PROBLEMS OF GEOCOSMOS

Saint-Petersburg State University 

Proceedings of the 7th International Conference 

PROBLEMS OF GEOCOSMOS 

St. Petersburg, Petrodvorets 

May 26-30, 2008 

Editors: V.N. Troyan, M. Hayakawa, V.S. Semenov 

Saint-Petersburg 

2008

Editors: V.N. Troyan, M. Hayakawa, V.S. Semenov. Proceedings of the 7th International 

Conference “Problems of Geocosmos”. – SPb., 2008 – 505 p. 

ISBN 978-5-9651-0303-4 

Copyright @ 2008 All rights 

reserved by V.A. Fock Institute of 

Physics, Physical Faculty, 

Saint-Petersburg State University

Proc. of the 7th Intern. Conf. "Problems of Geocosmos" (St. Petersburg, Russia, 26-30 May 2008): Contents 

C O N T E N T S 

SOLAR-TERRESTRIAL PHYSICS 

Amerstorfer, U.V., H.V. Erkaev, and H.K. Biernat: KELVIN-HELMHOLTZ INSTABILITY IN 

FINITE LARMOR RADIUS MHD AND CONSEQUENCES AT VENUS . . . . . . . . . . . . . . . . 

Artamonova, I.V., and S.V. Veretenenko: BARIC SYSTEM DYNAMICS DURING FORBUSH 

DECREASES OF GALACTIC COSMIC RAYS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Artemyev, A.V., L.M. Zelenyi, H.V. Malova, and V.Y. Popov: INSTABILITY OF THIN 

CURRENT SHEET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Avakyan, S.V., and N.A. Voronin: TRIGGER MECHANISM OF SOLAR-ATMOSPHERIC 

RELATIONSHIP AND THE CONTRIBUTION OF THE ANTHROPOGENIC IMPACT . . . . 

Badin, V.I.: MAGNETOMETRIC SPECTRA OF AURORAL CURRENTS COMPARED WITH 

THE DOPPLER RADAR MEASUREMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Baishev, D.G., E.S. Barkova, S.N. Samsonov, and K. Yumoto: SURGE-LIKE AURORAL 

STRUCTURES AND QUASI-PERIODIC PRECIPITATIONS OF ENERGETIC 

PARTICLES IN THE MORNING SECTOR: A CASE STUDY . . . . . . . . . . . . . . . . . . . . . . . 

Benevolenskaya, E.E.: NEW RESULTS OF SOLAR ACTIVITY AND MAGNETIC FIELD ON 

THE SUN (REVIEW) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Cherneva, N.V., G.I. Druzhin, and A.N. Melnikov: DIRECTION-FINDING OF A RARE 

PHENOMENON OF A THUNDERSTORM OVER KAMCHATKA ON THE 

REGISTRATION DATA OF VLF RADIATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Chugunova, O., V. Pilipenko, G. Zastenker, and N. Shevyrev: MAGNETOSHEATH 

TURBULENCE AND MAGNETOSPHERIC PC3 PULSATIONS . . . . . . . . . . . . . . . . . . . . . . 

Denisenko, V.V., A.V. Kitaev, and H.K. Biernat: TWO DIMENSIONAL MODEL OF MAGNETIC 

FIELD TRANSFER THROUGH THE MAGNETOTAIL DUE TO PLASMA FLOW IN THE 

PLASMA SHEET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Dergachev, V.A.: SECULAR AND LARGE-SCALE CHANGES IN SOLAR ACTIVITY, 

COSMOGENIC ISOTOPES AND CLIMATE CHANGES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Divin, A.V., V.S. Semenov, and D.B. Korovinskiy: STRUCTURE OF THE ELECTRON 

DIFFUSION REGION OF THE RECONNECTION PROCESS . . . . . . . . . . . . . . . . . . . . . . . . . 

Doronina, E.N., and A.A. Namgaladze: THE INFLUENCE OF NEUTRAL GAS HEATING AND 

COOLING ON THE DAY-TIME EQUATORIAL NEUTRAL DENSITY MINIMUM 

FORMATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Erkaev, N.V., V.S. Semenov, and H.K. Biernat: LOW FREQUENCY CURRENT SHEET 

OSCILLATIONS RELATED TO MAGNETIC FIELD GRADIENTS . . . . . . . . . . . . . . . . . . . . 

i 

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Grib, S.A., and V.B. Belakhovsky: ON THE INFLUENCE OF SECONADARY RAREFACTION 

WAVE ON THE GEOMAGNETIC FIELD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Gubchenko, V.M.: ON A NEW PARAMETER OF SPACE WEATHER AND TOPOLOGY OF 

THE EARTH’S MAGNETOSPHERE BASED ON THE FORM FACTOR OF THE 

INCOMING SOLAR-WIND PARTICLE-VELOCITY DISTRIBUTION FUNCTION . . . . . . . 

Guglielmi, A.V., B.I. Klain, and O.D. Zotov: ANHARMONICITY OF THE ULF 

GEOELECTROMAGNETIC WAVES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Ievenko, I.B., S.G. Parnikov and V.N. Alexeyev: PHOTOMETRIC STUDY OF PULSATING 

PRECIPITATIONS OF THE RING CURRENT ENERGETIC PARTICLES AT LATITUDES 

OF THE OUTER PLASMASPHERE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Ivanova, V., V. Semenov, H. Biernat, and S. Kiehas: APPLICATION OF RECONSTRUCTION 

METHOD BASED ON TIME-DEPENDENT PETSCHEK-TYPE RECONNECTION TO 

THEMIS DATA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Kharitonov, A.L., G.A. Fonarev, S.V. Starchenko, and G.P. Kharitonova: THE METHOD OF THE 

EXTRACTION OF EQUATORIAL EFFECTS OF THIN MAGNETOSPHERE LAYER OF 

THE EARTH FROM RESULTS OF GEOMAGNETIC MEASUREMENTS OF LOW-ORBIT 

MAGSAT, CHAMP SATELLITES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Kiehas, S.A., V.S. Semenov, N.N. Volkonskaya, V.V. Ivanova, and H. K. Biernat: 

RECONNECTION–ASSOCIATED ENERGY TRANSFER . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Kleimenova, N.G., O.V. Kozyreva, J. Manninen, and T. Turunen: MODULATION OF THE 

RIOMETER ABSORPTION AND WTISTLER-MODE CHORUS BY Pc5 GEOMAGNETIC 

PULSATIONS EXCITED BY THE SOLAR WIND PRESSURE OSCILLATIONS . . . . . . . . 

Kleimenova, N.G., O.V. Kozyreva, S. Michnowski, M. Kubicki, and N.N. Nikiforova: MAGNETIC 

STORM EFFECTS IN THE ATMOSPHERIC ELECTRIC FIELD VARIATIONS . . . . . . . . . 

Knyazeva, M.A., and A.A. Namgaladze: AN INFLUENCE OF THE MERIDIONAL WIND ON 

THE LATITUDINAL LOCATION OF THE ENHANCED ELECTRON DENSITY 

REGIONS IN THE NIGHT-TIME IONOSPHERIC F2-LAYER AND PLASMASPHERE OF 

THE EARTH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Korovinskiy, D., V. Semenov, A. Divin, and H. Biernat: ANALYTICAL MODEL OF 

COLLISIONLESS MAGNETIC RECONNECTION BASED ON THE SOLUTION OF 

GRAD-SHAFRANOV EQUATION COMPARED TO THE PIC-SIMULATION . . . . . . . . . . . 

Kozyreva, O.V., and N.G. Kleimenova: STORM-TIME Pc5 GEOMAGNETIC PULSATIONS 

ANALYSIS BASED ON A NEW ULF-INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Kuznetsova, N.D., and V.V. Kuznetsov: IMPLICATIONS OF VOLCANISM AND 

GEOMAGNETIC FIELD POLARITY REVERSALS INTO THE CLIMATE 

VARIABILITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Lazutin, L.L.: CREATION OF SOLAR PROTON BELTS DURING MAGNETIC STORMS: 

COMPARISON OF TWO MODELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Maksimenko, O.I., G.V. Melnik, and O.Ja. Shenderovska: SPATIAL DISTRIBUTION OF 

MAGNETIC STORM FIELDS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

ii 

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Martynenko, O.V.: THE MODEL INTEGRATION SCHEME OF THE FRAMEWORK 

ATMOSPHERE MODEL (FRAM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Maulini, A.L., A.L. Kotikov, A. Gavrasov, and V.I. Odintsov: ANALYSIS OF CLUSTER AND 

IRIS RIOMETER DATA OBTAINED DURING EXPERIMENTS ON IONOSPHERIC 

MODIFICATION CARRIED OUT 16 FEBRUARY 2003. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Mingalev, I.V., O.V. Mingalev, H.V. Malova, L.M. Zelenyi, A.A. Petrukovich, and A.V. Artemyev: 

ASYMMETRICAL CONFIGURATIONS OF THIN CURRENT SHEETS IN THE EARTH’S 

MAGNETOTAIL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Mocnik, K.: ON CLOSING A GAP IN SPACETIME PHYSICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Moskaleva, E.V., and O.V. Soloviev: INVESTIGATION OF THE SCATTERING OF VLF FIELD 

AT A THREE-DIMENSIONALIONOSPHERIC IRREGULARITY, ASSOCIATED WITH 

RED SPRITES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Myagkova, I.N., E.E. Antonova, S.N. Kuznetsov, Yu.I. Denisov, B.V. Marjin, and 

M.O. Riazantseva: SUB-RELATIVISTIC ELECTRON PRECIPITATION AT HIGH 

LATITUDES: LOW-ALTITUDE SATELLITES OBSERVATIONS . . . . . . . . . . . . . . . . . . . . . 

Myagkova, I.N., V.V. Kalegaev, S.Yu. Bobrovnikov, S.P. Likhachev, and D.A. Parunakian: HIGH 

LATITUDE MAGNETOSPHERE DYNAMICS DURING MAGNETIC STORMS: 

ENERGETIC PARTICLE DATA FROM LOW-ALTITUDE SATELLITES AND GLOBAL 

MAGNETOSPHERIC MODELING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Nikolskaya, K.I.: ON A CLOSE RELATION BETWEEN THE STATIONARY SOLAR WIND 

VELOCITIES AND THE SOLAR MAGNETIC FIELDS . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Parunakian, D.A., V.V. Kalegaev, S.Yu. Bobrovnikov, and W.O. Barinova: SINP SPACE 

MONITORING DATA CENTER PORTAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Ponomarev, E.A., N.V. Cherneva, and P.P. Firstov: FORMATION OF LOCAL ATMOSPHERIC 

ELECTRIC FIELD UNDER THE INFLUENCE OF IONIZATION FACTORS . . . . . . . . . . . . 

Posratschnig, S., V.S. Semenov, M.F. Heyn, I.V. Kubyshkin, and S.A. Kiehas: OBSERVATIONAL 

SIGNATURES OF CONSECUTIVE RECONNECTION PULSES . . . . . . . . . . . . . . . . . . . . . . 

Pulkkinen, T.I., M. Palmroth, K. Andreeova, and T. Laitinen: GLOBAL SIMULATIONS: WHAT 

DO THEY TELL ABOUT THE LARG E-SCALE MAGNETOSPHERIC DYNAMICS. . . . . . 

Raspopov, O.M., V.A. Dergachev, and E.G. Guskova: ON A COMBINED INFLUENCE OF LONG- 

TERM SOLAR ACTIVITY VARIATIONS AND GEOMAGNETIC DIPOLE CHANGES ON 

CLIMATE CHANGE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Raspopov, O.M., and S.V. Veretenenko: SOLAR ACTIVITY, COSMIC RAYS AND CLIMATE 

CHANGE (ON THE 75 TH ANNIVERSARY AND IN MEMORY OF 

PROF. M.I. PUDOVKIN) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Rossolenko, S.S., E.E. Antonova, I.P. Kirpichev, Yu. I. Yermolaev, N.N. Shevyrev, and 

O.M. Chugunova: MAGNETOSHEATH TURBULENCE AND THE LOW LATITUDE 

BOUNDARY LAYER FORMATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Samsonov, A.A., Z. Němeček, J. Šafránková, and L. Přech: INTERACTION OF OBLIQUE 

INTERPLANETARY SHOCKS WITH THE BOWSHOCK . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

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Sasunov, Yu., and V.S. Semenov: ANALITICAL INVESTIGATION OF 3D IMPULSIVE 

MAGNETIC RECCONECTION USING GREEN FUNCTION IN FRAME OF 

INCOMPRESSIBLE MHD APPROXIMATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Sedykh, P.A., and E.A. Ponomarev: ON THE NATURE OF PLASMA INHOMOGENEITIES IN 

THE MAGNETOSPHERE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Sedykh, P.A., E.A. Ponomarev, V.D. Urbanovich, and O.V. Mager: THE STRUCTURALLY 

ADEQUATE MODEL OF MAGNETOSPHERIC PROCESSES 85-08 . . . . . . . . . . . . . . . . . 

Shevchenko, I.G., V.A. Sergeev, M.V. Kubyshkina, and V.Angelopoulos: STANDARD DATA- 

BASED MAGNETOSPHERE MODELS TUNING FOR THEMIS PROJECT . . . . . . . . . . . . . 

Sormakov, D.A., V.A.Sergeev, V.Angelopoulos, and A.V. Runov: FLAPPING-STRUCTURES 

AND BURSTY BULK FLOWS IN THE MAGNETOTAIL NEUTRAL SHEET FROM 

MHD MODELING RESULTS AND FROM THEMIS MULTI-SPACECRAFT 

OBSERVATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Tyasto, M.I., N.G. Ptitsyna, I.S. Veselovskii, and O.S. Yakovchuk: SPACE CLIMATE AND 

HISTORICAL DATA OF THE RUSSIAN MAGNETIC NETWORK: RETROSPECTIVE 

ANALYSIS OF THE SEPTEMBER 1859 SUPERSTORM . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Veretenenko, S.V., V.A. Dergachev, and P.B. Dmitriyev: SOLAR ACTIVITY EFFECTS ON THE 

CHARACTERISTICS OF FRONTAL ZONES IN THE NORTH ATLANTIC . . . . . . . . . . . . . 

Volkov, M.A., and N.Yu. Romanova: THE FORMATION OF THE FIELD-ALIGNED CURRENTS 

DURING DIPOLARIZATION OF THE EARTH MAGNETIC FIELD . . . . . . . . . . . . . . . . . . . 

Zelenyi, L.M., H.V. Malova, V.Y. Popov, A.V. Artemyev, and A.A. Petrukovich: THE MODEL OF 

MULTISCALE THIN CURRENT SHEET WITH TWO-TEMPERATURE PLASMA 

COMPONENTS: THE COMPARISON WITH EXPERIMENTAL DATA . . . . . . . . . . . . . . . . 

Zubova, Yu.V., A.A. Namgaladze, and L.P. Goncharenko: MODEL INTERPRETATION OF THE 

UNUSUAL F-REGION NIGHT-TIME ELECTRON DENSITY BEHAVIOUR 

OBSERVED BY THE MILLSTONE HILL INCOHERENT SCATTER RADAR 

ON APRIL 16-17, 2002 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

CONDUCTIVITY OF THE EARTH 

Cherevatova, M.V.: DEEP STUCTURE OF THE KARELIAN PART OF THE FENNOSKANDIAN 

SHIELD (SEISMOLOGICAL AND GEOELECTRICAL RESEARCH) . . . . . . . . . . . . . . . . . . 

Kovtun, A.A., and I.L. Vardaniants: MANTLE ELECTROCONDUCTIVITY OF THE 

FENNOSCANDIAN SHIELD BY THE RESULTS OF COMBINED INTERPRETATION OF 

DEEP MTS AND GLOBAL MVS DATA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Plotkin, V.V., A.Yu. Belinskaya, P.A. Gavrysh, and BEAR Working Group: PRELIMINARY 

RESULTS OF THE BEAR DATA PROCESSING WITH APPLICATION OF NONLOCAL 

RESPONSE FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Vagin, S.A.: ONE- AND TWO-DIMENSIONAL INVERSION OF MAGNETOTELLURIC DATA 

BY THE REGULARIZATION SVD METHOD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

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Zhamaletdinov, A.A., A.N. Shevtsov, T.G. Korotkova, B.V. Efimov, M.B. Barannik, V.V. Kolobov, 

P.I. Prokopchuk, Yu.A. Kopytenko, Ye.A. Kopytenko, V.S. Ismagilov, M.Yu. Smirnov, 

S.A. Vagin, Ye.D. Tereschenko, A.N. Vasiljev, M.B. Gokhberg, and T. Korja: THE DEEP 

TENSOR CSMT SOUNDING WITH INDUSTRIAL POWER LINES AT THE EASTERN 

PART OF THE FENNOSCANDIAN (BALTIC) SHIELD (FENICS EXPERIMENT) . . . . . . . 

NONLINEAR GEOPHYSICAL METHODS 

Avsjuk, Yu.N., Yu.S. Genshaft, A.Ja. Saltykovsky, Yu.F. Sokolova, and S.P. Svetlosanova: 

INFLUENCE OF TIDAL FORCES (THE EARTH – MOON – SUN SYSTEM) ON SOME 

GEOLOGICAL PROCESSES IN THE EARTH’S CRUST . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Knyazeva, I.S., and D.A. Milkov: MULTIFRACTAL AND TOPOLOGICAL ANALYSIS OF 

SOLAR MAGNETIC FIELD COMPLEXITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Oposhnyan, O.L., D.I. Ponyavin, and N.G. Makarenko: NONLINEAR ANALYSIS OF CAUSAL 

RELATIONSHIPS BETWEEN SOLAR AND GEOMAGNETIC TIME-SERIES BY MEANS 

OF SYMBOLIC DYNAMICS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Uritsky, V.M., and N.I. Muzalevskaya: MULTISCALE INTERMITTENCY IN PHYSICS AND 

PHYSIOLOGY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Zotov, O.D., and B.I. Klain: FRACTAL CHARACTERISTICS OF THE SOLAR AND 

MAGNETOSPHERIC ACTIVITIES AND FEATURE OF THE AIR TEMPERATURE 

DYNAMICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Zotov, O.D., B.I. Klain, and N.A. Kurazhkovskaya: STOCHASTIC RESONANCE IN THE 

EARTH’S MAGNETOSPHERE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

PALEOMAGNETIC RECONSTRUCTIONS, PALEOINTENSITY AND ROCK 

MAGNETISM AS PHYSICAL BASIS OF PALEOMAGNETISM 

Burakov, K.S., and I.E. Nachasova: RESEARCH OF SHORT-PERIODICAL VARIATIONS OF 

INTENSITY OF THE GEOMAGNETIC FIELD IN SECOND HALF OF FIRST 

MILLENNIUM BC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Burakov, K.S., and I.E. Nachasova: DATING OF THE CERAMIC MATERIAL FROM 

MONUMENT “MAISKAJA GORA”, USING DATA ABOUT INTENSITY OF THE 

GEOMAGNETIC FIELD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Demina, I., Yu. Farafonova, and T. Koroleva: SIMULATION OF DIFFERENT SCRIPTS OF THE 

MAIN GEOMAGNETIC FIELD VARIATIONS ON THE BASE OF THE FORECAST OF 

THEIR SOURCES DYNAMICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Gnibidenko, Z.N.: THE LAST GEOMAGNETIC REVERSAL MATUYAMA-BRUNHES IN 

LOESS-PALEOSOL SEQUENCES OF PRIOBSKOE PLATEAU . . . . . . . . . . . . . . . . . . . . 

Guskova, E.G., O.M. Raspopov, A.L. Piskarev, and V.A. Dergachev: MAGNETISM AND 

PALEOMAGNETISM OF THE RUSSIAN ARCTIC MARINE SEDIMENTS . . . . . . . . . . . . . 

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Pilipenko, O.V., N. Abrahamsen, Z.V. Sharonova, and V.M. Trubikhin: PALEOMAGNETIC 

RECORD OF KARADJA LATE PLEISTOCENE SECTION REFLECTS GLOBAL 

VARIATIONS OF THE GEOMAGNETIC FIELD AND PALEOENVIRONMENTAL 

CHANGES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Starchenko, S.V.: PLANETARY CONVECTION AND MAGNETIC STABILITIES . . . . . . . . . . . . . 

Starchenko, S.V., and M.S. Kotelnikova: CONVECTION STABILITY AND THE EARTH’S TYPE 

PLANETARY MAGNETISM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Starchenko, S.V., and A.M. Soward: ANALYTIC CONVECTION SOLUTION AND THE EARTH’ 

TYPE PLANETARY MAGNETISM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

SEISMOLOGY 

Bakhmutov V.G., and A.A. Groza: THE DILATANCY-DIFFUSION MODEL: NEW 

PROSPECTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Boykov, A.M.: ABOUT NON-LINEAR DYNAMICS APPLIED TO DEPTH FRACTURES, 

CONRTOLLING HIGH SEISMICITY AREAS IN DAGHESTAN . . . . . . . . . . . . . . . . . . . . . . 

Il’chenko, V.L.: WAVE DISTRIBUTION OF ANISOTROPY OF ELASTIC PROPERTIES OF 

ROCK SAMPLES COLLECTED ALONG SECTION FROM THE SURFACE . . . . . . . . . . . . 

Krasnoshchekov D.N., and V.M. Ovtchinnikov: UPPER SOLID CORE’S FABRIC CONSTRAINED 

BY PKiKP CODA OBSERVATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Kuznetsov, I.V., and V.V. Kuznetsov: AVALANCHE-LIKE NUCLEATION OF CRACKS 

THROUGH FRACTURE KINETICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Silaeva, O.I., A.V. Ponomarev, A.A. Khromov, S.M. Stroganova, and T.I. Rudenko: TEMPORAL 

VARIATIONS IN GEOPHYSICAL FIELDS AS A MANIFESTATION OF THE 

NONLINEAR ROCK PROPERTIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

SEISMIC-ELECTROMAGNETIC PHENOMENA 

Gaivoronskaya, T.V.: COMPARATIVE ANALYSIS OF IONOSPHERIC VARIATIONS BEFORE 

STRONG EARTHQUAKES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Hayakawa, M., A.P. Nickolaenko, T. Ogawa, and M. Komatsu: COMPARISON OF 

EXPERIMENTAL AND MODEL Q-BURSTS IN TIME DOMAIN . . . . . . . . . . . . . . . . . . . . . 

Kudintseva, I.G., A.P. Nickolaenko, and M. Hayakawa: FINE STRUCTURE OF ELECTRIC 

PULSED FIELD ABOVE THE BENT STROKE OF LIGHTNING . . . . . . . . . . . . . . . . . . . . . . 

Lementueva, R.A., A.A. Gvozdev, and E.L. Irisova: STRESSES IN ROCK SAMPLES AND 

ELECTROMAGNETIC RELAXATION TIMES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

vi 

386 

391 

397 

403 

406 

412 

416 

421 

429 

432 

437 

440 

446 

451


Mullayarov, V.A., V.I. Kozlov, and A.V. Ambursky: OPPORTUNITIES OF USING OF 

ELECTROMAGNETIC SIGNAL OF LIGHTNING DISCHARGES FOR THE REMOTE 

SENSING OF SEISMIC ACTIVITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Ohta, K., J. Izutsu, K. Furukawa, and M. Hayakawa: ANOMALOUS EXCITATION OF 

SCHUMANN RESONANCES ASSOCIATED WITH HUGE EARTHQUAKES, CHI-CHI 

(CHINA, 1999) NIIGATA-CHUETSU (JAPAN, 2004), NOTO-HANTOU (JAPAN, 2007), 

OBSERVED AT NAKATSUGAWA IN JAPAN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Rozhnoi, A., M. Solovieva, and O. Molchanov: VARIATIONS OF VLF SIGNALS RECEIVED ON 

DEMETER SATELLITE IN ASSOCIATION WITH SEISMICITY . . . . . . . . . . . . . . . . . . . . . 

Sergeenko, N.P., M.V. Rogova, and A.V. Sazanov: SEISMIC TRAVELLING IONOSPHERE 

DISTURBANCES AT F2-REGION IN TIME OF HELIOGEOPHYSICAL 

DISTURBANCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Sholpo, M.E.: TESTING OF THE METHOD FOR THE CONVERSION OF THE MT APPARENT 

RESISTIVITY CHANGES INTO THE RELATIVE CHANGES IN THE ROCK 

ELECTRICAL RESISTIVITY USING THE 2D MODEL OF THE GEOELECTRIC 

STRUCTURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Smirnova, N.A., and A.A. Isavnin: FRACTAL CHARACTERISTICS OF ULF EMISSIONS 

REGISTERED IN THE HIGH LATITUDE SEISMIC-QUIET REGION OF 

SPITSBERGEN ISLAND . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Varlamov, A.A., and N.A. Smirnova: PECULIARITIES OF THE ULF EMISSION FRACTAL 

CHARACTERISTICS OBTAINED AT THE STATIONS OF 210 GM . . . . . . . . . . . . . . . . . . . 

Zolotov, O.V., A.A. Namgaladze, I.E. Zakharenkova, I.I. Shagimuratov, and O.V. Martynenko: 

SIMULATIONS OF THE EQUATORIAL IONOSPHERE RESPONSE TO THE SEISMIC 

ELECTRIC FIELD SOURCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

vii 

457 

461 

467 

473 

478 

483 

487 

492

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Proceedings of the 7th International Conference "Problems of Geocosmos" (St. Petersburg, Russia, 26-30 May 2008) 

1026ØÓ7 × 1026�ÓÒ××��Ô�Ò��Ò�ÓÒØ��×�Þ�Ó�Ø��ÔÐ�×Ñ�ÐÓÙ�×ËÙ�ÐÓ××Ö�Ø�× 1

Î�ÒÙ×�ØØ��Ñ��Ò�ØÓÔ�Ù×��ÓÙ×�×ÔÐ��ÙÔÓÒØ��Ò�Ù�Ò�Ó�Ø��Ò�Ø�Ä�ÖÑÓÖÖ��Ù×Ó�Ø�� ÓÒ×ÁØ�×�××ÙÑ��Ø��ØØ��Ñ��Ò�Ø��Ð��×Ô�ÖÔ�Ò��ÙÐ�ÖØÓØ��ÓÛÚ�ÐÓ�ØÝ�Ò�Ø��ØØ��ÓÙÒ��ÖÝ �ÖÓ××Û��Ø��ÔÐ�×Ñ��Ò��×�Ø×ÔÖÓÔ�ÖØ��×��×��Ò�Ø�Ø��Ò�×× Ì��××ØÙ�Ý��Ñ×ØÓ�ÒÚ�×Ø��Ø�Ø��ÔÖÓÔ�ÖØ��×Ó�Ø��Ã�ÐÚ�ÒÀ�ÐÑ�ÓÐØÞ�Ò×Ø��Ð�ØÝ�ÒØ��Ú��Ò�ØÝÓ� 

�ÓÖÒ�ÖÖÓÛ�ÓÙÒ��ÖÝÐ�Ý�Ö×Û��Ö�Ø��ÓÒÄ�ÖÑÓÖÖ��Ù×�×Ó�Ø��ÓÖ��ÖÓ�Ø��Ø��Ò�××Ó�Ø��ÓÙÒ��ÖÝ Ð�Ý�ÖØ��Ä�ÖÑÓÖÖ��Ù××�ÓÙÐ�ÒÓØ��Ò��Ð�Ø��Ì��×Ñ��Ò×Ø��Ø��Ø�ÓÒ�ÐØ�ÖÑ×�ÒØ��ÕÙ�Ø�ÓÒ ��Ò�Ø�Ä�ÖÑÓÖÊ��Ù×ÅÀ� 

��Ð��Ò�Ö�ÐÐÝØ��×�Ø�ÖÑ×ÓÑ��ÖÓÑØ��ØØ��ØØ��Ú�ÐÓ�ØÝ��×ØÖ��ÙØ�ÓÒ×Ð��ØÐÝ��Ú��Ø�×�ÖÓÑ� Å�ÜÛ�ÐÐ��Ò Ó�ÑÓØ�ÓÒ��Ú�ØÓ��ÒÐÙ��Ö�×�Ò��ÖÓÑØ��ÝÐÓØÖÓÒÑÓØ�ÓÒÓ�Ø��ÓÒ×�Ò�Ò�Ð�ØÖÓÑ��Ò�Ø� Ì��×�ØÓ��ÄÊÅÀ��ÕÙ�Ø�ÓÒ×ÓÒ×�×Ø×Ó�Ø��ÕÙ�Ø�ÓÒÓ�ÑÓØ�ÓÒ�ÒÐÙ��Ò�Ø��ÓÒØÖ��ÙØ�ÓÒÓ�Ø�� 

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�Ò�Ø��Ø�Ð�Ûρ ∂v 

∂t + ρ(v · ∇)v + ∇Π + ∇ · ˆ G − 1 

(B · ∇)B = 0, 

µ0 

∂ρ 

+ ∇ · (ρv) = 0, 

∂t 

∂B 

− ∇ × (v × B) = 0, 

∂t 

� 

d p 

dt ρκ ÉÙ�ÒØ�ØÝΠ��ÒÓØ�×Ø��ØÓØ�ÐÔÖ�××ÙÖ�Û��×Ø��×ÙÑÓ�Ø��ÔÐ�×Ñ��Ò�Ø��Ñ��Ò�Ø�ÔÖ�××ÙÖ� 

� 

= 0. 

Π = p + B2 

Ð�Ý�Ö v�×Ø��ÙÐ�Ú�ÐÓ�ØÝρØ��Ñ�××��Ò×�ØÝBØ��Ñ��Ò�Ø��Ð��Ò�p�×Ø��ÔÐ�×Ñ�ÔÖ�××ÙÖ�Ì��Ò�Ø��Ð ÓÒ��ÙÖ�Ø�ÓÒ�ÐÐÓÛ×Ø��Ú�ÐÓ�ØÝØ��Ò×�ØÝ�Ò�Ø��Ñ��Ò�Ø��Ð�ØÓ��Ò��ÖÓ××Ø��ÓÙÒ��ÖÝ 

, 

2µ0 

z��Ü�×�ÑÓÙÒØ×ØÓ�Ö��Ò×��ÀÙ�� 

G�ÓÖØ��ÓÓÖ��Ò�Ø�×Ý×Ø�ÑÛ��Ö�Ø��Ñ��Ò�Ø��Ð��×Ô�Ö�ÐÐ�ÐØÓØ�� 

B0 = B0z(x) ˆz, v0 = v0y(x) ˆy, ρ0 = ρ0(x). Ì��Ñ��Ò�Ø��Ð��×Ô�ÖÔ�Ò��ÙÐ�ÖØÓØ��Ú�ÐÓ�ØÝ�Ò�Ø��Û�Ú�ÒÙÑ��ÖB0 ⊥v0 ||k Ì��ÝÖÓÚ�×Ó×�ØÝØ�Ò×ÓÖˆ ⎛ � � � � � � ⎞ 

∂vx ∂vy ∂vx ∂vy ∂vy ∂vz 

⎜ −ρν + ρν − −2ρν + 

Û��Ö�ν�×Ø��×Ó��ÐÐ��ÝÖÓÚ�×ÓÙ×Ó��ÒØ��Ò��× 

⎜ ∂y ∂x ∂x ∂y ∂z ∂y ⎟ 

⎜ � � � � � � ⎟ 

ˆG 

⎜ ∂vx ∂vy ∂vx ∂vy ∂vx ∂vz ⎟ 

= ⎜ ρν − ρν + 2ρν + ⎟ , 

⎜ 

∂x ∂y ∂y ∂x ∂z ∂x ⎟ 

⎜ � � � � 

⎟ 

⎝ ∂vy ∂vz ∂vx ∂vz 

⎠ 

−2ρν + 2ρν + 0 

∂z ∂y ∂z ∂x 

ν = 1 

4 R2 L ΩL 

= 1 

4 RL vt 

= 1 

4 

v 2 t 

ΩL 

= kb T 

2eB 

2

Ø��Ò��Ú��Ù�Ð�ÝÖÓÚ�×Ó×�ØÝØ�Ò×ÓÖ×Ó��ÓÒ×Ô��× Ó�Ø��ÓÒ×�Ò�mØ��Ñ�××Ó�Ø��ÓÒ×ÁÒ�ÑÙÐØ��ÓÒÔÐ�×Ñ�Ø��ÝÖÓÚ�×Ó×�ØÝØ�Ò×ÓÖ�×Ø��×ÙÑÓ� 

T/m�×Ø��Ø��ÖÑ�ÐÚ�ÐÓ�ØÝe�×Ø��ÙÒ�Ø��Ö��kb�×�ÓÐØÞÑ�ÒÒ×ÓÒ×Ø�ÒØTØ��Ø�ÑÔ�Ö�ØÙÖ� 

�Ö��××ÙÑ��Ò�Ñ�ÐÝ×ÓÐ�ÖÛ�Ò�ÔÖÓØÓÒ××Ù�×Ö�ÔØÔ�Ò��ÓÒÓ×Ô��Ö�ÓÜÝ��Ò�ÓÒ××Ù�×Ö�ÔØÓ Ì��××Ý×Ø�ÑÓ��ÕÙ�Ø�ÓÒ× δp�Ò�δBÀ�Ú�Ò��ÒÑ�Ò�Ø��ÔÔÐ��Ø�ÓÒØÓØ��×�ØÙ�Ø�ÓÒ�ØÎ�ÒÙ×ØÛÓ�ÓÒ×Ô��× �×Ð�Ò��Ö�Þ��ÒÓÖÑ�Ð�Þ��Ò�Ø��Ò×ÓÐÚ��ÒÙÑ�Ö��ÐÐÝ�ÓÖØ��Ô�ÖØÙÖ��Ø�� 

Û�Ø�RL � 

= vt/ΩL�Ò�ΩL = eB/m�×Ø��ÓÒÄ�ÖÑÓÖÖ��Ù×�Ò��Ö�ÕÙ�ÒÝÖ�×Ô�Ø�Ú�ÐÝvt = 

2kb 

��ÖÓÙÒ�ÔÖÓ�Ð�×�Ö��Ú�Ò�Ý×��ÙÖ� ��Ö×ØÓ��ÐÐ�Ø��ÓÖ�Ø��Ð�×��×ÓÒ×��Ö��ØÓ×�ÓÛØ��Ò�Ù�Ò�Ó�Ø��Ò�Ø�Ä�ÖÑÓÖÖ��Ù×Ì��Ù×�� ØÓ��Ò�Ø�Ä�ÖÑÓÖÊ��Ù× ÕÙ�ÒØ�Ø��×δρ δv 

v0(x) = 1 

2 (vup + vlow) + sign(Dv0y) 1 

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6


BARIC SYSTEM DYNAMICS DURING FORBUSH DECREASES OF 

GALACTIC COSMIC RAYS 

I.V. Artamonova 1 , S.V. Veretenenko 2 

1 Institute of Physics, St.Petersburg State University, St.Petersburg, 198504, Russia, e-mail: 

artamonova@hotbox.ru; 2 Ioffe Physico-Technical Institute of the Russian Academy of Sciences, 

St.Petersburg, 194021, Russia 

Introduction 

Abstract. Short-time effects of galactic cosmic ray (GCR) variations on the baric system evolution at 

middle latitudes of the North Atlantic were investigated. A noticeable pressure growth after the sharp 

GCR intensity decreases (Forbush-decreases) was found, the maximum of pressure being observed 

over Scandinavia and the northern region of the European part of Russia on the 4 th day after the event 

beginning. It was shown that the detected pressure growth was caused by more intensive anticyclone 

development in the region of climatic Arctic front. It was suggested that the particles which 

precipitate in the regions of the Arctic (E ~ 20−80 MeV) and Polar (E ~ 2−3 GeV) fronts may 

influence the processes of cyclone and anticyclone formation in frontal regions. 

The variations of the cosmic ray flux are now considered as one of most important agents linking solar 

activity and the lower atmosphere. The studies of solar activity influence on the formation and evolution of 

extratropical cyclones are of significant importance, because the weather conditions at middle latitudes strongly 

depend on the cyclones forming over the North Atlantic and the North Pacific oceans. In particular, 

Veretenenko and Thejll (2004) showed that precepitations of high-energy solar protons into the Earth’s 

atmosphere resulted in the increase of cyclone activity near Greenland. Tinsley and Deen (1991) found a 

decrease of vortex area index (VAI), i.e., a weakening of cyclogenesis during Forbush decreases of galactic 

cosmic rays (GCR), mainly at the latitudes ~40-65°N over oceans. Pudovkin et al. (1997) also showed that 

according to the data of aerological soundings in Sodankylä (Finland, φ ≈ 67°N), Forbush decreases were 

accompanied by an increase of pressure, with the maximum being observed on the +3/+4 day after the event 

onset. These results were in good agreement with zonal pressure variations in the latitudinal belt 50-75°N 

according to Pudovkin and Babushkina (1992). Veretenenko and Artamonova (2005) revealed, that the pressure 

increase over Scandinavia and the northern region of the European part of Russia during Forbush decreases of 

GCR took place due to more intensive formation of blocking anticyclones in this region. 

In this work we continue studying the baric system dynamics during Forbush-decreases of galactic 

cosmic rays on the base of the extended statistical data and show that the pressure increase areas turn to be in the 

regions of the climatic position of the main atmospheric fronts. 

Experimental data analysis 

We analysed daily averaged values of geopotential heights (GPH) of the main isobaric levels 1000, 850, 

700, 500, 300 and 200 hPa using NCEP/NCAR “reanalysis” data (Kalnay et al., 1996) to investigate the effects of 

Forbush-decreases on the variations of pressure in the lower atmosphere. 

We selected 48 Forbush decreases during the cold half of the year (October-March) for the period 1980- 

2006 using the Apatity neutron monitor data (http://pgi.kolasc.net.ru/CosmicRay). The events selected for our 

study had to satisfy the following criteria: 

а) on the first day of the event the decrease of the neutron monitor counting rate exceeded 1% relative to 

the undisturbed level which was calculated by averaging the data over 5 days before the event onset; 

b) the amplitude of the Forbush-decrease exceeded 2.5% relative to the undisturbed level; 

с) no intensive solar proton fluxes (i.e. with the intensity I >100 proton·cm -2 ·s -1 ·sr -1 ) for particles of 

energy E >10 MeV had to be observed during the first days of the Forbush-decrease. 

7


The events were selected for the cold period (October-March), because in this half of the year the 

maximum intensity of cyclonic activity is observed. The superposed epoch analysis was used to calculate the 

mean pressure deviations from the undisturbed level, which was obtained by averaging the GPH data over 10 

days before the event onset. The day of the event onset was considered as the zero day. 

The mean variations in geopotential heights of the isobaric surface 1000 hPa during Forbush decreases 

under consideration are presented in Fig.1. The white lines indicate the areas, where the statistical significance of 

the deviations is above 0,95 and 0,99 according to the Student t-criterion. As it seen from the figure, a slow 

pressure growth takes place near the south-eastern coasts of Greenland on the first days (0/+1 days) after the 

Forbush decrease onset. Then, the area of the increasing pressure extends in the north-eastern direction and 

reaches its maximum on the +3/+4 days after the Forbush decrease beginning, covering all Scandinavia, the north 

of European part of Russia and the Arctic Ocean coasts. The deviations from the undisturbed level in this region 

amount to ∼ 60-70 gp.m. 

Latitude, deg. 

80 

60 

40 

20 

80 

60 

40 

20 

80 

60 

40 

20 

80 

60 

40 

20 

-50 0 

-1 day 

50 

0.95 

0.99 

-50 0 

0 day 

50 

-50 0 

1 day 

50 

-50 0 

2 day 

50 

0.95 

0.99 

0.99 

0.95 

0.99 

0.95 

40 

20 

0 

-20 

-40 

40 

20 

0 

-20 

-40 

40 

20 

0 

-20 

-40 

40 

20 

0 

-20 

-40 

80 

60 

40 

20 

80 

60 

40 

20 

80 

60 

40 

20 

80 

60 

40 

20 

Longitude, deg. 

0.95 

0.99 

0.99 

0.95 

0.95 

0.99 

-50 0 50 

3 day 

0.95 

0.95 

0.99 

0.99 

-50 0 

4 day 

50 

0.95 

0.99 

-50 0 

5 day 

50 

0.99 

-50 0 

6 day 

50 

Fig. 1 Mean variations in geopotential heights (in gp.m) of the isobaric level 1000 hPa in the 

course of GCR Forbush decreases for 48 events (1980-2006, cold half of year). White lines 

show the areas where the effects are significant at 0,95 and 0,99 confidence level. Black and 

blue lines show the climatic position of the Arctic and Polar fronts in January, respectively 

[Khromov and Petrosyants, 1994]. 

Variations in geopotential heights of the isobaric levels 1000, 850, 700, 500, 300 and 200 hPa on the +4 

day after the Forbush decrease onset, which is the day of the greatest pressure increase, are shown in Fig.2. White 

lines show the areas where the effects are significant at 0,95 and 0,99 confidence level according to the Student tcriterion. 

We can see a noticeable pressure growth at all the isobaric levels, but the most significant effects take 

place near the Earth’s surface. The effect weakens with the increase of the altitude. 

The data in Fig. 2 show also the climatic position of the main atmospheric fronts at middle latitudes in 

January according to Khromov and Petrociants (1994). Atmospheric fronts are rather narrow transition bands 

between air masses with different thermal characteristics which are formed over different kinds of surface. The 

8 

0.95 

0.95 

0.99 

0.99 

40 

20 

0 

-20 

-40 

40 

20 

0 

-20 

-40 

40 

20 

0 

-20 

-40 

40 

20 

0 

-20 

-40


Arctic front separates in winter the cold Arctic air over Greenland from the warmer air of middle latitudes over 

the ocean, whereas the Polar front separates the air mass of middle latitudes from the tropical air mass. The main 

atmospheric fronts are of particular interest for the studies, because the cyclonic activity at extratropical latitudes 

is closely related to these fronts. Most of extratropical cyclones arise and undergo significant changes in their 

evolution namely at the Arctic and Polar fronts. Indeed, the most appreciable pressure deviations are observed in 

the regions of the climatic position of these fronts, i.e. in the areas of intensive cyclogenesis. This allows the 

suggestion that a possible reason of the observed pressure deviations may be the changes in cyclone and 

anticyclone evolution. 


80 

60 

40 

20 

80 

60 

40 

20 

80 

60 

40 

20 

Level = 1000 hPa 

-50 0 50 


-50 0 50 


0.95 

0.95 

0.99 

0.95 

0.99 

-50 0 50 

0.95 0.99 

0.95 0.99 

0.99 

0.95 

0.99 

0.95 

40 

20 

0 

-20 

-40 

-60 

40 

20 

0 

-20 

-40 

-60 

40 

20 

0 

-20 

-40 

-60 

80 

60 

40 

20 

80 

60 

40 

20 

80 

60 

40 

20 



-50 0 50 


0.95 

0.99 

0.95 

-50 0 50 


-50 0 50 

0.95 

0.99 

0.95 

0.99 

Fig. 2 Mean variations in geopotential heights (in gp.m) of the isobaric levels 1000, 850, 700, 

500, 300 and 200 hPa on the +4 day after the Forbush-decrease beginning for 48 events (1980- 

2006, cold half of year). White lines show the areas where the effects are significant at 0,95 

and 0,99 confidence level. Black and blues lines show the climatic position of the Arctic and 

Polar fronts in January, respectively [Khromov and Petrociants, 1994]. 

To check this assumption, the weather chart analysis was carried out. The weather charts provide 

comprehensive information about atmospheric conditions at the moment of observation, in particular, about the 

spatial distribution of air masses and their characteristics, the atmospheric fronts and the different baric systems 

such as cyclones and anticyclones, troughs and crests. An example of the synoptic situation on the +3/+4 days of 

the Forbush decrease which started on the 13 January 1988 is presented in Fig.3. 

9 

40 

20 

0 

-20 

-40 

-60 

40 

20 

0 

-20 

-40 

-60 

40 

20 

0 

-20 

-40 

-60


Fig. 3. Example of synoptic situation on the +3/+4 days of the GCR Forbush decrease starting on 

the 13 January 1988. 

We can see that on the +3 day (16 January 1988, left panel) the high pressure area (1025 hPa in the 

center) is formed over the north of Scandinavia at the cold front of the cyclone with the center over Taimyr 

peninsula. The cold front stretches along the Arctic coast of Eurasia. There is also an occluded cyclone over 

Greenland, the pressure in its center is 960 hPa. On the next day (right panel) the cold front is displaced to the 

south, the pressure in the anticyclone reaches 1030 hPa, its area increases noticeably and covers both Scandinavia 

and the north of the European part of Russia. The cyclone near Greenland does not move and rapidly fills up to 

980 hPa. Similar processes were found to occur in most cases. 

Thus, the results of synoptic analysis showed that, as a rule, after the Forbush decrease onset the 

transformation of intensive mobile cold anticyclones into slowly-moving ‘blocking’ anticyclones takes place. 

These anticyclones create an obstacle for the transport of air masses from the North Atlantic to the continent. This 

process results in the decrease of intensity as well as in the slowing or even in the stop of cyclones, which usually 

move to the east (or to the north-east) in the zonal flow. As a result, the pressure over Scandinavia and the north 

of the European part of Russia starts to growth. 


80 

70 

60 

50 

40 

30 

20 

0.3 GV 

0.5 GV 

0.9 GV 

2 GV 

3 GV 

4 GV 

5 GV 

0.1 GV 

7 GV 

9 GV 

Polar front 

2 GV 

11 GV 

12 GV 

13 GV 

14 GV 

Arctic front 

-80 -60 -40 -20 0 20 40 60 80 


gp.m 

Fig. 4. Mean variations in geopotential heights (in gp.m) of the isobaric level 1000 hPa on the +4 

day after the Forbush-decrease beginning, superposed by the geomagnetic cutoff rigidity (R, GV) 

map, and the climatic position of the main atmospheric fronts at middle latitudes in January 

[Khromov and Petrociants, 1994]. 

10 

40 

20 

0 

-20 

-40 

-60


According to Shea and Smart (1983), the geomagnetic cutoff rigidities in the areas of most intensive 

anticyclone activity vary from ~ 0,2 GV to 0,4 GV (the Arctic front region) and from ~2 GV to 3,5 GV (the Polar 

front region), that corresponds to the energies ~ 20−80 MeV and ~ 2−3 GeV, respectively . The geomagnetic 

cutoff rigidity map and the climatic position of the main atmospheric fronts at middle latitudes in January 

[Khromov and Petrociants, 1994], are shown in Fig. 4. As it seen from the figure, the main atmospheric fronts 

under study turn to be in the zones of precipitation of particles with the minimum energy ~20−80 MeV (the 

Arctic front) and ~ 2−3 GeV (the Polar front). The intensity of cosmic particles with such energies is strongly 

modulated by solar activity that allows considering them as the most probable link between solar activity and the 

lower atmosphere. An intensification of anticyclones in the regions of particle precipitations with the indicated 

energies seem to provide new evidence that the variations of these particles are involved in the physical 

mechanism of solar activity effects on the formation and development of extratropical baric systems. 

Conclusions 

This investigation showed that Forbush decreases of galactic cosmic rays are accompanied by the 

noticeable pressure growth at middle and high latitudes, the most significant effects were found in the regions of 

the climatic Arctic front stretching from the Greenland coasts to the Arctic coasts of Eurasia and of the Polar 

front in the eastern part of the North Atlantic. The result obtained suggest that the pressure changes associated 

with the events under study are due to the changes in the intensity of cyclonic activity (i.e. formation and 

development of extratropical cyclones and anticyclones) in these regions. 

The synoptic analysis showed that the observed pressure increase in the Arctic front region was really 

caused by the changes in the evolution of mobile anticyclones forming in the rear of frontal cyclones. It was 

revealed that after the Forbush-decrease onset these anticyclones transformed very often to so called ‘blocking’ 

anticyclones slowing their movement over Scandinavia and, thus, creating an obstacle for the movement of 

North-Atlantic cyclones in the eastern direction. This process contributed to the pressure increase over 

Scandinavia. The results obtained are in good agreement with the previous studies by Pudovkin et al. (1997) 

who revealed a growth of pressure in all the troposphere at Sodankylä station (Finland) and with the studies by 

Tinsley and Deen (1991) who showed a decrease of cyclonic vorticity at middle latitudes associated with 

Forbush-decreases of GCR. 

We suggest that the cosmic particles having sufficient energies to reach geomagnetic latitudes of the 

Arctic front (E ~ 20−80 MeV) and of the Polar front (E ~2−3 GeV) may take part in the processes of cyclone 

and anticyclone formation and development in the frontal regions. 

References 

Kalnay, E., et al. (1996), The NCEP/NCAR 40-Year Reanalysis Project, Bull.of Amer.Met.Soc., 77, 437-472. 

Khromov, S.P., and M.A. Petrociants (1994), Meteorology and climatology, Mosk.Gos.Univ., Moscow. 

Pudovkin, M.I., and S.V. Babushkina (1992), Influence of solar flares and disturbances of the interplanetary 

medium on the atmospheric circulation, J. Atm. Sol.-Ter. Phys, 54 (7/8), 841-846. 

Pudovkin, M.I., S.V. Veretenenko, R. Pellinen and E. Kyrö (1997), Meteorological characteristic changes in the 

high-latitudinal atmosphere associated with forbush-decreases of galactic cosmic rays, Adv.Sp.Res., 20(6), 

1169-1172. 

Shea, M.A., and D.F. Smart (1983), A world grid of calculated cosmic ray vertical cutoff rigidities for 1980, in: 

18 th International Cosmic Ray Conference Papers, 3, 415-418. 

Tinsley, B.A., and G.W. Deen (1991), Apparent tropospheric response to MeV-GeV particle flux variations: a 

connection via electrofreezing of supercooled water in high-level clouds?, J.Geophys.Res., 96, 283-296. 

Veretenenko, S.V., and I.V. Artamonova (2005), Forbush-decrease of galactic cosmic rays influence on the 

cyclone processes intensity at the middle and high latitudes, in: Proc. of IX Int. Solar Physics Conf., (GAO 

RAN, Pulkovo, St.Petersburg, 4-9 July 2005), 11-16. 

Veretenenko, S.V., and P. Thejll (2004), Effects of energetic solar proton events on the cyclone development in 

the Nirth Atlantic, J.Atm.Sol.-Ter.Phys., 66, 393-405. 

11


INSTABILITY OF THIN CURRENT SHEET 

A. V. Artemyev 1 , L.M. Zelenyi 1 , H.V. Malova 1,2 , V.Y. Popov 1,3 

1 Space Research Institute, RAS, Moscow, e-mail: ante0226@gmail.com 

2 Institute of Nuclear Physics, Moscow State University 

3 Physics Department, Moscow State University 

Abstract. Eigenmodes of thin anisotropic current sheet (TCS) are studied in this work. Growth 

rate of kinetic ion-wave resonance instability is found as a function of TCS parameters. It is shown 

that there exist two possible polarizations for symmetric and asymmetric modes with positive and 

negative values of the growth rate both for sausage-kink and tearing-twisting instabilities. 

Introduction. Theory of eigenmodes of current sheet (CS) instability can be used for describing of various 

dynamical processes in Earth’s magnetosphere. For example, tearing instability was studied as a reason of 

magnetic reconnection of CS (Coppi et al. 1966). Various of drift modes 

(Daughton 1999, Artemyev et al. 2008a) can describe oscillation motions of CS (Sergeev et al. 2004, 

Petrukovich et al. 2006). But for different models of initial equilibrium one can obtain different values of 

frequency and growth rate from linear theory of instability. Therefore it is interesting to study the properties 

of CS perturbations that are close to observation data (Runov et al. 2006). In this work we investigate TCS 

model (Zelenyi et al. 2004) and we show that the comparison of this model with experimental observation of 

CS gives a good result (Artemyev et al. 2008b). 

Model of TCS. The model we propose (Zelenyi et.al 2004) contains electron and ion components. In our 

approach the parameter is small: bn = Bz B0 

< 0.3 ( B0 is the magnitude of the magnetic component Bx ( z ) ), 

B 0 ~ 0 ). In this 

as a consequence ions can be taken into account as unmagnetised near neutral line of CS ( ( ) 

case equations of motion might be solved by using quasi-adiabatic integral of motion 

(Sonnerup 1971, Buechner and Zelenyi 1989). 

I z = ∫ mivz dz 

In a case of a constant magnetic field at the edges of the system I z 

2 

= mi v⊥ ωi 

( ωi is gyrofrequency of ions 

2 2 

in the edges of the system). Therefore, one can use full ion energy 0 i ( ⊥ ) 

to construct ions velocity distribution in each point of the system (Zelenyi et.al 2004): 

2 

{ ω ( 0 ω ) } 

W = m v� + v 2 + eϕ and invariant z I 

f ~ exp − I − W − I − v 

(1) 

i i z i z D 

This velocity distribution corresponds to ion flows moving from the edges of the system toward the center 

along magnetic field lines with the velocity v D . Ions turn the direction of motion in neutral plane of CS from 

W > ω I ). Ions with such behaviour are called 

X to Y direction and then leave the system (it happens if 0 i z 

“Speiser” ions. The main parameter characterizing this plasma population is ε = vTi vD 

( vTi is thermal ion 

velocity). In the case W0 < ωiI 

z ions become trapped and their distribution function is taken as thermal 

Maxwellian distribution. 

Electrons are magnetized everywhere inside CS in the case Bz ≠ 0 . Therefore in our model we use drift 

approach for electron component (Zelenyi et.al 2004). In this case electron current density can be written as: 

[ E× B] 

c c 

je⊥ = − enec + 2 2 [ B×∇ ⊥ p⊥e ] + 4 ( p� e − p⊥e 

) ⎡ × ( ∇) 

⎤ 

B B B 

⎣B B B⎦ 

(2) 

Here e n is the electron density, p⊥e and e p� are perpendicular and parallel pressure components, and 

B = 

2 2 

Bx + Bz 

. Last term in (3) corresponds with curvature electron drift and in the central region of CS 

2 

( B x ( 0 ) ~ 0 ) this term is proportional to Bz − . Because parameter bn = Bz B0 

is small the electron current in 

the central region of CS is larger than ion. On the other hand ion current density profile is wider than electron. 

As a result several different spatial scales are presented in TCS (figure 1). 

12 

x


Tearing instability. Tearing instability is a 

symmetrical mode of plasma perturbation (perturbed 

component of vector potential A1 ( z) = A1 ( − z) 

) which 

is periodical along magnetic field direction 

~ exp( ikx x − iωt ) . Growing of tearing perturbation is 

supported by resonance interaction of unmagnetized 

particles with plasma waves in the central region of CS 

( B x ~ 0 ). For the first time Harris CS model (Harris 

1962) was used for instability investigations where 

electrons were considered as resonance particles 

(Coppi et al. 1966). But the nonzero normal 

component of magnetic field Bz ≠ 0 always is present 

in Earth’s magnetosphere. Electrons become 

Figure 1. Electron and ion current 

magnetised by B z magnetic component and resonance 

density and plasma density 

interaction is dominated by ions (Schindler 1974, 

Galeev and Zelenyi 1976). The stabilization effect of magnetized electrons (Lembége and Pellat 1982) 

makes Harris CS stable to tearing perturbation (Pellat et al. 1991). 

There exist several models of CS equilibrium which are alternative to Harris CS with Bz ≠ 0 (Sitnov et al. 

2006, Birn et al. 2004, Zelenyi et al. 2004). Also one can investigate tearing-like perturbation along 

directions which are not coinciding with magnetic field lines and propagate under the angle 

θ = arctan ( k y kx 

) to it. In our work we study tearing perturbation in model of TCS (Zelenyi et al. 2004) for 

which lager store of free energy was found (Zelenyi et al. 2008). 

Kink and sausage instability. Symmetric wave perturbation exp{ i − iωt} two values of arctan ( k y kx 

) 

kr has two well known modes for 

θ = . If θ = 0 (direction along magnetic field) perturbation is named tearing and 

if θ = π 2 (direction along the current j y ) perturbation is named sausage. Sausage mode was investigated 

for Harris CS (Lapenta and Brackbill 1997, Daughton 1999). But several features of structure can be a reason 

of the difference in behaviour of this mode in TCS . 

Asymmetric mode ( A1 y ( − z) = − A1 y ( z) 

) with θ = π 2 is named kink perturbation. This mode is 

investigated for Harris CS (Kuznetsova and Zelenyi 1985, Daughton 1999). It was shown that for TCS this 

perturbation has larger growth rate than for Harris one and larger period of oscillation (Artemyev et al. 

2008a). Because of substantial storage of free energy in TCS model with Bz ≠ 0 the modes with angle not 

only θ = π 2 can exist in the neutral plane of this CS. Therefore, it this work we take into account various 

modes of instability with different values of angel θ . 

Energy principle. Necessary conditions of CS instability. In this section we consider energy function of 

( 2) 

the second order of perturbation W for TCS and for Harris CS with Bz ≠ 0 . We start from standard 

( 2) 

equation for W (Schindler 2006): 

2 

2 

( 2) B1 1 f̃ 1 j 

W = ∫ dr − ∑ 8π 2 ∫ j ∂f0 j ∂H 0 j 

1 ∂j 

q 

0 2 

j res 

drdp −∑ 1d d −∑ 

1 f1 j d d 

j 2c 

∫ A r p 

∂ 0 

j c ∫ vA r p 

A 

(3) 

= z i − iωt f̃ = f − ∂f ∂A A 

res 

− f . The resonance part of perturbed 

Here we use ( ) { } 

A1 A1 exp kr and 1 j 1 j ( 1 j 0 ) 1 1 j 

res 

distribution function f 1 j can be obtained for each models of CS independently. In the presence of the 

normal component of magnetic field B z electrons are magnetized near the neutral plane and perturbation of 

their density corresponds with magnetic field perturbation 

Schwartz inequality to rewrite equation (4): 

n1 = n0 ( B1z Bz 

) . In this case one can use 

13


2 

2 

2 1 1 p0 B1z 

1 ∂j 

q 

0 2 

j 

res 

= ∫ + 2 

1 1 1 j 

8π 2 ∫ −∑ − 

Bz j 2c 

∫ ∑ 

∂A0 

j c ∫ 

( ) B 

W dr dr A drdp vA f drdp Here we use p n ( z)( T T ) 

= + . To obtain equation for perturbed vector potential one should take first 

0 0 i e 

( 2) 

variation over W : 

2 2 

2 

d A ⎛ 1 k 1 ∂j 

⎞ 0 

kx 

− 4π 2 ⎜ − ⎟ A1 − 4π 

p0 A 2 1ye 

y 

dz ⎝ 4π 

c ∂A0 

⎠ Bz 4π 

res 

= − j 

c 

2 

Here we take into account that B1z = ikx A1 

y and ∆ A1 = d A1 2 2 

dz − k A 1 , where k = k + k . 

2 2 2 

x y 

2 2 

To solve equation (6) for tearing perturbation ( k = k ) one should write the following inequality: 

2 2 2 −1 

( r) = 4π + − ∂j ∂ A < 0 . In the case U ( ) > 0 

U k p k B c 

* 

1 ~ exp( z k ) − 

then ( ) 

x 0 x z 

0 0 

x 

(4) 

(5) 

r there exist only trivial solution 

2 

A and growth rate of instability has negative value. If one use 1 p0 Bz 

B B is necessary condition of CS instability. For 

f z = . In this case we obtain kL < bn 

for tearing instability in Harris CS. 

This inequality ( kL < bn 

) was before obtained in 1982 (Lembége and Pellat 1982). 

In TCS model the shear of bulk velocity vy ( z) is characteristic therefore one can study inequality 

2 −2 

( ) > ( ) ( ) , which takes the following form ( ) 

v z u kL b f z 

y n 

Figure 2. Examination of necessary criteria of CS instability for TCS model. 

( ) 1 − 

2 

Determining the profiles ( ) 0.5ε 

( ) ( ) ( ) 

−1 3 −2 

v y T n 

−1 3 2 −2 

( vy z vT ) 0.5ε 

( kL) bn f ( z) 

> . 

F z = kL f z v z v b as a function of z coordinate one can 

find region with Fv ( z ) < 1 in the centre of CS (figure 2). Presence of region with v ( ) 1 

exist of possibility of developing of tearing perturbation in TCS. 

14 

F z < shows that there


Sufficient condition of CS instability. To obtain sufficient condition of instability one should find 

res res 3 

nontrivial solution of equation (5) with resonance term j = e∫ v fi d v . Resonance part of perturbed 

res 

distribution function f i can be fund by standard way from linearized Vlasov equation (Lapenta et al. 1997, 

Daughton 1999, Silin et al. 2002). Also we applies Coulomb calibration for the perturbed vector potential, 

div A 1 = 0 . One could consider two different polarizations of perturbations of vector potential A 1 . First 

polarization is presented in the form A1 = A1 xe x + A1 

ye y (Galeev and Zelenyi 1976, Silin et al. 2002). 

Coulomb calibration then imposes the following condition of components of the perturbed vector potential: 

A cosθ + A sinθ = 0 . Perturbations with such polarization are suppressed when θ → π 2 . Perturbation 

1x y 

with another polarization A1 = A1 ye y + A1 

ze z (Lapenta and Brackbill 1997) can be developed also for 

θ = π 2 . In this paper we will consider below both kinds of polarization. 

For the polarization of vector potential 1 A in a form A1 = A1 xe x + A1 

ye y , it is more convenient to consider 

single equation for its magnitude 

A = A + A instead of the system of two equations for each of these 

2 2 

1 1x 1y 

components. It is straight forward, because 1x A and 1y A are linearly coupled (i.e. 1 1 tan 

x y 

Coulomb calibration: 

− − 

res 

{ ( 1 4π z cos θ ) 0.5 ( y ) cos θ} ( , θ, 

, ) 

2 2 2 2 4 1 2 

1 0 0 1 1 

A = − A θ ) by 

d A dz − k + p B − c ∂j ∂ A A = − j z A t (6) 

For another type of polarization A1 = A1 ye y + A1 

ze z one could solve the single equation for A 1y like it was 

done by Lapenta and Brackbill (1997) for the sausage mode ( θ = π 2 ). Contrary to previous works we 

extended our results for perturbations at arbitrary angles (not only θ π 2 

= )neutral plane ( , ) 

− − 

res 

{ ( 1 0.5 cos θ ) 0.5 ( ) } ( , θ, 

, ) 

2 2 2 2 2 1 

1y 0 z y 0 1y 1y 

x y propagating: 

d A dz − k + p B − c ∂j ∂ A A = − j z A t (7) 

Because the resonant current densities, 

t 

∫ 

0 

( − ) ( ) 

res 

j ~ K t t′ A t′ dt′ 

1 

, depends on 

time, equations (6) and (78) could be 

considered as evolutionary equations and 

could be solved by method of finite 

elements (Lapenta and Brackbill 1997, 

Daughton 1999). Then one could obtain 

corresponding eigenfrequencies and 

growth rates as a function of TCS 

parameters, wavenumbers k and 

propagation angles θ . 

The resulting growth rates as a function of 

propagation angles θ for both 

polarizations are shown in figure 3. As 

one can see, both symmetric polarization 

modes have equal positive values of Figure 3. Growth rate as a function of angle θ for two 

growth rate in the case of tearing polarizations. Parameters have following values: 

instability ( θ = 0 ), but asymmetric modes τ = 3 , L = 0.8ρi , kL = 0.3, 

b n = 0.1 . 

are suppressed when θ → 0 . While the 

perturbation angle θ increases perturbation with the polarization A1 = A1 xe x + A1 

ye y become suppressed. 

But perturbation having another polarization ( A1 = A1 ye y + A1 

ze z ) become correspondingly sausage or kink 

instabilities ( θ = π 2 ). In the range θ ~ π 2 the perturbation growth rate become larger than the one of 

tearing mode ( θ ~ 0 ). Thus the vector potential perturbations in propagating along the direction of the 

currents are more probable than perturbation of the tearing mode type (i.e. waves moving along x direction). 

Also the asymmetric perturbations at θ = π 2 have larger growth rate than the symmetric one like it was 

obtained in Harris CS (Daughton 1999). 

15


The growth rate of symmetric mode with polarization A1 = A1 ye y + A1 

ze z as a function of wavenumber k is 

shown in figure 4. As one can see, the range of wavenumbers with positive values of the growth rate is wider 

than the one in classical Harris CS (Daughton 1999). Maximum value of the growth rate for different values 

kL∈ 0.8,1.8 . Real part of frequency in this region of 

of propagation angle belongs to interval [ ] 

wavenumbers acquires values ω [ ] ω 

∈ 0.01, 0.035 i (this range is the same for both symmetric and asymmetric 

modes). These values are much smaller than in the ‘classical’ case of thin Harris CS (Lapenta and Brackbill 

1997, Daughton 1999) because real part of frequency corresponds to the diamagnetic drift frequency 

ω = k v = kv sinθ 

, where v DM is the velocity of diamagnetic drift, and in Harris CS where most of the 

* 

y DM DM 

current is produced by diamagnetic effect vDM ~ dn dz anddensity gradients are much lager than in 

anisotropic CS with few embedded layers (Artemyev et al. 2008a). 

Discussion and Conclusion. The results of 

linear analysis of low frequency wave-like 

instabilities in propagating in the vicinity of 

neutral plane of TCS are discussed in this 

paper. We have shown that unstable modes 

could have two different types of 

polarization as well as two symmetries. One 

of them is suppressed at θ ~ π 2 while the 

second has maximum of growth rate at such 

direction of propagation (this case 

corresponds to the classical sausage mode). 

Growth rate as a function of both the 

amplitude of wavevector and its direction is 

obtained. We have shown that TCS tearing Figure 3. Growth rate as a function of magnitude of 

instability might have positive values of wavenumber k for polarizations A = Aye y + Aze 

z . 

growth rate contrary to the Harris CS with 

Bz ≠ 0 (Pellat et al. 1991). Detailed 

Parameters have following values: τ = 3 , L = 0.6ρi , 

discussion of this devoted to the investigation of marginally stable TCSs is given in paper by Zelenyi et al. 

(2008). 

Because the direction of drift velocity for each CS is always predefined (the direction of current) its low 

frequency eigenmodes if become unstable should have properties of drifts waves. This characteristic is 

similar to the one for Harris CS model (Lapenta and Brackbill 1997, Daughton 1999) but anisotropic TCS 

model predicts at least 4-5 smaller characteristic frequency than earlier Harris type models. 

Conceptually we would like to stress the point coming from our analysis that perturbations observed within 

CS, even if assumed to belong to CS eigenmodes class (non-eigenmode transient events could also exist in 

magnetotail), could have complicated structure with mixed polarizations and symmetric/asymmetric 

characteristics. 

This work was supported in part by the RF Presidential Program for State Support of Leading Scientific 

Schools (project no. NIII-472.2008.2), the Russian Foundation for Basic Research (project nos. 08-02-00407, 

06-05-90631). 

References. 

Artemyev, A.V., L.M. Zelenyi, Kh. V. Malova, and V.Yu. Popov (2008a), Effect of the Normal Component 

of the Magnetic Field on the Kink Instability of the Earth’s Magnetospheric Current Sheet. Plasma Physics 

Report, 34(9), 771-779. 

Artemyev, A., Petrukovich A., Zelenyi L., Malova H., Popov V., Nakamura R., Runov A., Apatenkov S. 

(2008b), Comparison of multi-point measurements of current sheet structure and modern analytical models. 

Annales Geophysicae, 26, 2749–2758. 

Birn, Joachim, Schindler, Karl, Hesse, Michael (2004), Thin electron current sheets and their relation to 

auroral potentials. J. Geophys. Res., 109(A2), doi: 10.1029/2003JA010303. 

Büchner J., and Zelenyi L.M., (1989). Regular and chaotic charged particle motion in magnetotaillike field 

reversals: 1. Basic theory of trapped motion. J. Geophys. Res., 94(10), 11821-11842. 

16


Coppi, B., Laval G., and R. Pellat (1966), Dynamics of the geomagnetic tail. Phys. Rev. Letters., 16(26), 

1207-1210. 

Daughton, W. (1999), The unstable eigenmodes of a neutral sheet, Phys. Plasmas, 6(4), 1329-1343. 

Galeev, A.A., and Zelenyi L.M. (1976), Tearing instability in plasma configurations, Zhurnal 

Eksperimental'noi i Teoreticheskoi Fiziki, 70(6), 2133-2151. In Russian. 

Harris, E.G. (1962), On a plasma sheet separating regions of oppositely directed magnetic field. Nuovo 

Cimento. 23, 115. 

Kyznetsova M.M., L.M.Zelenyi, (1985), Stability and structure of perturbations of the magnetic surfaces in 

the magnetic transitional layers, Plasma Phys. & Controlled Fusion, 27(4), 363-387. 

Lapenta, G., and Brackbill, J.U. (1997), A kinetic theory for the drift-kink instability. J. Geophys. Res. 

102(A12), 27,099-27,108. 

Lembege B., Pellat R. (1982), Stability of a thick two-dimensional quasineutral sheet. Phys. Fluids., 25(11), 

1995-2004. 

Pellat, R., Coroniti F. V., and Pritchett, P. L. (1991), Does ion tearing exist? Geophys. Res. Lett. 18, 143–146. 

Petrukovich, A. A., Zhang, T. L., Baumjohann, W., Nakamura, R., Runov, A., Balogh, A., Carr, C.(2006), 

Oscillatory magnetic flux tube slippage in the plasma sheet. Annales Geophysicae, 24, 1695-1704. 

Runov, A., V.A. Sergeev, R. Nakamura, W. Baumjohann, S. Apatekov, Y. Asano, T. Takada, M. Volwerk, Z. 

Voros, T.L. Zhang, J.-A. Sauvaud, H. Reme, and A. Balogh (2006), Local structure of the magnetotail 

current sheet: 2001 Cluster observations. Annales Geophysicae, 24, 247-262. 

Schindler, K. (1974), A Theory of the Substorm Mechanism. J. Geophys. Res., 79(19) , 2803-2810. 

Schindler, K. (2006), Physics of Space Plasma Activity. Cambridge University Press, ISBN: 9780521858977. 

Sergeev, V., Runov A., Baumjohann W., Nakamura R., Zhang T. L., Balogh A., Louarnd P., Sauvaud J.-A., 

Reme H.(2004), Orientation and propagation of current sheet oscillations. Geophys. Res. Lett., 31(5), doi: 

10.1029/2003GL019346. 

Silin, I., Büchner J., Zelenyi. L. (2002), Instabilities of collisionless current sheets: theory and simulations. 

Physics of Plasmas. 9(4), 1104-1112. 

Sitnov, M. I., Swisdak M., Guzdar P. N., Runov A. (2006), Structure and dynamics of a new class of thin 

current sheets. J. Geoph. Res. 111(A8), doi: 10.1029/2005JA011517. 

Sonnerup, B.U.Ö. (1971). Adiabatic particle orbits in a magnetic null sheet, J. Geophys. Res., 76, 8211-8222. 

Zelenyi, L. M., H. V. Malova, V. Yu. Popov, D. Delcourt, and A.S. Sharma (2004), Nonlinear equilibrium 

structure of thin currents sheets: influence of electron pressure anisotropy, Nonlinear Processes in 

Geophysics, 11, 1-9. 

Zelenyi, Lev, Artemyev Anton, Malova Helmi, Popov Victor (2008), Marginal stability of thin current sheets 

in the Earth’s magnetotail. Journal of Atmospheric and Solar-Terrestrial Physics. 70, 325-333. 

17


TRIGGER MECHANISM OF SOLAR-ATMOSPHERIC RELATIONSHIP 

AND THE CONTRIBUTION OF THE ANTHROPOGENIC IMPACT 

S.V. Avakyan, N.A. Voronin 

All-Russian Scientific Center S.I. Vavilov State Optical Institute 

Birgevaja line, 12, St. Petersburg, 199034, Russia, e-mail: avak2@mail.ru, avak@soi.spb.ru 

Abstract. A unified approach is suggested to the problem of impact of both space and several 

anthropogenic sources on the weather and climate changes. This impact is conducted by 

microwave ionospheric radiation with is generated both solar flares and by corpuscular 

precipitations from magnetosphere. Precipitations of electrons and proton fluxes from radiation 

belts take place during geomagnetic storms and also as result rocket launches, technological 

activity and at work of powerful radio transmitters. 

We suggest three-stage radio-optical trigger mechanism for the influence of solar flares and geomagnetic 

storms on the weather characteristics. The first stage is an increase in generation of the 

microwave radiation which penetrates from the ionosphere to the earth surface. The second stage 

is a change in the proportion of water vapour to water clusters caused by increased microwave radiation. 

The third stage is a change of the atmosphere transparence in the absorption bands of water 

vapour and clusters. The atmosphere transparence determines the fluxes of solar irradiance 

coming down as well as flux of the thermal radiation coming out from the underlying surface. 

These fluxes form the basis of the thermal balance and affect the weather and climate characteristics 

of the lower atmosphere. 

The maximum of secular cycles solar activity was observed in eighties last century. Since 1985 the 

total solar irradiance and ionizing fluxes have been decreasing but geomagnetic activity (aa - index) 

has been going up till 2003. Only during the last few years geomagnetic activity also started decreasing. 

This means that negative trends have come both for solar and geomagnetic activities. We 

suppose that according to our mechanism the natural global warming will go down to lower levels. 

Introduction 

The physical mechanism for natural global climate changes which happened during the last several 11th 

solar cycles is considered. The mechanism explains how agents of solar and geomagnetic activities together 

affect low-atmospheric processes: with help the flux of microwaves from ionosphere, which are generated 

during solar flares and geomagnetic storms due to the excitation of Rydberg states of atoms and molecules 

in upper atmosphere by fast ionospheric electrons. It is here very important for climatic changes, that 

the maximum of seculars (near one hundred and near of two hundred years) cycle solar activity was observed 

in eighties last century. 

In this paper are considered: 

1) the novel radiooptical the three-stage trigger mechanism of the solar flare and geomagnetic storms 

influence at the weather and climate characteristics. [1]. 

2) forecasting of future climatic changes – a namely decrease of natural contribution of global warming, 

if take into account the sum of solar and geomagnetic activity together. 

3) role of the new anthropogenic factor of the weather and climate – the experimentally registered precipitations 

of electrons from the radiation belts occurring during the period of work of power transmitters 

over the cyclotronic frequencies. 

Microwave radiation from ionosphere during solar flares and geomagnetic storms as well as microwave 

bursts from the Sun are supposed to control the condensation processes in the low atmosphere and thus 

affect the weather. This physical mechanism is based on taking into account the excitation of Rydberg states 

of atoms and molecules in generation of the ionospheric microwave radiation and in realization of the 

dissociative recombination of cluster ions in troposphere [1]. 

Recently we can read [2]: “We show that over the past 20 years, all the trends in the Sun that could 

have had an influence on the Earth’s climate have been in the opposite direction to that required to explain 

the observed rise in global mean temperatures... Our results show that the observed rapid rise in global mean 

temperatures seen after 1985 cannot be ascribed to solar variability, whichever of the mechanisms is invoked 

and no matter how much the solar variation is amplified”. Indeed, since 1985 the total solar irradiance (this 

irradiance is the total solar energy flux received at the top of the Earth’s atmosphere) and EUV/X-ray ionizing 

fluxes have been decreasing. But geomagnetic activity (aa - index) has been going up till 2003 (+ 0.3 % / 

year), Fig. 1. Only during the last few years (on October 2007) geomagnetic activity also started decreasing 

(- 5.7 % / year). This means that negative trends after 2003 have come both for solar and geomagnetic activi- 

18


aa-index 

40 

35 

30 

25 

20 

15 

1980 1985 1990 1995 2000 2005 

Years 

Fig. 1. Trends of the monthly аа-index of geomagnetic activity 

before and after 2003. 

ties. We suppose that according to our 

mechanism the natural global climate 

changes will go down to lower levels. 

There are also the change of sign for 

next trends of atmospheric parameters before 

and after 2000-2001: 

- the Earth’s albedo decreased during the 

period 1984 – 2000/1 and increase after the 

year 2000/1 [3], 

- the content of water vapour increased in 

the atmospheric depth during the period 

1980 – 2000 and decrease after the year 

2001 (Kyrghyzstan, lake Issyk-kul station 

[4]), 

- the total contents of ozone these decades, 

on the contrary, decreased, that has led to 

growth of a erythemal radiation in day time 

which also has started to decrease only with 

year 2000, then the content of ozone is increase 

[5]. 

Change of a sign on trend of total influence 

of solar and geomagnetic activity in 

generation of microwave radiation has actually occurred on 1-3 years earlier 2003, as was reflected in terms 

of change of signs in trends of the contents vapour of water, methane and ozone. 

About the novel radiooptical trigger mechanism of solar-weather and climate links 

In according to [6] it is necessary to propose the unknown trigger mechanism of ionospheric disturbance 

downward transfer into the troposphere under the action of the solar and geomagnetic activity factors 

(solar ionizing radiation and corpuscular fluxes from radiation belts) because the natural energy of weather– 

climate phenomena is very high. Avdyushin and Danilov [6] justified than such a necessity is related to the 

fact that the energy of the short waves (including the ionizing range) solar radiation, as well as that of corpuscles 

(electrons) from radiation belts and solar protons, cannot directly affect the troposphere because 

these fluxes do not reach the troposphere, being usually absorbed at much higher altitudes. Therefore, the effect 

of the solar ionizing radiation and corpuscular fluxes on the mesosphere and thermosphere should be 

somehow transferred downward, to the troposphere. Indeed, the mechanism of the effect of increasing solar 

activity on weather characteristics during geomagnetic disturbances due to the known Forbush decrease in 

the intensity of galactic cosmic rays was discovered (see [7] and references therein). However, these researchers 

repeatedly noted that solar flares, which lead a geomagnetic disturbance - magnetic storm - by approximately 

two days, also affect the weather characteristics, first of all, cloudiness. The effect of an increase 

in the UV (and X-ray) flux is registered several hours after a solar flare. This is directly related to the response 

of the degree of atmosphere transparency to the appearance of an enhanced flux of electromagnetic 

(UV) flare emission, when accompanying fluxes of the disturbed solar wind and SCRs have not yet reached 

the Earth’s orbit [7]. 

During the last decades the influence of galactic cosmic rays (GCR) and solar cosmic rays (SCR) on 

the cloudness has been studies in detail. The factors of influence are Forbush decrease of GCR and sporadic 

increase of SCR. However these events are rare. For instance, geomagnetic storms (with Kp more than 5) 

occur 20-80 times per year and solar flares (class greater than M5) take place 50 times per year [8] whereas 

Forbush decrease of 3 % and more occurs only 2-4 times per year and solar proton events at energy than 100 

MeV take place 5 times per year that is approximately ten times lesser. 

We propose to solve this problem in a new way by introducing a “three-stage trigger.” The first stage 

is transformation of the energy factors of solar (increased flux of ionizing radiation) and geomagnetic (precipitating 

corpuscles from radiation belts) activities in the ionosphere into the flux of microwaves, penetrating 

to the Earth’s surface within the troposphere. This is a direct trigger (initiating triggering mechanism) 

since direct information relation between the upper atmosphere and the entire troposphere originates precisely 

during this stage, which was previously ignored in the solar–terrestrial coupling [9]. The second stage 

is regulation of the production and destruction rates of water cluster ions at altitudes where the condensation 

19


mechanism operates and initiates the generation of cloud and aerosol layers in the lower atmosphere (at altitudes 

higher than 3–4 km; i.e., in the zone of influence of galactic cosmic rays) and stratosphere (in the zone 

of SCR absorption) [10]. In this stage taking into account Rydberg states excitation at the preliminary stages 

of association and dissociation of clusters (as well as ionized clusters) of water vapour and carbon dioxide. 

The rates of association and dissociation processes depend strongly on the magnitude of the Rydberg state 

orbital quantum number. An increase in the orbital quantum number by one results in a decrease of crosssections 

of the dissociation processes by an order of magnitude. According to the developed theory [9]. this 

increase in the quantum number is caused by stimulated absorption of the ionospheric microwave radiation 

quanta as well as solar radiobursts radiation quanta during the periods of increased solar and geomagnetic activity 

(or anthropogenic precipitation impact). 

The third stage consists in the evident role of formed clouds and aerosol layers in weather–climate 

phenomena via absorption and reflection of certain part of the solar radiant energy and thermal flux from the 

underlying surface by these formations [10]. There is various role cloudiness in global warming. According 

to [11], the net radiative properties of a cloud are mainly depend on its altitude and optical thickness. Optically-thin 

clouds at high and middle altitudes cause a net warming due to their relative transparency at short 

wavelengths but opacity in the IR region, whereas thick clouds produce a net cooling due to the dominance 

of the increased albedo of short-wave solar radiation, and according to [12], the role of high clouds in the radiation 

budget of the earth-atmosphere system depends on optical depths; high thin cloud acts to warm the 

atmosphere, while high thick cloud cools. Thus, the decrease in high clouds can reduce both the warming 

and cooling effect to the system. But it is clear that because of relatively low power of the ionospheric microwave 

radiation (in comparison with atmospheric energy) its influence on the clusterization leads to formation 

of optically-thin clouds at the high altitudes. 

On the whole, the proposed three stage physical mechanism is an intensifying process since a low energy 

of cosmic factors regulates fluxes of incoming and outgoing radiation in the lower atmosphere owing to 

strong energy variability. According to numerous calculations [7, 10], even 6% weakening of the solar radiant 

energy flux due to reflection and absorption at altitudes of several kilometers can explain the observed 

contribution of solar and geomagnetic activities to weather phenomena. In addition, resonance absorption 

can participate in this process because the characteristic microwave emission of ionospheric nitrogen and 

oxygen molecules in Rydberg transitions in the lower atmosphere by Rydberg excited nitrogen and oxygen 

molecules participating (as an ambient gas) in collisional dissociative recombination of cluster ions from water 

vapor and carbonic acid molecules [13]. 

We emphasize that all stages of the proposed novel radiooptical mechanism are experimentally confirmed: 

(i) the microwave ionospheric emission, which intensifies during solar and magnetic storms, was detected 

in [14, 15]; 

(ii) the regulation of humidity at altitude higher than 3 km by the solar microwave emission and flares 

was registered in [16, 17]; 

(iii) a direct influence of solar flares and magnetic storms on the total cloudiness is distinctly registered 

[18, 19, 20]. 

Our contribution consists in that we determined the mechanism of generation of the ionospheric microwave 

emission in transitions between highly excited (Rydberg) states and used the processes of dissociation 

and association of complex ions well known in physics of atomic collisions [13, 21, 22, 23] via intermediate 

Rydberg levels. In the case of association (i.e., formation of clusters), the process proceeds through the 

addition of proton to parent molecules owing to their high affinity to proton. Produced ions are neutralized 

when electron is trapped at a Rydberg orbital. The orbital moment, the value of which can change during absorption 

of quanta of the microwave emission from the ionosphere, is the main characteristic of Rydberg levels 

affecting the rate of the considered elementary processes. 

Rydberg microwave emission of ionosphere during precipitation of electrons from the radiation 

belts caused by radio transmitters 

Industrial greenhouse effect is usually suggested as a cause of global rise of the surface temperature 

over the last few decades. In this paper we propose to draw attention the new anthropogenic component – influence 

of powerful radio transmitters (navigation and communication) on the particles in radiation belts of 

the Earth. This anthropogenic factor affects mainly the electrons from inner and outer belts over the cyclotronic 

frequencies i.e. frequencies of the Larmor precession. These frequencies belong to very low frequency 

(VLF) range: from few to few tens kilo Hertz. 

20


Surface transmitters with such frequency have power up to 1 Mw that cause precipitations and result 

in optical emission above the transmitter. Intensity of these emissions is of the same scale with the aurora of 

the class two or more in the international IBC II system. Thus, precipitations simulated by VLF transmitters 

we suggest to consider as anthropogenic analogue of the aurora caused by magnetic storm. 

Let us estimate contribution of this phenomenon into microwave radiation of ionosphere, which according 

to experiment [1 16, 17] and its interpretation suggested in [1, 24] could control processes of condensation 

and cloud generation in the lower atmosphere. Previously, we considered global geomagnetic 

storms in the problem “Sun-weather” [24] and showed that during geomagnetic storms microwave radiation 

from Rydberg states, caused by ionospheric fast electrons (secondary electrons and Auger electrons), controls 

rate of cluster generation as well as during solar flares. 

We take into account results [13] connected with influence of the orbital quantum number (l) of the 

Rydberg state on the rate of dissociative recombination of cluster ions. These results show that this rate decrease 

when high l levels are filled when strong fluxes of the microwave radiation appear [1, 24]. This could 

activate cyclonic activity [25]. Moreover generation of optically thin clouds of the upper layer might cause 

warming of the near surface air [11]. 

Thus we can make very important for the modern climatology conclusion that two important features 

of the modern climatic change: (a) global warming and (b) permanent increase in cyclone number (192 cyclones 

from 1970 to 1992 and 162 over the next 10 years [25, 26]) have the same nature – global increase of 

the number and power of VLF transmitters particularly near maritime coast regions where the cyclogenesis 

takes place. This conclusion is based on analysis on intensity of the stimulated electronic precipitations 

which are comparable with the precipitations during the global geomagnetic storms. Results of measurements 

performed by the satellite DEMETER [27, 28] confirm very high extent of disturbance of radiation 

belts and ionosphere during night above the zone of work of VLF transmitters both in Northern Hemisphere 

(transmitter NAA in USA with coordinates 44°39 N, 67°17 W), and in Southern Hemisphere (transmitter 

NWC in Australia with coordinates 21°47 S, 114°09 E). Areas of the stimulated electronic precipitations and 

areas of perturbed ionosphere are linked either with the magnetic force line at which the surface VHL transmitter 

is situated or with the magnetic line at which effect of radio wave on the pitch angle of electron, captured 

in radiation belt, takes place. In full agreement with the law of latitudinal drift in dipole magnetic field 

there is some expanding of the perturbed region eastward thus area of the stimulated perturbations reach a 

half of million of square kilometers [28]. Every time perturbation of less scale are observed in magnetic conjugate 

area. In accordance with our calculations [29] rate of the optical excitation of ionosphere in the conjugate 

point and hence, generation of microwave radiation from Rydberg states reaches 10 % of the effect in 

the point of the transmitter work. Intensity of precipitations corresponds to the main phase of geomagnetic 

storm. This conclusion is made by us after comparison of the data [27, 28] considering the scale [8], with the 

results of measurements of fluxes of electrons precipitating from radiation belts during global geomagnetic 

storms performed by satellites “Kosmos-348” [ 30] and “Kosmos-381” which had radiometric equipment 

made in State Optical Institute [31]. Actually, according to [31, 32] increases in electronic fluxes, precipitating 

to middle latitudes from radiation belts, occur during periods on 2-3 hours over the main and recovery 

phase with energies at least 300 times larger than 2.5 and 25 KeV. This regards also to latitudes more than 

45° for both day and night conditions in both hemispheres. But just these increases of electron precipitation, 

stimulated by work of VFL transmitter are registered by DEMETER satellite [27] even over the lower latitudes. 

Experiment [27] showed also that stimulated precipitations correlate well with the level of geomagnetic 

perturbation. Fluxes, registered by DEMETER are few order of magnitude higher than levels measured 

by the satellite “Oreol-2” for the same energy of electrons in the work [33] for discrete forms of aurora. 

Thus precipitation of electrons from radiation belts, registered over periods of VFL transmitters have 

fluxes close to that from the global magnetic storm. Such storm is accompanied by intensive emission of all 

the upper atmosphere [29] which is aurora. Hence, according to results of our investigation [1, 24, 9, 34] 

these simulated precipitations of electrons to ionosphere should cause excitation of Rydberg states with the 

corresponding emission of microwave radiation with intensity up to 10 –12 – 10 –11 W сm –2 [24]. It should be 

noted, however, that we have not enough information on the spectra of electrons precipitating due to influence 

of VLF transmitters [27, 28, 35, 36] that brings some limitations in energy estimations. High altitude 

experiments [1, 24] showed that microwave emission in 2-10 cm range might influence process of cluster 

generation in the lower atmosphere. According to our hypothesis [1, 24] that should reflect in changes of the 

weather and climate parameters. Since radio and VLF transmitters are both products of the industrial activity 

of 20 th century probably it is necessary to take into account its geography and working regime when research 

solar-weather and solar-climate phenomena. 

21


Conclusion 

The new radiooptical mechanism of the action of solar and geomagnetic activity on the weather and 

the climate is substantiated. Suggest integral approach to the problem of the control of weather and climatic 

changes by both the natural - space sources and by some anthropogenic (technogenic) actions. In this case is 

examined the united agent of this control - microwave emission of the terrestrial ionosphere, which appears 

with atoms and molecules excitation of gases of the upper atmosphere by fast ionospheric electrons into the 

highly excited (Rydberg) states. Fast ionospheric electrons with the energies more than 10 - 15 eV are 

formed with the photoionization of the upper atmosphere under the effect of X-ray and extreme UV solar radiation, 

with the corpuscular precipitations both in the period of geomagnetic storms and under the anthropogenic 

influences. The latter (emission of powerful radio stations, electric power lines, starting space rockets, 

industrial activity) ensure the locality of precipitations (because the most of them induce VLF emissions) 

and, correspondingly, the local action of the microwave radiation of the ionosphere on the weather characteristics. 

Additionally locality they ensure coastal effect, and thunderstorms, is possible also connection with 

breakings of the earth's crusts, the centers of the preparation of earthquakes. 

The negative trends after 2003 have come both for solar and geomagnetic activities. We suppose that 

according to our mechanism the natural global climate changes will go down to lower levels. Role of the new 

anthropogenic factor of weather and climate changes – the experimentally registered precipitations of electrons 

from the radiation belts occurring during periods of work of powerful transmitters over the cyclotronic 

frequencies – also is discussed. 

Acknowledgements 

The authors would like to thank for the moral support the foreign collaborators of the International 

Science and Technology Center project #3878: A.D. Aylward, APL/UCL. UK; A. Belehaki, NOA, Greece; A. 

Hilgers, ESA/ESTEC, Netherlands; J. Lilensten, LPG, France. 

References 

1. Avakyan, S.V., N.A. Voronin (2006), Condensation Process in the Low Atmosphere and Microwave Radiation 

of the Sun and Ionosphere, in: Proceeding of the VI International Conference “Problem of Geocosmos”. 

2006. SPbSU. 24-28. 

2. Lockwood, M. and C. Frohlich (2007), Recent opposite directed trends in solar climate forcing and the 

global mean surface air temperature, Proc. Royal Soc. A., doi: 10.1098/rspa.2007.1880. 

3. Climate change. Scientific assessment and policy analysis. Ed. R van Dorland, 2006, 154 pp. 

4. Arefiev, N.N. et al. (2006), Water vapour in atmospheric dept of North Tien Shan, Physics of Atmosphere 

and Ocean (in Russian), 48, 5, 803-815. 

5. Feister, U., J. Junk, and M. Woldt (2008), Long-term solar UV radiation reconstructed by Artificial Neural 

Networks (ANN), Atmos. Chem. Phys. Discuss., 8, 453–488. 

6. Avdyushin, S.I. and A.D. Danilov (2000), The Sun, Weather, and Climate: A Present Day View of the 

Problem (Review), Geomagn. Aeron. 40 (5), 3–14 [Geomagn. Aeron. 40, 545–555]. 

7. Pudovkin, M.I. and O.M. Raspopov (1992), Mechanism of the Effect of Solar Activity on the State of the 

Lower Atmosphere and Meteorological Parameters: A Review, Geomagn. Aeron. 32 (3), 1–22. 

8. S.E.C. User Notes. Issue 28. January. 2000. 7 pp. 

9. Avakyan, S.V. and N.A. Voronin (2007), On the Possible Physical Mechanism of the Effect of Solar and 

Geomagnetic Activity on Phenomena in the Lower Atmosphere, Issled. Zemli Kosm., 2, 23–30. 

10. Kondrat’ev, K.Ya. and G.A. Nikol’skii (1995), Solar Activity and Climate. 1. Observational Data. Condensation 

and Ozone Hypotheses, Issled. Zemli Kosm., 5, 3–17. 

11. Kirkby, J., and A. Laaksonen (2000), Solar variability and clouds, Space Sci. Rev., 94, 1/2, 397-403. 

12. Tsushima, Y. (2005), Report of the 2nd International SOWER Meeting, SPARC Newsletter, 24, 24. 

13. Bates, D.R. (1981), Electron-ion recombination in an ambient molecular gas, J. Phys. B., 14, 18, 3525- 

3534. 

14. Forsyth, P.A., W. Petrie, and B.W. Currie (1950), On the Origin of Ten Centimeter Radiation from the 

Polar Aurora, Canad. J. Res., Ser. A, 28 (3), 324–335. 

15. Bondar’, L.N., K.M. Strezhneva, and V. S. Troitsky (1975), Sporadic Background Radioemission, Solar 

Activity, and Auroras, Astron. Vestn., 9 (4), 210–217. 

22


16. Krauklis, V.L., G.A. Nikol’skii, M.M. Safronova, E.O. Shults (1990), On the conditions of appearance of 

abnormal peculiarities of aerosol attenuation of ultra-violet radiation under high transparency of the atmosphere, 

Optics of Atmosphere (in Russian), 3, 3, 227-241. 

17. Nikol’skii, G.A., E.O. Shults (1991), Time-spectral variations of the residual attenuation in the ultra-violet 

range of spectrum, Optics of Atmosphere (in Russian), 4, 9, 961-966. 

18. Dmitriev, A.A. and T.Yu. Lomakina (1977), Cloudiness and Space X Rays,” in Solar Activity Effects in 

the Lower Atmosphere, Ed. by L.R. Rakipova (Gidrometeoizdat, Leningrad, ), 70–77 [in Russian]. 

19. Veretenenko, S.V. and M.I. Pudovkin (1994), Effects of GCR Forbush Decreases in Total Cloudiness 

Variations, Geomagn. Aeron. 34 (4), 38–44. 

20. Veretenenko, S.V. and M.I. Pudovkin (1996), Variations of Total Cloudiness during Solar Cosmic Ray 

Events, Geomagn. Aeron. 36 (1), 153–156 [Geomagn. Aeron. 36, 108–111]. 

21. Mark, T.D. and A.W. Castleman, Jr. (1985), Experimental Studies on Cluster Ions, Adv. At. Mol. Phys. 

20, 65–172. 

22. Biondi, M.A. (1982), Electron–Ion Recombination in Gas Phase, Appl. At. Coll. Phys., Ed. by E.W. 

McDaniel and W. L. Nighan, Vol. 3, pp. 173–189. 

23. Gallas, J.A.C., G. Leuch, H. Wallher, and H. Figger (1985), Rydberg Atom: High Resolution Spectroscopy 

and Radiation Interaction Rydberg Molecules, Adv. At. Mol. Phys., 20, 413–466. 

24. Avakyan, S.V., N.A. Voronin (2006), Possible mechanisms for the influence of heliogeophysical activity 

on the biosphere and the weather, Opticheski Zhurnal, (J. Opt. Technol. – in Englich, 73, 4, 281-285), 2006, 73, 

4, 78-83. 

25. Ivanov, K.G. (2007), Correlation between tropical cyclones and magnetic storms over the 23 th cycle of solar 

activity, Geomagn. and aeronomy., 47, 3, 394-398. 

26. Golitsyn, G.S. (1997), Statistics and energy of tropical cyclones, Dokl. RAS, 354, 4, 535–538. 

27. Sauvaud, J.A., A.R. Maggiolo, C. Jacquey, M. Parrot, J.-J. Berthelier, R.J. Gamble, and C.J. Rodger (2008), 

Radiation belt electron precipitation due to VLF transmitters: Satellite observations, Geophys. Res. Lett., 35, 

L09101. doi:10.1029/2008GL033194. 

28. Parrot, M., J.A. Sauvaud, J.J. Berthelier, and J.P. Lebreton (2007), First in-situ observations of strong ionospheric 

perturbations generated by a powerful VLF ground-based transmitter, Geophys. Res. Lett., 34, L11111. 

doi:10.1029/2007GL029368. 

29. Avakyan, S.V. (2001), Impact of the impulse X-ray source on the optics of upper atmosphere considering 

the Auger effect, Opticheski Zhurnal, (J. Opt. Technol. – in Englich), 68, 4, 5-11. 

30. Lashtovichka, J. (1980), Precipitation of energetic (E=20-150 KeV) electrons over the middle latitudes, 

Geomagn. and Aeronomy, 20, 5, 800-883. 

31. Avakyan, S.V., M.P. Bolgartseva, A.I. Efremov, I.A. Krinberg, A.P. Kulakov, V.S. Petrov, A.L. Podmochensky, 

I.M. Pribylovsky, G.V. Sazonov, Yu.N. Shaulin (1974), The fluxes of electrons during the magnetic 

storm 14-15 December 1970 according to data of the satellite “Kosmos-381”, Issledovania Geomagn. and aeronomy., 

32, 158-161. 

32. Avakyan, S.V., A.I. Vdovin, V.F. Pustarnakov (1994), Near-Earth space ionization and penetration radiations, 

Handbook, St. Petersburg, Gidrometeoizdat, 501 p. 

33. Val'chuk, T.E., Yu.I. Gal'perin, Zh. Kran'e, L.M. Nikolaenko, Zh.-A. Sovo, Ya.I. Fel'dshtein (1979), Diffusion 

auroral zone. IV. Latitudinal pattern of precipitation of the auroral particles into ionosphere and structure 

of the plasma sheath in the magnetospheric tale, Kosmicheskie Issledovanya, 17, 4, 559-579. 

34. Avakyan, S.V (2008), Physics of the solar-terrestrial connections: results, problems and new approaches, 

Geomagn. and Aeronomy, 48, 4, 1-8. 

35. Inan, U.S., T.F. Bell, J. Bortnik, J.M. Altbert (2003), Controlled precipitation of radiation belt electron, J. 

Geoph. Res., 108. A5, 1186. 

36. Datlowe, D. (2006), Differences between transmitter precipitation peaks and storm injection peaks in lowaltitude 

energetic electron spectra, J. Geoph. Res., 111, A12, 202. 

23


MAGNETOMETRIC SPECTRA OF AURORAL CURRENTS COMPARED 

WITH THE DOPPLER RADAR MEASUREMENTS 

V.I. Badin 

Pushkov Institute of Terrestrial Magnetism, Ionosphere, and Radio Wave Propagation, 

IZMIRAN, Troitsk, Moscow Region, 142190, Russia 

Abstract. Doppler radar measurements have revealed the enigmatic frequencies of 1.3, 1.9, 2.6, 

3.2–3.4 and probably 0.6–0.8 mHz associated with the auroral activity. The frequencies are nearly 

invariant, i.e. repetitively observed at independent activity events. This study applies the spectral 

analysis to the 10-second magneto-difference data obtained by the IMAGE magnetometer 

network. The proposed technique analyzes events of moderate to very low activity of the auroral 

electrojet observed at the southward and northward IMF. Each selected event, except that of the 

lowest activity, displayed a quasi-stationary auroral arc, with its position being retained within a 

narrow interval of latitudes. The magneto-difference data used consist of the differences between 

the meridional components of the magnetic fields detected by neighboring magnetometers of the 

meridional array of instruments. Distinct equidistant harmonics can be revealed by the 

spectrograms. Their spectral peaks indicate different frequencies varying from case to case, but the 

frequency distances between adjacent peaks tend to coincide with or closely approach the invariant 

Dopplerometric frequencies. An important new feature is that the lower frequencies dominate at 

southward IMF while higher at northward. This fact indicates that the ULF signals observed at the 

auroral activity cannot be explained by the MHD modes solely. The proposed explanation 

interprets the low-frequency harmonics as the spectra of the auroral currents generated by some 

rotating sources associated with the magnetospheric convection. The spectrograms obtained for the 

very low activity demonstrate a pattern that can be attributed to the MHD spectrum alone. In 

general, the ULF spectra observed apparently contain the low-frequency harmonics of some 

intramagnetospheric sources and the MHD response to both internal and external sources. 

Introduction 

The Doppler radar and magnetometric measurements, carried out at high latitudes during periods of 

the considerable auroral activity, have revealed some discrete frequencies, namely those of 1.3, 1.9, 2.6, 3.2– 

3.4 and probably 06–0.8 mHz [1, 2]. These frequencies demonstrate significant stability or invariance; i.e. 

nearly identical frequencies are repetitively observed at independent activity events. To reveal these 

frequencies statistically in the magnetometric data, an additional filtering, which extracts highly polarized 

signals typical for the magnetic field line resonance, is usually used [1-3]. A critical analysis of the highlatitude 

magnetometric data undertaken in [3] questioned the stability of the discrete frequencies revealed. At 

the same time, the stability of these frequencies was surprisingly supported by the low-latitude (L=1.6) 

observations [4]. 

The magnetohydrodynamic (MHD) modes of the magnetospheric cavity located between the 

magnetopause and the plasmapause were proposed for an explanation of the physical origin of these 

signals [2]. However, the well-known theory of such MHD modes treated as coupled compressionaltransverse 

oscillations [5] and the numerical computations of magnetospheric dipole MHD spectra [6] 

indicate significantly higher frequencies for these modes. Namely, the frequencies of all modes in these 

spectra must exceed 5 mHz, since the compressional waves propagating along the shorter transverse size of 

the magnetospheric cavity add to the spectrum the frequencies which are higher than those of the transverse 

waves propagating along the magnetic field lines. Thus, the MHD spectra of these modes must be shifted 

into higher frequencies, and the shift must exceed the frequency distance between successive spectral 

components determined by the quantization step of transverse waves. 

The contradiction with the theory, in fact, leaves the origin of the discrete auroral frequencies 

unknown. On the other hand, the frequencies of the range can be associated with a direct influence of the 

solar wind and explained by small changes in the Chapman-Ferraro current induced by variations in the 

dynamic pressure of the solar wind [7, 8], although such explanations require some additional reasons for the 

invariance or stability of the discrete auroral frequencies. The goal of the present work is to apply a special 

spectral analysis to the magnetometric data, in order to examine the origin and stability of the discrete 

frequencies revealed. 

24


Data selection and processing 

To apply spectral analysis, the time series studied must approach stationary as closely as possible. 

Trying to satisfy this requirement, we can select the auroral events in which the auroral arcs remain quasistationary, 

being retained within narrow intervals of latitudes. The all-sky-camera (ASC) keograms recorded 

over long activity periods can be very helpful for this purpose. Figure 1 showing the Longyearbyen keogram 

(negative) for 17.01.2000 presents a pertinent example. We can see that the auroral arc continually moves 

Fig. 1. Keogram shows the aurora retained in a narrow latitudinal interval during 20:00-00:00 UT 

along the meridian, being nevertheless retained within a comparatively narrow interval of latitudes. The 

meridional motion of the arc introduces the low-frequency noise into the magnetometric data, and this noise 

severely impedes the analysis. 

The subsequent spectral analysis is executed as follows. For the every pair of neighboring 

magnetometers in the meridional array of instruments, the detected meridional magnetic fields are subtracted 

from each other forming the magneto-difference signals. These magneto-difference signals eliminate 

contributions of distant sources of magnetic fields thus extracting the fields of the nearest sources, which 

predominantly are the Hall currents flowing in the ionosphere at the given latitudes. Further, the periodogram 

analysis using the Tukey-Hanning spectral window is applied, with the width (resolution) of the window 

being individually adjusted for each pair of magnetometers that is for each latitudinal interval. For this 

purpose, the analysis is formulated as solving an inverse problem of searching for the spectral window 

resolution that gives us the most probable equidistant spectral peaks fitted to the data. 

The proposed technique can be risky, of course, when the equidistant spectral model becomes 

inconsistent with the physics of the phenomena in study. On the other hand, the equidistant or nearly 

equidistant spectra are very typical for numerous physical generators and resonators which can be probable 

sources of discrete spectra. There is a little probability that the equidistant spectrum turns out to be 

completely inconsistent with the physics. Nevertheless, to take account of opposite situations, an alternative 

formulation of the inverse problem is in searching for the most prominent spectral peaks resembling the 

Fejer kernel, since we seek for discrete frequencies. In either case, the proposed technique can be quite 

appropriate when we have convincing physical reasons to expect some discrete equidistant spectra in the 

signals detected. Approximate solutions of the inverse problem can be found by the trial and error method. 

We can accelerate the trial and error procedure reducing the spectral resolution successively, until we find 

the lowest applicable resolution, below which the spectrum starts to disappear. Some additional reasons for 

this technique can be found in [9]. 

Results and discussion 

The first event subjected to the examination is a period of a rather low activity of the auroral 

electrojet indicated by the IMAGE activity index IE0 and Kp=0+, while the solar wind 

parameters by the density N=3cm -3 and velocity V=700km/s. Figure 2 presents spectrograms for five pairs of 

auroral magnetometers. The spectrograms corresponding to higher latitudes are shown above those for lower 

latitudes. Each spectrogram is marked by the maximum amplitude of the magneto-difference signal in nT 

25

(the first number), two three-letter abbreviations of the station names for each pair, and the frequency 

distance between adjacent spectral peaks 

in mHz (the last number). The ordinate and abscissa axes show the 

non-normalized power densities and frequencies in mHz, respectively. 

We can see all spectral peaks obtained indicate frequencies 

above 5 mHz that well agrees with the MHD theory and 

7 NAL-LYR 4.6 computations. All spectrograms show nearly equidistant harmonics, 

though there are no standard harmonic relations, in which all 

16 LYR-HOR 3.7 

frequencies are proportional to the first main frequency. Nevertheless, 

we can recover standard relations, if we translate each spectrum as a 

whole to lower frequencies until the harmonic proportionality appears. 

According to this translation, we can identify two different types of 

32 HOR-BJN 2.0 

spectra. The spectra of the first type require translations or frequency 

shifts which exceed the frequency distance between adjacent peaks, 

i.e. exceed the frequency step of the spectrum. On the contrary, the 

spectra of the second type require frequency shifts below the step of 

25 BJN-SOR 2.2 the spectrum. 

The origin of the spectra of the first type (three spectrograms 

at the bottom 

of Fig. 2) can be attributed to the magnetospheric cavity, 

6 SOR-MAS 

in accordance with the MHD theory of coupled compressionaltransverse 

modes [5]. These spectra correspond to the closed (dipole) 

magnetic field lines and describe the magnetospheric MHD response 

0 4 8 12 16mHz 

Fig. 2. Spectra for quiet conditions. 

to perturbations. The origin of the spectra of the second type (two 

spectrograms at the top of Fig. 2) remains unknown, although we can 

associate these spectra with the plasma sheet. 

The second event in study is that of the moderate activity 

of 

IE0 and the same 

solar wind parameters observed January 01, 2000 during 12:00- 

21 NAL-LYR 3.8 16:00 UT. Figure 3 presents the spectrograms for this case, and the 

notations are similar to those in Fig. 2. The spectrogram obtained for 

the stations BJN-SOR beneath the aurora represents the strongest 

56 LYR-HOR 3.4 magneto-difference signal and is shown by the thick curve. The 

spectrograms obtained equatorwards from the aurora (three spectra at 

the bottom of Fig. 3) predominantly display the spectra of the first 

type, which can be identified as the MHD modes. Though the strong 

signal penetrates from the arc through the conversion of Alfven waves 

into magneto-acoustic waves, the signals of the MHD origin dominate 

83 HOR-BJN 2.4 in this portion of the auroral oval, especially at the equatorward edge. 

On the contrary, the spectrograms obtained beneath and polewards 

from the aurora demonstrate the spectra of the second type. The 

168 BJN-SOR 2.5 frequency steps (between adjacent peaks) of these equidistant spectra 

tend to coincide with or closely approach the Dopplerometric 2.6 and 

3.4 mHz. 

79 SOR-MAS 2.8 

The 

third of examined events corresponds to the disturbed 

conditions of IE

Nonnormalized 

spectral power 


29 NAL-LYR 3.5 

frequencies obtained for the quiet conditions. If we associated the 

origin of the second-type spectra with the MHD modes, neither 

geomagnetic, nor solar wind parameters could explain such an 

unusual behavior. No doubt that the magnetosphere could not inflate 

in size by half an order of magnitude. 

37 LYR-HOR 1.9 

A general and important property of the second-type spectra 

is that the frequency step of the spectrum increases with latitudes at 

the poleward edge of the auroral oval. This feature also cannot be 

explained 

by the MHD modes, since the length of magnetic field 

103 HOR-BJN 0.9 lines increases with latitudes and must, therefore, result in an 

opposite behavior. 

An attempt to understand harmonic relations in the secondtype 

spectra can help to clarify the origin of these signals. Indeed, the 

243 BJN-SOR 0.8 magnetic variations contained in magneto-difference signals are 

predominantly attributed to the magnetic fields of the Hall currents 

flowing in the E layer of the ionosphere. It is well known that the 

114 SOR-MUO 1.8 ionosphere as a whole (including the neutral gas dragged by drifting 

ions) partially corotates with the convecting magnetospheric 

plasma [10]. The velocity of this corotation, of course, is below the 

50 PEL-OUJ 0.9 

velocity of the magnetospheric plasma. The corotating ionosphere 

moves the Hall currents with respect to ground magnetometers, and 

this motion introduces the Doppler shifts in the magnetometric 

frequencies. These Doppler shifts can be observed only at high 

4 NUR-TAR 2.6 

latitudes, where the magnetospheric convection provides rather high 

plasma velocities. 

If we assume that the second-type spectra are generated by 

the rotating magnetospheric plasma, the frequency shifts in harmonic 

0 4 8 12 16mHz 

relations of these spectra can be attributed to the Doppler shifts in the 

Fig. 4. Spectra for southward IMF. 

magnetometric data. Since the ionospheric corotation is only partial, 

these Doppler shifts turn out to be below the rotational frequencies of 

the sources, i.e. below the frequency steps of the second-type spectra. Such interrelations can also explain 

the 

uncertainties in the high-latitude magnetom etric data revealed in [3]. Indeed, the Doppler shifts in 

magnetometric 

data introduce different ground frequencies, which in fact can represent a single set of the 

magnetospheric 

frequencies. This also explains why the low-latitude data [4] support the stability of 

Dopplerometric frequencies, whereas the high-latitude data do not. 

An evident objection to the proposed hypothesis is that the obtained frequencies seem to be too 

high 

for the magnetospheric convection with the plasma velocities about 1000m/s and below. This is so, 

indeed, 

for 

the large-scale convection of the planetary size. In addition to the large-scale convection, some 

comparatively small-scale plasma vortices were recently observed 

by the SuperDARN HF radars [11]. 

Rather 

small spatial scales of these structures can probably provide the required rotational frequencies. 

Acknowledgments 

The author is grateful to M.G. Deminov for fruitful discussions 

The magnetometric 

data were granted by the institutes maintaining the IMAGE Magnetometer Array. 

This work was supported by the Russian Foundation for Basic Research, project code 07-05-00104. 

References 

1. Samson, J.C., T.J. Hughes, F. Creutzberg, D.D. Wallis, R.A. Greenwald, and J.M. Ruohoniemi 

(1991), Observations of a detached, discrete arc in association with field line resonances, J. Geophys. 

Res., 96, 15683-15695. 

2. Samson, J.C., B.G. Harold, J.M. Ruohoniemi, R.A. Greenwald, and A.D.M. Walker (1992), Field 

line resonances associated with MHD waveguides in the magnetosphere, Geophys. Res. Lett., 19, 

441-444. 

3. Ziesolleck, C.W.S. and D.R. McDiarmid (1995), Statistical survey of auroral latitude Pc 5 spectral 

and polarization characteristics, J. Geophys. Res., 100, 19299-19312. 

27


4. Francia, P. and U. Villante, Some evidence of ground power enhancements at frequencies of global 

magnetospheric modes at low latitudes (1997), Ann. Geophysicae, 15, 12-23. 

5. Kivelson, M.G. and D.J. Southwood (1986), Coupling of global magnetospheric MHD eigenmodes 

to field line resonances, J. Geophys. 

Res., 91, 4345-4351. 

6. Lee, D.-H. and R.L. Lysak (1991), Monochromatic 

ULF wave excitation in the dipole 

magnetosphere, J. Geophys. Res., 96, 5811-5817. 

7. Korotova, G.I. and D.G. Sibeck (1 995 ) , A case study of transient event motion in the magnetosphere 

and in the ionosphere, J. Geophys. Res. ,100, 35-46. 

8. Kepko, L. and H.E. Spence (2003), Observations of discrete, global magnetospheric 

oscillations 

directly driven by solar wind density 

variations, J. Geophys. Res., 108, 1257-1270. 

9. Badin, V.I. (2007), Spectral studies of the auroral currents, in: Physics of Auroral Phenomena, Proc. 

XXX Annual Seminar, Apatity, 2007, 51-54. 

10. Fedder, J.A. and Banks P.M. (1972), 

Convection electric fields and polar thermospheric winds, 

J. Geophys. Res., 77, 2328-2340. 

11. Grocott, A. and T.K. Yeoman (2006), SuperDARN observations of ionospheric convection during 

magnetospheric substorms, in: Int. Conf. Substorms-8, 81-86. 

28


1 

SURGE-LIKE AURORAL STRUCTURES AND QUASI-PERIODIC 

PRECIPITATIONS OF ENERGETIC PARTICLES IN THE MORNING 

SECTOR: A CASE STUDY 

1 

1 

D.G. BaishevP P, E.S. BarkovaP P, S.N. SamsonovP P, K. YumotoP 

P PYu.G.Shafer Institute of Cosmophysical Research and Aeronomy SB RAS, Yakutsk, 677980, 

2 

Russia, e-mail: HTbaishev@ikfia.ysn.ruTH; P PSpace Environment Research Center, Kyushu University, 

Fukuoka, Japan 

Introduction 

Abstract. Relationship between series of surge-like auroral structures and quasi-periodic 

precipitations of energetic particles registered in the morning sector during 1900-2200 UT on 

November 8, 2004 is studied. This event has been analyzed on the data from all-sky TV camera at 

Tixie (ϕ=71.6° N, λ=128.9° E), riometer and magnetometer chain at around 190° geomagnetic 

longitude and measurements of energetic particle fluxes aboard geostationary LANL satellites. 

Surge-like auroral structures expanding by about 4° in latitude appeared in the field-of-view of TV 

camera with a periodicity of 12-20 min and were accompanied by the intense geomagnetic 

pulsations in the Pi3 range and quasiperiodic oscillations in the riometer absorption. A peak-to-peak 

value of geomagnetic pulsations in the H and Z components was ~600 nT and exceeded the 

amplitude in the D component by factor of 3. It is found that variations of discrete aurora intensity in 

latitude one-to-one correspond to quasi-periodic oscillations in the riometer absorption observed at 

Tixie and are in an antiphase to the riometer pulsations at more southern station of Dzhardzhan 

(ϕ=69.0° N, λ=124.2° E). 

The auroral picture on the morning side is complex. Omega bands, torch-like structures and pulsating aurora 

drifting eastward with a convection speed are registered with the all-sky camera [Akasofu, 1974]. It is now 

well known that auroral omega bands and Ps6 quasiperiodic magnetic pulsations are manifestations of the 

same phenomena [Saito, 1978]. Ps6 pulsations are preferentially observed in the Y and Z components of the 

magnetic field. 

Steen et al. [1988] described the unusual rare event in which a gradual transition between Ps6 pulsations with 

auroral torches and surgelike pulsations with quasiperiodic variations in auroral intensity were observed 

during a substorm. The period of surge-like auroral structures is the manifestation of a series of individual 

substorms occurring on the morning side. 

On the morning side at 1900-2200 UT we observed 10 successive auroral structures like auroral surges 

which drifted to the east and were accompanied by Pi3 magnetic pulsations. We present results of the 

detailed study of relationship between auroral structures, quasiperiodic precipitations of energetic particles 

and magnetic field variations. 

Observations 

The dynamics of aurora and long-period oscillations of the magnetic field in the morning sector during 1900- 

2200 UT on November 8, 2004 are studied by data of the all-sky TV camera at the Tixie (TIX, ϕ=71.6° N, 

λ=128.9° E), riometer and magnetic stations of the 190° MM. The TV camera provided high-resolution 

optical measurements of aurora in white light [Shiokawa et al., 1996]. 

Ground-based measurements were supplemented by the satellite observations. The WIND satellite was 

located far upstream at the distance of X~190 RBeB in GSM coordinates. The estimated time delay of ~33 min 

is calculated between the satellite and the magnetopause. Measurements of energetic particle fluxes aboard 

the geostationary LANL satellites in the morning sector were used. 

29 

1 

2 

P


Figure 1b shows that the beginning of negative bay in the H component of the magnetic field at ~1736 UT 

coincides with a sharp southward turning of the IMF (Figure 1a). The sudden excursion of IMF BBzB at ~0805- 

0820 UT (Figure 1a) triggered a substorm that was manifested in the increase of westward electrojet 

intensity at Tixie (Figure 1b). One can see that the H and D component variations at both stations are similar. 

Taking into account the Z component, we can suppose that the westward electrojet center is between the 

Tixie and Zhigansk but closer the Tixie (Figures 1b and 1c). 

Figure 1. IMF BBzB from WIND satellite shifted by ~33 min (a), magnetic field variations at Tixie 

and Zhigansk (ZGN, ϕ=66.8° N, λ=123.4° E) (b-d), the TV keogram in north-south direction (e) 

in the morning sector (~01-07 MLT). Variation of the poleward auroral boundary caused by the 

passage of 10 successive surge-like structures is shown by open circles in Figure 1b. 

30


Figure 2 shows the development of aurora during substorm. This is evident from Figure 2 that the westward 

electrojet intensification is accompanied by eastward expansion of the auroral bulge (TV frames at 1841- 

1844 UT in Figure 2). From 1906 to 2147 UT the Tixie all-sky TV camera registered 10 surge-like structures 

drifting 

to the east when they crossed the station zenith. 

Figure 2. Eastward expansion of the auroral bulge and 10 surge-like structures observed by the 

Tixie TV camera. 

31


Figure 1e presents the TV keogram in north-south direction showing latitudinal variations of the auroral 

intensity. The distinctly visible poleward boundary of auroral intensity is probably caused by the passage of 

surge-like structures over the station. One can see that surge-like auroral structures expanding by about 4° in 

latitude 

appeared in the field-of-view of TV camera with a periodicity of 12-20 min. 

Standard magnetograms in Figure 1 illustrate the connection of Pi3 geomagnetic pulsations with the surgelike 

structures. The correspondence is very good showing the correlation between the surge-like structures 

and variations of the magnetic field, which are the most intense in the H and Z components (Figures 1b and 

1c). A peak-to-peak value of geomagnetic pulsations in the H and Z components was ~600 nT (Figures 1b 

and 1c) and exceeded the amplitude 

in the D component by a factor of 3 (Figure 1d). 

Figure 3 demonstrates 

the measurements of energetic particles from the geostationary LANL satellites 

(Figures 

3b, 3c, 3d) and variations of the riometer absorption observed at the Tixie (Figure 3f) and 

Dzhardzhan (DZD, ϕ=69.0° N, λ=124.2° E) (Figure 3e) during the time of interest. The variations of 

poleward boundary of aurora intensity (Figure 3f) one-to-one correspond to quasi-periodic oscillations in the 

riometer absorption observed at the Tixie (Figure 3f) and are in an antiphase to the riometer pulsations at the 

more southern station of Dzhardzhan (Figure 3e). 

Figure 3. The location of observational stations and LANL-97 satellite (cross) at 19 UT on 

November 8, 2004 (a), energetic electron fluxes measured by 1991-080 (194.9° E) (b) and 

LANL-97 (145.7° E) (c) satellites, partial electron density in energy band of 50-225 keV 

registered by LANL-97 (solid line) and 1991-080 (dashed line) satellites (d), riometer 

absorption at DZD (e) and TIX (f). Large circle in Figure 3a is the TV camera field of view at 

the Tixie. The poleward boundary of surge-like auroral structures is shown by open circles in 

Figure 3f. 

Satellite measurements show that the distinct quasiperiodic variations in aurora, riometer absorption and 

magnetic field began to be registered, when high-energy electrons injected during a substorm reached the 

observation meridian (190° MM). 

On the basis of experimental data analysis one can assume the following. The mechanism, which links the 

surge-like structures with quasiperiodic oscillations of the magnetic field and riometer absorption, can be 

32


described within the model by Yamamoto et al. [1997]. Most likely, the surge-like auroral structure is a 

manifestation of the interchange instability occurring in the hot plasma torus (HPT) in the magnetosphere. 

According to the riometer data, a latitudinal size of torus is ~3° and the HPT particles are concentrated to a 

closed region. 

Conclusions 

The Tixie all-sky TV camera registered the appearance of 10 surge-like structures in the morning sector in 

the time interval of 1900-2200 UT on November 8, 2004. Auroral structures expanding by about 4° in 

latitude were observed with a periodicity of 12-20 min and accompanied by the intense geomagnetic 

pulsations in the Pi3 range and quasiperiodic oscillations in the riometer absorption. A peak-to-peak value of 

geomagnetic pulsations in the H and Z components was ~600 nT and exceeded the amplitude in the D 

component by a factor of 3. 

It is found that variations of discrete aurora intensity in latitude one-to-one correspond to quasi-periodic 

oscillations in the riometer absorption observed at the Tixie and are in an antiphase to the riometer pulsations 

at the more southern station of Dzhardzhan. We suggest that the surge-like auroral structures are a 

manifestation of the interchange instability occurring in the hot plasma torus in the magnetosphere. 


This work was supported by RFBR grant 06-05-96118, by the Program of Presidium of RAS no.16 p.3 and 

by INTAS grant 06-1000013-8823. 

References 

Akasofu, S.-I. (1974), A study of auroral displays photographed from the DMSP-2 satellite and from the 

Alaska meridian chain of stations. Space Sc., Rev., 16, 617-725. 

Saito, T. (1978), Long-period irregular magnetic pulsations, Pi 3. Space Sci. Rev., 21, 427-467. 

Shiokawa, K., et al. (1996), Auroral observations using automatic instruments: relations with multiple Pi2 

magnetic pulsations, J. Geomag. Geoelectr., 48, 1407-1410. 

Steen, A., P.N. Collis, D. Evans, G. Kremser, S. Capelle, D. Rees, and B.T. Tsurutani (1988), Observations 

of a gradual transition between Ps6 activity with auroral torches and surgelike pulsations during strong 

geomagentic disturbances. J. Geophys. Res., 93(A8), 8713-8733. 

Yamamoto, T., S. Inoue, and C.-I. Meng (1997), Formation of auroral omega bands in the paired region 1 

and region 2 field-aligned current system. J. Geophys.Res., 102(A2), 2531-2544. 

33


NEW RESULTS OF SOLAR ACTIVITY AND MAGNTIC FIELD 

ON THE SUN (REVIEW) 

1, 2 

Elena E. Benevolenskaya 

1 Stanford University, W.W. Hansen Experimental Physics Laboratory, Stanford, CA 94305, USA, 

e-mail:Elena@sun.stanford.edu; 2 Pulkovo Astronomical Observatory, St. Petersburg, 196140, 

Russia 

Abstract. For the last decade the solar space missions (e.g. Yohkoh, Coronas, Ulysses, SOHO) make a 

progress in the investigations of the solar activity in Photosphere, Corona and solar wind. The Hinode 

and Stereo space labs continue the progress of previous missions and extend our knowledge about the 

solar activity, an evolution of vector magnetic field, a structure of photosphere, chromosphere and 

corona. Upcoming Solar Dynamics Observatory will investigate the vector magnetic field, corona and 

solar irradiance with a purpose to understand the nature of the solar cycle on the base of the highresolution 

images. 

In this paper, I review the recent and most important results of the investigation of the solar activity 

from the interior to the corona and their relationship to the dynamo theory. 

Introduction 

The last decade and present of observations of the Sun from Space are called ‘The golden Ages of Solar 

Physics’. And it is not surprised due to the new data and results. If we go to the ‘ADS abstract search 

system’ and type, for example, keyword ‘SOHO’ (Solar and Heliospheric Laboratory) in ‘abstract 

words’, we get more than 5000 references. 

Investigations of the Sun from the Space enable see our Sun in the invisible wavelength which is no 

observable from the ground Observatories, such as Extreme Ultraviolet (EUV) and X-ray. 

Here is a brief list (not the whole) of the most important space mission contributed to solar cycle studies: 

YOHKOH (31.08.1990-14.12.2001), CORONAS-F (31.07. 2001-6.12.2005), SOHO started on 2 

December 1995, ULYSSES (10.06.1990-03.03.2008), TRACE (April 1998-current). 

And, it is new space laboratories: STEREO, which launched on October 25, 2006 and HINODE (Solar-b) 

has been observing the Sun since 22 September 2006. Each mission has its own signature. 

Yohkoh has measured the X-ray Solar corona by Soft X-ray Telescope (SXT) with two filters: Al 5-12 A° 

and Al/Mg/Mn (AlMg) 6-13 A°. Examples of images for filter AlMg (Tsuneta et al. 1991). 

Figure1. Left panel: Solar X-ray coronal image from YOHKOH shows the plasma heated up to the 3MK (bright 

features). Middle panel: EUV corona from SOHO/EIT telescope. Right panel: Line-of-sight component of the 

magnetic field measured by MDI (Michelson Doppler Imager) on the board SOHO (white color shows a positive 

polarity, a negative polarity is marked by black). 

Large-scale hottest features were detected and observed several times in the solar corona in the hightemperature 

Mg XII line (T= 5–20 MK, Tmax = 10 MK) with the soft X-ray telescope of the SPIRIT 

34


instrumentation complex onboard the CORONAS-F spacecraft. Zhitnik et al. (2003) phenomenologically 

described such features as long-living plasma bodies with bright orbed cores, localized at a height of 0.1–0.3 

solar radii, and darker legs, probably giant loops, connecting the cores with active regions. 

Ulysses spacecraft flied over the poles of the Sun, climbed its maximum latitude of 80.2 degrees North on 

31 July 1995 with the last passing on 14 January 2008. Figure 2 shows the decreasing of the temperature 

distribution above the solar Polar Regions. 

Figure 2. The temperature of the Sun’s polar coronal holes as measured by the SWICS instrument on board Ulysses 

(Credit to Ulysses). 

Among the numerous results of HINODE let’s look at the X-ray jets which are observed in the solar polar 

atmosphere (e.g. Kulhane et al. 2007; Filippov, Golub and Koutchmi 2007; Savcheva 2007). Recent results 

(Shimojo 

et al. 2007; Shimojo 2008) reveal that over 70% of jets occur in mixed polarity regions and X-ray 

jets in the polar coronal hole are not always associated with the kG-patches (kilo Gauss magnetic field). 

Some X-ray jets are associated with very weak magnetic field. And, the jets are strongly associated with the 

emerging/cancelling magnetic flux. 

The series of wonderful EUV images from two satellites with fine resolution of A (head) and B (behind) of 

the Solar TErrestrial RElations Observatory 

(STEREO) provide 3D reconstruction of the coronal loops 

and 

corona (Aschwanden et al. 2008a, 2008b). 

SOHO (Solar and Heliospheric observatory) is the leader in the list of the space observatories not only 

due to the numerous publications; SOHO demonstrates 

a successful international collaboration inside the 

SOHO 

teams and collaborations with other teams among the solar and the heliospheric society. 

Birth of the Solar Cycle 

"On January 4, 2008, a reversed-polarity sunspot appeared—and this signals the start of Solar Cycle 24" 

(David Hathaway of the Marshall 

Space Flight Center, HASA deadlines) 

Figure 3. Left image: Sun in continuum. Right image: MDI (Michelson Doppler Imager) 

magnetogram. White color 

shows a positive polarity, black is marked a negative polarity. 

35


The sunspot, 1 NOAA 981 at the latitude N30 o and at the carrington longitude (L) equals 246 o , has emerged 

in the same longitudinal region as sunspot NOAA 980 of the old polarity (S06 o , L239 o ). 

n March 28 8 the cycle 23 returned: three big sunspots ( 1 NOAA 987, NOAA 988, and NOAA 989) 

atitude 25 o -35 o O , 200 

appeared and they were all old cycle spots. After that, the Sun was practically blank. Usually, the beginning 

of the new cycle corresponds to the appearance of sunspots with a new polarity at the l 

, and 

the all sunspots of the old polarity, that are located close to the equator, are disappeared. But, there is a 

period of the overlapping of two cycles when both sunspots with the old and the new polarity coexist on the 

Sun. On October 5, 2008 the sunspot (NOAA 1003) of the new cycle appeared in the southern hemisphere at 

23 o latitude and at 222 o carrington longitude (L). It has disappeared rapidly, and next several days we 

observe plages instead of sunspot in the same place. On 11 October 2008, small sunspot (NOAA 1004) 

emerged at S08 and L188 and one more (NOAA 1005) at higher latitude in the North (N26, L116). During 

the next day two plages 1003 NOAA (S23, L222) and NOAA 1004 (S08, L188) have coexisted with the 

sunspot (NOAA 1005) in the North which coordinates are N26 o and L116 o . 

The tendency of the solar cycle to appear at the preferred longitudes was found by Benevolenskaya, 

Hoeksema, Kosovichev and Scherrer (1999) and Bumba, Garcia, and Klvana (2000). 

Figure 4. Left panel: Synoptic maps of the solar magnetic field for Carrington rotations (CR) 1911–1934 derived from 

the SOHO/MDI magnetograms during the activity minimum between cycles 22 and 23. Values of the line-of-sight 

component of the magnetic field are represented in light and dark colors for positive and negative polarities, 

respectively. The gray scale shows magnetic field in the range from -10 to 10 G. 

Right panel: More detailed synoptic magnetic maps for Carrington rotations 1916–1923. The plots indicate the NOAA 

sunspot number for selected active regions. Bins are 1 o square and extend to latitude ±65 o . (Benevolenskaya et al., 

1999). 

hich is shown in more detail in Figure 4 (right panel). One major zone occurred at longitudes 240 o – 

80 o and lived over a year. This longitude was active from CR 1911 to CR 1917 (region 1 The transition from old (cycle 22) to new flux (cycle 23 ) is largely concentrated in the interval CR 1916- 

1923, w 

2 

NOAA 8006) 

1 NOAA sunspot region number reached 9999 and rolled over to 0000 on 16 June 2002. 

36


in the southern hemisphere and from CR 1916 to CR 1918 (NOAA 7997) in the northern hemisphere. This 

active 

zone of old flux, which was gradually decaying and migrating westward, reactivated in CR 1923, 

when a new-cycle complex of solar activity (NOAA 8046) emerged in the southern hemisphere at longitude 

~280 o . Another interesting strong active zone developed at 160 o –200 o and drifted slowly westward. This 

zone of old-cycle flux first appeared in the southern hemisphere in CR 1916 (NOAA 7999) and persisted in 

CR 1917 (8007A); then in CR 1918 new cycle flux emerged in this zone at latitude 20 o S. During CR 1920 

one of the last regions of the old cycle appeared at longitudes 200 o –240 o in the northern hemisphere (NOAA 

8020) and decayed over the next two rotations; then, in CR 1923 a new cycle region appeared in the same 

hemisphere but at higher latitudes. In CR 1920 and 1921 both “new” (8021 and 8027) and “old” (8020 and 

8029A) fluxes existed at the same longitude of .210 o , but in different hemispheres. We see a similar 

coexistence of “new” (8006) and “old” (8005) regions in the southern hemisphere in CR 1917. 

In both active longitude zones the old-cycle magnetic flux was replaced by new cycle flux. 

Solar magnetic flux emerging 

There are several types of the solar magnetic flux emerging. The first 

is the bipolar emerging which 

associated 

with the activity complexes. It is observed in ephemerical regions (Harvey and Zwaan 1993; 

Hagenaar 2000), and in small magnetic loop structure in the quiet Sun, according the Hinode data (Centeno, 

et al. 2007). The next, it is a unipolar magnetic flux emerging which related to polar faculae. Mechanism of 

forming of the unipolar magnetic flux emerging suggested by Lamb, DeForest, Hagenaar, Parnell and Welsh 

(2008) is represented in Figure 5. 

Figure 

5. Two possible scenarios for detecting negative (black) flux while hiding 

the 

positive (white) component. 

(a) The cross section of the positive end of the flux tube is larger, so the weaker 

average field does not exceed the tracking detection threshold. 

(b) Each end of the flux tube is not detectable by itself, but if two or more likepolarity 

ends come together, the average field strength can exceed detection 

limitations for that polarity only. In this case the tubes are not newly emerging, 

so the positive ends could be arbitrarily far away at the time of detection 

(Figure 4, Lamb et al. 2008). 

Helioseismology points out on the 

multiple fluxes emerging. “However, the magnetic flux rate reveals two 

or three peaks of intensive flux emergence; each was about one day long. It appears that the active region 

was formed by multiple magnetic flux emergence events.”(Kosovichev, Duvall 2008). 

Figure 

6. Model of the Emerging Flux Region. White and 

dark 

ovals represent the footpoints observed with Stokes 

V. The solid lines stand for magnetic tubes above the 

photosphere and the dashed lines for those below the 

Photosphere. An emerging flux region (EFR) is a young 

active region (AR) where magnetic flux loops emerge 

from underneath the photosphere. (Otsuji et al., 2007). 

Figure 6 (i.e. Figure 9 in Otsuji et al., 2007) shows a model of this EFR. The temporal evolution of the 

observed flux emergence will be as follows: (1) A magnetic flux tube emerges from 

the intergranular lane 

(17:54 UT). (2) The flux tube splits along its axis into two parts (flux tubes 1 and 2). (3) After the emergence 

of flux tubes 1 and 2, newly emerged flux tubes appear (flux tubes 3–6). These emergences of flux will be 

these observed by Pariat et al. (2004) and simulated by Isobe et al. (2007). 

One remarkable new finding from Hinode is the discovery of ubiquitous horizontal magnetic fields in the 

quiet internetwork regions (Lites et al. 2007). The stronger horizontal fields 

occur separately from the 

37

vertical fields. The vertical fields occur mainly in the intergranular lanes. The horizontal fields occur over 

the bright granules, but avoid the brightest portions of the granules. They most commonly occur at the outer 

edges of the granules. Horizontal fields are not associated with the stronger network elements; they are a 

phenomenon of the internetwork only. 

Polar magnetic field and dynamo theory 

The polar magnetic fields on t he Sun have been an attractive subject for solar researches since Horace and 

Harold Babcocks measured them in solar cycle 19 ( Babcock and Babcock 1955). One of the remarkable 

features of the polar magnetic fields is their reversal during the maxima of 11-year sunspot cycles (Babcock 

and Livingston 1958; Babcock 1959). To understand the origin of the polar magnetic field reversals many 

investigators employed the mean-field dynamo theory (e.g. Dikpati et al, 2004). But, now, the question is 

raised. What is a new we know about the polar magnetic field? 

Figure 7. Azimuthally averaged intensity of the solar corona as a 

30 

function of latitude and time in the EUV lines: (a) 304 A° , (b) 171 A° , 

0 

-30 

- 

(c) 195 A° , and (d) 284 A° , and the corresponding line-of-sight 

photospheric magnetic field values: (e) |B | and (f) B (red shows the field 

of the positive polarity, and blue the negative polarity). The dashed 

curves show the high-latitude magnetic neutral lines. 

Study of the EUV from SOHO/EIT and the X-ray from YOHKOH 

data 

revealed a large scale connectivity in the corona between 

polar regions and the following parts of complexes of solar 

activity in the rising phase of the solar cycle (Benevolenskaya, 

Kosovichev, Scherrer 2001; Benevolenskaya, Kosovichev, Lemen, 

Slater, Scherrer 2002). 

In the longitudinally averaged coronal 

EUV maps (Figure 7), we 

see 

in each hemisphere two sets of migrating structures: low- 

latitude structures that migrate toward the equator following |B| 

and high-latitude structures that migrate toward the poles parallel 

to the magnetic neutral lines. However, these coronal structures 

are located 15 

d onnecting 

the following parts of complexes of solar 

o –20 o higher in latitude than the neutral line. In the 

EUV data, the polar branches of coronal activity started in 1997 

almost simultaneously with the equatorial branch and reached the 

lower and upper boundaries of our synoptic maps (±83 o 60 

60 

) in early 

2000. The polar branches are easily identified in 304, 171, and 195 

A° maps. The bright coronal structures detected in the EUV data 

from SOHO/EIT, which migrated to the poles during the rising 

phase of the solar cycle, were formed by density enhancements in 

the poleward footpoints of magnetic field lines connecting the 

magnetic fields of the following parts of active regions with the 

polar field (Figure 8). It was suggested that giant coronal loops 

together with meridional circulation and turbulent diffusion play 

very important role in polar magnetic field reversals. Part of the 

magnetic flux from mid-latitude goes to plasma heating inside 

these loops (Figure 8). After the polar magnetic field reversals, the 

situation is changed. The transequatorial loops connected the 

following parts of the activity complexes or sunspot complexes are 

prevail (Figure 9). 

Gopalswamy, Lara, Yashiro, Howard (2003) proposed that 

coronal mass ejections (CMIs) associate with these closed configurations of the magnetic field c 

activity with the open magnetic flux of polar regions. And, CMIs 

may be really an important mechanism of the magnetic field decay in the polar reversals. Moreover, 

according to Von Steiger, Zurbuchen, Kilclenmann (2006), the number of CME displays latitude 

dependence: polar CME’s are greater on the rising phase of solar cycle. 

304A 

a) 

60 

30 

0 

-30 

-60 

171A 

b) 

60 

195A 

30 

0 

-30 

-60 

60 

c) 

284A 

30 

0 

-30 

-60 

60 

d) 

|B||| 

30 

0 

-30 

-60 

60 

e) 

B|| 

30 

0 

-30 

-60 f) 

1997 1998 1999 

year 

2000 

latitude (deg) 


38


Coronal topology before the polar magnetic field reversals 

Figure 8. Left panel: Soft X-ray image from Yohkoh spacecr 

aft. Right panel: correspondent topology of the 

magnetic field. Lc- is a Carrington longitude of the central meridian of the 

Sun. 

o 

Figure 9. Left panel: Topology of the magnetic field. Right panels: EUV image of Fe IX, X (171 A ) from 

/SOHO/EIT (upper) and MDI/SOHO (bottom) images. 

Fisk and Schwadron (2001) suggested that the polar magnetic field reversals occurred because of the 

diffusion 

of open magnetic field lines on the solar surface (due to transport and decay) that were reconnected 

with closed loops. Cohen, Fisk, Roussev, Toth and Gombosi (2006) have considered the two-dimensional 

transport model of open magnetic flux on the surface of the Sun. The diffusion process represents: 

39


1) diffusion of the filed line footpoints and 2) diffusion due to reconnection of open field lines with closed 

loops. They demonstrated that the rate of emergence of flux on the photosphere can control the magnitude of 

meridional flow. But, they found that the effect of diffusion due to magnetic reconnection is significant for 

the case of structured magnetic configuration (solar minimum conditions) and it small for the case of 

unstructured magnetic configuration (solar maximum conditions). 

Abramenko, Fisk, Yurchishin (2006) found that the coronal hole which forms after the polar magnetic field 

reversals (2002-2003) displays the local minimum for the rate of emergence of new magnetic flux. Dipole 

emergence rate in quiet sun exceeds twice that in Coronal holes. 

However, Hagenaar, Schrijver, and DeRosa (2008) have found that the emergence frequency of ephemeral 

regions does not depend on the presence of coronal holes. Instead, 

the frequency of ephemeral regions is 

found to depend on the degree of flux imbalance in the photosphere. This explains the observations by 

Abramenko, Fisk, & Yurchyshyn (2006) that fewer ephemeral regions emerge in quiet Sun inside coronal 

holes, than outside coronal holes. 

The surface-diffusion or transport models explain the polar magnetic field reversals as a result of turbulent 

diffusion, 

meridional circulation and differential rotation (e.g. Wang, Sheeley and Nash, 1991; Schrijver 

and Title 2001). Schrijver, De Rosa, Title (2002) also point out that the transport process leads to a transport 

of closed connections from equator to pole even as open solar flux is transported from the high latitudes to 

the equator. Fox, McIntosh and Wilson (1997) described the evolution of the large-scale fields and their 

association with polar coronal holes. Their question was whether the polar fields resulted from the local 

polar dynamo or not. There is no a certain answer to this question. But, Durrant, Turner and Wilson (2002) 

have observed that high-latitude flux emergence can affect the evolution of individual high-latitude plumes, 

but this flux does not seriously affect the whole reversal times of the polar magnetic field. However, the 

polar magnetic elements involve in the supergranular motion, solar rotation and reflect the subsurface 

gradient of angular velocity (Benevolenskaya, 2007). 

Conclusion 

The current and future high- (low-) resolution solar observations 

enable to investigate physical processes at 

the all levels on the Sun (convection zone, photosphe re, 

chromosphere, and corona), simultaneously. SOHO 

and others missions show how our Sun is variable. In this paper I reviewed the present results with focus on 

the solar cycle studies. Because of the next solar space laboratory, Solar Dynamics Laboratory (SDO), is 

coming to replace SOHO with a purpose to understand the nature of the solar cycle. 

References 

Abramenko, V. I., Fisk, L. A. and Yurchyshyn V. B. (2006), The rate of emergence of magnetic dipoles in 

Coronal holes and adjacent quiet-sun regions, ApJ, 641, L65-L68 

Aschwanden, M. J., Wuelser, L.-P, Nitta, N. V., Lemen, J.R. (2008a), First 3D Reconstructions of Coronal 

loops with the STEREO A and B Spacecraft.I. Geometry, ApJ, 679, 827-842 

Aschwanden, M. J., Nitta, N. V., Wuelser, L.-P., Lemen, J.R. (2008b), First 3D Reconstructions of Coronal 

loops with the STEREO A+B Spacecraft. II.Electron Density and Temperature 

Measurements, ApJ, 680 

(2), 1477-1495 

Babcock, 

H. W., and Babcock, H. D. (1955), The Sun’s magnetic field, 1952-1954, ApJ, 121, 349-366 

Babcock, H. W., Livingston W. C. (1958), Changes in the Sun’s polar magnetic field, Science, 127, 1058 

Babcock, H. D. (1959), The Sun’s polar magnetic field, ApJ, 130, 364-365 

Benevolenskaya, E. E., Hoeksema , J. T., Kosovichev, A. G. and Scherrer, P. H. (1999), The interaction of 

new and old magnetic fluxes at the beginning of solar cycle 23, ApJ, 517, 

L163-L166 

Benevolenskaya, E. E., Kosovichev, A. G. and Scherrer, P. H. (2001), Detection of high-latitude waves of 

solar coronal activity in extreme-ultraviolet data from the Solar and heliospheric observatory 

EUV 

imaging telescope, ApJ, 554, L107-L110 

Benevolenskaya, 

E. E., Kosovichev, A. G., Lemen, J. R., Scherrer, P. H., Slater, G. L. (2002), Large-scale 

solar coronal structures in soft X-ray and their 

relationship to the magnetic flux, ApJ, 571, L181-L185 

Benevolenskaya, E.E., (2007), Rotation of the magnetic elements in Polar Regions on the Sun, Astron. 

Nachr., 328 (10), 1016-1019 

40


Bumba, V., Garcia, A., and Klvana, M. (2000), Longitudinal distributions of solar magnetic fields and 

activity during the ending and starting periods of activity cycles, Solar Phys., 196, 403-419. 

Cohen, O., Fisk, L. A., Roussev, I. I., Toth, G. and Gombosi, T. I. (2006), Enhancement of photospheric 

meridional flow by reconnection processes, ApJ, 645, 1537-1542 

Culhane, L. et al., (2007), Hinode EUV study of Jets in the Sun’s South Polar corona, Publ. Astron. Soc. 

Japan, 59, S751-S756 

Dikpati, M., de Toma, G., Gilman, P. A., Arge, C. N., White, O. R. (2004), Diagnostics of polar field 

reversal in solar cycle 23, 

using the a flux transport Dynamo model, ApJ, 601, 1136-1151 

Fisk, L.A., Schwadron, N.A. (2001), The behavior of the open magnetic field on the Sun, ApJ, 560, 425-438 

Durrant, C.J., Turner, J., Wilson, P.R. (2002), Bipolar magnetic fields at high latitude, Solar Phys., 

211, 103- 

124 

Fox, P., McIntosh, P., Wilson, P.R. (1998), Coronal holes and the polar field reversals, Solar Phys., 171, 

375-393 

Filippov, B., Golub, L. and Koutchmi, S. (2007), X-ray jet Dynamics in Polar Coronal Hole Regions, eprint 

arXiv:0711.4320, 

p 1-11 

Gopalswamy, N., Lara, A., Yashiro, S., Howard, R. A. (2003), Coronal Mass Ejections and Solar Polarity 

reversal, ApJ, 598, L63-L66 

Hagenaar, H., Schrijver, C., and DeRosa, M. (2008), Ephemeral bipolar regions in coronal holes, ASP 

Conference Series, 383, 343-346 

Isobe, H., Tripathi, D., & Archontis, V.,(2007), Ellerman bombs and jets associated with resistive flux 

emergence, ApJ, 657, L53-L56 

Kosovichev, A.G., Duvall, T.I. Jr. (2008), Local helioseismology and magnetic flux emerging, ASP series, 

383, 59-70 

Lamb, D.A., DeForest, C.E., Hagenaar, H.J., Parnell, C.E. and Welsch, (2008), Solar magnetic tracking II. 

The apparent 

unipolar origin of quiet-Sun flux, ApJ, 674, p.520-529. 

Lites, B., et al. (2007), Hinode observations of horizontal quiet Sun magnetic flux and ‘Hidden turbulent 

magnetic flux’, Publ. Astron. Soc. Japan, 59, S571-S576, 

Otsuji, K. et al. (2007), Small-Scale Magnetic-Flux Emergence Observed with Hinode Solar Optical 

Telescope, Publ. Astron. Soc. Japan, 59, S649–S654 

Pariat, E., Aulanier, G., Schmieder, B., Georgoulis, M. K., Rust, D. M., and Bernasconi, P. N. (2004), 

Resistive Emergence of undulatory flux tubes, ApJ, 614, 1099-1112 

Savcheva, A, A (2007), Study of Polar jet Parameters Based on Hinode XRT observations, Publ. Astron. 

Soc. Japan, 59, S771-S778 

Schrijver, C. J., Title, A M. (2001) On the formation of polar spots in sun-like stars, ApJ, 551, 1099-1106 

Sch rijver, C. J., De Rosa, M. L. , Title A.M. (2002) What is missing from our understanding of long-term 

solar and heliospheric activity, ApJ, 577, 1006-1012 

Shimojo, M, et al. (2007), Fine structures of solar X-ray Jets observed with the X-ray telescope aboard 

Hinode, Publ. Astron. Soc. Japan, 59, S745-S750 

Shimojo, M. (2008), The relationship between the magnetic field and the coronal activities in the polar 

region, COSPAR, E23-003-08, p.1 

The SOHO Mission, Kluwer Academic Publisher, 1995, Eds. B. Fleck, V. Domingo, A. Poland, 531 p. 

The First results from SOHO, Kluwer Academic 

Publisher, 1997, Eds. B. Fleck and Z. Svestka, 799 p. 

Tsuneta, S., et al. (1991), The soft X-ray telescope for the SOLAR-A mission, Sol. Phys., 136, 37-67 

Von Steiger, R., Zurbuchen, T.H., Kilclenmann, A. (2006), Latitude distribution of interplanetary coronal 

mass ejection, 36th COSPAR Scientific Assembly, CDRON #2327 

Wang, Y.-M, Sheeley, N. R. Jr., Nash, A.G. (1991) A new solar cycle model including meridional 

circulation, ApJ, 383, 431-442 

Zhitnik, I.A., Bugaenko, O.I., Ignat’ev, A.P., et al. (2003), Dynamic 10 MK Plasma Structures Observed in 

Monochromatic Full-Sun Images 

by the SPIRIT Spectroheliograph on the CORONAS-F Mission, Mon. 

Not. R. Astron. Soc., 338, 67–71. 

41


DIRECTION-FINDING OF A RARE PHENOMENON OF A 

THUNDERSTORM OVER KAMCHATKA ON THE REGISTRATION DATA 

OF VLF RADIATION 

Cherneva N.V., Druzhin G.I., Melnikov A.N. 

Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS, Kamchatka, 684034, 

Russia, e-mail: nina@ikir.kamchatka.ru 

Abstract. A strong thunderstorm front has passed over Kamchatka in August 2007. On August 27 

strong thunderstorm discharges have been visually observed in Paratunka, Kamchatskiy krai. 

Visually observable thunderstorms are very rare in Kamchatka. This phenomenon is considered to 

occur 1-2 times a year. Moreover it is difficult to locate this phenomenon. In the region during 

thunderstorm formation and during its visual observation the registration of thunderstorm 

discharges was carried out by VLF-direction-finder in Paratunka. Hour dependence of 

thunderstorm discharges as well as azimuthal distribution is presented over whole period of the 

observation of thunderstorm activity. Comparison of direction-finding and meteorological 

characteristics was carried out. The analysis of thunderstorm dynamics according to the data of 

VLF radiation and meteorological parameters points to the fact that sudden change of wind 

direction entails the increase of quantity of thunderstorm discharges in a thunderstorm source. 

Introduction 

The greatest frequency of lightning discharges being the basic sources of VLF radiation, is 

observed on the continents in near equatorial zone. There are known three world lightning centers: 

African, Australian and American. There is a set of local lightning cells on the planet, except of 

world centers, which are basically observed above a land and less often above the sea. The 

electromagnetic signals from lightning discharges can be distributed at great distances - hundred 

and thousand kilometers and are called atmospherics. The maximum of spectral density at radiation 

from a lightning is on frequencies ~10 kHz (a wave-length is 30 kms). The signals from lightning 

are distributed on such frequencies along the waveguide Earth – ionosphere. The world data about 

lightning discharges in "real time" are used for study the phenomena of cyclones and tsunami with 

the purpose of the weather prediction and dangerous weather phenomena. 

There is a world network of lightning site (World Wide Lightning Location Network - 

WWLLN), which includes 26 working reception stations of lightning located worldwide, capable to 

within several hundreds kilometers to define a site and quantity of lightning discharges on all Earth 

(Fig.1, Rodger et al., 2006). 

Fig.1. Locations and hosts of the 25 VLF receiving stations operating in the VLF World Wide 

Lightning Location Network on April 2006. 

42


The continuous registration of electromagnetic radiations with the use VLF direction finder, 

coming from lightning discharges from distances three - five thousand kilometers, is carried out at 

the observatory point “Paratunka” of Institute of Cosmophysical Research and Radio Wave 

Propagation FEB RAS. The registration is conducted in a range of frequencies from 3 up to 60 kHz. 

The signals from lightning sources are accepted by the aerial system consisting of two mutually 

perpendicular magnetic frame aerials and one rod electrical aerial. The voltages from the output of 

the aerial system apply on preliminary amplifiers which are taking place directly at the base of the 

aerial, then on the block of analogue and digital processing of a signal along the cable 

communication. After amplification and frequency filtrations, the transformations of a signal to the 

digital form, two daily files are created, in one of which the temporary forms of a signal are 

recording, in another – its parameters (date, time, root-mean-square meanings of output voltage, 

azimuths of arrival atmospherics). 

Data, received with the use of VLF direction finder, have allowed us to investigate lightning 

activity arising during moving of cyclones, taking place through Kamchatka (Druzhin, Cherneva, 

2005), and also at origin both moving of cyclones and typhoons in Pacific ocean (Mikhailov and 

etc., 2005). Daily direction finding data register very much lightning discharges. However, thunderstorms 

are observed visually seldom in Kamchatka, several times in a year. It is connected with 

various reasons, including that the equipment receives signals from lightning which are taking place 

in the large territory (from distances up to several thousand of km), and visually lightning can be 

observed from distances only up to 15 – 20 km. 

Thunder-storm in Kamchatka 

Powerful thunderstorm front had passed above Kamchatka in August, 2007. The lightning was 

observed on August 27 at the point “Paratunka” and was accompanied by numerous lightnings and 

thunders. The record of an electromagnetic signal was carried out with the use of VLF direction 

finder in the period of its passage. 

It is shown the distribution of lightning discharges (azimuth is counted from northern 

direction clockwise) as points (each point corresponds one lightning discharge) in the top part of 

Fig. 2 for the period from August 24 to August 29, 2007, at the bottom – total quantity of pulses an 

hour. The temporary dependence of a direction of a wind is imposed on azimuth distribution of 

lightning discharge on the data received from Kamchatka Hydrometcenter. 

Fig. 2. Lightning activity during its passage in August, 2007, azimuth distribution lightning 

discharges and direction of a wind (a); hour dependence of quantity lightning centre (b). 

43


It is shown in Fig. 2, that the maximal intensity lightning discharges was observed on 

August 26 at 7 o’clock on the world time (UT), i.e. at 20 o’clock on local Kamchatka time (LT). 

The next day, August 27, the lightning activity has fallen, but remained significant. The local 

maxima were observed in the evening in 15 LT on August 27 and morning in 8 LT on August 28. 

The intensity lightning discharges considerably have weakened next days. 

Also it is visible under consideration of Fig. 2, that the maximum quantity of lightning 

discharges has coincided with sharp change of the direction of a wind: from northern direction to 

southeaster on August 26; and from northern direction to southwester on August 27. It testifies that 

the sharp change of the direction of a wind results in increase of lightning discharges quantity in the 

center. The sharp change of the azimuth thunderstorm sources has taken place in the morning of 

August 27 at 8 o’clock LT. It is possible to consider, that at this time the thunderstorm centre has 

passed above the observation point “Paratunka”. Approximately in the same time the thunder-storm 

was observed visually. 

Let's make an estimation of a site of thunderstorm sources, having the items of the 

information on speed of a wind and about azimuth moving of a thunder-storm. The southern part of 

the Kamchatka peninsula is shown in Fig. 3, where the letter P designates the observation point 

“Paratunka”. Let's assume, that the epicenter of thunderstorm activity is in a point P, and width of 

the thunderstorm center has extent AB. As above mentioned, maximum thunderstorm activity has 

occured on August 26 at 20 o’clock LT (Fig. 2). The thunder-storm was observed in west, and the 

thunder-storm has come to the observation point later ~ 12 hours. Proceeding from it, we shall 

define distance (see Fig. 3) up to the centre of thunderstorm centre PG = V*T, where V- speed of a 

wind, T- time of passage of the thunder-storm centre. Substituting meanings V = 1.2 m/s, T = 12 h, 

we shall receive PG = 64 kms. 

Fig. 3. Location of observation point “Paratunka” – P, centre of lightning activity - G and size of 

lightning centre – AB. 

The thunder-storm on August 26 was observed basically in the range of azimuthal angles 

from 235 0 up to 315 0 (Fig. 2). Hence, the azimuthal angle, under which maximal lightning activity 

was observed, was ~90 0 . Therefore the width of lightning centre AB, determined from a triangle 

PAB (Fig. 3), makes about PG, i.e. ~ 65 kms. 

Distance up to of the lightning centre can be estimated also on temporary and spectral 

characteristics of atmospherics. The examples of temporary variations of atmospherics and their 

frequency spectra are given in Fig. 4. It is visible, that at great distance away from the observation 

point, on August 24, (at the top of Fig. 4) the temporary form of a signal is smooth (without sharp 

emissions), and the maximal amplitude in a spectrum of a signal falls on frequency ~ 8 kHz. As far 

as the thunder-storm is approaching, on August 25, the form of a signal becomes less smooth, and 

there are the components on frequencies 12 - 15 kHz in the frequency spectrum, except of 

frequency 8 kHz. Near to the observation point, on August 26 and 27, the form of a signal gets the 

form of short pulses, frequency the spectrum extends and higher frequencies are prevailed. 

44


Fig. 4. Dependence of the temporary forms of atmospherics (at the left) and their frequency spectra 

(on the right) during passage of the thunder-storm above Kamchatka in August, 2007. 

Conclusions 

The fact that the intensity of lightning discharges in the area of Kamchatka is low, can be 

caused that the nearest observation points are located at distances some thousand kilometers. In 

Russia, with the exception of Moscow, there are no observation points, included in a world 

network, for lightning activity (Fig. 1). Therefore with the purpose of making up a deficiency the 

decision is accepted to establish in Kamchatka the observation points for lightning identical 

WWLLN. Works on the set of VLF equipment are spent now. The exacter distribution of lightning 

activity in the area of Kamchatka can be received when the point "Paratunka" will be a member of 

WWLLN. 

REFERENCES: 

Rodger C.J., Werner J. B., Brundell, Lay E. H., Thomson N. R., Holzworth R. H., Dowden R. L. 

Detection efficiency of the VLF World-Wide Lightning Location Network (WWLLN): 

initial case study. Ann. Geophys., 2006. V. 24. P. 3197–3214. 

Druzhin G.I., Cherneva N.V. Direction finding of lightning sources, connected with Kamchatka 

cyclones. Coll. of reports XXI rus.conf. “Distribution of Radio Wave”. Yoshkar-Ola. 2005. 

V.1. P.421-424. 

Mikhailov Yu.M., Mikhailova G.A., Kapustina O.V., Druzhin G.I., Cherneva N.V. Possible 

atmospheric effects in low ionosphere on observations of atmospheric noises during tropical 

cyclones. Geomagnetizm and Aeronomy. 2005. V.45. №6. P. 824-839. 

45


MAGNETOSHEATH TURBULENCE AND MAGNETOSPHERIC 

PC3 PULSATIONS 

O. Chugunova 1,2 , V. Pilipenko 1,2 , G. Zastenker 1 , and N. Shevyrev 1 

1 Space Research Institute, Moscow; e-mail: ch_olga@nln.ru 

2 Institute of the Physics of the Earth, Moscow 

Abstract. The terrestrial magnetosheath (MSH) is not merely a homogeneous turbulent layer 

between the magnetopause and bow shock (BS), but a structured medium with complex dynamics 

determined both by interplanetary parameters and internal processes. Using the high-resolution 

magnetic and plasma data from Interball-1 (IB1) satellite, we have marked out several typical 

turbulent domains: (a) upstream BS (UBS); (b) post-shock (PBS) downstream BS; (c) transitional 

region; and (d) inner MSH. In contrast to the existing paradigm that the upstream waves in the 

foreshock (FSH) are the primary source of magnetospheric Рс3 pulsations, we suggest that their 

actual source is a turbulence in the MSH. Analysis of IB1 observations shows that both the MSH 

turbulence and ground Pc3 pulsations are controlled by the IMF orientation in respect to the BS 

normal. We suppose that the hypothesis about the MSH as a primary source of Pc3 disturbances 

gives a possibility for a new look on the problem of ULF wave origin. 

Introduction 

The turbulent magnetosheath (MSH) region between the bow shock (BS) and magnetopause is of special 

importance to the solar-terrestrial physics, because in fact the magnetosphere interacts not with the solar 

wind (SW), but with the MSH. The MSH turns out to be not merely a homogeneous turbulent layer, but a 

structured medium with complex dynamics determined both by interplanetary parameters and internal 

processes. The magnetic and plasma turbulence inside the MSH is not directly related to the turbulence of 

the SW, but to a considerable extent is due to intrinsic MSH processes [Shevyrev et al., 2003; Shevyrev & 

Zastenker, 2005]. 

According to the dominating view in geophysics the primary source of Рс3 pulsations is upstream waves 

(UW) the BS front. UW are excited by the ion-cyclotron instability (ICI) of energetic protons reflected from 

the BS. The particle and wave population are especially intense in the foreshock (FSH) part of the region 

upstream the BS (UBS). The UW are supposedly convected by the SW flow through the BS and penetrate 

somehow via the MSH into the magnetosphere. The further Pc3 wave propagation and mode conversion 

inside the magnetosphere are well studied. However, all the attempts to trace the propagation of UW from 

the FSH through the MSH into the magnetosphere failed [Engebretson et al., 1991]. Nonetheless, the 

viewpoint has widely spread that namely the FSH is the primary source of magnetospheric Рс3 pulsations. 

This notion is supported by the statistical relationship between intensity of UW in the FSH and cone angle q 

(more strictly, by the angle θBn between the BS normal and IMF): intensity of UW is suppressed upstream a 

quasi-perpendicular (Q⊥) BS (θBn > 45°) and enhanced upstream a quasi-parallel (Q||) BS (θBn < 45°). The 

same statistical regularities are observed for magnetospheric Рс3 pulsations. Moreover, the theory of ICI 

predicts that the UW frequency f is to be proportional to the IMF magnitude B. Indeed, the linear statistical 

dependence: f[mHz]=gB[nT] (where g = 4.4–6.0 mHz/nT) was observed both for UW, and for 

magnetospheric Pc3 waves (though not very firmly) [Russell and Hoppe, 1981]. 

On the basis of these results, the notion prevails that the FSH is the source of both UW and 

magnetospheric Pc3 pulsations. In contrast to this view, here we suggest that the actual source of Pc3 

pulsations is not UW, but turbulence in the MSH. The presented here analysis of high-resolution 

observations of plasma flow and magnetic field by IB1 spacecraft shows that both the MSH turbulence and 

ground Pc3 pulsations are controlled in a similar way by the IMF orientation, namely by θBn angle. In 

addition, the case and statistical analysis of IB1 passes through the MSH has enabled us to reveal several 

typical turbulent domains. 

Estimated characteristics of magnetic and plasma fluctuations 

Using 1-sec IB1 data of the three-component magnetic field B (in GSE coordinates) and integral flux of ions 

F measured by the Faraday cup oriented Sunward along the spacecraft spin axis the following parameters 

have been estimated: 

46


• Relative level of magnetic field magnitude fluctuations δB/B (standard deviation of B normalized to 

the mean B), characterizing the magnetic field compression; 

• Relative level of magnetic field component fluctuations δBy/B; 

• Relative level of the plasma flux fluctuations δF/F, it has been assumed that plasma density N 

fluctuations provide a main contribution to fluctuations of F; 

• Relative «compression» of plasma in oscillations C=(δF/F)/(δB/B), characterized by the ratio 

between normalized F and B fluctuations, introduced similar to [Song et al., 1994]; 

• Measure of magnetic field direction fluctuations RB, namely 

N 

∑ i 

2 

N 

∑ i 

2 

N 

∑ i 

2 1/2 

i= 1 i= 1 i= 

1 

RB = 1 − (1/ N)[( X ) + ( Y ) + ( Z ) ] 

where N is a number of measurements, and Xi, Yi, Zi are the direction cosines of B. For purely compressional 

disturbances RВ →0, for chaotic in all directions fluctuations RВ →1. 

• Correlation coefficient RBF between variations of В and F; 

• Spectral coherency γ and phase shift Δϕ (the latter has sense under a sufficiently high coherency, e.g. 

γ > 0.3) between variations of В and F, using the modified Welch periodogram method. The spectral 

estimates have been averaged in the Pc3-4 frequency range 10–60 mHz; 

• Spectral indices PB and PF, characterizing the slope of the power spectral density S(f) ~ f -P of B and 

F fluctuations in the inertial interval 0.0001–0.5 Hz; 

• Ratio between minimal and maximal eigenvalues of the minimum variance analysis (MVA) matrix 

λmin/λmax, characterizing the anisotropy of fluctuations; 

• Angle between local В and effective wave vector k, determined from MVA ψBk = arсcos(kB); 

We have used the angle θBn between IMF and the BS normal at a point at the BS, where the plasma flow 

through IB1 in the MSH is traced back to the BS determined with the Spreiter et al. [1966] model, using 1min 

WIND or ACE data. The BS is modeled by relationships from Shue et al. [1997]. All these parameters 

have been estimated in a running 10-min (20-min for the spectral indexes) window with 50% overlapping. 

Cases studies 

The analysis of many individual orbits demonstrates that several characteristic domains may be outlined: the 

UBS, which under favourable IMF orientation, namely Q BS, is observed as the FSH; post-shock (PSH) 

downstream the BS; transitional region between PSH and inner MSH, and inner MSH. 

As a typical example we consider an event on June 16, 1997, when IB1 moves from the SW towards the 

magnetosphere. Variations of the magnetic and plasma fluctuation parameters along the orbit are shown in 

Fig. 1. The values of θBn during this event (bottom panel in Fig. 1) indicate on the prevalence of Q⊥ BS 

condition. The behavior of magnetic and plasma fluctuations in these domains may be characterized as 

follows: 

UBS: 00.00–00.40 UT. IB1 trespassed the BS around 00.40 UT. The moderate level of fluctuations is 

observed: δF/F ~ 0.18 and δB/B ~ 0.2. Magnetic field fluctuations are compressional, RB ~ 0.1–0.3, and 

anisotropic, λmin/λmax ~ 0.1–0.2. The plasma compression is high C ~ 0.9. Variations of B and F are coherent 

γ ~ 0.6–0.8 and in-phase Δϕ ~ 3 о , RBF ~ 0.6–0.8. 

PSH: 00.45–01.10 UT. Fluctuations of B and F are significantly enhanced as compared with FSH: 

δB/B~0.3, δF/F~0.3. Fluctuations of B direction are more chaotic RB ~ 0.4, and more isotropic λmin/λmax~0.4. 

The contribution of B orientation oscillations to magnetic noise can be seen also from deviations between 

δBy and δB wave powers. Plasma compression is high C ~ 1.1. Fluctuations of B and F become non-coherent 

γ < 0.3, RBF ~ 0. 

Transitional region: 01.10–01.35 UT. The intensity of fluctuations is substantially suppressed: 

δB/B~0.08, δF/F~0.09. Coherency of these fluctuations is low (γ ~ 0.2, RBF ~ 0). Oscillations of В are mainly 

compressional (RB ~ 0.01) and anisotropic (λmin/λmax ~ 0.3). Plasma compressibility is still high (C ~ 0.8). 

MSH: 01.35–03.00 UT. Intensity of magnetic fluctuations steadily grows: δB/B~0.15, whereas the 

intensity of plasma fluctuations keeps nearly at the same level δF/F~ 0.1. Oscillations of B are mainly 

compressional (RB ~ 0.01), and anisotropic (λmin/λmax ~ 0.15). Oscillations of B and F become more coherent 

γ ~ 0.4, but rather out-of-phase (Δϕ ~ 80 о , RBF ~ –0.3), whereas plasma compression is not high (C ~ 0.6). 

The spectral index PB is noticeably higher (~2.5) than in the PSH (< 1.5). 

Summarizing this and other observations, the following characteristic domains may be selected: 

47


• FSH – the UBS region filled with coherent and in-phase oscillations of В and F (like fast 

magnetosonic waves), most evident for the Q conditions; 

• PSH – the narrow region in the MSH downstream the BS (both for Q and Q⊥ BS) with very 

intense non-coherent fluctuations of F and В. Magnetic fluctuations are nearly isotropic and fluctuate both in 

magnitude and direction; 

• Transitional region between PSH and inner MSH with low intensity В and F fluctuations; 

• Inner MSH with coherent, but out-of-phase, oscillations (like diamagnetic or slow magnetosonic 

disturbances). Magnetic fluctuations are anisotropic and mainly compressional. 

Additional to these, the region of the MSH near the magnetopause may be outlined [Denton et al., 1995], 

which is not considered here. Further, this classification scheme is verified with the statistical analysis of 

other similar events. 

Fig. 1. Variations of the 

magnetic and plasma fluctuation 

parameters along the IB orbit on 

June 16, 1997 in the following 

domains indicated as follows: 

FSH, PSH, transitional region, 

and MSH. The following 

parameters are shown (from top 

to bottom): the total B[nT], 

normalized magnitudes of 

magnetic and plasma fluctuations 

δB/B (solid line), δBy/B (dashed 

line), and δF/F (dotted line); 

plasma flux F [10 -8 cm -2 s -1 ]; 

correlation coefficient RBF 

between variations of В and F; 

plasma compression C; phase 

shift Δϕ [degrees]; spectral 

coherency γ in the Pc3-4 

frequency range 10–60 mHz; 

measure of magnetic field 

direction fluctuations RB; angle 

ψBk; the MVA parameter 

λmin/λmax; spectral indices PB 

(solid line) and PF (dotted line); 

and angle θBn. 

Statistical dependence of magnetic and plasma fluctuations on IMF orientation 

We have analyzed 11 events of the IB1 crossing the BS and surrounding layers in 1996–1999. The statistical 

distributions of all the parameters versus the corresponding θBn values are presented as scatter plots in Fig. 2 

for the following domains: UBS/FSH (blue dots), number of 10-min (20-min) intervals is N = 217(76); PSH 

(green dots), N = 147(30); and inner MSH (red dots), N = 203(72). Data points corresponding to the 

48


transitional region (N = 168) have been omitted to make plots more readable. The visual inspection of the 

scatter plots shows the following regularities: 

In the UBS, as expected, the magnetic fluctuations δB/B are statistically more intense in the FSH (θBn < 

45º). The same tendency is observed in PSH and MSH regions: fluctuations are more intense under Q 

condition, but less evident and with a larger dispersion. However, the plasma fluctuations δF/F demonstrate 

evident dependence on θBn in all regions. 

The spectral properties of the plasma and magnetic field turbulence change upon the transition from the 

FSH to PSH (green dots are statistically lower than blue dots). Moreover, the dependencies on θBn are 

different in different domains: the index PB decreases in the FSH with increase of θBn , whereas in the MSH 

the tendency is opposite.Thus, the magnetic and plasma turbulence in the MSH is not the same, but just more 

intense, than those in the FSH. 

According to the coherency γ between B and F oscillations in ULF range, there is a clear distinction 

between the regions: oscillations are coherent in the FSH, non-coherent in the PSH, and have moderate 

coherency in the MSH. In the UBS the oscillations of B and F are more coherent under the conditions of Q 

than under Q⊥ BS. 

The correlation coefficient RBF between B and F oscillations is clustered around specific values in all 

three domains. In the UBS RBF ~ 0.8 under Q BS and becomes more dispersed under Q⊥ BS. In the MSH 

coefficient RBF becomes negative: RBF ~ –(0.1–0.8), being more widely dispersed under Q BS. 

Under Q BS the measure of magnetic field direction fluctuation RB is rather widely dispersed in all 

domains and in PSH fluctuations of B direction are more chaotic: here RB mainly > 0.2, whereas in other 

domains RB < 0.2. Under Q⊥ BS RB is clustered at low values 0.1, which indicates that variations of B are 

mainly compressional. 

49 

Fig. 2. The statistical 

distributions of parameters 

δB/B, δF/F, γ, RBF, PB, PF, 

λmin/λmax, RB, C, (panels a-i, 

respectively) versus the 

corresponding θBn for the 

following domains: FSH 

(blue dots), PSH (green), 

and MSH (red). 

The linear regression 

approximations for 

parameters with statistically 

significant correlation 

coefficient (r>0.4) are 

shown by dashed lines.


The magnetic oscillations are anisotropic, as measured by the parameter λmin/λmax, in the UBS and inside 

the MSH under any orientation of IMF. In the UBS magnetic oscillations are more isotropic under Q BS 

(λmin/λmax is distributed in the range 0.1–0.6) than under Q⊥ BS (λmin/λmax 0.2). In the PSH magnetic 

oscillations become more isotropic: λmin/λmax > 0.3. Plasma oscillations tend to be more compressional 

(higher С) under Q⊥ BS. In all domains the wave vector of magnetic fluctuations is directed at large angle to 

B: ψBk ~ 40°–80° (not shown). This may signify that these fluctuations are more elongated along B than 

across it. 

The visual impression has been validated by the regression analysis (approximation by 

linearization). Fig. 2 shows the approximation lines for parameters with statistically significant 

correlation coefficient (r > 0.4). The comparison of the regression lines show that the same 

dependencies on θBn as in the FSH are observed in the PSH and inside the MSH for all parameters 

besides the spectral index PB. The statistically significant correlation (r indicated in brackets) have 

been found for the following dependences on θBn: 

FSH: δF/F (–0.45), PB (–0.73), PF (–0.78), RBF (–0.58); 

PSH: δF/F (–0.54), RB (–0.52), RBF (–0.53); 

MSH: δF/F (–0.51), RB (–0.45), δB/B (–0.41), PB (0.49), RBF (–0.46). 

Mechanisms of the turbulent region formation 

The statistical analysis confirms that many features of magnetic and plasma fluctuations in the FSH and 

MSH are not the same. Thus, the turbulence and waves downstream the BS are not just an enhancement of 

SW turbulence and upstream waves. This may to be the indication on the occurrence of different generation 

mechanisms in these regions: 

In the FSH upstream waves were established to be generated by ICI of ion beams, reflected upon 

interaction of SW flow with BS [Le and Russell, 1992]; 

In the PSH some fast-growing (explosive?) instability must operate. Any slow-growing disturbances due 

to a kinetic instability cannot interpret the observations because they will be removed fast from this region by 

SW plasma flow. Fast growth of unstable oscillations may be facilitated by a high level of seed disturbances, 

resulted from a theoretically predicted increase of FSH fluctuations upon transition through BS; 

In the MSH the magnetic and plasma oscillations are generated by a relatively slow-growing (possibly, 

mirror) instability caused by unstable plasma. 

50 

Fig. 3. The ULF observations during 

March 21, 1997 at IB1 (magnetic field 

magnitude B and component By, 

plasma flux F) and on the ground 

stations A80, A81, P3, and P4 (H 

components). Corrected geomagnetic 

latitudes of stations are indicated near 

right-hand sides of panels). The 

bottom panel shows the angle θBn. The 

moment of the IB crossing the BS 

(~12.45 UT) is marked as BS.


Is the upstream waves a source of magnetospheric Pc3 pulsations? 

According to the existing paradigm, UW in the FSH are the primary source of magnetospheric Рс3 

pulsations. These waves supposedly transmit somehow through the turbulent MSH into the magnetosphere. 

Here we put forward a hypothesis that in fact the source of Pc3 pulsations is not the FSH, but the MSH itself! 

The following event March 21, 1997 is an example of the IMF orientation control of ULF oscillations in the 

MSH and Pc3 waves on the ground (Fig. 3). During this event IB1 was in the MSH till 12.45 UT. Due to the 

IMF orientation change, the transition from Q⊥ to Q|| BS occurred in the period from 11.50 to 12.00 UT: θBn 

decreased from ~90º to ~0º. This transition caused a noticeable increase of the intensity of plasma and 

magnetic fluctuations in the MSH. 

The ground ULF activity has been monitored by the search-coil magnetometers (sampling rate 2Hz) in 

Antarctica at sub-auroral latitudes (stations А80, А81), and at cusp latitudes (stations Р3, Р4). 

Simultaneously with the increase of the intensity of plasma and magnetic fluctuations in the MSH, the 

enhancement of Pc3-4 wave activity is observed at ground stations in the morning sector of the 

magnetosphere. 

The spectral analysis shows that the oscillations of B and F in the MSH are not featureless noise, but have 

a highlighted frequency ~0.02–0.03 Hz (not shown). This frequency band corresponds to Pc3-4 frequency 

observed on the ground. However, the ground Pc3-4 waves are more narrow-band, possibly due to the 

magnetospheric resonance effects. 

Conclusion 

Analysis of many events has shown that the direct wave penetration from the FSH into MSH is never 

observed, which makes the assumption about the FSH origin of the magnetospheric Pc3 pulsations 

questionable. On the other hand, the known statistical relationship between the Pc3 activity and IMF cone 

angle may be interpreted from another view point, as follows. The energy of super-sonic SW flow transforms 

at the BS not only in heat, but in the excitation of various plasma and field pulsations by different 

mechanisms. In the FSH waves are known to be generated by the kinetic instability of reflected protons. 

The instability mechanisms in the MSH are to be different for Q⊥ and Q|| BS. At Q⊥ BS the tangential B 

rapidly increases, simultaneously with the plasma pressure. As a result, the growth of β is relatively small, 

but increase of the anisotropy A is substantial. At Q|| B is normal to the boundary and does not change. 

Therefore, the jump of plasma pressure results in substantial increase of β (up to 6–7), whereas the increase 

of A is insignificant (A~0.5). Thus, the physical conditions at Q⊥ and Q|| BS are to be favorable for different 

types of instabilities (e.g., mirror ICI). It is essential that an instability in the MSH downstream Q|| BS has to 

generate more intense oscillations. Further, the excited intense fluctuations of B and plasma are convected by 

the MSH flow to the magnetopause, buffet the boundary of the magnetosphere, and excite the 

magnetospheric compressional waves. The magnetosphere responses resonantly on external large-scale 

disturbances in the Pc3-4 frequency range only. 

Despite limited statistics of the events analyzed, we suppose that the proposed hypothesis gives 

possibility to look from a new point on the problem of the ULF wave origin in the magnetosphere and 

deserves more thorough study and validation. 

Acknowledgements. This study is supported by the INTAS grants 05-1000008-7978, 05-1000008-8050 and 

RFBR grant 07-02-00198. 

References 

Engebretson, M. J., et al. (1991) J. Geophys. Res., 96, 3441. 

Denton R. E., et al. (1995) J. Geophys. Res., 100, 5665. 

Le G., C.T. Russell (1992) Planet. Space Sci., 40, 1203. 

Russell C.T., M.M. Hoppe (1981) Geophys. Res. Lett., 8. 615. 

Shevyrev N.N., et al. (2003) Adv. Space Research, 31/5, 1389. 

Shevyrev N.N., G.N. Zastenker (2005) Planet. Space Science, 53. 95. 

Shue J.-A., et al. (1997) J. Geophys. Res., 102. 9497. 

Song P., et al. (1994) J. Geophys. Res., 99, 6011. 

Spreiter J.R., et al. (1966) Planet. Space Sci., 14. 223. 

51


TWO DIMENSIONAL MODEL OF MAGNETIC FIELD 

TRANSFER THROUGH THE MAGNETOTAIL DUE TO 

PLASMA FLOW IN THE PLASMA SHEET 

V.V. Denisenko 1,2 , A.V. Kitaev 1 , H.K. Biernat 3 

1 Institute of Computational Modelling, Krasnoyarsk 660036, 

Russia, e-mail: denisen@icm.krasn.ru; 

2 Siberian Federal University, Krasnoyarsk 660041, Russia; 

3 Space Research Institute, Austrian Academy of Sciences, 

Schmiedlstrasse 6, Graz 8042, Austria 

Abstract A two dimensional steady state model of magnetic field transport to the magnetotail 

is developed. A kinematic MHD approach is used, in which the velocity and 

conductivity distributions are taken as given. The used velocity distributions in the 

plasma sheet approximate the satellite data. The value of the effective electric conductance 

of the plasma sheet of about 100S is chosen to fit the observed features of the 

magnetic field stretching into the tail. 

1 Introduction 

Dissipative processes in the magnetosphere plasma, in particular anomalous resistivity of the plasma 

have essential influence on processes in magnetosphere of the Earth [2]. The condition of a frozenin 

magnetic field in the plasma sheet would lead to accumulation of magnetic field tubes in the 

magnetotail, and to almost constant magnitude of the magnetic field in the tail lobes. On the other 

extreme case of low conductivity of plasma the convective transfer of the geomagnetic field to the 

distant tail would be insignificant and a dipole-like magnetic field would fast decrease with the 

distance from the Earth. We believe that the magnetotail is formed as an outcome of convective 

transfer and diffusion of geomagnetic field in the plasma sheet. 

The purpose of the present paper is to study influence of conductivity of plasma in the plasma 

sheet on magnitude of magnetic field in the tail lobes. A simple stationary model of the geomagnetic 

field transfer in the tail by plasma flow in the plasma sheet is considered. In the model the geometry 

of the plasma sheet is defined, and flow velocity in the plasma sheet also is considered as given and 

it is set on the base of satellite measurements. This simplification reduces the problem to a linear 

problem for the magnetic field distribution in a specific area. 

2 Kinematic MHD 

When velocity V is given, the steady-state 2-D equations for magnetic induction B in isotropic 

conductor with given conductivity σ are the following 

∂Bx 

∂z 

− ∂Bz 

∂x + µ0σVxBz − µ0σVzBx = µ0σE 0 y, 

∂Bx 

∂x 

+ ∂Bz 

∂z 

These equations can be obtained from Maxwell equations and Ohm’s law 

j = σ(E + [v × B]), 

= 0. (1) 

when all parameters are independent of time and y and vectors V,B are in the x, z plane. 

The electric field E = (0, Ey, 0) is a given constant E 0 y in such a model. 

By the solution of (1) the current density j = (0, jy, 0) can be calculated as 

µ0jy = ∂Bx 

∂z 

52 

− ∂Bz 

∂x .


If there is an ideal conductor behind the boundary Γ of the domain Ω then 

Bn | Γ = B 0 n(l), 

where l – arc length at the boundary, indexes l and n mark tangential and normal components. 

We analyze an important particular case when the density ρ = const and σ = const, or the 

case with constant ratio at each stream line σ/ρ = const, when the current function β can be 

constructed because of the mass conservation law div(ρv) = 0: 

µ0σVx = − ∂β 

∂z , µ0σVz = ∂β 

∂x , 

Then the equations (1) can be written 

with the tensor coefficient 

� 

β dΩ = 0. 

roty(κB) = µ0σE 0 y, div B = 0 (2) 

κ = 

� 

1 β 

−β 1 

Since it is invariant in respect of rotation around z axis, the equations (2) simulate some process 

in a hyrotropic medium. 

3 Energy method 

The operator of the boundary value problem for the equations (2) is not a self-adjoint one. To avoid 

difficulties of numerical solution of such a problem we invent a new statement of the same problem 

that has self-adjoint operator. A use of new potentials instead of the usual vector potential permits 

to set up a boundary value problem with a symmetric positive definite operator. The principle of 

energy minimum is valid for such a problem. Such a principle is used to design an effective finite 

element method for numerical solution. 

New unknown functions (F, P) are similar to the traditional potential and current function. 

The space that consists of pares of the functions (F, P), which satisfy the conditions 

� 

P | Γ = 0, F dΩ = 0, 

is the Hilbert space with the energy scalar product 

� � � � � 

ξ F 

[ , ] = 

η P 

� �T � 

grad ξ 1 −κ 

rot η 

T 

−κ κκT The minimum of the energy functional 

W(F, P) = 1 

2 [ 

� � � 

F F 

, 

P P 

gives the solution for the problem 

� � 

] − 

Ω 

� 

div(−grad F + β grad P) = 0 

. 

� � 

grad F 

rot P 

� 

Pµ0σE 0 � 

y dΩ + FB 

Γ 

0 n(l) dl 

div(β grad F − (1 + β 2 )grad P) = µ0σE 0 y 

�� 

��Γ 

� 

− ∂F ∂P 

+ β = B 

∂n ∂n 

0 n(l). 

It is equivalent to the original problem with notation 

dΩ. (3) 

B = −grad F + κ T rot P, (4) 

where T means transposition of the matrix. 

In view of (4) the quadratic form (3) is equal to the total energy of the magnetic field with 2µ0 

multiplier 

[ 

� 

F 

P 

� 

, 

� 

F 

P 

53 

� � 

] = B 2 dΩ.


4 Model magnetic field 

We use the model (1) inside the plasma sheet that occupies the rectangle |z| < 2.5 RE, x < 

−7 RE. No current is taken into account in the rest part of the magnetosphere and equations of 

magnetostatics are used there, which correspond (1) with σ = 0. Both components of the magnetic 

induction B are permanent at the interior boundary which separates the plasma sheet. 

The magnetopause is regarded as an ideal conductor with zero Bn. So we construct a model 

of closed magnetosphere. The surface of the Earth is also an ideal conductor and dipolar Bn is 

given there. The dipole is directed along z− axis that makes the model symmetrical with respect 

to z = 0 plane. So only the Northern half of the magnetosphere is presented later. Some formal 

boundary condition is used at the far part of the boundary at x = −200 RE, and this distance is 

chosen by test calculation large enough to have no influence on the field in the domain of interest, 

x > −100 RE. 

From the estimations [1] we obtain conductivities σ = 5 · 10 −6 S/m in the near-Earth plasma 

sheet at 15−35 RE and σ = 2·10 −6 S/m in the deep tail at about 100 RE with intervals (1/3÷3) of 

these values. These values give integral conductance of the plasma sheet Σ = 150, 60 S × (1/3 ÷ 3) 

if δz = 5 RE. So we use Σ = 100 S in our model and a few values around it. 

We use velocity distribution, that approximates the average data from [4] 

−Vx = V0 (1 − exp(x − x1)/x0) (5) 

with V0 = 400 km/s, x1 = −7 RE, x0 = 100 RE. In accordance with [3] there is flow to the Earth 

in the near-Earth plasma sheet at 19 −29 RE during quite time. So we also analyze a modification 

of (5) with velocity directed to the Earth in the near-Earth plasma sheet at 7 − 32 RE. Both 

approximations are shown in Fig. 1. 

The results of calculations are presented in Fig. 2-4. It is well seen how the magnetic field lines 

are pulled from the Earth by the moving conductor in comparison with the dipolar geomagnetic 

field in empty closed magnetosphere, that is presented in Fig. 2a. The model distributions of 

the components Bx, Bz are presented in Fig. 3,4. The magnetic field in the lobes increases with 

conductance of the plasma sheet, and Bx is close to the data [4] if Σ is about 100 S. 

The flow to the Earth in the near-Earth plasma sheet decreases the stretching very much as it is 

presented in Fig. 2d and Fig. 4, curves 3. Of cause it corresponds to the increase of Bz component 

that closes Bx in the near-Earth plasma sheet. 

The addition of the electric field increases current jy and so increases Bx in the lobes. Fig. 3c 

and curves 1 in Fig. 4 demonstrate this effect for typical value Ey = 1 kV /RE that corresponds 

to 50 kV potential difference across the tail. 

5 Conclusions 

The designed model permits to explain the observed stretching of the geomagnetic field into the 

lobes. This simple model uses as given the stationary Vx(x) distribution in the plasma sheet, that 

has large variations and is not well known until now. The flow in the near-Earth plasma sheet 

is especially important since just there the conductor ”catch” magnetic field lines which are to 

be pulled into the tail. More detailed Vx(x) distribution aught be used for different geomagnetic 

conditions, since corresponding Vx(x) may vary ten times and change sign [3]. The presented 

magnetic field distributions mainly demonstrate the role of the conductor motion in the magnetotail 

formation. 

Acknowledgement. This work is supported by grant 07-05-00135 from the Russian Foundation 

for Basic Research, by grants 2.16 and 16.3 from the Rusiian Academy of Sciences, and 

by project I.2/04 from “ Österreichischer Austauschdienst”. It is also supported by the Austrian 

“Fonds zur Förderung der wissenschaftlichen Forschung” under projects P20341–N16 and P20145– 

N16. The authors are grateful to Prof. V. Sergeev for the discussion. 

54


600 

400 

200 

−Vx, km/s 

0 

0 50 100 150 200 −x,RE 

Figure 1: Vx distribution in the plasma sheet. Broken line – data [4]. Curves – two versions of our 

approximation. 

a 

b 

c 

d 

0 50 −x, RE 100 

Figure 2: Magnetic field lines in closed 2-D magnetosphere. Flux between neighbor lines 20 nT ∗RE. 

a – dipole in empty magnetosphere, that corresponds Σ = 0, and Σ = 100 S for the next models. 

b – flow from the Earth and zero Ey. c – flow from the Earth and Ey = 50 kV /50 RE. d – flow 

to the Earth in the near-Earth plasma sheet −7 RE > x > −32 RE and zero Ey. 

55


50 

40 

30 

20 

10 

0 

< −Bx >, nT 

� Σ = 200 

� � � 

Σ = 0 

0 10 20 50 −x,RE 100 

� 

10 

8 

6 

4 

2 

0 

Σ = 0 

Bz, nT 

� � 

Σ = 200 

� 

� � � � 

0 10 20 50 −x,RE 100 

Figure 3: Average magnetic field −Bx component in the Northern tail lobe (left) and Bz component 

in the plasma sheet (right) for Σ = 0, 25, 50, 100, 200 S. Dots – data [4]. 

50 

40 

30 

20 

10 

0 

1 

2 

3 

< −Bx >, nT 

0 10 20 50 100 

−x,RE 

� 

� � � � 

10 

8 

6 

4 

2 

0 

1 2 3 

� � 

Bz, nT 

0 10 20 50 100 

−x,RE 

� 

� � � � 

Figure 4: Average magnetic field −Bx component in the Northern tail lobe (left) and Bz component 

in the plasma sheet (right) for Σ = 100 S – curves 2, which are repeated from Fig. 3. Flow to the 

Earth up to Vx = 28 km/s in the near-Earth plasma sheet −7 RE > x > −32 RE is added – curves 

3, or Ey = 50 kV /50 RE is added – curves 1. Dots – data [4] 

References 

[1] Cattell, C.A. (1996). Experimental evaluation of the Lundquist number for the Earth’s magnetopause 

and magnetotail, J. Geophys. Res., 101, 27309-27316. 

[2] Liperovsky V.A., and M.I. Pudovkin (1983). Anomalous resistivity and double layers in the 

magnetospheric plasma. 181 pp., Publishing house ”Nauka”, Moscow. 

[3] Nishida, A., T. Mukai, T. Yamamoto, S. Kokubun, and K. Maezava (1998). A unified model of 

the magnetotail convection in geomagnetically quiet and active times, J. Geophys. Res., 103, 

4409-4418. 

[4] Slavin, J.A., E.J. Smith, D.G. Sibeck, D.N. Baker, R.D. Zwickl, and S.-I. Akasofu (1985). An 

ISEE-3 study of average and substorm conditions in the distant magnetotail, J. Geophys. Res., 

90, 10875-10895. 

56


SECULAR AND LARGE-SCALE CHANGES IN SOLAR ACTIVITY, 

COSMOGENIC ISOTOPES AND CLIMATE CHANGES 

Introduction 

V.A.Dergachev 

Ioffe Physico-Technical Institute of RAS, St.-Petersburg, 194021, Russia, e-mail: 

v.dergachev@mail.ioffe.ru 

Abstract. There is a grows body of evidence from a multi-proxy palaeoclimate records that 

hundred years and millennial years periodic climatic events have persisted during the last 10000 

years, as for instance the well-known “Little Ice Age” and cold episode about 2800 cal yr BP 

separated by about 2400-year time interval. Ice rafted debris in marine cores of the north Atlantic, 

which are attributed to changes in the north Atlantic deep water formation and probably forced by 

changes in solar activity, demonstrated about 1500-year cycles, which rather appear to reflect 

atmospheric circulation variations, ice sheet fluctuations and oceanographic changes. It is well 

established that the production of cosmogenic isotopes, such as 14 C and 10 Be, is modulated by solar 

activity and may thus serve as a proxy for solar activity changes. The 14 C and 10 Be signals from 

well-dated samples show similar trends during the last 10000 years. Removing the effects of the 

Earth’s magnetic field from the measured 14 C concentration in tree-ring yields the residual 

radiocarbon signal, which potentially reflects changes in solar activity. As demonstrated by 

spectral analysis of sunspot numbers and reflected in the 14 C proxies, solar activity displays a 

cyclic behavior with short-time, secular and large-scale periodicities. Hence, if solar activity is the 

driving force behind climate changes, these cyclicities should be observable in climate records. 

Evidence of warm and cold periods and of cyclic climate variability connected with secular and 

large-scale changes in solar activity are demonstrated by this work. Large-scale climate changes 

recognized as global events suggest periodicities of about 2400 years. The observed 210-year 

climate periodicity corresponds to secular changes in solar activity, such as the Maunder or 

Spoerer minimum. Direct solar forcing may account for a significant amount of the climate 

variations observed during the Holocene. 

The climate of the last millennium has been the subject of much debate in recent years, both in the scientific 

literature and in the popular media. The most debated issue in contemporary science is the cause or causes of 

global warming – the increase of approximately 0.8±0.1 0 C in the average global temperature near the 

Earth’s surface since 1900 year. The IPCC report (Climate Change 2007) concludes that the observed 

warming is due to the increase in anthropogenic greenhouse gas concentration in the atmosphere. As to the 

natural causes of global warming it is reported that the contribution of solar variability is negligible, to a 

certainty of 95%. 

Presently, there is a grows body of evidence from a multi-proxy palaeoclimate records that the earth’s 

climate experienced rapid cyclical climate change - medium-lived (hundred years) and long-lived (millennial 

years) periodic climatic events - during the last 10000 years. Proxy data document mid-Holocene warming 

of the Arctic as well as the Antarctic (Mayewski et al. 2004). This Holocene warming appears to be strongly 

linked to solar variability and not to the greenhouse gas forcing. 

In order to understand the Holocene climate history and the forcing for natural climate variability at 

decadal to millennial timescales during this epoch, records of climate variability to have the finest possible 

temporal resolution and greater chronological control. Documenting the extent and persistence of centennial- 

and millennial-scale variability requires global coverage. Proxy climate indicators include information 

obtained from documentary and cultural sources, ice cores, glaciers, boreholes, speleothems, tree-growth 

limits, lake fossils, mammalian fauna, coral and tree-ring growth, peat cellulose, pollen, phonological data, 

and seafloor sediments. On the assumption that the Sun and cosmic ray intensity are the major driver of 

climate changes (van Geel et al. 1999), the 14 C concentration record has been used as a measure of changes 

in cosmic ray flux, and solar activity in the past. 

Climate proxy records of high resolution are analyzed to demonstrate major changes in these variables 

over the Holocene. A comparison between these changes in climate and changes in cosmogenic isotopes is 

carried out to establish a relationship between solar variability and climate changes. The main archives in 

57


this study are hydrological and atmospheric circulation changes. Lake basins present highly sensitive 

archives because lake-level record can document past changes in the water budget in relation to climatic 

changes. In addition, hydrology is more important for people in some cases than temperature variability. 

EVIDENCE FOR REGULAR CLIMATIC CHANGES IN THE PAST 

During the Holocene large fluctuations in hydrology and atmospheric circulation, as revealed by a number of 

archives and proxies, took place on the continents with distinct amplitudes both in the Northern Hemisphere 

and in the tropics and subtropics. The main attention in continental palaeohydrology is devoted to the 

analysis of information from groundwater, mountain glaciers and permafrost, lake, wetland, soil and river 

systems. 

Lake levels are influenced by climatic parameters affecting both evaporation and precipitation. To 

reconstruct a Holocene mid-European lake-level record Magny (2004) used a data set of 180 radiocarbon, 

tree-ring and archaeological dates obtained from sediment sequences of 26 lakes in the Jura, the northern 

French Pre-Alps and the Swiss Plateau. The dates were separated into two groups, i.e. lower lake-level 

versus higher lake-level episodes. The phases of high lake-level are characterized by a deposition of more 

mineralized sediments, whereas the phases of low lake-level are characterized by an extension of peat or 

organic detritus accumulation in the nearshore areas. According to a quantitative reconstruction of climate 

variables, phases of higher lake-level coincide with an increase in annual precipitation, a decrease in summer 

temperature and a shortening of the growing season. Fig. 1 shows that the dates form clusters suggesting an 

alternation higher lake-level phases that point to a rather cold Holocene climate. There are clearly ca. 2000year 

quasi-periodicity in cold climate change. Thus, the mid-European lake-level record testifies to a 

significant instability of the Holocene climate. 

Fig. 1. Distribution of the dates of higher lake-level events reconstructed in the Jura mountains, the 

northern French Pre-Alps and the Swiss Plateau over the Holocene period (Magny, 2004). The vertical 

scales represent the number of dates for successive 50 years intervals between 12,250 and 0 cal yr BP. 

The Holocene wetting of the northern desert belt of Africa was studied by Gasse (2005). Lake, pollen 

and speleothem records registered weakening of the summer Indian and African monsoons and dry spans 

interrupted the Holocene wet period (Fig. 2). As can be seen from Fig.2, major Holocene droughts are 

repeated every 2000-2500 years. 

On the basis of the results of palynological research on two cores from the Song Hong (Red River) delta 

in the sub-tropical zone of Asia, centennial- to millennial-scale climate changes and human impacts during 

the Holocene were clarified by Li et al. (2006). Three cycles of cooling and warming were identified during 

the last 5000 year: a cool and wet climate during 4530–3340 cal yr BP, 2100–1540 cal yr BP, and 620–130 

cal yr BP, a warm and dry climate during 3340–2100 cal yr BP, 1540–620 cal yr BP and the present warm 

climate. The first and last cooling events correspond to global Holocene cooling events, the Neoglacial 

Period and the Little Ice Age, respectively. Each persisted for 500–1000 yr, and they occurred at intervals of 

1500–2000 years. 

58


Fig.2. Comparison of lake-level fluctuations in the Ziway-Shala Lake in the Sahara–Sahel (Hoelzmann 

et al. 1998) and Ethiopian Abhe Lake (Gasse 2000), reflected Indian and African monsoons, with dry spells 

due to major Holocene droughts (Gasse 2005). 

The storm chronology was inferred by Noren et al. (2002) from terrigenous sedimentations in-wash 

layers, which reflect rainfall events of exceptional intensity/duration in the 13 lake drainage basins in the 

northeastern United States. The frequency of storm-related floods in the northeastern United States has 

varied in regular cycles during the past 13,000 years, with a characteristic millennial periodicity. Maxima of 

terrigenous influx coincide with high storminess and flooding episodes in other records from the North 

Atlantic area, and with cool periods in Greenland and Europe as recorded in glaciers by Hormes et al. 

(2001). 

Presently, there is a growing body of evidence that short-lived periodic events have persisted into the 

Holocene epoch as for instance the 8200 cal BP and 2800 cal BP cold periods (e.g., Dergachev et al 2004; 

Veski et al 2004) together with the perhaps more well-known ‘Little Ice Age’ (Matthews and Briffa 2005). 

Neff et al. (2001) presented a high-resolution study of variation in the Indian Ocean monsoon during the 

time span from 9600 to 6100 BP derived from oxygen isotope variation (the stable isotopes are used to 

provide information concerning climate changes) in a Th/U dated speleothem from Oman. The speleothem 

δ 18 O values serve as a proxy for estimating variation in monsoon intensity by measuring past changes in δ 18 O 

of monsoon rainfall as recorded in speleothem calcite δ 18 O. In the time span from 8500 to 8000 cal year BP 

there are strong peaks at 8400, 8200 and 8000 cal yr BP with the 200-year periodicity (Neff et al. 2001) in 

δ 18 O data similar to the pattern of climate change during the Little Ice Age in the past millennium. As was 

shown by Fleitmann et al. (2003) from δ 18 O monsoon record in a stalagmite of Qunf Cave in Southern Oman 

(17°10’ N, 54°18’ E; 650 m above sea level), between 10,300 and 8000 BP decadal to centennial variations 

in monsoon precipitation are in phase with temperature fluctuations recorded in Greenland ice cores. Taking 

into account both the stalagmite and GRIP records, decadal scale intervals of reduced monsoon precipitation 

(more positive δ 18 O values) correlate with cooling events in Greenland and vice versa, as best expressed at 

9100 and 8200 BP. 

Olsen (2007) discussed the climate variability based on the Blinden Lake (Denmark) record in 

relation to regional and northern hemisphere climate by combining the sedimentological and geochemical 

evidence. An estimate of the paleolake water isotope composition (δ 18 Ow) and changes of the lake water 

level (ΔW) and thereby also an effective humidity were derived. Figure 3 presents the wavelet power 

spectrum of the inferred δ 18 Ow and ΔW values. 

Fig. 3. The absolute values of the wavelet coefficient using a morlet wavelet on the δ 18 Оw (lake water 

isotope composition) and on ΔW (lake water level) from Blinden Lake (Denmark) sediment. 

59


Both wavelet power spectra reveal a similar pattern, verifying that most of the observed variance is likely to 

originate from changes in the isotope composition of the lake water and probably reflects changes in the 

evaporation to inflow balance. The wavelet spectra suggest periodicities of mainly 210 years. 

CLIMATE CHANGES, SOLAR ACTIVITY AND COSMOGENIC ISOTOPES 

Understanding the mechanisms and history of natural climate variability is important for improving climate 

predictability and properly attributing ongoing climate changes to human and natural forcings. The general 

state of the Earth's climate is controlled by the balance of energy on the Earth received from the Sun and the 

amount of energy released back to space. The Sun provides more than 99% of the energy to the Earth’s 

climate. Causes of climate change involve any process that can alter this global energy balance. Energy from 

the Sun drives the Earth’s weather and climate. A number of studies have sought to find correlations between 

the changes in solar activity and the temperature of the Earth’s atmosphere. Good correlations have been 

found for the past millenium on a time scale of decades to centuries (e.g., Solanki et al. 2004). It should be 

particularly emphasized that solar activity during the Little Ice Age is extremely weak, and during the 

Medieval Warm Period is high. 

Cooling and glacier advances during the Little Ice Age are widespread at high northern latitudes. For the 

low altitudes new high resolution lacustrine records (Verschuren et al. 2000) show that equatorial East Africa 

experienced humid condition. In equatorial Africa, lake levels can be used as an indicator of climate 

changes. It is interest to consider past levels in Lake Victoria (Stager et al. 2005) and Lake Naivasha 

(Verschuren et al. 2000). Lake Victoria, located on the equator between the two main branches of the East 

African Rift Valley system is well situated to record large-scale climate events that affected not only tropical 

Africa but also the polar regions. About 90% of the lake's water arrives and exits through the atmosphere, 

making it extremely sensitive to changes in rainfall. The balance of this lake is regulated by evaporation 

processes as a result of solar variability 

Fig. 4 shows the comparison between each of the lakes and the proxy of solar activity – radiocarbon 

concentration (∆ 14 C) measured in tree rings. As can see from this figure the Victoria and Naivasha basins 

were unusually arid during Europe's Medieval Warm Period and unusually wet during cool phases of the 

globally distributed Little Ice Age. 

Fig. 4. Comparison of proxy records for changes in the hydrology with the proxy for solar activity based 

on the ∆ 14 C record. SWD is the shallow water depth. The minima of solar activity are W –Wolf, S –Spoerer, 

M – Maunder, D – Dalton. 

Comparison between atmospheric radiocarbon and hydrological data from tropical Africa demonstrates 

the relationship between a variable solar activity and climate. Maasch et al. (2005) compared eight welldated 

high-resolution records, reflecting the range and rate of change of atmospheric circulation and 

hydrology, obtained at latitudes extending from the Arctic to the Antarctic with the ∆ 14 C record over the 2 

millennia and showed that such relationship is seen on a global scale. 

Exact measurements of the 14 С concentration in year-by-year tree rings allow to trace continuous longterm 

changes in level of solar activity during more than the last 10 thousand years (Stuiver et al. 1998). 

Vasiliev and Dergachev (2002) analyzed the primary properties of the decadal data of ∆ 14 C record during the 

Holocene using power spectrum, time-spectrum and bispectrum analysis. They established that the 

amplitudes of the radiocarbon content vary periodically in time, the changes of amplitudes are synchronous 

in the wide frequency band. A bispectrum analysis of data demonstrates the existence of amplitude 

modulation with period of ~2400 years. In addition, a bispectrum analysis allows to classify three primary 

60


lines of the power spectrum: 710, 420 and 210 years, and was shown that the line component corresponding 

to 210 years has first harmonics. The long period of ~2400 years is the characteristic property of major 

climatic changes in Fig. 5. 

Fig. 5. Comparison of the Polar Circulation Index from GISP2 (Mayewski et al. 1997) with the mid- 

European lake-level fluctuations (Magny 2004), with the ice-rafting debris events in the North Atlantic 

Ocean (Bond et al. 2001), and with the atmospheric residual 14 C contcentration (Stuiver et al. 1998) during 

of the Holocene. 

The mechanism for the connection between solar variability and atmospheric circulation may be due to 

solar ultraviolet radiation or cosmic ray flux modulated by solar activity. Changes in ultraviolet radiation 

from the Sun may lead to a change in ozone production in the lower stratosphere accompanied by the change 

in tropospheric dynamics, whereas cosmic ray flux changes may directly lead to a change in global cloud 

cover, as demonstrated by the correlation between the variation in cosmic ray flux and the observed global 

cloud cover. An increase in the low cloud cover due to cosmic ray flux may lead to wetter and cooler 

conditions at different latitudes (Svensmark et al. 2007). 

CONCLUSION 

Thus, the analysis of the numerous varieties of proxy climatic records is indicative of high variability of the 

Holocene climate. Furthermore, palaeoclimate records reveal the presence of fairly regular quasi-periodic 

patterns of major large-scale global climate changes. A correlation of historical records of solar activity and 

climate change and also cosmogenic isotopes, proxies for solar activity, and millennial scale variability in 

palaeoclimate records demonstrates the connection between solar variability and climate change. As 

mentioned above, cosmogenic isotope records can be used as a measure of changes in solar activity and in 

cosmic ray flux in the past. More significant changes in the Holocene climate are characterized by a quasi- 

2400-year periodicity in cold conditions possibly caused by changes in solar activity. The Sun-climate 

relation is most clearly seen during the Little Ice Age. Additional study is needed to investigate the rate and 

change of atmospheric circulation in the past. The change in the processes of atmospheric circulation may 

alter the distribution of precipitation both high and low latitudes that may lead to the large fluctuations in 

lake levels, monsoon activity and redistribution of moisture and heat on the Earth’s surface. 


This work was supported by the Russian Foundation for Basic Research (projects 06-02-16268, 06-04- 

48792, 06-05-64200, 07-02-00379), Presidium of RAS (program «Environmental and Climatic Changes»), 

and Presidium of the St.-Petersburg Scientific Centre of RAS (Regional Programs). 

References 

Bond, G., Kromer, B., Beer, J., Muscheler, R., Evans, M.N., Showers, W., Hoffmann, S., Lotti-Bond, R., 

Hajdas, I., and G.Bonani (2001), Persistent solar influence on North Atlantic climate during the 

Holocene. Science, 294, 2130–2136. 

61


Climate Change 2007: The Physical Science Basis. Available at http://ipcc-wg1.ucar.edu/wg1/wg1report.html. 

Dergachev, V. A., Raspopov, O.M., van Geel B. and G. I. Zaitseva (2004), The ‘Sterno-Etrussia’ 

geomagnetic excursion around 2700 BP and changes of solar activity, cosmic ray intensity, and climate. 

Radiocarbon, 46, 661-681. 

Fleitmann, D., Burns, S.J., Mudelsee, M., Neff, U., Kramers, J., Mangini, A., and A.Matter (2003), Holocene 

forcing of the Indian monsoon recorded in a stalagmite from Southern Oman. Science, 300, 1737-1739. 

Gasse, F. (2000), Hydrological changes in the African tropics since the last glacial maximum. Quaternary 

Science Reviews, 19, 189–211. 

Gasse, F. (2005), Continental palaeohydrology and palaeoclimate during the Holocene. C. R. Geoscience, 

337, 79–86. 

Hoelzmann, P., Jolly, D., Harrison, S. P., Laarif, F., Bonnefille, R., and Pachur, H.-J. (1998), Mid-Holocene 

land-surface conditions in northern Africa and the Arabian peninsula: a data set for the analysis of 

biogeophysical feedbacks in the climate system. Global Biochemical cycles, 12, 35-51. 

Hormes, A., Müller, B.U., and C.Schlüchter (2001), The Alps with little ice: evidence for eight Holocene 

phases of reduced glacier extent in the central Swiss Alps. Holocene, 11, 255–265. 

Li, Z., Saito, Y., Matsumoto, E., Wang, Y., Tanabe, S., and Q.L.Vu (2006). Climate change and human 

impact on the Song Hong (Red River) Delta, Vietnam, during the Holocene. Quaternary International, 

144, 4-28. 

Maash, K.A., Mayewski, P.A., Rohling, E.J., Stager, J.C., Karlen, W., Meeker, L.D., and E.A.Meyerson 

(2005), A 2000-year context for modern climate change. Geografiska Annaler, 87A, 7-15. 

Magny, M. (2004), Holocene climate variability as reflected by mid-European lake-level fluctuations and its 

probable impact on prehistoric human settlements. Quaternary International, 113, 65–79. 

Matthews, J. A. and K. R. Briffa (2005), The ‘Little Ice Age’: Re-evaluation of an evolving concept. 

Geografiska Annaler Series a-Physical Geography 87A(1): 17-36. 

Mayewski, P.A., Holmgren, K., and 14 others (2004), Holocene climate variability. Quaternary Research, 

62, 243-255. 

Mayewski, P.A., Meeker, L.D., Twickler, M.S., Whitlow, S., Yang, Q., Lyons, W.B., and M.Prentice (1997), 

Major features and forcing of high-latitude northern hemisphere atmospheric circulation using a 

110,000-year long glaciochemical series. Journal of Geophysical Research, 102, 26345–26366. 

Neff, U., Burns, S.J., Mangini, A., Mudelsee, M., Fleitmann, D., and A. Matter (2001), Strong coherence 

between solar variability and the monsoon in Oman between 9 and 6 kyr ago. Nature, 411,290-293. 

Noren, A.J., Bierman, P.R., Steig, E.J., Lini, A., and J.A.Southon (2002), Millennial-scale storminess 

variability in the northeastern United States during the Holocene. Nature, 419, 821–824. 

Olsen J. (2007), Stable isotope mass spectrometry and AMS dating applied to a multi-proxy climate record 

from the Bliden Lake, Denmark. Ph.d. thesis, University of Aarhus, Department of Physics and 

Astronomy AMS 14 C Dating Centre, Ny Munkegade, bld 1520, DK-8000 Aarhus C. 

Solanki, S.K., I. G. Usoskin, I.G., Kromer, B., Schüssler, M., and J. Beer (2004), Climate: How unusual is 

today's solar activity? Nature, 431, 1084–1087.. 

Stager, J.C., Ryves, B.F., Cumming, L.D., Meeker L.D., and J.Beer (2005), Solar variability and the levels of 

Lake Victoria, East Africa, during the last millennium. Journal of Paleolimnology, 33, P. 243-251. 

Stuiver, M., Reimer, P.J., Bard, E., Beck, J.W., Burr, G.S., Hughen, K.A., Kromer, B., McCormac, G., van 

der Plicht, J., and M.Spurk (1998), Intcal98 radiocarbon age calibration, 24 000– 0 cal BP. Radiocarbon, 

40, 1041–1083. 

Svensmark, H., Pedersen, J.O.P., Marsh, N.D., Enghoff, M.B., and U.I.Uggerhøj (2007), Experimental 

evidence for the role of ions in particle nucleation under atmospheric conditions. Proceedings of the 

Royal Society, A 463 (2078), 385 – 396. 

van Geel, B., Raspopov, O.M., Renssen, H., van der Pflicht, J., Dergachev, V.A., and H.A.J.Meijer (1999), 

The role of solar forcing upon climate change. Quaternary Science Reviews, 18(3), 331–338. 

Vasiliev, S.S., and V.A.Dergachev (2002), The~2400-year cycle in atmospheric radiocarbon content: 

Bispectrum of 14 C data over the last 8000 years. Annales Geophysicae, 20, 115–120. 

Verschuren, D., Laird, K.R., and B.F.Cumming (2000), Rainfall and drought in equatorial East Africa during 

the past 1100 years. Nature, 403, L410–413. 

Veski, S., Seppa, H. and A. E. K. Ojala (2004), Cold event at 8200 yr BP recorded in annually laminated 

lake sediments in eastern Europe. Geology, 32(8), 681-684. 

62


STRUCTURE OF THE ELECTRON DIFFUSION REGION OF THE 

RECONNECTION PROCESS 

A.V. Divin, V.S. Semenov, D.B. Korovinskiy 

Institute of Physics, University of Saint-Petersburg, 198504, Russia, e-mail: andrey.div@gmail.com 

Abstract. In our work we employ particle-in-cell simulation of plasma for the study of magnetic 

reconection process. We explore details of the diffusive process inside dissipation region which 

breaks magnetic fields line. In the case of undriven two-dimensional collisionless simulation such 

diffusion is provided by divergency of electron pressure tensor. Far from X-point electrons follow 

magnetic field lines (gyrotropy); in the vicinity of X-point gyrotropy is lost and electrons behave 

non-adiabaticly. To guarantee quasistatic dynamics of the reconnection process, open boundary 

conditions are implemented in the code. 

The study of distribution functions shows their non-Maxwellian behaviour. We separate particles 

in velocity space by means of tracing them back over characteristic time scale. Those particles that 

stay in the vicinity of X-point are considered to be accelerating and trapped, whereas magnetized 

particles flow in from the outside of diffusion region. A qualitative model of electron pressure 

anisotropy based on bi-maxwellian nature of distribution function near X-point is proposed. 


There have been a long debate whether processes inside the electron diffusion region (EDR) control overall 

reconnection rate Me or they don‘t. In analytical models (e.g. [1], [2]) and numerical simulations ([3],[4], [5]) 

which include electron dynamics, properties of the EDR are found to adjust to that of the ion diffusion region 

and so ions believed to control reconnection rate. 

Hall term in the Ohm’s law does not provide for direct dissipative effects near X-point though it introduces 

the whistler waves, which remove reconnected flux the faster the smaller EDR size is. This dispersive property 

effectively supports finite reconnection rate for the EDR of arbitrarily small size and makes Me independent of 

the details of electron dynamics within field reversal [3], [1], etc.. We generally support this point of view, but 

results of kinetic simulations with Hall term excluded cast it into question [6] , fast reconnection in electronpositron 

plasma being the most prominent example [7]. We put aside the question of actual Me value and 

scalings and investigate in detail electron behaviour near X-point. 

In [6] size of EDR is estimated as the characteristic length of electron current sheet in the vicinity of 

X-point (indeed, being of the order of 10di >> de). In [8], [9] only the area within Ez ∼ = − 1 

ne ∇ · Pe is 

attributed to EDR. At the downstream ∇ · Pe changes sign and is compensated for by fast streaming electrons, 

forming long super-Alfvenic structure for which − 1 

c [ve × B]z > Ez is satisfied. Length of the electron jet 

varies significantly with time, being independent of reconnection rate and not damping fast reconnection [8]. 

Thus, electron demagnetization region develops two-scale structure with conventional short EDR and elongated 

electron current in the outflow region. This jet is claimed to be observed recently in one magnetopause crossing 

[14]. 

In next section we present results of kinetic simulation with focus on electron scale physics within inner 

EDR. Origin of electron pressure anisotropy is discussed. Two distinct plasma populations are separated, 

occupying different positions in the phase space and efficiently rendering ∇ · Pe contribution in the Ohm’s law. 

It is suggested this analysis could later be applied to the study of anisotropy in the outflow electron jet. 

2 Model description 

Simulations of two-dimensional magnetic reconnection are performed with the explicit particle-in-cell code 

P3D [10]. The code is utilized for the study of magnetic reconnection in a number of previous works (e.g. 

[10], [3], [8] ). P3D is electromagnetic full particle explicit code; Boris algorithm is used for the numerical 

solution of equation of motion. Electromagnetic field solver utilizes leapfrog scheme to advance fields in 

time. For the initial condition we take conventional Harris neutral current sheet Bx = B0tanh(y/λ), n(y) = 

n0cosh −2 (y/λ) + nb, with a background plasma nb = 0.2n0. Magnetic field is normalized to its maximum 

value in the lobes B0 and density is normalized to it current sheet maximum n0. A small initial GEM-type 

perturbation is added to ignite reconnection 

63


Ψ(x, y) = Ψ0cos 2πx 

cos 

Lx 

πy 

, (1) 

Ly 

where Lx and Ly are the size of computational box in ion inertial lengths di. In this work we report on the 

results of two runs: one with Lx = Ly = 19.2di (Run 1) and second with the size of computational box doubled 

Lx = Ly = 38.4di (Run 2). For the smaller run (Run 1) we extracted particle data (positions, velocities) to 

investigate particle motion in detail. Intensity of perturbation is Ψ0 = 0.3. We explore the EDR current layer 

in the phase when reconnection rate and main plasma parameters throughout the computational box enter the 

quasistationary state (t = 15Ω −1 

i for Run 1 and t = 20Ω −1 

i for Run 2). Here Ωi = eB0 

mic is ion gyrofrequency. 

The mass ratio is mi/me = 64, the temperature ratio Ti/Te = 3/2 for both runs. 

Open boundary conditions for fields 

and particles 

∂Bx,y 

∂x 

∂ne,i 

= 0, ∂Ey 

∂x = 0, Ex,z = 0, δBz = 0. (2) 

∂Ve,i 

= 0, 

∂x 

= 0, 

∂x 

T = T(t = 0), (3) 

are implemented at the exhaust boundaries to allow free outflow of plasma [11], [12] 

3 Results 

Figure 1: Current density jz in Run 1 (top), out-of-plane magnetic field Bz in Run 1 (bottom) 

Here we briefly present general results on the kinetic simulation of reconnection. 

Reconnection starts as initially imposed X-line perturbation drives system out of equilibrium. Details of 

non-stationary phase could be found in e.g. [12],[13]. As Me reaches the value of 0.1 ÷ 0.2, process turns to 

quasistationary phase ([8] and references herein). In the simulations by [6] slow decay of Me was claimed, but 

this result was considered to be controversial in recent works and attributed to the particular set of boundary 

conditions. 

64


Figure 2: Large-scale structure of the diffusion region. Left top: out-of-plane current density; left bottom: 

out-of-plane magnetic field. Right top: electron (thin) and ion (thick) velocity, dark: vx, gray: vz; thick dotted 

line: convection flow velocity vE = c E×B 

B 2 . Right bottom: components of the Ohm‘s law at x = x X(·), dark 

solid: − 1 

c [vi × B]z, dark dotted: − 1 

c [ve × B]z, gray solid: − 1 

ne ∇Pe, gray thin: Ez 

Reconnection electric field, first generated near the X-line, then spreads throughout all domain and ignites 

global convection. Magnetic field is frozen into plasma in inflow region and is pulled to the reconnection site 

near y=0. Configuration of smaller Run 1 represents quasistationary X-point (Fig.1 , upper, out-of-plane current 

is shown on background). 

Existence of two distinct species in the simulation (namely, ions and electrons) suggests that their motion 

is, strictly speaking, different at the regions of sharp magnetic field and flow gradients, reconnection being the 

case. That fact manifests itself as appearance of the Hall term in the Ohm’s law and formation of the typical 

quadrupolar pattern of out-of-plane magnetic field Bz. Value of Bz reaches its maximum of 0.2 ÷ 0.3 within 

several di from the X-line. Spatial extent of the quadrupolar pattern marks ion diffusion region as the area, 

where electrons and ions follow different trajectories. 

Spatial extent of the X-point is considerably larger than di estimations derived earlier. This significant result 

is further elaborated in recent works by [6],[8],[14] and others. Thus we increased domain size in the next Run 

2 to minimize the influence of boundaries on the reconnection dynamics, keeping results of Run 1 to deepen 

further into the vicinity of X-point by extracting particles distribution function there. Larger Run 2 better 

describes dynamics on ion scales and shows the opening of the exhaust in outflow with formation of shock-like 

structures between inflow and outflow regions. Electrons get accelerated first in EDR up to the electron Alfven 

velocity cAe = 

B0 √ , whereas ions remain under-Alfvenic well beyond the computational region. At Fig. 

4πneme 

2 (top right) magnetic field lines convection velocity vE = c E×B 

B 2 is marked by thick dotted line. Left part of 

the simulation box is displayed. vE velocity represents E × B drift and thus, for magnetized particles, should 

control their mean velocity. Fig. 2 suggests that magnetization happens somewhere far away from the X-line 

and require much larger box to observe it in simulation. In [6], [7], [8] , [9] computational boxes of the order 

of 100di were implemented to show that demagnetization region stretches up to the boundary and supports 

65


favourable conditions for slow plasmoid generation. Such mechanism of ’non-stationary’ reconnection could 

both slow or accelerate reconnection process and is studied by other authors. 

On the de scale from the y=0 plane a thin outflowing electron jet is streaming through magnetic field lines 

(Fig. 2, right top). We utilize kinetic Ohm’s law here to describe its properties. 

E + 1 

c ve × B = − 1 

ne ∇Pe − me 

� � 

∂ve 

+ (ve∇)ve 

e ∂t 

Following Fig. 2 (right top), electrons are accelerated by reconnection electric field directly near the X-line, 

where magnetic field is small. This jet is then slowly rotated in the direction of outflow. 

On Fig. 3 components of the Ohm’s law are plotted (left part of the simulation box). To a certain extent 

the electric field (thin gray line) displays quasistationarity and could be considered a constant (0.2 ÷ 0.3). 

Convective electric field − 1 

c [ve × B]z is thick dotted line. As expected, it falls to zero near X-point and 

reconnection electric field is supported by dissipative pressure anisotropy − 1 

(4) 

ne ∇ · Pe (largest contribution 

comes from − 1 ∂Peyz 

ne ∂y component, which is plotted in thick gray line). Electron diffusion region is located at 

around x = −3, where −1 c [ve × B]z < Ez condition is met. Rather than falling to zero, pressure anisotropy 

changes sign and thus supports fast super-Alfvenic electrons in the ouflow region. Following [8], [9] we call 

this area ’external electron diffusion refion’ (external EDR). Spatial scales of this structure are much larger than 

previously derived estimations of de ÷ di for EDR. Those jets being a feature of two-dimensional collisionless 

reconnection doesn‘t preclude fast reconnection rates Me [9]. Other terms (namely, −me � � 

∂ve 

e ∂t + (ve∇)ve as 

thin black, − 1 ∂Pexz 

ne ∂x as thick black) are presented in Fig.3 (bottom) and could be neglected. 

Size of the internal EDR in y direction scales as de and equals 1 

8 di for our mass ratio. This is verified 

on Fig. 2 by plotting components of the Ohm’s law for y varying from −4di to 4di. Convective electric 

field − 1 

c [ve × B]z (black dotted line) rapidly falls to zero at around y = 0.25di, whereas pressure anisotropy 

− 1 ∂Peyz 

ne ∂y (gray solid line) jumps to compensate for reconnection electric field (thin gray line). Thus it defines 

the region of interest from 0 to 0.5di in y direction right above the X-line where we further analyze electron 

distribution function and study the origin of pressure anisotropy. 

Figure 3: primary components of the Ohm‘s law at y = 0, gray thin: Ez, gray thick: − 1 

−1 c [ve × B]z (top); secondary components of the Ohm‘s law, thin black: −me e 

− 1 ∂Pexz 

ne ∂x (bottom) 

66 

� ∂ve 

∂t 

∂Peyz 

ne ∂y � 

+ (ve∇)ve 

; dark dotted: 

z 

, thick gray:


Sufficiently different motion of inflow plasma (gyration around flux tube) and demagnetized accelerated 

electrons (which are trapped around z=0 plane) suggests bi-maxwellian origin of the pressure anisotropy near 

X-line. Accelerating particles perform bounce motion near X-point on the characteristic time scale tb, which 

we assume to be ambient gyroperiod Ω −1 

ce in view of many other uncertainties. We trace electrons back in time 

over tb and separate between accelerating and magnetized particles based on their distance to X-point. Particles 

crossing z=0 plane are considered to be trapped, whereas those moving away from the X-line are magnetized 

and constitute magnetized inflow distribution. This method is applied to quasistationary phase of reconnection, 

allowing test particle approach. 

Distribution is sampled over the box of ∆x = 0.5, ∆y = 0.1 size, x = 2.2 (Run 1) and for y varying from 

y = 0 to y = 0.5di, which covers the extent of electron diffusion region in Y direction. The latter technique 

is applied for the box to identify particles of different origin. The result is displayed at Fig. 4. Accelerating 

particles are marked as gray point, whereas black represent inflow of magnetized particles. Fig. 4 (right picture, 

sample taken at y = 0.35 above X-line) implies that vast majority of particles, except the most energetic ones, 

appears to be magnetized and represents inflow distribution. Moving closer to the X-point more and more 

particles are trapped and demagnetized and perform meandering motion near y=0 plane. 

For Maxwellian distribution, presence of nonzero Peyz component represents a tilt of distribution function 

isosurfaces around x axis. In the EDR non-diagonal component of the pressure tensor is rendered as inflow 

particles and accelerated particles are well separated in the velocity space. To confirm this bi-maxwellian nature 

of pressure anisotropy, we plotted mean vy,vz, Peyz for inflow particles, accelerating particles and combined 

distribution as a function of y for x = x (X·) 

Large out-of-plane vz velocity of accelerated particles is clearly visible at Fig. 5 (left). Meanwhile, vy is 

almost zero (Fig 5., middle picture), what emphasizes their trapping around y = 0 plane. At the upper edge of 

the EDR, vy velocity of the inflow population should be close to the convection velocity of electrons inside ion 

diffusion region c E×B 

B 2 . At Fig. 5 (middle picture) inflow vy is plotted in thick black line, convection velocity 

is plotted in thin black line, and good correspondence between these two indicates magnetization of inflow 

component of plasma up to the electron diffusion region scales. Thus, at almost every y these populations 

occupy different parts of velocity space. Mean velocity vy of combined distribution converges to zero at y ≈ 0 

as is found in the stagnation point. 

We further check the anisotropy of electron distribution functions at Fig. 5 (right) by estimation of nondiagonal 

pressure term Peyz for these two sorts of particles. Inflow electrons are well thermalized (thick black 

line), whereas accelerated population is not thermalized (see Fig.5), what could be attributed to the influence 

of particles inflow from the y < 0 halfspace. Combined distribution (Fig. 5, right, dotted line) displays the 

required amount of Peyz to support reconnection electric field inside the EDR. 

v ey 

15 

10 

5 

0 

−5 

−10 

−15 

15 

15 

15 

Y=0.05 Y=0.15 Y=0.25 Y=0.35 

−10 0 

v 

ez 

10 

10 

5 

0 

−5 

−10 

−15 

−10 0 

v 

ez 

10 

10 

5 

0 

−5 

−10 

−15 

−10 0 

v 

ez 

10 

10 

5 

0 

−5 

−10 

−15 

−10 0 

v 

ez 

10 

Figure 4: Accelerated (gray points) and magnetized (black points) parts of electron distribution function in the 

vicinity of the X-point. More accelerated particles inside diffusion region (left picture), more magnetized above 

(right picture) 

4 Conclusion 

Kinetic simulation of reconnection is discussed. Reconnection dynamics displays all major features typical 

for collisionless process: separation between ion and electron scales, generation of Hall quadrupolar magnetic 

field in the ion diffusion region, existence of the diffusion process (in the form of anisotropic pressure) and 

67


v z 

10 

8 

6 

4 

2 

0 

−2 

0 0.1 0.2 0.3 0.4 0.5 

y/d 

i 

v y 

0.5 

0 

−0.5 

−1 

−1.5 

−2 

0 0.1 0.2 0.3 0.4 0.5 

y/d 

i 

P eyz 

2 

1 

0 

−1 

−2 

x 10−3 

3 

−3 

0 0.1 0.2 0.3 0.4 0.5 

y/d 

i 

Figure 5: Mean velocities and anisotropy for Fig.4. from y = 0 to y = 0.5di Magnetized particles: black thick 

line; accelerating particles: gray thick line; combined distribution: dotted line. vz velocity (left picture ), vy 

velocity, electron convection velocity c E×B 

B 2 (central picture), non-diagonal pressure term Peyz (right picture) 

acceleration of particles near neutral line. Formation of a long super-Alfvenic electron jet in the exhaust region 

is confirmed. The properties of this jet are unusual since it spans through the most of the computational domain 

(up to 50di ÷ 100di [6], [8], [9]), whereas electrons are expected to be well magnetized at much smaller 

scales. This question is definitely a matter of further research. In [9] this jet is supposed to be secondary 

for the reconnection problem and not precluding fast reconnection rates. We studied the origin of the pressure 

anisotropy in the inner EDR. Separation of electrons into trapped (accelerating) and inflow particles by means of 

tracing them back in time reveals the source of collisionless dissipation to be a significantly different properties 

of these two populations. At the most basic level such dissipation could be explained as the presence of a 

bi-maxwellian distribution, varying in y direction. In other words, electron pressure anisotropy naturally arises 

here as magnetized orbits (z > de) are gradually replaced by unmagnetized meandering trajectories, which 

occupy different region of the phase space. 

References 

[1] Biskamp, D., E. Schwarz, J. F. Drake (1995), Ion-Controlled Collisionless Magnetic Reconnection, Phys. 

Rev. Lett, 75, 3850 

[2] Korovinskiy, D. B., V. S. Semenov, N. V. Erkaev, A. V. Divin, and H. K. Biernat (2008), The 

2.5-D analytical model of steady-state Hall magnetic reconnection, J. Geophys. Res., 113, A04205, 

doi:10.1029/2007JA012852. 

[3] Shay, M. A., J. F. Drake, B. N. Rogers, and R. E. Denton (2001), Alfvenic collisionless magnetic reconnection 

and the Hall term, J. Geophys. Res., 106(A3), 3759-3772. 

[4] Birn, J., et al. (2001), Geospace Environmental Modeling (GEM) Magnetic Reconnection Challenge, J. 

Geophys. Res., 106(A3), 3715-3719 

[5] Hesse, M., K. Schindler, J. Birn, M. Kuznetsova (1999), Phys. Plasmas 6, 1781 (1999); 

DOI:10.1063/1.873436 

[6] Daughton, W. et al (2006), Fully kinetic simulations of undriven magnetic reconnection with open boundary 

conditions, Phys. Plasmas 13, 072101 

[7] Daughton, W., H. Karimabadi (2007), Collisionless magnetic reconnection in large-scale electronpositron 

plasmas, Phys. Plasmas 14, 072303; DOI:10.1063/1.2749494 

[8] Shay, M., J.F. Drake, M. Swisdak (2007), Two-Scale Structure of the Electron Dissipation Region during 

Collisionless Magnetic Reconnection, Phys. Rev. Lett., 99, 155002 

[9] J. F. Drake, M. A. Shay, M. Swisdak (2008), The Hall fields and fast magnetic reconnection, Phys. Plasmas, 

15,042306; DOI:10.1063/1.2901194 

68


[10] Zeiler, A., D. Biskamp, J. F. Drake et al. (2002), J. Geophys. Res., 107 (A9), 

1230,doi:10.1029/2001JA000287 

[11] Divin, A. V., M. I. Sitnov, M. Swisdak, and J. F. Drake, Reconnection onset in the magnetotail: 

Particle simulations with open boundary conditions, Geophys. Res. Lett., 34, L09109 (2007), 

doi:10.1029/2007GL029292 

[12] 12. Pritchett, P.L. (2001), Geospace Environment Modeling magnetic reconnection challenge: Simulations 

with a full particle electromagnetic code, J. Geophys. Res., 106, 3783 

[13] 13. Wan, W., G. Lapenta (2008), Electron Self-Reinforcing Process of Magnetic Reconnection, Phys. Rev. 

Lett., 101, 015001 

[14] 14. T. D. Phan, J. F. Drake, M. A. Shay, F. S. Mozer, and J. P. Eastwood (2007), Evidence for an Elongated 

(> 60 Ion Skin Depths) Electron Diffusion Region during Fast Magnetic Reconnection, Phys. Rev. Lett. , 

99, 255002 

[15] 19. Hesse, M.,J. Birn, M. Kuznetsova (2001),Collisionless magnetic reconnection: Electron processes and 

transport modeling, J. Geophys. Res., 106, 3721–3735 

[16] 20. Biskamp, D. (2000), Magnetic reconnection in plasmas, Cambridge University Press, ISBN 0521 

58288 1 

69


THE INFLUENCE OF NEUTRAL GAS HEATING AND COOLING ON THE 

DAY-TIME EQUATORIAL NEUTRAL DENSITY MINIMUM FORMATION 

E.N. Doronina, A.A. Namgaladze 

Murmansk State Technical University, Murmansk, Russia, e-mail: DoroninaEN@mstu.edu.ru 

Abstract. We have investigated the problem of the total mass density minimum near the equator 

found out by the CHAMP satellite at the height of 400 km. The Upper Atmosphere Model (UAM) 

was used in this study. In the UAM the temperature of neutral gas is calculated by the solution of 

the heat balance equation. We have studied the influence of various mechanisms of heating and 

cooling of neutral gas on the formation of the day-time equatorial minimum of temperature and 

density. For that we sequentially switched off the sources of heating and cooling: the Joule 

heating, solar UV and EUV radiations, heat of chemical reactions, magnetospheric sources of 

momentum and energy, and cooling by IR radiations. It has been found that these minima are the 

features of the tidal structure generated by the solar ionizing radiation and the rotation of the Earth. 

Introduction 

In this work we continue the research of the problem of the neutral temperature and total mass 

density minimum near the equator at heights of ∼400 km [Namgaladze et al., 2006]. The neutral gas density 

minimum near the equator (Figure1, the top panel) has been found in 2002 by the CHAMP satellite 

measurements [Liu et al., 2005; Forbes, Lu, 2005]. The NRLMISE-00 does not reproduce this minimum 

(see Figure 1). 

We have investigated this phenomenon using the Upper Atmosphere Model (UAM) [Namgaladze et 

al., 1998] and the empirical thermospheric model NRLMSISE-00 [Picone et al., 2002]. The UAM describes 

the thermosphere-ionosphere-plasmasphere system by means of numerical integration of the time-dependent 

3D continuity, momentum and heat balance equations for neutral, ion and electron gases and the equation for 

the electric potential. 

Figure 1 shows that the UAM reproduces the daytime minimum (Figure1, the bottom panel) which is 

not present in the NRLMSISE-00 calculations (Figure1, the middle panel). 

Fig.1 The global distribution of the total mass density at the height of 400 km: 

• the top panel – the CHAMP satellite measurements; 

• the middle panel – NRLMSISE-00; 

• the bottom panel – UAM. 

70


Using the UAM we have investigated the influence of various mechanisms of heating and cooling on 

the equatorial minima of neutral temperature and density by excluding terms responsible for heating and 

cooling from the heat balance equation consistently. 

In the UAM neutral gas temperature is calculated by solving of the heat balance equation: 

dT r r r r 

n 

m nn 

ncν 

n + nnkTn 

∇Vn 

= ∇( 

λn∇Tn 

) + PQn 

− PLn 

+ PTn 

, 

dt 

UV EUV J cor chem 

where P = P + P + P + P + P , = P ( CO2 

) + P ( NO) 

+ P ( O) 

, PQn – the heating 

Qn 

Qn 

Qn 

rate of neutral gas, PLn – the cooling rate of neutral gas, UV 

Qn 

Qn 

rate, P – the Joule heating rate, 

J 

Qn 

Qn 

Qn 

PLn Ln 

Ln 

Ln 

chem 

P nQ – the heat of chemical reactions, 

P – the UV heating rate, P – the EUV heating 

EUV 

Qn 

cor 

P Qn – the heat of magnetospheric 

electron precipitations, PLn CO ) – cooling by IR radiation CO2, PLn (NO) 

– cooling by IR radiation NO, 

( 2 

PLn (O) 

– cooling by IR radiation O. 

Results 

We studied the influence of low and high-latitude electric fields and magnetospheric electron 

precipitations on the formation of the day-time neutral temperature and density minima near the equator. The 

numerical experiments have been produced using the UAM for equinox conditions of March, 21, 2002 in 

three various variants: 

1 – with the constant potential drop across the polar cap equal 30 kV; 

2 – without the low-latitude electric field (equatorwards from 30 degrees of the magnetic latitude); 

3 – without the total electric field and magnetospheric electron precipitations. 

Other sources of heating and cooling are included. 

Fig. 2 Time variations of neutral gas density and temperature, h=410 km, at the geomagnetic meridian 

corresponding 1530 MLT: 

1 – with the constant potential drop across the polar cap equal to 30 kV; 

2 – without the low-latitude electric field; 

3 – without the total electric field and magnetospheric electron precipitations. 

Figure 2 shows the time variations of total mass density and neutral temperature at the height of 410 

km at the geomagnetic meridian corresponding 1530 MLT. These variations are in “magnetic latitude – time 

(days)” co-ordinates. We have concluded that the minima of neutral gas temperature and density do not 

71


depend on the equatorial anomaly, because they do not disappear after switching off the low- latitude electric 

field (variant 2). After switching off the high-latitude electric fields and magnetospheric electron 

precipitations (variant 3) the absolute values of temperature and density decrease, but character of their 

distribution does not change. Therefore, the equatorial minima of total mass density and neutral temperature 

are not related to the electric field and magnetospheric sources of momentum and energy. 

The thermal conditions of the thermosphere depend on many factors, besides of high-latitude sources 

of momentum and energy. Using the UAM we have performed following numerical experiments to study 

how heating and cooling sources influence on the formation of the equatorial minima of temperature and 

density. For this purpose we have excluded the terms responsible for heating and cooling sequentially from 

the heat balance equation. 

Fig. 3 The global maps of latitude-longitudinal distribution of the 

neutral temperature (left column) and total mass density (right column) 

at the height of 400 km for 1200 UT 

72


The calculation results are presented in Figure 3 as the global maps of latitude-longitudinal 

distribution of the neutral temperature (left column) and total mass density (right column) at the height of 

400 km for 1200 UT in following variants: 

4 – with UV heating only and total cooling of neutral gas; 

5 – with UV and EUV heating and total cooling; 

6 – with UV and EUV heating, heat of chemical reactions and total cooling; 

7 – with UV and EUV heating, heat of chemical reactions, Joule heating and total cooling; 

8 – with total heating of neutral gas and cooling by IR radiation CO2 only; 

9 – with total heating of neutral gas and cooling by IR radiation O only; 

10 – with total heating of neutral gas and cooling by IR radiation NO only. 

Figure 3 shows that in the variant 4 daily variations of neutral temperature and density are not 

present. 

Accounting the main energy source for upper thermosphere - the solar EUV radiation (variant 5) 

changes the character of distribution of temperature and density. The neutral temperature increases of about 

twice, and density – in two orders of magnitude. Daily variations of the temperature and density appear and, 

that the most important, the minima of the temperature and density are formed at the day-side near the 

equator with maxima at both sides from it. 

Other sources of neutral gas heating and cooling (variants 6-10) influence only on absolute values of 

temperature and density. 

Conclusions 

Equatorial minima of neutral temperature and density are not related to the electric field and 

magnetospheric sources of momentum and energy. 

We have found that these minimums are features of the tidal structure generated by the solar ionizing 

EUV radiation and the rotation of the Earth. 

Other sources of neutral gas heating and cooling influence only on absolute values of temperature 

and density. 

References 

Doronina, E.N., A. A. Namgaladze and M. Förster, A model interpretation of the CHAMP neutral mass 

density measurements, in: Proc. 6th Intern. Conf. "Problems of Geocosmos" (St. Petersburg, Petrodvorets, 

Russia, May 23-27, 2006). 

Liu H., Lühr H., Henize V., Köhler W. Global distribution of the thermospheric total mass density derived 

from CHAMP, J. Geophys. Res., V. 110, A04301, doi: 10.1029/2004JA010741, 2005. 

Forbes J.M., Lu G., Bruinsma S., Zhang X., Thermosphere density variations due to the 15-24 April 2002 

solar events from CHAMP/STAR accelerometer measurements, J. Geophys. Res., V. 110, A12S27, doi: 

10.1029/2004JA010856, 2005. 

Namgaladze A.A., Martynenko O.V., Namgaladze A.N. Global model of the upper atmosphere with variable 

latitudinal integration step, Geomagnetism and Aeronomy International, V.1, No.1, p.53-58, 1998. 

Picone J.M., Hedin A.E., Drob D.P., Aikin A.C. NRLMSISE-00 empirical model of the atmosphere: 

Statistical comparisons and scientific issues, J. Geophys. Res. 107 (A12), doi: 10.1029/2002JA009430, 2002. 

73


LOW FREQUENCY CURRENT SHEET OSCILLATIONS RELATED TO 

MAGNETIC FIELD GRADIENTS 

N. V. Erkaev 1,2 , V. S. Semenov 3 , H. K. Biernat 4,5 

1 Institute of Computational Modelling, Russian Academy of Sciences, Krasnoyarsk, Russia 

2 Siberian Federal University, Krasnoyarsk, 660036, Russia, e-mail: erkaev@icm.krasn.ru 

3 St.Petersburg State University, Russia 

4 Space Research Institute, Austrian Academy of Sciences, Graz, Austria 

5 Institute for Theoretical Physics, University of Graz, Austria 

Abstract 

One fluid ideal MHD model is applied for description of current sheet flapping disturbances 

appearing due to a gradient of the normal magnetic field component. The wave modes 

are studied which are associated to the flapping waves observed in the Earth’s magnetotail 

current sheet. In a linear approximation, solutions are obtained for the Harris-like behavior 

of the background electric current density and different profiles of the plasma density across 

the current sheet. The current sheet can be stable or unstable in dependence on the direction 

of the gradient of the normal magnetic field component. 


Flapping oscillations of the magnetotail current sheet have been detected by many spacecraft 

measurements. Namely, CLUSTER observations in the Earth’s magnetotail current sheet indicated 

the appearance of the wave perturbations propagating along the current sheet perpendicular 

to the magnetic field lines. The observed cases of such waves were first described by Zhang 

et al. (2002). A comprehensive statistical analysis of Sergeev et al. (2003, 2004), Runov et al. 

(2005a, 2005b, 2006), and Petrukovich et al. (2006) has proved the existence of such kind of 

waves, which were identified as the “kink”-like disturbances. The plasma sheet flapping waves 

are interpreted as quasi-periodic dynamical structures produced by almost vertical slippage motions 

of the neighboring magnetic tubes (Petrukovich et al., 2006). Data analysis yields a typical 

frequency of the flapping waves wf ∼ 0.035 s −1 (Sergeev et al., 2003). A group speed of the 

flapping waves, estimated from data analysis, is in a range of a few tens (30–70) kilometers per 

second (Runov et al., 2005a). Spatial amplitudes and wavelengths are of the order of 2 - 5 RE 

(RE is the Earth’s radius) (Petrukovich et al., 2006). In spite of good observational background 

for the flapping oscillations, a physical mechanism of this phenomenon has not been understood 

well. Several theoretical models were introduced, but each of them has difficulty in application 

to this effect. In particular, the Ballooning-type mode was proposed by Golovchanskaya and 

Maltsev (2005). This ballooning theory implies the condition, that the wave length scale is much 

less than the curvature radius of the magnetic field line. This condition is more suitable for the 

near Earth region, but it is not fulfilled in the magnetotail plasma sheet with a small normal 

component of the magnetic field. 

The second physical mechanism addresses to the drift kink modes investigated by Daughton 

(1999), Karimabadi et al.(2003) and Sitnov et al.(2004). A particular feature of these wave 

modes is that they can propagate only in the direction determined by the proton drift velocity. 

Another theoretical model was proposed by Erkaev et al. (2007) in a framework of MHD 

approach. In accordance to this model, MHD flapping modes can exist due to a gradient of the 

normal magnetic field component along the current sheet. 

In our present paper, we develop the approach of Erkaev et al. (2007, 2008). In particular, 

we analyze flapping wave dispersions for four different background density profiles. 

74


J 

Figure 1: Geometrical situation of the problem (left). Stable (a) and unstable (b) magnetic 

tubes (right). 

2 Basic equations 

We apply conventional equations of incompressible ideal magnetohydrodynamics (MHD) for 

nonstationary plasma sheet parameters 

� � 

∂V 

ρ + V · ∇V + ∇P = 

∂t 1 

B · ∇B, 

4π 

(1) 

∂B 

+ V · ∇B = B · ∇V, 

∂t 

(2) 

∂ρ 

+ V · ∇ρ = 0, 

∂t 

∇ · V = 0, ∇ · B = 0. (3) 

Here V, B, ρ, P are the velocity, magnetic field, plasma density and total pressure (sum of 

the magnetic and plasma pressures), respectively. We consider specific wave perturbations 

propagating across the magnetic field lines, which are much slower than the magnetosonic modes. 

In this case the incompressible approximation is quite reasonable. Our study is focussed on the 

wave modes existing due to a gradient of the Bz component in the magnetotail current sheet 

along the x direction. Here the Bx component has a gradient along the z direction, and thus 

we consider the two magnetic gradients as key factors for the current sheet oscillations. This 

approach, applied by Erkaev et al. (2008) for the flapping wave oscillations, was called as 

“Magnetic double gradient mechanism”. 

The background configuration shown in Figure 1 is considered to be rather simple with a 

weak dependence of the Bz component on the x coordinate 

B = [Bx(z/∆), 0, Bz(x/Lx)], V = 0. (4) 

Here ∆ is a half-thickness of the current sheet, and Lx is a length scale of the Bz variation along 

the current sheet. We introduce two dimensionless parameters ɛ = Bz(0)/Bxmax and ν = ∆/Lx, 

which are assumed to be small. 

We consider small perturbations of the magnetic field, total pressure and velocity, 

B = (Bx + bx, by, Bz + bz), ρ = ρ0 + ˜ρ, P = P0 + p, V = (vx, vy, vz). (5) 

As a first step, we make a simplifying assumption, that all wave perturbations propagating in 

the y direction do not depend on the x coordinate, and thus they are considered to be functions 

of time and two Cartesian coordinates (y, z). 

Linearizing equations (1–3) for the small perturbations, we also neglect small terms Bz∇zbz 

and Bz∇zby (∇z is a partial derivative with respect to the axis z), and retain the main term 

bx∇xBz. This is justified by the condition BzLx/(Bx∆) ≪ 1. 

75


3 Linear analysis of eigenmodes 

Inserting Fourier harmonics (∝ exp(iωt − iky)) in the linearized equations, we obtain finally a 

system of equations for Fourier amplitudes 

iωρ0vx = 1 

� 

� 

dBx dbx 

bz + Bz , 

4π dz dz 

(6) 

iωρ0vy − ikp = 0, iωρ0vz + dp 1 

= 

dz 4π bx 

dBz 

, 

dx 

(7) 

dvz dBz 

iωbz − Bz + vx 

dz dx = 0, iωby 

dvy 

− Bz = 0, 

dz 

(8) 

ωbx + dBx 

dz vz = 0, (9) 

dρ0 

iω ˜ρ + vz 

dz , −ikvy + dvz 

= 0. 

dz 

(10) 

Hereafter we assume that gradient dbz/dx is constant, and all other quantities do not depend 

on the x coordinate. From linearized equations (7–10), treated as a system of ordinary equations 

with respect to z, we derive a second order ordinary differential equation for the velocity 

perturbation 

where 

1 

ρ0 

� � 

d dvz 

ρ0 + 

dz dz 

¯ k 2 � � 

U(¯z) 

˜vz − 1 = 0, (11) 

¯ω 2 

U(z) = 1 ∂Bx 

4πρ0 ∂z 

∂Bz 

. (12) 

∂x 

We consider background plasma density and magnetic field profiles given by model formulas 

ρ0 = ρ ∗ /(cosh(αz/∆)) 2 , (13) 

Bx = B ∗ tanh(z/∆). (14) 

For 0 < α < 1, the current velocity determined as a ratio of the current and plasma densities 

has a maximum at the center of the current sheet. This maximum becomes less for larger α. 

The limit α = 1 corresponds to the case of a uniform current velocity. For uniform background 

plasma density (α = 0), Equation (11) is similar to that known from the theory of tearing 

mode instabilities (Pritchett et al., 1991). In this case spectral problem for equation (11) has 

analytical solutions corresponding to“kink”-like and “sausage”-like modes. The eigenfunctions 

are expressed via Legendre functions (P µ 

λ ) as follows 

where 

Vz = CP µ 

λ (tanh(z/∆)), λ = −1/2 + [1/4 + (k∆ωf /ω) 2 ] 1/2 , µ = −k∆, (15) 

ωf = 

� 

1 

4πρ 

B ∗ 

∆ 

∂Bz 

∂x = 

� 

1 

4πρ 

� � 

∂Bx 

∂z z=0 

∂Bz 

. (16) 

∂x 

The eigenfrequency is proportional to ωf , which can be real or imaginary, if the product of two 

magnetic gradients is positive or negative. The first case corresponds to the stable flapping waves 

propagating to the flanks of the current sheet, and the second case is related to the unstable 

situation in the current sheet. Both, stable and unstable situations are illustrated in Figure 1. 

For the “kink” mode, Vz is an even function of the z coordinate, which requires to fulfill 

condition λ = −µ = k∆. This relation between λ and k yields equation 

� 

k∆ = −1/2 + 1/4 + (k∆) 2ω2 f /ω2 . (17) 

76


Figure 2: Frequencies, group and phase velocities for α =0 (left) and α = 0.4 (right). 

From this equation we derive frequency as a function of wave number for the “kink” mode 

� 

k∆ 

ωk = ωf . (18) 

k∆ + 1 

For the sausage mode, Vz is an odd function, which vanishes at the center of the current sheet. 

This mode corresponds to condition λ = k∆ + 1 which leads to 

� 

k∆ + 3/2 = 1/4 + (k∆) 2ω2 f /ω2 . (19) 

This equation determines the “sausage” mode frequency 

ωs = ωf 

k∆ 

� (k∆) 2 + 3k∆ + 2 . (20) 

In case of nonuniform background plasma density (α �= 0), we found numerical solution. 

The normalized frequencies ωk,s/ωf and wave velocities are presented in Figure 2 for α = 0 

and α = 0.4. Similar plots for α = 0.6 and α = 0.8 are shown in Figure 3. This α parameter 

determines the model profile of the background plasma density (13). One can see at the figures, 

that in all cases flapping wave frequency is an increasing function of the wave number, and it 

has saturation for k → ∞. For a fixed wave number, the frequency tends to increase to a limit 

value, when the α parameter varies from 0 to 1. For larger α, behavior of the frequency as a 

function of wave number becomes more shallow for the most interval of k, besides very small 

wave numbers, where it has abrupt drop to zero. In the limit case α → 1, the frequency has 

a constant limit ω → ωf for each wave number. This is the case of uniform current velocity 

across the plasma sheet. The “kink” perturbations grow faster than the “sausage” ones. This 

instability can take place at some regions of the Earth’s magnetotail current sheet, where the 

Bz component decreases towards Earth. 

For example, we estimate the flapping frequency for the reasonable parameters corresponding 

to the current sheet conditions in the Earth’s magnetotail, 

Bx = 20 nT, Bz = 2 nT, ∆ ∼ RE, np = 0.1 cm −3 , k∆ = 0.7, ∂Bz/∂x ∼ Bz/Lx, Lx ∼ 5RE.(21) 

77


Figure 3: Frequencies, group and phase velocities corresponding to α=0.6 (left) and α = 0.8 

(right). 

Applying these parameters to Figure 2, we find the characteristic flapping frequency ωf ∼ 0.03 

s −1 , and also the group velocity Vg = 60 km/s, and phase velocity Vph = 274 km/s. 

4 Summary 

In a framework of the MHD approach, flapping waves and instability are analyzed in application 

to the magnetotail current sheet. Important factors for our theory are the gradients of Bx and 

Bz magnetic field components along the z and x directions, respectively. MHD solutions are 

obtained for the Harris-like current density profile across the sheet and different profiles of 

the background plasma density. The eigenfrequency and the growth rate for the “kink” and 

“sausage” modes are found. For both modes, the frequencies are monotonic increasing functions 

of the wave number. The corresponding wave group velocities are decreasing functions of the 

wave number, and they vanish asymptotically for high wave numbers. 

For the typical parameters of the Earth’s current sheet, the group velocity of the “kink”-like 

mode is estimated as a few tens of kilometers per second that is in good agreement with the 

CLUSTER observations. A strong decrease of the group velocity for high wave numbers means 

that the small scale oscillations propagate much slower than the large scale oscillations. Because 

of that, the propagating flapping pulse is expected to have a smooth gradual front side part, 

and a small scale oscillating backside part. 

The double gradient flapping waves studied in our model propagate in the direction perpendicular 

to the planes of the background magnetic field lines, and thus they can not be stabilized 

by the magnetic tension. For the “kink” mode, the magnetic field planes are just shifting with 

respect to each other. 

Acknowledgement. This work is supported by RFBR grants No 07-05-00776-a and No 

07-05-00135, by Programs 2.16 and 16.3 of RAS, and by project P17100–N08 from the Austrian 

“Fonds zur Förderung der wissenschaftlichen Forschung”, and also by project I.2/04 from “ 

Österreichischer Austauschdienst”. 

78


References 

Angelopoulos, V., W. Baumjohann, C. F. Kennel, F. V. Coroniti, M. G. Kivelson, R. Pellat, 

R. J. Walker, H. Luhr, and G. Paschmann (1992), Bursty bulk flows in the inner central plasma 

sheet, J. Geophys. Res., 97, 4027–4039. 

Daughton, W.(1999), Two-fluid theory of the drift kink instability, J. Geophys. Res., 104, 

28701. 

Erkaev, N. V., V. S. Semenov, and H. K. Biernat (2007), Magnetic double-gradient instability 

and flapping waves in a current sheet, Phys. Rev. Lett., 99, 235003. 

Erkaev, N. V., Semenov, V. S., and Biernat, H. K.: Magnetic double gradient mechanism 

for flapping oscillations of a current sheet, Geophys. Res. Lett., 35, L02111, doi: 

10.1029/2007GL032277, 2008. 

Golovchanskaya, I. V. and Y. P. Maltsev (2005), On the identification of plasma sheet flapping 

waves observed by Cluster, Geophys. Res. Lett., 32, L02102. 

Karimabadi, H., W. Daughton, P. L. Pritchett, and D. Krauss-Varban (2003), Ion-ion 

kink instability in the magnetotail. Linear theory, J. Geophys. Res., 108(A11), 1400, doi: 

10.1029/2003JA010026. 

Petrukovich, A. A., T. L. Zhang, W. Baumjohann, R. Nakamura, A. Runov, A. Balogh, and 

C. Carr (2006), Oscillatory magnetic flux tube slippage in the plasma sheet, Ann. Geophys., 

24, 1695–1704. 

Pritchett, P. L., F. V. Coronity, R. Pellat, and H. Karimabadi (2003), Collisionless reconnection 

in two-dimensional magnetic equilibria, J. Geophys. Res., 96, 11523. 

Runov, A., V. A. Sergeev, W. Baumjohann, R. Nakamura, S. Apatenkov, Y. Asano, M. 

Volwerk, Z. Vörös, T. L. Zhang, A. Petrukovich, A. Balogh, J.-A. Sauvaud, B. Klecker, and 

H. R‘eme (2005a), Electric current and magnetic field geometry in flapping magnetotail current 

sheets, Ann. Geophys., 23, 1391–1403. 

Runov, A., V. A. Sergeev, R. Nakamura, W. Baumjohann, T. L. Zhang, Y. Asano, M. 

Volwerk, Z. Vörös, A. Balogh, H. Reme (2005b), Reconstruction of the magnetotail current 

sheet structure using multi-point Cluster measurements, Planet. Space Sci., 53, 237–243. 

Runov, A., V. A. Sergeev, R. Nakamura, W. Baumjohann, S. Apatenkov, Y. Asano, T. 

Takada, M. Volwerk, Z. Vörös, T. L. Zhang, J.-A. Sauvaud, H. R‘eme, and A. Balogh (2006), 

Local structure of the magnetotail current sheet: 2001 Cluster observations, Ann. Geophys., 

24, 247–262. 

Sergeev, V., A. Runov, W. Baumjohann, R. Nakamura, T. L. Zhang, M. Volwerk, A. Balogh, 

H. Reme, J. A. Sauvaud, M. Andre, and B. Klecker (2003), Current sheet flapping motion and 

structure observed by Cluster, Geophys. Res. Lett., 30, 1327, doi:10.1029/ 2002GL016500. 

Sergeev, V., A. Runov, W. Baumjohann, R. Nakamura, T. L. Zhang, A. Balogh, P. Louarn, 

J.-A. Sauvaud, and H. R‘eme (2004), Orientation and propagation of current sheet oscillations, 

Geophys. Res. Lett., 31, L05807, doi:10.1029/2003GL019346. 

Sitnov, M. I., M. Swisdak, J. F. Drake, P. N. Guzdar, and B. N. Rogers (2004), A model 

of the bifurcated current sheet: 2. Flapping motion, Geophys. Res. Lett., 31, L09 805, 

doi:10.1029/2004GL019473. 

Zhang, S. T. L., W. Baumjohann, R. Nakamura, A. Balogh, K.-H. Glassmeier (2002), A wavy 

twisted neutral sheet observed by Cluster, Geophys. Res. Lett., 29, 10.1029/2002GL015544. 

79


ON THE INFLUENCE OF SECONADARY RAREFACTION WAVE ON 

THE GEOMAGNETIC FIELD 

Grib S.A. 1 , Belakhovsky V.B. 2 

1 - Central Astronomical Observatory of Russian Academy of Sciences, Saint-Petersburg, 

Russia, 2 - Polar Geophysical Institute of Kola Scientific Center, Apatity, Russia 

E-mail: Belakhovsky@mail.ru 

Abstract. On the basis of solar wind data from the WIND satellite, magnetic field data 

from GOES satellite and ground-based magnetic data the influence of secondary rarefaction wave 

on the geomagnetic field is examined. This secondary rarefaction wave is arising in the 

magnetosheath during the interaction of interplanetary shock wave with the bow shockmagnetopause 

system. The secondary rarefaction wave decreases the magnitude of the magnetic 

field during SSC. 

Introduction. It is known that arrival of interplanetary shock wave to the Earth’s magnetosphere 

cause compression of magnetosphere and SSC (sudden storm commencement) event, which may be the 

beginning of the magnetic storm. The interplanetary shock wave is characterized by step increase of solar 

wind density, velocity and magnetic field. 

The field of SSC is consisting of field on the low latitudes (DL) and polar latitudes (DP) (1). DP 

consists of main impulse (MI) and preliminary impulse (PI). The currents on the magnetopause cause DL 

field, while the currents in polar ionosphere cause DP field [Araki T., 1994]. 

D = DL + DP + DP 

SSC 

[Grib et al., 1979] theoretically show that during interaction of during interaction of interplanetary 

shock wave with the bow shock-magnetopause system the secondary rarefaction wave in the magnetosheath 

is arisen. The mechanism of interaction of interplanetary shock wave with the bow shock-magnetopause 

system schematically is shown by (2). The result of interaction of interplanetary shock wave S2 with the bow 

shock S1bow are two shock waves (forward and backward) and tangential discontinuity T. Then refracted 

shock wave moves through the magnetosheath. The result of interaction of refracted shock wave S4 with the 

magnetopause Tm are the rarefaction wave R, magnetopause Tm and shock wave S5 moving inside the 

magnetosphere. This rarefaction wave R reflects from the rear side of the bow shock S′′bow and the secondary 

rarefaction wave R′ moves to the magnetopause. 

S 

S 

R 

2→ 

← 

→ 

S 

T 

4→ 

m 

S 

'' 

bow 

1bow 

→ S 

→ R T S 

m 

→ R'T 

S 

m 

3bow← 

5→ 

5→ 

In papers [Samsonov et al., 2006, 2007] MHD-simulation of the interaction of interplanetary shock 

wave with the bow shock and magnetopause and passing of the shock wave through the magnetosheath were 

performed. It was shown that result of the interaction of the fast shock wave with the magnetopause gives a 

shock wave or a rarefaction wave. But even the product of the interaction of shock wave with rear side of the 

bow shock is the rarefaction wave that consistent with results obtained in the work [Grib et al., 1979]. 

In the work [Safrankova J. et al., 2007] on the basis of MHD-simulation it was shown that during 

interaction of interplanetary shock wave with the bow shock at first it is seen the motion of the bow shock in 

antisunward direction and then in sunward direction. Possibly this motion is the result of the interaction of 

interplanetary shock wave with the magnetopause. 

80 

PI 

T S 

4→ 

MI 

( 1) 

( 2)


In the paper [Zhuang et al., 1981] on the basis of ISEE satellite data the existence of rarefaction 

wave reflected from the magnetopause is confirmed. The attempts to detect secondary rarefaction wave in 

the magnetosheath is too difficult due to turbulence and vortexes in the magnetosheath. 

So the purpose of this paper is to show how secondary rarefaction wave may influence on the 

geomagnetic field. 

Methods. 

We choose events when the rise time of solar wind dynamic pressure equals more than 5 min, 

because secondary rarefaction wave need approximately 3-5 min to arrive to the magnetopause after an 

arrival of the interplanetary shock wave. We choose such events in order to show that the rarefaction wave 

does not exist in the solar wind but is the result of the interaction of interplanetary shock wave with the bow 

shock-magnetopause system. 

81 

Due to the limitation of the paper we consider only 

two SSC events: on 6 May 2005 and on 9 July 

2006. We examine 1-min magnetic data from the 

WIND, GOES satellites and H-component of the 

magnetic filed from the ground-based stations. 

We examine GOES satellite data when the 

GOES is located on the dayside magnetosphere 

because magnetopause currents an influence on the 

dayside magnetic filed. But when the GOES is 

located on the nightside the decrease on the 

magnetic field is observed. This decrease of the 

magnetic field on the nightside geostationary orbit 

is associated with tail currents. The dependence of 

magnetic filed at geostationary orbit is shown in 

[Kokubun, S., 1983]. 

On the ground we choose low latitude 

geomagnetic stations because H-component of the 

magnetic field at this latitudes well correlate with 

the solar wind dynamic pressure [Russell, C. T., 

1992]. We choose the events when the satellite is 

located near the Sun-Earth line.


Results. 

6 May 2005. On the fig.1 the total 

magnetic field, solar wind dynamic pressure 

and thermal pressure are shown. The WIND 

satellite is located in the point (214, -2, 23) Re 

in the GSE coordinate system. Rise time of the 

solar wind dynamic pressure is equal 6.5 min. 

Dst-index during this event is equal 2 nT, so 

this is SI event. SSC event registered on the 

Earth at 13.05 UT. 

On the fig.2 the total magnetic field is 

shown on GOES-12 satellite, which located at 

08.00 MLT during SSC event. Corrected 

geomagnetic coordinate is shown in the 

brackets. The rise time on GOES-12 is equal 5 

min. 

On the fig.3 the H-component of low 

latitude stations is shown. The vertical line 

gives the magnetic field in nT. The rise time on 

the low-latitude stations is equal 4-5 min. 

9 July 2006. Total magnetic field, solar 

wind dynamic pressure and thermal pressure are shown by fig.4. The WIND satellite is located at 

the point (262, -15, 21) Re in the GSE coordinate system. Rise time of the solar wind dynamic pressure is 

equal 8.5 min. 

On the fig.5 the total magnetic field is shown on GOES-11 and GOES-12 satellites, which are 

located at 15.00 MLT and 17.00 MLT during SSC event. Corrected geomagnetic coordinate is shown in the 

brackets. Rise time on GOES-11 is equal 6 min and rise time on GOES-12 is equal 7 min. 

On the fig. 6 the H-component of low latitude stations is shown. On the vertical line the magnetic 

field is shown in nT. The rise time on the low-latitude stations is equal to 5-7 min. 

Discussion. 

So we see that from two examined cases that the rise time on the ground and at the geostationary 

orbit are less than rise time of the solar wind dynamic pressure. [Koval A. et al., 2005] show that parameters 

of interplanetary shock wave during propagation thought the solar wind are similar and parameters of the 

shock wave strongly change during propagation through the magnetosheath. 

82


The variations of the H-component of the geomagnetic field at the low-latitude stations 

quantitatively depend on the variations of the solar wind dynamic pressure. See for example formulae (3) 

from [Siscoe G.L., 1968]. 

∆B 

= k − 

SSC 

( pS 

pS 

0 

It is known that two main factors determine SSC rise time: orientation and velocity of interplanetary 

shock. When interplanetary shock is highly inclined the SSC rise may be longer than the rise time of the solar 

wind dynamic pressure [T.Takeuchi et al., 2002]. Velocity of shock is greater in the interplanetary medium 

than in the magnetosheath. So shock with smaller velocity would produce greater SSC rise time. 

Besides taking into account these two factors we consider that the rise time observed at the Earth’s 

surface would be smaller than the observed rise time because orientation of the shock and smaller shock 

velocity increase the SSC rise time. 

In all cases we see that rise time of the magnetic field on the ground and at geostationary orbit are 

proportional to the rise time of solar wind dynamic pressure. At the same time the magnetic field on the 

ground and in the magnetosphere in all cases less than rise time of the solar wind dynamic pressure. We 

associate these differences in the rise time with an influence of secondary rarefaction wave on the 

geomagnetic field. 

Conclusions. We obtain that the magnitude of the magnetic field decrease during SSC event. We 

suppose that this decrease is associated with the generation of secondary rarefaction wave appearing in the 

magnetosheath during the interaction of interplanetary shock wave with the bow shock-magnetopause 

system. 

The data from the WIND and GOES satellites ware taken from the site http://cdaweb.gsfc.nasa.gov/. 

The data from the ground-based stations ware taken from the site http://swdcwww.kugi.kyoto-u.ac.jp/ 

Acknowledgements. The work of the first author was supported by the Russian Foundation for 

Basic Research (project no. 08-01-00191) and by Department of the Physics Science (program 16). 

The work of the second author was supported by the Russian Foundation for Basic Research (project 

no. 06-05-64374) and by Presidium of the Russian Academy of Science (program 16). 

References 

Araki, T. A physical model of the geomagnetic sudden commencement // Solar wind sources of 

magnetospheric ultra-low-frequency waves. Geophys. Monograph, Ser. AGU. Washington, D.C.81, p.183- 

200, 1994. 

Grib, S.A., B.E. Briunelli, M. Dryer, and W.-W. Shen. Interaction of interplanetary shock waves with 

the bow shock-magnetopause system, J. Geophys. Res., 84, 5907-5921, 1979. 

Kokubun, S. Characteristics of storm sudden commencement at geostationary orbit, J. Geophys. 

Res., 88, p. 10025-10033, 1983. 

Russell, C. T., Ginskey, M., Petrinec, S., Le, G. The effect of solar wind dynamic pressure changes 

on low and mid-latitude magnetic records // Geophys. Res. Letters, 19, p.1227-1230, 1992. 

Samsonov A.A., Sibeck D.G., Imber J. MHD simulation for the interaction of an interplanetary shock 

with the Earth’s magnetosphere // J. Geophys. Res., vol.112, A12220, 2007. 

Samsonov A.A., Nemecek Z., Safrankova J.. Numerical MHD modeling of propagation of 

interplanetary shock through the magnetosheath // J. Geophys. Res., vol.111, A08210, 2006. 

Safrankova J., Nemecek Z., Prech L., Samsonov A.A., Koval A., Andreeova K.. Modification of 

interplanetary shocks near the bow shock and through the magnetosheath // J. Geophys. Res., vol.112, 

A08212, 2007. 

Siscoe G.L., Formisano V., Lazarus A.J. Relation between geomagnetic, sudden and solar wind 

pressure changes –an experimental investigation// J.Geophys.Res, 73, №15, р. 4869, 1968. 

Takeuchi T., Russell C. T., Araki T. Effect of the orientation of interplanetary shock on the 

geomagnetic sudden commencement // // J.Geophys.Res., 107, A12, 1423, 2002. 

83 

) 

( 3)


Zhuang H.C., Russel C.T., Smith E.J., and Gosling J.T. Three-dimensional interaction of 

interplanetary shock waves with the bow shock and magnetopause: a comparison of theory with ISEE 

observations // J.Geophys. Res.V.86, A7, p. 5590-5600, 1981. 

84


ON A NEW PARAMETER OF SPACE WEATHER AND TOPOLOGY OF 

THE EARTH’S MAGNETOSPHERE BASED ON THE FORM FACTOR OF 

THE INCOMING SOLAR-WIND PARTICLE-VELOCITY DISTRIBUTION 

FUNCTION 

V.M. Gubchenko 

Institute of Applied Physics, Russian Academy of Science, 603950 Nizhny Novgorod, Russia, 

e-mail: ua3thw@appl.sci-nnov.ru 

Abstract. We consider the result of theoretical analysis of the 3D global classical Chapman- 

Ferraro problem (CFP) where unmagnetized plasma flow inductively interacts with the resting 

magnetic dipole. As a result, we obtain the 3D magnetosphere topology with a tail, magnetopause 

and the energy/pulse exchange with the SW flow. We take into account the VDF form factor to 

describe the incoming hot collisionless plasma flow. The electromagnetic part of the 

magnetosphere structures (magnetopause and magnetotail) with large spatial scales of non-MHD 

nature are determined by the dimensionless parameter GV of the incoming SW flow. Parameter GV 

is the ratio of the large-scale diamagnetic current to the resistive current in the magnetospheric 

plasma. This parameter is determined by the kinetic effects of the moving plasma and depends on 

the VDF form factor. Calculations of GV in the kinetic CFP are based on simplification of the 

nonlinearity by division of plasma particles into a “flyby” group forming the moving medium and 

a “trapped” group forming the resting magnetization. Parameter GV that we introduced here is a 

new parameter of space weather, which is related to the properties of the kinetic inductive 

electromagnetic mode of a hot collisionless moving plasma formed by the “flyby particles”. In 

particular we find that the parameter GV governs the topology of the electromagnetic part of the 

structure. We obtain the adiabatic/bifurcation transition with return from the resistive state GV 1. This can explain in a new way the effects of the magnetic substorm. Parameter GV is the 

ratio of the “momentum anisotropy”, which is determined by a flow of resonant particles, to the 

“energy anisotropy” determined by a flow of nonresonant particles. The dimensionless parameter 

GV as a function of the form factor of the VDF of the incoming flow can be rewritten via the ratio 

of the squared anomalous skin scale to the squared magnetic Debye scale. New dispersion scales 

in a plasma induced by the SW flow are responsible for “thick” and “thin” structures. 

1. Introduction. Inner and outer parts of the magnetosphere 

Space weather is at the beginning of a chain of events connecting the state of space which is filled by 

the solar wind plasma with the topological state of the 3d magnetosphere formed by the “outer” and the 

“inner” parts. Finally, the chain is connected via polar Birkeland currents with the state of the global 

electrojet formed in the Earth’s atmosphere/ionosphere. The electrojet heats the atmosphere, which 

inductively interacts with large scale electrical power line systems generating hazardous geomagnetically 

induced currents (GIC) (Fig. 1). 

Space weather is characterized by a group of dimensionless parameters determined from plasma 

theory or observations as functions of the incoming solar wind plasma parameters such as plasma 

concentration nw , solar wind velocity v' , thermal velocity of the species α , and interplanetary magnetic field 

v 

Bw r . We include in the analysis of the space weather a form factor of the particle velocity distribution 

function (VDF) f (v) 

(Fig. 1, Fig. 2). All these physical parameters are measured by modern space probes. 

r 

85


Fig.1. Earth’s “outer” magnetosphere with a 3d magnetotail, a magnetopause and a mantle formed by the “flyby” 

particles and “inner” part inside a sphere formed by the “trapped” particles from the solar wind plasma flow with 

velocity v ' and the VDF f (v) 

(left side). Electrojets formed on the Earth’s atmosphere (center). Power lines and GIC 

under the jets (right side). 

r 

2. Chapman-Ferraro problem in kinetics and two dimensionless parameters of the solar wind 

The physical parameters in dimensionless form, which characterize the state of space weather, are a 

result of the classical Chapman-Ferraro problem (CFP) consideration. The CFP is a basic 3d global nonlinear 

problem of the space plasma physics and in the CFP under study is the process of plasma flow inductive 

interaction with the resting magnetization (X ) 

r r 

r r r 

μ with generation of the inductive current j = jr 

+ jd 

, 

which we divide into two physically different components: “resistive” r j 

r 

and “diamagnetic” , d j 

r 

which are 

related to the resistive (conductive) and polarization currents in a plasma. 

Fig.2. Similarity in the multi-ray structure of the far magnetotail (left side) and of the ray structure of a separate 

coronal streamer in the solar corona (center). Proton velocity distribution functions (VDF) f (v) 

of the solar wind 

measured by a space probe with velocity anisotropy and “core” and ”halo” elements (right side). 

r 

The CFP solution clarifies the 3d global topology of the magnetosphere and the energy/pulse 

exchange with the solar wind flow. Solar streamer is another 3D object of space plasma with similar physics 

for applications of the CFP solutions. The streamer is visible in optics, and we obtain complimentary data for 

mutual testing of the Earth magnetosphere and Solar streamer physics (Fig.2). 

There are phenomenological MHD and more realistic kinetic approaches taking into account the 

VDF form factor in the solution of the CFP and in the description of the incoming hot collisionless plasma 

flow. Evolving from 1931, this problem was finally as the subject of nonlinear global MHD approach to 

plasma. Since the end of the 80s the large scale self-consistent kinetic (LSK) approach to the 3d CFP is 

under development analytically [1,2] and since the beginning of the 90s, numerically [3]. 

The only dimensionless parameter for the plasma flow provided by the ideal MHD in the case of 

Bw = 0 

r 

is the Mach number M = v'/ 

cs 

. When M < 1 , D’Alambere motion with no drag takes place. When 

M > 1 we get the formation of the shock wave cone structure provided by potential ϕ fields describing 

longitudinal acoustic waves and we obtain the pressure drag force action. The Mach number M is not 

86


related to the formation of elongated electromagnetic magnetotail/streamer structures provided by the vector 

potential A r field describing transversal inductive fields. The definition of Mach number based on dispersive 

properties of the sonic waves in the flow, and these properties are not so sensitive to the choice between 

MHD and kinetic approaches to the plasma modeling. It is weak dependence of the acoustic wave dispersion 

properties ω = ( k) 

k is chosen among ideal M HD, nonideal MHD and kinetics. On the basis of the 

Mach 

c s 

2 1/ 

2 

number we obtain the aerodynamic coefficient cx = δ /( M −1) 

related with a form factor δ ( r0 

) of the 

magnetization (X ) 

r r 

μ with a scale r 0 , which, along with dynamic pressure, determines the aerodynamic drag 

force on the magnetosphere due to sonic wave radiation in the supersonic regime M > 1. 

The electromagnetic part of the magnetosphere/streamer is determined by the dimensionless 

parameter G V which is a new parameter for the incoming flow characteristic, considered further as a space 

weather parameter and related to excitation by a flow of transversal e.m. vector potential A r fields. This 

parameter characterizes the topological state of the magnetosphere with two basic elements: 

magnetopause/mantle and magnetotail with neu sheet inside as well as the state of the solar 

streamer with the ray structures. The parameter V ≈ j d / jr 

which we call a “quality” characterize ratio of 

densities of the large-scale dia gnetic current d j to the resistive current tral current 

G 

ma 

j r components excited in plasma 

r r 

flow by the magnetization μ (X ) . We note that in a common case, electromagnetic properties of the flow are 

characterized by the tensor of the dielectric permittivity ij ( , k ) 

r 

ε ω . Parameter 

G V describes the particular 

rr 

electromagnetic properties of the solar wind flow calculated for ω = kv' 

as app lied to the stationary 

solution 

of the CFP. Thus, G V does 

n metrical form factor 

of the (X ) 

r 

2 2 r 

the geo ~ exp( X / 2r0 

) μ 

r 

not depend o 

− 

defined by the scale r 0 . 

We get the “resistive” state solar wind when G V > 1 where the 

magnetotail/streamer is absent. 

Parameter G V as a dissipative parameter is much more sensitive to the choice between the nonideal 

MHD model, where dissipation is postulated, and the kinetic 

plasma model where dissipation is self- 

−1 

consistent with VDF form. In the ideal MHD, G V = 0 and the magnetosphere/streamer 

formed by 

r 

tangential discontinuities provided by diamagnetic current of density jd 

. Inst ead of G V , we can operate 

2 −1/ 

2 

with the “loss” angle GV 

= ctgγ 

V or with “reactivity” angle ϕ V ensuring cosϕV 

= ( 1+ 

GV 

) for the 

magnetosphere and streamer equivalent ele ctro-technical circuits (Fig.3). 

On the other hand the parameter Rem = r 0 / rskin 

. is the magnetic Reynolds number defined by the 

r r 

spatial scale r 0 of magnetization μ (X ) and a skin scale r skin which is defined by the resistive properties of 

the plasma. 

The parameter characterizes the role of the flow conductivity and defines the ideal conductor 

Re m → ∞ and nonconductive 

media Rem → 0 in the limiting cases. Another parameter is the magnetic 

Debye number D M = r0 

/ rDM 

, which characterizes the role of diamagnetic currents around magnetization 

r r 

μ (X ) . The quantity r DM is the diamagnetic scale related to the plasma pressure anisotropy, and in 

particular, to the dynamical pressure of the flow and defines diamagnetic currents thickness relative to r 0 in 

2 2 2 2 

the moving media. It can be shown that G V ≈ jd 

/ jr 

= Rem/ 

DM 

= rskin 

/ rDM 

is independent of the r 0 value 

and is characteristic of the incoming flow only. Determination 

of the parameter G V from the CFP solution 

strongly depends on the physical model of plasma flow. 

87


Fig.3. Resistive and diamagnetic components of the current density generated in a plasma by transversal e.m.f. 

j 

jr d 

Et provided by magnetization motion in plasma. The angle V 

γ is the loss angle and the angle V 

ϕ is the reactivity 

angle (fig. at the upper left corner). Electro-technical models for transversal ( A r - field) and longitudinal (ϕ - field) 

parts of the magnetosphere fields (left and right). Resistor is related with resistive current j and inductance L 

Rt r 

with diamagnetic current , capacity C related to part of the convective electrostatic field. The inductance is a coil 

jd t 

N = V 

El 

which has G internal loops (two figs on the right for multiloop and no loops coil). The longitudinal e.m.f. 

provided by magnetization motion. Capacity C is related to plasma polarization and resistor Rl 

with wake and sonic 

wave radiation. 

3. The flow regimes and solutions of the CFP. The “quality” parameter in kinetics. Thin and thick 

induced scales and two types of the flow anisotropy 

Calculations of the G ≈ j / j in the kinetic approach are based on simplification of the nonlinear 

V 

d 

r 

CFP by method of division of plasma particles into a “flyby” group forming the “moving media” with 

r r r 

excited currents j = jr 

+ jd 

, which are related to the “outer” part of the magnetosphere, and the “inner” 

part, which is based on a “trapped” group forming the resting prescribed magnetization (X ) 

r r 

μ as a 

“quasiparticle” provided by the magnetic dipole and magnetic toroid components in (X ) 

r r 

μ . In this outer 

part, the motion of particles only disturbed by the direct motion, and a self-consistent kinetic solution of the 

r 

Vlasov equation can be found by the perturbation method in terms of the tensor ε ij ( ω, 

k ) . In a plasma with 

r 

r 

isotropic VDF f (| v |) , we obtain the diagonal tensor with two equal transversal components ε t ( ω, 

k ) and 

r 

r 

one longitudinal component ε l ( ω, 

k ) , which is expressed via the form factor of f (| v |) . 

r r r r r r 

Magnetization μ ( X ) = μd 

( X ) + μτ 

( X ) is formed by the Earth’s magnetic dipole and the ring 

r r 

current. The first is the magnetic dipole part of magnetization μ (X ) with N and S “magnetic poles” and 

d 

the magnetic moment μ0 r . This part is formed by the magnetic dipole of the Earth and the circular 

part of the ring current in the inner magnetosphere (CRC). The second part is a toroidal part 

r r r r 

( X ) ∇ × τ ( X ) with the toroidal moment τ r . This part is formed by the partial ring current (PRC). In 

μτ = 0 

our further consideration the vectors μ0 r , τ 0 

r and v' r are orthogonal to each other, forming the “inner” 

magnetosphere or the solar “helmet” structure over active region. It can be shown that μ πr 

I , 

2 

τ πr 

Iτ 

, where and are the integral currents forming magnetic dipole and magnetic 

toroid. We call the parameter 

3 

0 = ( 4 / 3) 

0 Iμ Iτ 

Γ = I / I a toroidality of the inner magnetosphere/solar active 

τμ 

τ 

μ 

region. For the Earth Γτμ ≤ 1 and for the Sun Γτμ ≥ 1. 

r r r 

The resulting electromagnetic field A = Aτ 

+ Aμ 

after the solution of the Maxwell equations has 

two components related to two components of the magnetization (X ) 

r r 

μ : 

88 

0 = 

0 

μ


r ∂M 

G r ∂M 

G r 

A = μ ( x − y ) , 

μ 0 ∂Y 

0 ∂X 

0 

2 

2 2 

2 

r ∂ MG 

r ∂ MG 

∂ MG 

r ∂ MG 

r 

Aτ 

=τ 0( 

x0 

+ ( + ) y0 

− z0) 

. 

2 2 

∂X∂Y 

∂X 

∂Z 

∂Z∂Y 

The outer “dipole part” of the field Aμ r is related to the magnetopause/mantle field provided by the 

“two wire” current structure with two ± opposite currents. The inner “toroidal” part τ is provided 

by “ 

Ar 

θ ” type cylindrical toroid current structure in the magnetotail. Generation of the potential field 

ϕ by moving magnetization, which is equivalent here to the moving electric dipole polarization is 

not considered here. 

These components are expressed via derivatives of the characteristic function 

M 

r 4π 

( X , r0 

, v') 

= 

( 2π 

) 

∫ 

r r 

r 

2 2 

exp[( −k 

r0 

/ 2) 

+ ikX 

] 

dk 

r r , 

2 

k D ( k , kv' 

) 

G 3 

r 

T 

r 

2 2 2 

where DT ( ω, k) 

= 1− 

( ω / c k ) εt 

( ω, 

k) 

and ε t ( ω, 

k ) is the transversal part of the dielectric 

r 

r 

permittivity tensor ε ( ω, 

k ) . When ( ω , k ) = 0 we have e.m. field modes in plasma and get 

ij 

D T 

plasma resonance. 

r 

The real part of the complex value ε t ( ω, 

k ) is related to diamagnetic properties of the flow 

r r 

and forms the current jd 

, and the imaginary part of ε t ( ω, 

k ) is related to resistive properties of the 

r r r 

flow and forms the resistive current jr 

. Vectors jd 

and jr 

are collinear in an isotropic plasma, but 

have different spatial distribution and differently depend on e.m. field. 

In the kinetic approach to the CFP, there are three physically different “regimes” of flow. We have 

the “subsonic regime”, which is realized for the solar streamer generation v '< 

c > 

v >> c which describes the plasma as an MHD medium [3]. For the 

first two cases [1,2], the characteristic function can be represented as 

I 

x 

e 

s 

∞ 

2 2 

1 

ξ ⊥ Re m 

M G ( χ, ρ ⊥ , Re m , GV 

) = dξ 

⊥ξ 

⊥ J 0 ( ξ ⊥ρ 

⊥ ) exp( − ) I x ( ξ ⊥ , χ, 

Re m ) 

πr 

∫ , 

2 

0 

G 

0 

∞ 

2 2 

2 2 

ξ x Re m ( ξ ⊥ + ξ x ) 

( ξ ⊥ , χ, 

Re m , GV 

) = 2Re∫ 

dξ 

x exp( iξ 

x χ − ) 

, 

2 

2 ( ξ + ξ ) − i | ξ | ξ + G ξ 

where χ = x / rG 

, ρ ⊥ = r ⊥ / rG 

are dimensionless cylindrical coordinates and krG is a 

dimensionless wave vector with the cylindrical components 

r r ξ = 

ξ ⊥ and ξ x . Here, Rem = r 0 / rG 

is the 

r 

magnetic Reynolds number and r = r is the anomalous skin depth expresed via f (| v |) [1]. 

skin 

G 

From the expression given above we see the key role of the parameter GV 

called “quality” which 

r 

determined by form factor of the VDF f (| v |) . Parameter GV 

governs the 3d topology due to the variable 

character of the dispersion in the denominator of the characteristic function M G ( X , GV 

) . We have a 

transition from the “resistive” state with a long ray structured magnetic tail to the diamagnetic 

r 

G > 1, 

which explains in the nonadiabatic transition the effects of the magnetic 

V 

substorm and the effect of coronal mass ejection (CME). 

The parameter 

G ≈ κ / κ 

V 

V 

D 

89 

G 

2 

⊥ 

s 

2 

x 

s 

e 

x 

e 

V 

2 

x


as the ratio of diamagnetic to resistive current is determined in a hot collisionless isotropic plasma by the 

ratio of the “momentum anisotropy” κ ≈ v'πf 

( v') 

provided by the “resonant” particles to the “energy 

∫ 

G 

2 

2 

anisotropy” κ ≈ −2v' 

du( 

∂f 

/ ∂u 

) of the “nonresonant” particles of the flow providing the flow 

D 

dynamical pressure. For the Maxwellian plasma f = f we have G v' 

/ v


ANHARMONICITY OF THE ULF GEOELECTROMAGNETIC WAVES 

A.V. Guglielmi 1 , B.I. Klain 2 , O.D. Zotov 2 

1 Institute of Physics of the Earth, RAS, Moscow, Russia, e-mail: guglielmi@mail.ru; 

2 Geophysical Observatory Borok, IPE, RAS, Borok, Russia, e-mail: ozotov@inbox.ru 

Abstract. The theory of ponderomotive forces predicts the anharmonicity of standing Alfvén 

waves. The goal of our work is to find an experimental evidence of the anharmonicity of Alfvén 

oscillations of the Earth’s magnetosphere by using the ground based observation of the ULF waves 

in the Pc3 frequency band. The method of remote diagnostics of the oscillating magnetic shells, 

the spectral-polarization method and the method of synchronous detection are used. As the result 

the true signs of anharmonicity of the ULF waves are found. 

Keywords: Alfvén waves, ULF electromagnetic waves, ponderomotive forces. 

1. INTRODUCTION 

There are two reasons to believe that the ULF electromagnetic waves in the magnetosphere are the 

nonlinear waves. The first reason is that the energy density of the magnetic field oscillations is of the order 

of the background plasma pressure. The second one is that the ULF and other types of electromagnetic 

waves in the magnetosphere arise mostly as a consequence of plasma instabilities. This results in the selfexcitation 

of the diversity of nonlinear wave structures. A common property of the nonlinear waves is the 

appearance of time-averaged ponderomotive forces providing the specific mechanisms of the wave-particle 

interaction [Lundin and Guglielmi, 2006]. 

Ponderomotive forces of a standing Alfvén wave acts such that the plasma is pushed out of the nodes 

and gathers at the antinodes of the electric field. This results in specific anharmonicity effects in the 

oscillations. It would be very useful to analyze the observational manifestations of anharmonicity. With this 

aim we have proposed new methods for analyzing ULF wave data. One method is based on the location of 

the oscillating magnetic shells. One more method is based on the analyzing of the amplitude dependence of 

the wave polarization by using the Stokes parameters. (More general approach is based on the extraction of 

the nine Roman’s invariants from the wave data.) At last, the synchronous detection method may be used to 

study the nonlinear generation of the 2 nd harmonics. In this paper we describe shortly some preliminary 

results. 

2. ULF RANGEFINDER 

The ground based method of remote diagnostics of the oscillating magnetic shells by using the socalled 

ULF rangefinder is described in the paper (Lundin and Guglielmi, 2006). This method provides a way 

of estimating the distance x along the meridian from the observation point to the magnetic shell which 

R 

resonantly oscillates with the period T. It has been found that the distance and the period are both amplitude 

dependent, suggesting that the standing Alfvén waves in the magnetosphere exhibit the nonlinear property of 

anharmonicity. Here we would like to present some additional analysis of the experimental data presented in 

the above-mentioned paper. 

First of all let us note that by analogy with a mechanical oscillator we can really expect the 

nonlinearity to cause effects of anharmonicity of the standing Alfvén oscillations. In particular, the quadric 

dependence of the period on the oscillations amplitude is expected: T = T0+ χI 

. Here T0 

is the period of 

2 

infinitesimal oscillations ( I → 0 ), χ is the coefficient of nonlinearity, I ∝ H is the intensity, and H is the 

amplitude. We would like to discuss the questions: How to detect the anharmonicity, and how to estimate the 

coefficient χ by observation of the ULF oscillations? 

91


The quest for anharmonicity is complicated by the fact that there exists the dependence of the 

eigenperiods on the L-value of the oscillating magnetic shell. It is not easy to discover the weak nonlinear 

effect of anharmonicity on the background of this pronounced linear dependence. To get over the difficulty 

the following routines may be applied. The first way is to study I dependence of T at x R = const , and the 

second one is to study H dependence of x at T = const . Actually this implies that the variation of the 

value x or T is bounded by the narrow limits. 

R 

Period, sec 

25 

24 

23 

22 

21 

20 

R 

0,5 1,0 1,5 2,0 2,5 3,0 

Normalized intensity 

r = -0.53 

Fig. 1. The period–intensity relation. The solid line is the linear regression function. The dash curves 

show the regression band with 90% confidence interval. 

At first we consider the limitation x R < 120 km. The scatter plot in Fig. 1 shows the dependence of 

2 

period T on the dimensionless intensity I = ( H / Hm) 

, where H m = 334 µA/m is the mean amplitude of 

oscillations. The regression line T = 23.2 −0.94 

I shows that the coefficient of anharmonicity is negative: 

χ ≈ − 0.94 s. (1) 

Now, we would like to study the dependence of x on I at T = const. (In actual practice the 

condition T = const implies that the relative variation of the period is bounded by the narrow limits). We 

found 33 couples of events over the interval of distances − 200 < xR 

< 500 km. The amplitude is varied over 

the interval 100 < H < 600 µA/m. The difference of the amplitudes δ H in a couple is typically ± 100 µA/m. 

And lastly, we have calculated the value δ xR / δ H for each couple. The Fig. 2 shows that the value 

δ x / δ H is positive in most cases (25 positive and 8 negative values). The mean is equal to 0.6 km /mA , 

R 

so that 

2 

δxR/ δI ≈ 10 km 

at H = Hm. 

It must be noted that the reference value δxR/ δ I = 0 corresponds to the harmonic Alfvén 

2 

oscillations. The t-test of mean δxR/ δ I = 10 km 

against this reference value indicates that δxR/ δI ≠ 0 

with 95% confidence. Therefore, it is very probable that we have detected the anharmonicity of Alfvén 

oscillations. 

92 

R 

2 

(2)


Fig. 2. The distribution of the events (see the text). 

Now we would like to discuss briefly the relation between the values χ and δ x / δ I . These values 

are considered as two independent estimates of anharmonicity of the Alfvén oscillations. The coefficient of 

nonlinearity χ is derivable from the equation 

which follows from the equation 

χ 

⎛ ⎞⎛ ⎞ 

⎜ ⎟⎜ ⎟ , (3) 

⎝ ⎠⎝ 

⎠ 

∂T 

δ x 

=− R 

∂xR 

δ I 

∂T ∂T 

δT( x , I) = δx 

+ δI 

= 0. 

(4) 

∂x ∂I 

R R 

R 

The condition δ T = 0 corresponds roughly to the sampling of couples of the events. The first term 

−3 

-1 

in the right-hand side of equation (3) is of the order of ∂T / ∂xR≈6.5⋅ 10 km s (Guglielmi, 2006). The 

2 

second term is of the order of δxR/ δI ≈ 10 km. 

Hence the equation (3) leads to a conservative estimate 

χ ≈− 0.65 s of the coefficient of nonlinearity. Alternatively, we had derived the value χ ≈− 0.94 s by using 

the Fig. 1. This independent result is in rather good agreement with the estimate χ ≈− 0.65 s if it is 

considered that the number of data points in the Fig. 1 is small. 

It must be noted that the parameters χ and δ xR / δ I may be determined also by using the meridian 

chain of magnetic observatories. 

3. STOKES PARAMETERS 

A priori information on the polarization properties of the ULF geoelectromagnetic fields is widely 

employed in geophysics. The method of magneto-telluric sounding of the Earth’s crust which is based on the 

using of the polarization relation E/H is the well known example of this sort. The other interesting examples 

have been presented in the recent review papers (Guglielmi, 2006, 2007): 

a. The relation ( E/ Z)sinθis used in the hydromagnetic diagnostics of the Earth’s 


b. A specific polarization of the seismoelectromagnetic waves in the so-called picture plane 

allows us to detect the weak coseismic magnetic signals. 

93 

R


c. The relation Z/H is used in an attempt to predict the earthquakes. 

Here E and H are the horizontal components of the electric and magnetic fields, Z is the vertical 

component of the magnetic field, and θ is the phase angle between the E and Z oscillations. 

In addition we would like to mention a new approach to study the ULF geoelectromagnetic field 

(Guglielmi et al., 2007). This is the spectral-polarization method which rests on the evaluation of the Stokes 

parameters at a given point on the earth’s surface. It allows estimating of the Alfvén resonant frequency by 

using the ground-based observation of the Pc3-4 magnetospheric oscillations. The spectral-polarization 

method is scheduled to use in the Geophysical Observatory Borok (Φ = 54.05 o , Λ = 119.44 o , L = 2.9) in the 

frame of BARS project (“Study of the Alfvén Resonances in Borok”). It has been elaborated the special 

equipment, the appropriate software support, and the field test of the method has been provided. The result 

shows that the spectral-polarization method may be apparently used for the estimating of the Alfvén resonant 

frequencies. We have made the special attention to the study of anharmonicity of the Pc3-4 waves. 

4. SYNCHRONOUS DETECTION 

The theory of the finite-amplitude standing Alfvén waves predicts the phenomenon of frequency 

doubling. It has been found by use of both numerical simulations (Rankin et al., 1994) and perturbation 

theory in the second (lowest) order of nonlinearity (Dmitrienko, 2005). However, as we know, the magnetic 

observations of the frequency doubling were absent hitherto. The goal of our work in the frame of BARS 

project is to fill this gap by using the method of synchronous detection method which allows to identify a 

weak signal against the background of interferences (Guglielmi and Zotov, 2007). It is not easy to observe 

the phenomenon since the spectrum of Alfvén oscillations of the magnetosphere is non-equidistant, and 

therefore the nonlinear oscillations at a frequency twice than the frequency of pumping oscillations are out of 

resonance. Oscillogram and Fourier-spectrum do not show the effect of frequency doubling. To overcome 

this specific difficulty we have used the synchronous detection method which allows us to identify the 

desired weak signal against the background of interferences. 

Fig. 3. Spectrum of oscillations (left panel) and synchronous detection of the frequency doubling 

(right panel). 

As an example let us consider Fig. 3. The Pc3 oscillations have been registered on 9 April 2007, at 

10-12 UT at GO Borok. In Fig. 3 we see that the spectrum (left panel) has the pronounced maximum at the 

frequency of 50 mHz. We see also that the spectral analysis does not allow us to detect the effect of 

frequency doubling. In contrast, the application of the synchronous detection method (right panel in Fig. 3) 

leads to conclusion that the oscillations with frequency of 100 mHz are really generated. We believe that this 

is the nonlinear effect of frequency doubling because the spectrum of linear oscillations of the 

magnetosphere is evidently non-equidistant. 

The key innovation here is as follows: By using the method of synchronous detection it has been 

established that the effect of frequency doubling may be clearly detected. Even being small, effect of the 2 nd 

harmonic generation will has important geophysical consequences, e.g., for the development of nonlinear 

hydromagnetic spectroscopy of the space plasma. 

94


5. SUMMARY 

The search for manifestations of anharmonicity of the ULF electromagnetic oscillations has been 

made by using of new methods for analyzing ULF wave data. The main result of this work is that we found 

the experimental evidences of the anharmonicity of magnetospheric oscillations in the Pc3 frequency band. 

Acknowledgments. We would like to thank A.S. Potapov and N.A. Zolotukhina for the valuable discussions. 

The work was supported by RFBR grants 06-05-64143 and 07-05-00696. 

REFERENCES 

Dmitrienko, I.S. (2005), Nonlinear generation of the second harmonic, Geomag. Aeron., 45(2), 168-175. 

Guglielmi, A.V. (2006), Problems of the physics of geoelectromagnetic waves, Phys. Solid Earth , 42(3), 

179-192. 

Guglielmi, A.V. (2007), Ultra-low-frequency electromagnetic waves in the Earth’s crust and 

magnetosphere, Physics – Uspekhi, 50(123), 1197-1216. 

Guglielmi, A.V., B.I. Klain, O.D. Zotov, A.S. Potapov, and N.A. Zolotukhina (2007), Polarization of the 

ULF geoelectromagnetic waves, in: Proc. 10 th International Seminar "Low-frequency wave 

processes in space plasma" (Zvenigorod, 12-16 November 2007), Abstract № 1.9. 

Guglielmi, A.V., and O.D. Zotov (2007), Anharmonicity of ULF oscillations: Detection of the frequency 

doubling, in: Proc. 10 th International Seminar "Low-frequency wave processes in space plasma" 

(Zvenigorod, 12-16 November 2007), Abstract № 2.6. 

Lundin, R., and A. Guglielmi (2006), Ponderomotive forces in Cosmos, Space Sci. Rev., 127(1), 1-116. 

Rankin, R., P. Fricz, V.T. Tikconchuk, J.C. Samson (1994), Nonlinear standing shear Alfven waves in 

the Earth’s magnetosphere, J. Geophys. Res, 99, 21291-21301. 

95


PHOTOMETRIC STUDY OF PULSATING PRECIPITATIONS OF THE 

RING CURRENT ENERGETIC PARTICLES AT LATITUDES OF THE 

OUTER PLASMASPHERE 

I.B. Ievenko, S.G. Parnikov and V.N. Alexeyev 

Yu. G. Shafer Institute of Cosmophysical Research and Aeronomy, Yakutsk, 677980, Russia, 

ievenko@ikfia.ysn.ru 

1. Introduction 

Abstract. Investigation results of a diffuse aurora and stable auroral red arc dynamics based 

on spectrophotometric observations at the Yakutsk meridian (CGMC: 57° N, 199° E) are presented. 

The detailed relationship of the development of pulsating variations of the N2 + band intensity 

to the formation of SAR arc equatorward of the DA boundary is shown. The basic types of the 

particle pulsating precipitation spectra in the frequency region of 0.02-1 Hz are analysed. The delay 

of 0.1-0.5 s in the particle pulsating precipitation development in the latitude interval of ~4 o 

(∆L=0,5-0,7 RE) has been revealed. 

It is known that stable auroral red (SAR) arcs are the consequence of interaction of the outer plasmasphere 

(plasmapause) with energetic ions of the ring current (Rees and Akasofu, 1963; Cole, 1965, 1970; 

Kozyra et al, 1997). The diffuse aurora (DA) is caused by the low-energy electron precipitation from the 

plasma sheet. During substorms we observe the intensity increase of DA and its equatorward extension up to 

the plasmapause projection which is mapped by the SAR arc appearing at that time. (Ievenko, 1999; Ievenko 

et al, 2008). 

It is also known that the precipitation of low-energetic electrons and also energetic neutral atoms (ENA) 

of a ring current can cause the enhancement of the 557,7 and 630,0 nm emission in the nightglow at mid and 

low latitudes during substorms (Rassoul et al., 1993; Ievenko, 1994). Recently DeMajistre et al. (2005) have 

shown the relationship of mid-latitude aurora to the ENA precipitation by data from the IMAGE satellite. 

Ievenko (1995) has established that during the substorm recovery phase the luminosity pulsations in the 

427.8 nm N2 + emission due to the pulsating precipitation of energetic particles are usually observed at SAR 

arc latitudes. This phenomenon unambiguously indicates to the penetration of ring current energetic particles 

into the outer plasmasphere during the substorms. 

Here we present the new data, which confirm and supplement the above mentioned results of spectrophotometric 

observations at the Yakutsk meridian. Three type of the particle pulsating precipitation spectra 

in the frequency region of 0.02-1 Hz are analysed. 

2. Methods and Results of Observations 

The observation of DA and SAR arcs is carried out using the digital meridian-scanning photometer 

(MSP) with two channels of parallel registration of the 630.0 and 557.7 nm [OI] emissions. In order to 

analyze, the MSP data are presented in this work as isophots of the surface brightness of the 557,7 and 

630,0 nm emissions in a projection to the Earth's surface for the luminosity heights of 110 (DA) and 450 

(SAR arc) km, respectively (keograms). The keograms were calculated without taking into account the 

Van Rhijn effect. 

The registration of pulsating variations of the N2 + band intensity (391.4 and 427.8 nm) in the nightglow 

and the diffuse aurora with a high time resolution (sampling frequency of 10-100 Hz) was carried out by 

three wide-angle photometers with fields of view of 20° and frequency characteristic widths of 0-10 Hz. 

Luminosity pulsations were registered at fixed zenith angles 45º S, 0º(Z) and 73º N. The registration of the 

427.8 nm and 630.0 nm emissions intensity in the magnetic zenith was carried out by four channel photometer. 

To determine time intervals when the magnetospheric convection is enhanced, the measurement data of 

the IMF and the solar wind (SW) velocity from the ACE spacecraft are used. Time intervals for a substorm 

expansion phase were identified using magnetograms at the low-latitude stations. Some examples of complex 

analysis of the new data of photometric observations at the Yakutsk meridian are presented below. 

In Fig. 1 the example of observations on February 8, 2000 shows that during the decrease of southward 

IMF BZ at 1530-1630 UT the DA decay in the 557,7 emission in the northern part of sky took place (see 

96


Fig. 2. Study of pulsating variations of the N2 

Fig. 1 a,b). After a sharp southward turn of IMF BZ at 

1654 UT (dawn-dusk EY increase) the brightening 

and equatorward expansion of DA started. The SAR 

arc was formed in the vicinity of DA equatorial 

boundary after the substorm expansion phase onset at 

~1740 UT. Further the SAR arc moved equatorward 

through a zenith of optical observation station (see 

Fig. 1c). A significant increase of the 630.0 nm emission 

intensity in the magnetic zenith of station took 

place during the formation and brightening of SAR 

arc (see the plots in Fig. 1d). From ~1800 UT the zenith 

photometer registered splashes of the 427.8 nm 

emission intensity at SAR arc latitudes. In the 630.0 

nm emission these splashes were not observed. 

e splashes of quasi-harmonic 

puls 

+ 

emissions at the latitudes of diffuse aurora and 

SAR arc during the substorm on February 8, 2000. 

From top to bottom: (a) power spectrum of luminosity 

pulsation in the frequency ragion of 0.2-1 Hz; (b) plots 

of the N2 + emission variations for three registration di- 

Fig. 1. Relationship of the diffuse aurora dynamrections: 73º N, Z and 45º S (see Fig. 1). 

ics to changes of the southward IMF BZ and the 

appearance of SAR arc during the substorm on 

February 8, 2000. 

From top to bottom: (a) variation of the IMF BZ in 

view of the transport time (dТ). (b) and (c) meridianscanning 

photometer data as keograms in 557.7 and 

630.0 nm emissions. In the keogram in the 557.7 nm 

emission the location of view field of photometers for 

the N2 + emissions registration is shown. Z is a zenith 

of observation station. The substorm expansion phase 

onset is identified by the low-latitude magnetograms 

of the Kanoya station (in Figure they are not presented). 

(d) plots of the 427.8 nm and 630.0 nm emissions 

registered in magnetic zenith of the station. In 

the plots a grey column indicates the time interval of 

the observation and spectral analysis of luminosity 

Fig. 2 shows the analysis example of photometric observations of the particle pulsating precipitations on 

February 8, 2000 (see Fig. 1). In Fig. 2 it is seen that the development of luminosity pulsations began at 

∼1745 UT with a maximum in the power spectrum in the frequency ragion of 0.2-0.4 Hz. In this case, the Nphotometer 

registered luminosity pulsations in the region of active DA after the onset of substorm expansion 

phase at 1740 UT. At this time, the development of pulsations at latitudes of the forming SAR arc was registered 

with the Z and S photometers (see Fig. 1). From 1830 to 1840 UT the form and spectrum of luminosity 

pulsations in the zenith and in the south were sharply changed. One can see th 

ations with discrete maxima in the power spectrum at frequencies from 0,4 to 0,8 Hz. These luminosity 

pulsations were developed at latitudes of SAR arc equatorward of DA. 

97


Fig. 3 Diffuse aurora and SAR arc dynamics during 

the enhancement of dawn-dusk SW Ey and substorms 

on February 7, 2000. 

From top to bottom: (a) variation of the EY component of 

SW electric field in view of the transport time (dТ). The 

rest is as in Fig. 1. 

Fig. 4 Analysis of luminosity pulsations in the 

N2 + emissions at the latitudes of diffuse aurora 

and SAR arc during the flaming aurora in N1 on 

February 7, 2000. 

The data are presented as in Fig. 2. 

In Fig. 3 the second example of photometric 

observations shows of the DA and SAR arc dynamics 

during the whole night of February 7, 2000. In 

this event SAR arc was registered from the start of 

optical observations during the recovery phase of 

weak magnetic storm. Equatorward extension of 

DA from northern horizon began during the in- 

crease of SW Ey after the turn of IMF Bz to the south at ~1230 UT. During the expansion phase of first substorm 

the brightening of DA and SAR arc occurred. DA was extended up to polar edge of the SAR arc. The 

speed of SAR arc equatorward shift increased. 

The second substorm caused the brightening of SAR arc in the south and occurrence of the second 

smearing 

red arc (red band) equatorward of DA in the 557.7 nm emission. The increase of the 630.0 nm 

emission intensity was observed in the magnetic zenith during the SAR arc brightening. During this substorm 

a flaming aurora in N1 were visually observed. At this time the zenith photometer registered the intensity 

splashes of the N2 

. It is seen that the dynamic spectra 

of p 

sually occurs during the flaming aurora. 

+ 427.8 nm emission (see Fig. 3d) 

Fig. 4a, b shows the dynamics of the luminosity pulsations in the N2 + emissions at the latitudes of diffuse 

aurora and SAR arc during the flaming aurora in N1 on February 7, 2000 

ulsations in the frequency range of 0.2-1 Hz in N1 (in the flaming aurora) and in the red band region (S) 

equatorward of DA are similar. The spectra are noisy ones with the transient amplification of separate harmonics. 

The amplitude of harmonics in the flaming aurora in N1 approximately is greater by a factor of five 

than the amplitude of harmonics at latitudes of the red band. In the frequency region of 0.02-0.2 Hz (bottom 

panel in Fig. 4a) the increase of pulsation period in time u 

In Fig.5 the third example of photometric observations shows of the DA and SAR arc dynamics on February 

11, 2000 during the convectional activity enhancement without intense substorms. It is seen that during 

98


Fig. 5 Observation of the diffuse aurora and SAR 

arc dynamics on February 11, 2000 during the 

convectional activity enhancement without intense 

substorms. The data are presented as in Fig. 3. 

Fig. 6 Dynamics of luminosity pulsations in the 

N2 + emissions at the latitudes of diffuse aurora 

and SAR arc during the convectional activity 

enhancement on February 11, 2000. 

The data are presented as in Fig. 3. In the bottom 

panel the time interval of correlation analysis of the 

luminosity pulsations is indicated by a gray column. 

a changing dawn-dusk Ey from 1430 UT took place smoothly brightening and equatorward expansion of DA 

in the 557.7 nm emission. The intensification of quasi-stationary activity caused the formation of the redband 

and the short-term SAR arc equatorward of DA and zenith of observation station. In the region of an 

amplified red luminescence at 1630-1900 UT the intensity splashes of the 427.8 nm emission were observed 

in the magnetic zenith (see Fig. 5d). Auroral activity slowly decreased after 1800 UT at a northern IMF Bz. 

Fig. 6 shows the analysis results of luminosity pulsations in the N2 + emissions during observations of DA 

and SAR arc dynamics on February 11, 2000 (see Fig. 5). It is seen that the development of luminosity pulsations 

began at ~ 1630 UT synchronously in three directions. At this time the N- photometer registered the 

pulsations in DA. Simultaneously Z and S-photometers did it at latitudes of a forming SAR arc (see keogrms 

in Fig. 5). Dynamic spectra of the luminosity pulsations in three directions are similar and have discrete 

maxima in the frequency range of 0.05-0.1 Hz. The amplitude of harmonics in the power spectrum of pulsations 

in DA is approximately greater by an order of the amplitude of harmonics at latitudes of the SAR arc. 

3. Discussion 

The analysis of photometric observations submitted above shows a clear manifestation of enhancement 

of the SW dawn-dusk electric field after the turn of the IMF BZ to the south in the equatorward extension of 

DA. The formation and/or brightening of SAR arcs in the three events are most likely connected with a fast 

penetration of energetic particles of a developing ring current into the outer plasmasphere during the sub- 

storm expansion phase or the intensification of quasi-stationary activity as in the third example. The devel- 

99


opm minosity pulsations in the N2 + ent of lu 

emissions at SAR arc latitudes during the recovery phase of sub- 

storms unambiguously 

indicates to the appearance of energetic particles in the plasmasphere. 

Considered 

examples of the photometric observations show three types of the luminosity pulsations in 

the N2 

in DA and at 

SAR 

+ emissions. The general property of pulsating precipitations at SAR arc latitudes in the event on February 

8, 2000 is the occurrence of quasi-periodic pulsation splashes with discrete maxima in the power spectrum 

at frequencies from 0,4 to 0,8 Hz. In (Ievenko et al, 2008) it is supposed that this type of luminosity 

pulsations (pulsating precipitations) is caused by a self-modulation of electron - cyclotron instability on the 

bounce resonance in the cold plasma region of the outer plasmasphere on the basis of Bespalov and 

Trakhtengerts (1985). 

Two next observation examples show the connection between the luminosity pulsations 

arc latitudes. In these events the high similarity degree of pulsation spectra in various regions of the 

subauroral luminosity was observed. 

In Fig. 7 presents the time delay change between different channels of the pulsation registration during 

the flaming aurora on February 7, 2000. The time delay was determined by a function of cross- correlation 

for each minute on the basis of data with sampling frequency of 100 Hz. On the plots one can see the vari 

Fig. 7 Plots of the time delay change between 

different channels of the pulsations registration 

during the flaming aurora on February 7, 

2000. 

Fig. 8 Registration fragment of luminosity pulsations 

in the N2 + emissions for two directions: 73°N and 

45°S on February 11, 2000 (see Fig. 6). 

able time delay of 0.05-0.15 s of the pulsations equatorward of DA relative to the pulsations in the flaming 

aurora region in N1. 

Figure 8 shows the registration fragment of luminosity pulsations in the N2 

for two time intervals are specified. The time delay of the pulsations at 

SAR 

,5in 

these cases can be caused by the propagation of hydromagnetic waves from the region 

+ emissions for two directions: 

73°N and 45°S on February 11, 2000. On the plot of the cross- correlation coefficients and the time delays 

between signals N and S-photometers 

arc latitudes relative to the pulsations in the diffuse aurora region in N1 is equal to 0.3 and 0.5 s with 

the cross correlation coefficients ~0.9 respectively. 

The revealed time delay in the luminosity pulsations development in the latitude interval of ~4 o (∆L=0 

0,7 RE) gives the basis to suppose, that the appearance of pulsating precipitations at latitudes of the SAR arc 

(outer plasmasphere) 

of source (pulsations in the diffuse aurora) inwards the magnetosphere. 

4. Conclusion 

On the basis of detailed analysis of new observation 

data of the DA and SAR arc dynamics dur- 

ing the substorms we summarize as follows. The formation and/or the brightening of SAR arcs in 

the considered events are most likely connected with a fast penetration of energetic particles of a 

developing ring current into the outer plasmasphere during the substorms. The development of luinosity 

pulsations in the N2 iguously indicates to the apergetic 

particles in the plasmasphere. 

that: 

+ m 

emissions at SAR arc latitudes unamb 

pearance of en 

We 

suppose 

in the first case the particle pulsating precipitations at the SAR arc latitudes arise in the outer plasmasphere 

as a result of a self-modulation of cyclotron instability on the bounce resonance; 

100


in events on February 7 and 11, 2000 the particles pulsating precipitations in the outer plasmasphere are 

coupled to the propagation of hydromagnetic waves from the region of source (pulsations in the DA) inwards 

the magnetosphere. 

Acknowledgments. 

The geomagnetic data were provided in WDC C2 for Geomagnetism, Kyoto 

(http://swdcwww.kugi.kyoto-u.ac.jp/index.html). The data on solar wind and IMF were obtained in the ACE 

Science Center (http://www.srl.caltech.edu/ACE/ASC/level2/index.html). 

References 

Bespalov, P.A. and V.Yu. Trakhtengerts (1985), Automodulation of cyclotron instability at bounceresonance. 

Magnetospheric Research. 7, 40-43, IZMIRAN, Moscow, (In Russian). 

Cole, K.D. (1965), Stable auroral red arcs, sinks for energy of Dst Main phase. J.Geophys.Res. 70, 7, 1689- 

1706. 

Cole, K.D. (1970), Magnetospheric processes leading to mid-latitude 

auroras. Annales de Geophysique. 26, 

1, 187-193. 

DeMajistre, R., P.C. Brandt, T.J. Immel, et al. (2005), Storm-time enhancement of mid-latitude ultraviolet 

emissions due to energetic neutral atom precipitation, Geophys. Res. Lett. 32, L15105, 

doi:10.1029/2005GL023059. 

Ievenko, I.B. (1994), Dynamics of diffuse aurora and SAR-arc during substorm. Geomagnetism and Aeron- 

omy. 33, 5, 599-611, (In Russian, English translation). 

Ievenko, I.B. (1995), Substorm-induced pulsed particle precipitations in the SAR arc region. Geomagnetism 

and Aeronomy. 35, 3, 331-338, (In Russian, English translation). 

Ievenko, I.B. (1999), Effects of magnetospheric activity on the plasmasphere as inferred from observations 

of diffuse aurora and SAR arc. Geomagnetism and Aeronomy. 39, 6, 697-703, (In Russian, English 

translation). 

Ievenko I.B., S.G. Parnikov, V.N. Alexeyev (2008), Relationship of the diffuse aurora and SAR arc dynamics 

to substorms and storms Adv. Space Res., Vol. 41/8, pp. 1252-1260, DOI: 10.1016/j.asr.2007.07.030. 

Kozyra, J.U., A.F. Nagy, D.W. Slater (1997), High-altitude energy source(s) for stable auroral red arcs. Reviews 

of Geophysics, 35, 2, 155-190. 

Rassoul, H.K., R.P. Rohrbaugh, B.A. Tinsley, D.W. Slater (1993), Spectrometric and photometric observations 

of low - latitude aurora. J. Geophys. Res. 98, A5, 7695-7709. 

Rees, M.H., S. Akasofu (1963), On the association between subvisual red arcs and Dst (H) decrease. Planet. 

Space Sci. 11, 1, 105-107. 

101


APPLICATION OF RECONSTRUCTION METHOD BASED 

ON TIME-DEPENDENT PETSCHEK-TYPE 

RECONNECTION TO THEMIS DATA 

V. Ivanova 1 , V. Semenov 2 , H. Biernat 1 , S. Kiehas 1 


A-8042 Graz, Austria, e-mai: biglion@inbox.ru; 

2 Institute of Physics, St.Petersburg State University, St.Petersburg, Russia 

Abstract. Remote-sensing method based on 2D time-dependent Petschek-type reconnection model is applied 

to a tailward propagating dual NFTE (nightside flux transfer event) observed by THEMIS B spacecraft 

in the magnetotail on 22 February 2008 around 04:35 UT. The method utilizes magnetic time series as an 

input and provides the reconnection electric field and and the location of X-line as an output. The recovered 

electric field reaches 1.3 mV/m at the maximum. The location of X-line is estimated to be 18–20 Re in the 

tail. 

Introduction 

Recently, a novel remote-sensing technique was introduced (Semenov et al., 2005), which allows to reconstruct 

a time-varying reconnection rate and an X-line location from single spacecraft magnetic data. The technique 

was successfully applied to both: isolated reconnection events in the magnetotail (Ivanova et al., 2007), like 

NFTEs (nightside flux transfer events) or TCRs (traveling compression regions), and composite reconnection 

events consisting of several successive NFTE/TCR-signatures (Ivanova et al., 2008). 

To exploit the reconstruction tool, one needs (1) a record of reconnection-associated bipolar magnetic variations, 

obtained in the tail lobes or, at least, at the plasma sheet periphery/PSBL (plasma sheet boundary layer), 

and (2) an estimate of a propagation velocity of these bipolar structures (needed to convert reconstruction results 

to dimensional values). Up to now the reconstruction method was applied to CLUSTER observations 

only. As it was stated above, the technique itself require single spacecraft measurements. However, use of 

multiple spacecraft, like CLUSTER, has an obvious advantage: propagation velocity of NFTE/TCR-structures 

can be estimated by multi-point timing. 

In this paper we present first application of our method to magnetotail data obtained by THEMIS. We investigate 

a composite reconnection event consisting of two bipolar variations observed by THEMIS B spacecraft 

in the tail on 22 February 2008 around 04:35 UT. A necessary estimate of propagation velocity is obtained by 

tracing a reconnection-associated structure through the sequence of THEMIS spacecraft. 

Reconstruction technique based on time-dependent 

Petschek-type reconnection 

In this section we give a brief description of the reconstruction tool developed on the basis of 2D timedependent 

Petschek-type reconnection model. For technical details we refer the reader to Semenov et al. 

(2005), who developed the reconstruction technique for symmetric configurations (like the magnetotail) in the 

limit of an incompressible plasma, and to Ivanova et al. (2007), who extended it to a compressible plasma and 

configurations with possible asymmetry (like the magnetopause). 

The model of time-dependent Petschek-type reconnection (Heyn and Semenov, 1996) generalizes the classic 

Petschek mechanism for an unsteady regime. The unsteady solution allows to simulate different reconnection 

regimes (impulsive, quasi-stationary, intermittent) and, thus, to investigate dynamics of the reconnection 

process depending on a variable reconnection rate. It also describes the current sheet state after reconnection 

has ceased. 

102


In the frame of this model the reconnection rate (the electric field at the X-line) is prescribed a priori as 

an arbitrary function of time restricted by the causality: E(t) ≡ 0 for t ≤ 0. Local appearance of the electric 

field leads to a decay of the current sheet into a system of MHD discontinuities and shocks (Heyn et al., 1988), 

which form two outflow bulges containing accelerated plasma (Figure 1). Once reconnection ceases (i.e. the 

electric field at the X-line drops to zero), the outflow bulges detach themselves from the reconnection site and 

move in opposite directions along the current sheet. 

The model is analytical and is predicated on a number of simplifying assumptions: (i) the reconnecting 

domains are uniform; (ii) the initial current sheet contains no normal component and is thin enough to be 

approximated by a tangential discontinuity; and (iii) the reconnection electric field is much less than the electric 

field calculated from the background magnetic field and the Alfven velocity E ≪ EA = vAB0/c (Petschek, 

1964). 

Perturbations caused by the moving outflow bulges in the surrounding medium are found from the set of 

compressible ideal MHD equations linearized with respect to the constant background. External perturbations 

(observed outside the bulges) can be written in the form of a convolution integral: 

Bz(t, x, z) = 

�t 

0 

dτKz(τ, x, z)E(t − τ). (1) 

Here E is the reconnection electric field, x and z are the observational coordinates along and normal to the 

current sheet, counted from the reconnection site (X-line). 

The kernel of convolution Kz(τ, x, z) contains information on: (1) medium parameters; (2) waves and 

discontinuities launched by reconnection; and (3) position of observation with respect to X–line. Physically, 

the kernel characterizes the response of the medium to an elementary, delta-shaped pulse of reconnection (Penz 

et al., 2006). 

External perturbations are caused by bending of magnetic field lines around the outflow bulge and, since the 

shape of the bulge depends on the time profile of E(t), they, naturally, reflect all changes in the reconnection 

rate (see equation (1)). For an intermittent electric field consisting of two successive pulses the model predicts 

a dual bipolar Bz-variation and a dual Bx-compression (Figure 2). 

Figure 1: Time-dependent Petschek-type reconnection 

model: Current sheet separating two 

plasma domains with opposite magnetic fields decays 

into a system of MHD discontinuities and 

shocks, which form two outflow bulges propagating 

in opposite directions with the Alfven speed. 

E 

Bz, Δ Bx 

0.1 

0.05 

0 

0 1 2 3 4 5 6 7 8 

0.2 

0.1 

0 

Bx 

Bz 

−0.1 

0 1 2 3 4 

time 

5 6 7 8 

Figure 2: Dual reconnection pulse and the corresponding 

magnetic field perturbations. 

Qualitative agreement between model predictions and spacecraft observations gave rise to an idea of inverting 

the problem. The inverse solution gives the reconnection electric field if magnetic perturbations are known 

(whereas the direct solution defines perturbations for the specified electric field). Indeed, if the magnetic variation 

Bz(t) at some observational point (x, z) is known (from spacecraft measurements), the relation (1) can be 

103


seen as an integral equation for the unknown electric field E(t). Employing a standard method for solving integral 

equations of the convolution type, namely, the method of Laplace transforms, we get a simple relationship 

between Laplace images of the electric field, the Bz-variation, and the convolution kernel: 

E(p) = Bz(p) 

. (2) 

Kz(p) 

Once the position of the spacecraft with respect to the X-line is known, the inverse Laplace transform 

of relation (2) gives E(t). In reality, of course, the relative spacecraft location is not known a priori. To 

find it, a minimization procedure is utilized as follows: A trial spacecraft position (˜x, ˜z) is assumed and the 

corresponding reconnection electric field ˜ E(t) is obtained. Since the trial coordinates are not correct in general, 

the function ˜ E(t) is usually negative on a part of the time interval. However, the real electric field must be 

positive. Therefore, the absolute value | ˜ E(t)| is then inserted into the direct solution to obtain the magnetic 

field variations Bz, Bx. Minimizing the standard deviation between the calculated Bz, Bx and those measured 

by the spacecraft, one can find both, the optimal electric field E(t), and the position of the X-line with respect 

to the spacecraft. 

To wind up the description of the technique, we should emphasize that our method requires magnetic data 

collected outside the disturbing bulge (since it exploits the inverted external solution). The method can be applied 

to isolated reconnection events and to composite reconnection events (consisting of several NFTE/TCRsignatures) 

as well. 

Application to THEMIS event on 22 February 2008, 4:35 UT 

We now apply the technique described above to an NFTE observed by THB spacecraft in the magnetotail 

during a substorm on 22 February 2008 around 4:35 UT. We shall not discuss ground signatures of the substorm, 

noting only that they included Pi2 pulsations at Pine Ridge station, increase of THEMIS AE index to 

200 nT and the aurora intensification at 68◦ magnetic latitude, near the location of THB, C, D, E footpoints 

(Angelopoulos et al., 2008, Supporting Online Material). Here we concentrate on those magnetotail aspects of 

the substorm, which are relevant to our purpose. 

At the time of interest THEMIS spacecraft were located as shown in Figure 3. In accordance with a value 

of the observed Bx–component, probes THB and THC were located in the southern periphery of the plasma 

sheet (BTHB x ∼ −19 nT, BTHC x ∼ −22 nT), whereas THD and THE were situated deep inside the plasma 

sheet, slightly to the north from the neutral sheet (BTHD x ∼ +2 nT, BTHE x ∼ +5 nT). All the probes detected 

substorm–related plasma sheet activity around 4:35 UT. 

Figure 3: Positions of THEMIS spacecraft on 22 February 2008 around 04:35 UT in (x, z) GSE plane. 

At 4:35:16 UT the probe THB detected commencement of a dual bipolar structure with the main negative 

pulse in Bz preceded by the smaller positive pulse (Figure 4, left panel). One can see that (1) change of sign 

of the Bz–variation approximately coincides with the extremum of Bx–variation, and (2) vz–component of 

the ion velocity anticorrelates with Bz–component. These properties are typical for nightside flux transfer 

events (Sergeev et. al., 1992), which are believed to be associated with reconnection in the tail. Interpreting 

104


THB observations in favor of reconnection we may conclude (from the +/− polarity of Bz–variation) that the 

NFTE–bulge was propagating tailward, i.e. the X-line was located Earthward of THB. 

To our opinion, there is an ambiguity in the interpretation of THC observations (Figure 4, middle panel). 

Owing to indistinct character of magnetic field and velocity variations at THC, it is not clear whether the probe 

observed a bipolar Bz–variation of −/+ polarity (stating from 4:33:45) or positive Bz–deflection (stating from 

4:34:20)? In the first case observations would be interpreted as the passage of an Earthward propagating 

bulge, which NFTE–properties (phase shift between Bz and Bx, correlation between Bz and vz) are not wellpronounced. 

In the second case the data from THC may be interpreted as the onset of reconnection inflow 

towards the neutral sheet. Indeed, as one can see, the positive Bz–deflection is accompanied by the northward 

plasma flow. In both cases the X-line should be located tailward of the probe THC and, possibly, very close to 

it (if the second interpretation is right). 

The neighboring probes THD/THE detected similar signatures: transient dipolarization at 4:36:50 and 

Earthward flow up to 600 km/s at maximum (Figure 4, right panel). An interesting thing is that the flow onset 

preceded dipolarization by ∼ 50 s at THD and by ∼ 30 s at THE. Dipolarization (sudden increase of the 

Bz–component) is usually interpreted as arrival of the reconnected flux (carried by the NFTE–bulge). It is 

important to note that the plasma flow speed observed simultaneously with the onset of transient dipolarization 

was ∼ 300 km/s on both spacecraft. 

Figure 4: Observations of THEMIS probes B, C, D on 22 February 2008 around 04:35 UT. 

Since we do not know unambiguously the moment when THC captured the reconnection signal, we can 

not estimate definitely the propagation velocity of the NFTE–bulge: the delay ∆t = 185 s (4:36:50-4:33:45) 

and the distance R = 6.9 Re between THC and THD give the speed of Earthward propagation v ∼ 240 km/s; 

the delay ∆t = 150 s (4:36:50-4:34:20) corresponds to the speed v ∼ 290 km/s. The latter value is congruent 

with the plasma flow (∼ 300 km/s) detected at the dipolarization front and is used a preferable normalization 

unit to convert reconstruction results to dimensional form. 

Three different variants of reconstruction have been tried: (1) using only first pulse (4:35:16 — 4:38:00 

UT), (2) only second pulse (4:38:00 — 4:42:00 UT), and (3) using both pulses as one input (4:35:16 — 4:42:00 

UT). Normalization of THB magnetic data was done with respect to B0 = 19 nT and T0 = 60 s (a typical 

duration of a reconnection pulse). Minimization of the standard deviation with respect to x exhibited existence 

of a well-pronounced minimum (Figure 5). In all three cases the obtained X-line location is nearly the same: 

between -18 and -20 Re (the differences do not exceed the accuracy of the method). The recovered electric 

field consists of two pulses with total duration of ∼ 6 min. The amplitude of the first pulse is ∼ 0.7 mV/m, of 

the second one ∼ 1.3 mV/m. 

105


The reconstructed X-line location is in a good agreement with a primitive timing, based on the capture time 

and positions of THB (tB,xB) and THD (tD,xD): 

(xD − xX) − (xX − xB) = v(tD − tB). 

Here v is the propagation speed of the NFTE–bulge and xX is the GSM coordinate of the reconnection site. 

Varying v from 200 to 1000 km/s and assuming 10 s error of tB and tD, we get the dependence xX(v) shown 

in Figure 6. One can see, the argument v ∼ 300 km/s corresponds to the reconnection site at xX ∼ −18.5 Re. 

StD 

70 

60 

50 

40 

30 

20 

10 

0 

−12 

−14 

−16 

−18 −20 

x [Re] 

X 

Figure 5: Distribution of the standard deviation 

StD as function of X-line location. 


−22 

−24 

−26 

Reconnection Site [Re] 

−17 

−18 

−19 

−20 

−21 

−22 

Reconnection Site 

Lower Boundary 

Upper Boundary 

−23 

200 300 400 500 600 

v [km/s] 

700 800 900 1000 

Figure 6: Dependence of X-line location on propagation 

velocity. 

This work is supported by RFBR grant No. 07–05–00776a, by RFBR/CRDF grant No. 07–05–91109, by the 

Austrian “Fonds zur Förderung der wissenschaftlichen Forschung” under project P20145–N16, and by project 

No. I.12/04 from the “Österreichischer Austauschdienst”. Also acknowledged is support by the Austrian 

Academy of Sciences, “Verwaltungsstelle für Auslandsbeziehungen”. 

References 

Heyn, M., H. Biernat, R. Rijnbeek, and V. Semenov (1988), The structure of reconnection layers, J. Plasma 

Physics, 40, 235–252. 

Heyn, M., and V. Semenov (1996), Rapid reconnection in compressible plasma, Phys. Plasmas, 3, 2725– 

2741. 

Ivanova, V., V. Semenov, T. Penz, I. Ivanov, V. Sergeev, M. Heyn, C. Farrugia, H. Biernat, R. Nakamura, and 

W. Baumjohann (2007), Reconstruction of the reconnection rate from Cluster measurements: Method 

improvements, J. Geophys. Res., 112, A10226, doi:10.1029/2006JA012183. 

Ivanova, V., V. Semenov, I. Ivanov, H. Biernat, and S. Kiehas (2008), Reconstruction of time-varying reconnection 

rate and X-line location, submitted to Ann. Geophys. 

Penz, T., V. Semenov, V. Ivanova, M. Heyn, H. Biernat, and I. Ivanov (2006), Green’s function of compressible 

Petschek–type magnetic reconnection, Phys. Plasmas, 13, 052108. 

Petschek, H. E. (1964), Magnetic field annihilation, in: Physics of solar flares, ed. by W. Hess, NASA 

Spec. Publ., 50, 425–440. 

Semenov, V., T. Penz, V. Ivanova, V. Sergeev, H. Biernat, R. Nakamura, M. Heyn, I. Kubyshkin, I. Ivanov 

(2005), Reconstruction of the reconnection rate from Cluster measurements: First results, J. Geophys. 

Res., 110, A11217, doi:10.1029/2005JA011181. 

Sergeev, V., R. Elphic, F. Mozer, A. Saint–Marc, and J. Sauvaud (1992), A two–satellite study of nightside 

flux transfer events in the plasma sheet, Planet. Space Sci., 40, 1551–1572. 

106


THE METHOD OF THE EXTRACTION OF EQUATORIAL EFFECTS OF 

THIN MAGNETOSPHERE LAYER OF THE EARTH FROM RESULTS OF 

GEOMAGNETIC MEASUREMENTS OF LOW-ORBIT MAGSAT, CHAMP 

SATELLITES 

A.L. Kharitonov 1 , G.A. Fonarev 2 , S.V. Starchenko 1 , G.P. Kharitonova 1 

1 Pushkov Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation of Russian 

Academy of Science, Troitsk, 142190, Russia, e-mail: ahariton@izmiran.ru, 2 Geoelectromagnetic 

Research Center of Integrated Institute of the Earth Physics of Russian Academy of Science, 

Troitsk, 142190, Russia 

Abstract. The activities in the field of differential magnetic measurement from satellites СНАМР and 

МАGSАТ were continued. An apart from of refinement of an anomaly field of sub-sinusoidal 

anomalies presumably connected to a magnetic non-uniformity of a thin magnetosphere layer was 

detected. The differential spatial-temporal magnetic measurements ( DSTM ) aboard MAGSAT 

satellites is alternative for direct gradient methods (DM) of the registration of long-wave variations 

needlessly of satellite spatial measurements (SWARM - satellite). The extraction of magnetic 

anomalies by two methods (with two magnetometers – DM and one magnetometer - DSTM) increases 

confidence to outcomes of the interpretation. The measured with the satellite differential 

magnetic data has allowed to create algorithm for extraction of anomalies connected with thin 

magnetosphere layer. 

Introduction 

One from new methods of extraction of equatorial geomagnetic field effects connected with the thin 

magnetosphere plasma layer at a hum noise of the geomagnetic field connected with the other ionospheremagnetosphere 

and internal sources of the Earth are the methods of differential spatial-temporal magnetic 

(DSTM) analysis. The main magnetic field (Fm) of Earth’s core was previously eliminated from the 

MAGSAT, CHAMP satellite measured geomagnetic field (Fe) data. The residual geomagnetic field (Fr) is 

present in magnetic anomalies of tectonosphere origin (Fa) and variation of a permanent magnetosphereionosphere 

field (Fv). The partial derivative of the geomagnetic field per time from the schedules the vector 

components of the low-orbit satellite MAGSAT, CHAMP was calculated. The extraction of equatorial 

magnetic anomaly effects from the data of the partial derivative of vector component geomagnetic field per 

time is made better, than from the measured geomagnetic field. For extraction from the MAGSAT, CHAMP 

low-orbit satellite geomagnetic data of the equatorial anomaly effects of the magnetosphere thin layer and 

the tectonosphere effects we shall consider the formulas of differential spatial-temporal magnetic (DSTM) 

analysis, from which we leaned at computer calculations. For improving the situation with extraction of 

equatorial anomaly effect of magnetosphere thin layer from a hum noise of the MAGSAT, CHAMP loworbit 

satellite geomagnetic data, the algorithm of high-frequency filter of the Lagrange to values of a 

combinational partial derivative of the geomagnetic field per time was applied. 

The results of activity in the field of differential spatial temporary magnetic (DSTM) measurements 

from MAGSAT, CHAMP satellites are presented. The method of differential spatial-temporal magnetic 

MAGSAT, CHAMP measurements (DSTM) is alternative of the standard horizontal gradient method of the 

registration of variations. The extraction of magnetic anomalies by two gradient methods (with diverse towed 

magnetometers and DSTM) increases confidence to outcomes of the interpretation. 

DSTM Method of processing of the geomagnetic data of “MAGSAT” and “СНАМР” satellite of Earth 

Differential spatial-temporal magnetic (DSTM) analysis with the use of the time partial derivative is 

applied in a broad band of speeds from drifting ice up to satellites. The DSTM essence consists of selection 

of virtual temporary measuring base 

Δt = ϋ ΔL, 

where ϋ - speed of the driven magnetometer, ΔL - section of a path or virtual spatial measuring base. It is 

necessary, that during Δt one from increments Fa or Fv was less sensitivity of the magnetometer (έ). Fa and 

Fv - accordingly one from the component of magnetic anomaly field in driven coordinate system and 

magnetic variation. Then Fa or Fv will be absent on a differential curve. At Δt


data of the towed installation with diverse in space by magnetometers [Fonarev et al., 1997]. In case of 

MAGSAT, CHAMP satellite magnetic measurement surveys of such capability is not present. However, in 

case of satellite magnetic surveys on the recurring orbits with very close coordinates, is possible that also 

allows successfully use the DSTM method. In the solution of this problem the large help can be rendered by 

reliable satellite magnetic measurements by vehicles “МАGSАТ” and “СНАМР” [Rotanova et al., 2004; 

Rotanova et al., 2005]. The doubtless virtue of satellite surveys consists of speed of realization of magnetic 

measurements in huge territories that saves to correct of errors connected with the changes of the secular 

variation of the geomagnetic field. But thus, observed geomagnetic field from “СНАМР”, “MAGSAT” 

artificial satellites of the Earth (ASE) is total reflection of various determined and random physical processes 

and appearances happening in various layers of the Earth. By one from methods of separation of a magnetic 

field of the Earth is a method of differential magnetic measurement. 

The “СНАМР” or “MAGSAT” satellite survey of the geomagnetic field in considered temporary 

period, it can be presented as a sum of “constant” and “permanent” fields stipulated by sources, located both 

inside the Earth, and outside of boundaries of the hard Earth (magnetosphere sources) [Kharitonov et al., 

2005]. It is possible to consider study spatial-temporary structures of the geomagnetic field (Fs), measured 

aboard satellites [Rotanova et al., 1999, Tsvetkov et al., 2004] as a sum of vectors of several components of 

geomagnetic field: 

Fs(ϕ, λ, h, t) = Fm(ϕ, λ, h, t) + Fa(ϕ, λ, h, t) + Fv(ϕ, λ, h, t), (1) 

where Fm – the component of vector of an induction of the main geomagnetic field stipulated by sources in 

the core of the Earth; Fa – the component of vector of an induction of the geomagnetic field stipulated by 

heterogeneities of mantle of the Earth; Fv - component of vector of an induction of the permanent 

geomagnetic field stipulated by sources external magnetosphere origin and irregular earthquake signals; ϕ, 

λ, h, t – geographic latitude, longitude, altitude and time of measurement point. 

Usually for the description of a main geomagnetic field is used the spherical harmonic series of the 

Gauss. For calculations the model of the main geomagnetic field with the length of a series equal to 13 

harmonics developed [Bondar et al., 2000]. For the analysis of a spatial structure of the geomagnetic field 

conducted mathematical processing and interpretation along 100 orbits ASE “СНАМР” covering territory 

from 0 up to 60 degrees of east longitude and within the limits of geographical altitudes from + 60 up to - 60 

degrees [Rotanova et al., 2005]. 

Thus, the difference fields for each from selected of hundred orbits was calculated. The obtained 

thus difference fields are stipulated external magnetosphere current systems and internal sources of the 

Earth: by a magnetization at the Earth’s crust, electromagnetic heterogeneities in the mantle of the Earth, is 

present small component, connected with accidental errors of measurements. 

One from methods of allocation of a magnetic field connected with the interned Earth’s mantle 

heterogeneities of researched regions at a hum noise of the field connected with external solarmagnetosphere 

sources and earthquakes too are the methods differential magnetic investigations [Fonarev et 

al., 1997; Fonarev, 2005, Kharitonov et al., 2005; Tsvetkov et al., 2004]. As, was shown above, from the 

satellite measured data the main magnetic field (Fs) was previously eliminated. The residual field is present 

in regional magnetic anomalies of mantle origin (Fa) and variation of a variable magnetic field (Fv). In the 

schedule of change of values of the module (Ba), the vertical component (Za), the east component (Ya) of the 

incremental geomagnetic field, northern component (Xa) of the incremental geomagnetic field is shown, 

which a visible, that in all components of an incremental geomagnetic field is very complex on a hum noise 

of anomalies. For extraction from the satellite magnetic data of the anomalies of the external origin and the 

earthquake signals we shall consider the formulas differential magnetic investigations, from which we leaned 

at computer calculations [Fonarev et al., 1997; Fonarev, 2005; Kharitonov et al., 2005; Kharitonov et al., 

2006]. If the satellite is gone rectilinearly along an axis Х with the speed ϋ, the magnetometer installed on 

board of satellite, through a slice of time equal Δt = 1 s can calculate through expression 

F(ϕ, λ, h, t) = Fs(ϕ, λ, h, t) [exp(- i w Δt) – 1] exp(- i w t), (2) 

where Fs - component of vector of an induction, w = (2π / T) - circular frequency of the measured field. 

It is possible to determine of slice of times Δtv and Δtа, at which difference of the residual 

geomagnetic field under the data of the satellite СНАМР Fv and Fa will be less sensitivity of the 

magnetometer (έ) installed on board this satellite, from the formula (3). 

Δtv < ε / (Wv Fv), Δtа < ε / (Wа Fа) (3) 

However, there is one limitation of the given DSTM method, when it is impossible to divide variations of the 

variable geomagnetic field called by sources of the external origin and earthquake signals and measured on 

band of the satellite by anomalies of the “constant” field, created by sources in the lithosphere of the Earth. 

Wа Fa = Wv Fv (4) 

108


The virtual spatial measuring base (ΔL) of a DSTM method for the satellite with the magnetometer will be 

on board is determined from the following formula 

ΔL = υ Δt , (5) 

where ϋ – the speed of motion of a satellite in the orbit of the Earth. 

Horizontal size (L) of a large internal magnetic anomaly in a projection to an earth surface make 

about 1000 km from the data of CHAMP satellite. Then the temporary period (Т) internal magnetic anomaly 

will make about 125 s from formula (6). 

Т = L / ϋ (6) 

The inequalities (3) determine working intervals of a DSTM method of processing of the satellite 

data. It is known, that the sensitivity (έ) of the component magnetometer installed on board a satellite 

СНАМР makes approximately 0.1 nT. It is known also, that the amplitude of diurnal variations of 

geomagnetic activity even of a perturbed variable magnetic field of mean and lower altitudes, as for 

example, at the observatory Moscow, makes about Fv = 30 nT. Then because of set forth above data it is 

easy to calculate values Δta and Δtv. The outcomes of calculations for a various component (Bav, Zav, Yav, 

Xav) partial derivative of the geomagnetic field per time are analysed. Though the Kursk magnetic anomaly 

is already looked through in some components, but the high-frequency filter of the Lagrange was applied for 

the best filtration of noise. It is justified, as at Δt = 1 s. The condition Sin (w Δt)


Fig. 2. The sharp changes DSTM values in DAWN pass № 14 of MAGSAT satellite (between max values in 

latitude from ~ +1 0 to ~ +12 0 , longitude = 115 0 .8 E) are connected with the effect of thin magnetosphere 

layer of 02.11.1979, UT = 22h 38 m in the geomagnetic equator region. The horizontal axis is the 

geographical latitude in degree and vertical axis is the partial derivative of geomagnetic field value. 

Conclusions 

1. All components of the geomagnetic field X, Y, Z, B, measured aboard MAGSAT, CHAMP satellites 

hardly noised from sources of the variable geomagnetic field of the internal origin and consequently is 

scarlet are informative at extraction anomalies of thin magnetosphere plasma layer. 

2. All components of the partial derivative of the geomagnetic field on time (DSTM) from the data of a 

satellite MAGSAT, СНАМР select anomalies connected with thin magnetosphere layer better, than simply 

from values of the magnetic anomaly field. 

3. The application of high-frequency filters of the Lagrange of a combinational partial derivative of the 

geomagnetic field on time (DSTM), from the data of a satellite СНАМР gives the most good outcomes at 

extraction of a field connected with sources external magnetosphere origin (thin magnetosphere layer) on a 

hum noise of a variable field of internal origin. 

The activity is executed by support of Russian Foundation of the Basic Research grant № 07- 

05-90006 Вьет_a. 

References 

Bondar, T.N., I.A. Burdelnaja, V.P. Golovkov, T.I. Zvereva (2000), Main geomagnetic field model and 

space-time structure of external, internal and induced geomagnetic variations derived from 

satellite magnetic survey, Proc. 3-rd Intern. Science Team Meeting, Grasse, France. 

Rotanova, N.M., A.L.Kharitonov, A.Kh.Frunze and S.V.Filippov, D.Yu.Abramova (2005), Magnetic 

anomaly fields from CHAMP satellite measurements over Kursk magnetic anomaly territory, 

Geomagnetism and Aeronomy, 45, 5, 712-719. 

Serkerov, S.А., E.I.Kuldeev (2005), Determination of density of rocks of an intermediate layer with 

application of an interpolation polynomial of the Lagrange, Informations of high schools. 

Petroleum and gas, 3, 22-30. 

Fonarev, G.А. (2005), Gradient measurements with the driven magnetometer, Geomagnetism and 

Aeronomy, 45, 4, 576-579. 

Kharitonov, А.L., G.A.Fonarev, L. Eppelbaum, P.V. Kishcha (2005), Use differential satellite 

110


magnetometry for separation of the fields external (solar) and internal origin, Proc. of Russian 

conference " Experimental and theoretical researches of the bases of forecasting helio geophysic 

activity ", Troitsk, 335-340. 

Tsvetkov, Yu.P., N.M.Rotanova, A.L.Kharitonov (2004), Structure of magnetic anomalies on gradient to 

measurements in a stratosphere, Geomagnetism and Aeronomy, 44, 3, 412-418. 

Kharitonov, A.L., G.A.Fonarev, G.P.Kharitonova, S.A.Serkerov (2006), Structure of deep 

heterogeneities of the mantle from the satellite magnetic and gravity data, Abstracts of 10-th 

Symposium on Study of the Earth's Deep Interior (SEDI-2006), Prague, 16. 

Rotanova, N.M., A.L. Kharitonov, A.Kh. Frunze (2004), Anomaly crust field from satellite 

measurements: their processing and interpretation, Annals of Geophysics, 47, 1, 179-190. 

Fonarev, G.A., V.S. Shneyer, S.P.Gaidash (1997), Marine magnetic survey (MMS) and geomagnetic 

variations, Abstracts of the International Conf. on Marine Electromagnetics, London, 7. 

111


RECONNECTION–ASSOCIATED ENERGY TRANSFER 

S. A. Kiehas 1 , V. S. Semenov 2 , N. N. Volkonskaya 2 , V. V. Ivanova 1 , H. K. 

Biernat 1,3 


8042 Graz, Austria, e–mail: stefan.kiehas@oeaw.ac.at; 

2 Institute of Physics, St.Petersburg State University, St.Petersburg, Russia 

3 Institute of Physics,University Graz, 8010 Graz, Austria 

Abstract. Magnetic reconnection leads to well-known features which can be observed in the Earth’s 

magnetosphere, such as flux transfer events (FTEs), bursty bulk flows (BBFs) or traveling compression 

regions (TCRs). The compression of the magnetic fields due to the appearance of a plasma bulge can 

be observed in the form of a compression region, traveling together with the plasma flow regions. Also 

these regions carry energy. In this work we investigate the kinetic energy output of the reconnection 

process as well as the magntic energy appearing inside TCRs. For this purpose, we use a time-dependent 

analytical Petschek model of magnetic reconnection and investigate the spatial and temporal distribution 

of the energy due to the reconnection process. We apply this method to a substorm event on September 

19th, 2001, examining Cluster data. As input parameter, disturbances in Bz, associated with the appearance 

of six TCRs during this substorm, are used in order to determine the energy transport by these 

TCRs. 


Besides the change in the magnetic field line topology, the conversion of magnetic field energy into kinetic 

plasma energy is one of the most crucial results of the reconnection process. The reconnection 

model proposed by Petschek (1964) describes reconnection as steady–state process with a temporally constant 

reconnection electric field and standing shocks. Since processes in nature appear to be impulsive 

and non–stationary, Semenov et al. (1984) and Biernat et al. (1987) extended the Petschek model to 

a time–dependent description of magnetic reconnection by implementing a varying reconnection electric 

field which first builds up and finally drops to zero again. This leads to the formation of enclosed outflow 

regions (OR), bounded by shocks. The magnetic field lines from both sides of the current sheet are 

connected via these shocks. After reconnection ceased, i.e., the reconnection electric field vanished, the 

outflow regions detach from the initial reconnection site and propagate in opposite directions along the 

current sheet as shown in Figure 1. Since these regions contain accelerated plasma and are associated with 

the reconnected field lines, they act as transporter of mass, reconnected magnetic flux and energy. Due to 

Figure 1: Sketch of the plasma outflow regions (OR) and the magnetic field lines configuration due to 

reconnection. 

112


the reconnection process, the magnetic field line density in the wake of the outflow regions is rarefied and 

above and beneath these regions it is enhanced. This compression region of magnetic field lines above and 

beneath the plasma flow regions was identified as “traveling compression region” (TCR) for magnetotail 

applications (Slavin et al., 1984). The first interpretation of TCRs was associated with the appearance 

of a traveling bulge in the magnetotail plasma sheet, causing the lobe magnetic field compression. The 

plasma bulge can be seen as plasma outflow region due to tail reconnection. This relation with magnetotail 

reconnection in the course of magnetic substorms is confirmed due to the observation of TCRs following 

substorm onset or intensification (Slavin et al., 1993). 

In the following we investigate the energy budget of the reconnection process based on a 2D time– 

dependent reconnection model for incompressible plasmas and take advantage of Cluster observations 

of a series of six TCRs in order to apply theoretical results to the energy transport associated with TCRs. 

2 The energy inside the outflow region 

Neglecting first order effects, the plasma with densityρis accelerated to Alfvénic speed vA due to the 

reconnection mechanism, and thus, the kinetic energy of this plasma, which is captured inside the OR, is 

given as 

W uhp 

k 

1 

= 

2 ρ v2 � 

A dV, 

OR 

where we consider only the OR in the upper half plane (uhp), due to a later comparison with the associated 

compression region above this OR. All equations appear in cgs units. 

The integral over the OR can be found by integrating along the shock surface, which is given as (Biernat 

et al., 1987), 

f (t, x)= c 

x Er 

vA B0 

� 

t− x 

vA 

� 

, (1) 

with c, vA, B0 and Er as speed of light, Alfvén velocity, background magnetic field, and reconnection 

electric field, respectively. x denotes the distance to the initial reconnection site and t=0 refers to the start 

of the reconnection process. Thus, the kinetic energy inside the OR per unit length of the reconnection line 

appears as 

W uhp 

k 

� vAt 

cρvA 

= x E (t− x/vA) dx. (2) 

2B0 0 

With the magnetic flux as F(τ)= � E(τ) dτ and by introducing the function G(τ)= � F(τ) dτ (see also 

Semenov et al., 2004), we find for t≫1, 

W uhp 

k 

= c vA B0 

8π 

t F0, (3) 

with F0 as the total amount of reconnected flux produced during the reconnection process. 

The change of the magnetic energy in the outflow region is given for t≫1 (Semenov et al., 2000), 

OR, uhp 

∆WB =− c vA B0 

t F0. (4) 

8π 

Comparing Equations (3) and (4) shows that the decrease in the magnetic field energy corresponds 

to the kinetic energy of the plasma, i.e., magnetic energy is converted into kinetic plasma energy, which 

simply represents the conservation of energy densities. 

3 The energy above the outflow region 

Due to the appearance of the plasma outflow region, the magnetic field in the region above the outflow 

regions gets disturbed, i.e., the magnetic field density in this region is enhanced. With the initial background 

magnetic field exhibiting only an x–component, the magnetic field in the compression regions B1 exhibits in 

a 2D configuration a component in x in the form Bx=B0+B (1) 

x and in z, Bz=B (1) 

z , where B0 corresponds to 

the background magnetic field and B (1) 

x,z to disturbances in the magnetic field due to compression region. The 

113


additional magnetic field energy in the compression region appears with the vector potential A=(0, A, 0) 

of the form B=∇×A, as 

WB= B0 

� 

A|z0dx. 4π 

(5) 

The magnetic vector potential can be written in the form of an integral over Bz, 

A|z0 = 

� 

With the boundary condition of the magnetic field (Semenov et al., 2004), 

Equations (5)–(7) give for t≫0, 

B (1) c 

|z0 z = 

vA 

� 

2E 

� 

t− x 

B (1) 

z |z0dx. (6) 

vA 

� 

− x 

E 

vA 

′ 

� 

t− x 

vA 

�� 

, (7) 

W TCR 

B = c vA B0 

t F0. (8) 

4π 

A comparison of the the magnetic energy inside the TCR, i.e., above the OR from Equation (8) with the 

amount of kinetic energy inside the OR from Equation (3) shows that the amount of magnetic energy inside 

the TCR is two times bigger than the kinetic energy of the plasma. This means that the reconnection process 

leads not only to a conversion of magnetic energy into kinetic plasma energy, but also to a redistribution 

of magnetic energy, leading to regions of enhanced magnetic field energy and this magnetic field energy is 

bigger than the kinetic energy of the plasma. 

4 Application to a series of six TCRs 

On September 19th, 2001, Cluster with a barycenter position at (X, Y, Z) = (−18.6, 5.3, 0.35) detected 

a series of six TCRs in the Earth’s magnetotail between 20:57:18 UT and 21:55:10 UT. The associated 

substorm is discussed in detail in Borälv et al. (2005). The Cluster s/c were located in the lobe region 

during the time of interest (interrupted by several excursions into the plasmasheet). Five of these TCRs 

exhibited a south–to–north reversal in Bz, indicating an earthward propagation of these TCRs (the first 

TCR is shown in Figure 2), whereas one TCR (the fourth one) was moving tailward, manifested in the 

north–to–south turning in Bz. This is also confirmed by time–of–flight (TOF) analysis performed by Slavin 

et al. (2003), leading to propagation speeds of the earthward propagating TCRs of about 400 to 600 km/s 

and about 260 km/s for the tailward propagating TCR. 

An interesting feature can be found for the second and third TCR. The magnetic field observations (Figure 

Bz 

2 

1.5 

1 

0.5 

0 

−0.5 

−1 

20:54:02 20:57:02 21:00:02 21:03:02 21:06:02 

time (UT) 

Figure 2: First TCR: Detrended Bz data observed by Cluster spacecraft during 20:54:02 and 21:07:02 UT. 

The typical bipolar signature is visible for all spacecraft. 

114


B [nT] 

Bx [nT] 

By [nT] 

Bz [nT] 

35 

30 

25 

20 

−20 

−25 

−30 

−35 

10 

0 

−10 

10 

0 

−10 

21:08:02 21:09:02 

time (UT) 

21:10:02 

Figure 3: Second TCR: Total magnetic field B, and Bx, By, and Bz for the second TCR. The different 

behavior of C1 (black), C2 (red), C4 (blue) data on the one hand and C3 (green) data on the other hand is 

due to the location of the first mentioned spacecraft inside the plasma bulge and C3 outside. 

3) give rise to the assumption that only C3 was located in the lobe, whereas all other s/c were swept over by 

the plasma bulge. The plasma density and energy flux spectrograms form C1 and C3 (not shown) confirm 

this result, since C1 detects enhanced plasma density and high–energy ions during the appearance of the 

second and third TCR, but C3 detects mainly lobe–like plasma properties. Since we need observations of 

the magnetic field outside the OR, we can only use observations made by C3 for the second and third TCR 

(shown in Figure 4). 

With the relation B (1) 

z = ∂A 

∂x and dx=vAdt, we find a relation between the magnetic field energy and the 

Bz disturbance from Equation (5), 

WB= vA 2 B0 

4π 

� � 

B (1) 

|z0 z dt dt. (9) 

Hence, we use observations from Cluster spacecraft outside the plasma flow regions to determine the 

amount of magnetic energy inside the TCRs. The kinetic energy of the plasma inside the outflow region 

can be calculated via � 2 ρv 

Wk= dV. (10) 

2 

With a typical particle density inside the plasma sheet of n=0.5 cm −3 , and the hydrogen ions as main 

contributors to the plasma sheet population, the densityρcan be found to beρ=8.5·10 −25 g/cm 3 . The 

velocity of the TCR, obtained via TOF analysis from Slavin et al. (2003) can be seen as average bulk flow 

velocity of the plasma in the underlying outflow region, since the TCR propagates together with the plasma 

bulge. We approximate the shape of the outflow region as that of an ellipse, which gives an area of 

A=π a b, 

115


Bx 

Bz 

−26 

−28 

−30 

−32 

−34 

4 

2 

0 

−2 

21:18:02 21:20:02 21:22:02 21:24:02 21:26:02 21:28:02 

time (UT) 

Figure 4: Third TCR: Bx and Bz observed by C3. The increase in|Bx| at 21:23:34 UT indicates a TCR and 

is consistent with the variation in Bz. 

with a and b as semi–major and semi–minor axis, corresponding to the half x– and half z–elongation of 

the outflow region, respectively. For calculating the kinetic energy, we use half of this area, since we 

compare the kinetic and magnetic energies for one lobe–hemisphere. According to Slavin et al. (2003), 

the z–elongation can be approximated for the second and third TCR as 0.5 RE, and we assume a similar 

z–elongation for the other TCRs as well. 

The elongation in x–direction can be found as x=vAT, with vA as propagation speed of the plasma and T as 

the duration of the reconnection pulse. The calculations are based upon our two–dimensional reconnection 

model. Therefore, the calculations are done per unit length of the reconnection line. Thus, the volume of 

the outflow region is approximated to be V= 2.55 RE 3 . 

We have to exclude the fifth (tailward) TCR since the Bz signal is not clearly identifiable (see Kiehas et al., 

submitted). The results are shown in Table 1. 

TCR1 TCR2 TCR3 TCR4 TCR6 

Wk 2.4·10 10 2.4·10 10 7.1·10 10 1.8·10 10 2.4·10 10 

WB from C1 5.9·10 10 n/a n/a 3.6·10 10 6.6·10 10 

WB from C2 7.8·10 10 n/a n/a 5.2·10 10 n/a 

WB from C3 2.4·10 10 2.8·10 10 7.9·10 9 4·10 10 5.4·10 10 

WB from C4 7.4·10 10 n/a n/a 4.5·10 10 5.14·10 10 

Average WB from C1–C4 5.9·10 10 2.8·10 10 7.9·10 9 4.3·10 10 5.7·10 10 

WB/Wk 2.4 1.1 0.1 2.4 2.4 

Table 1: Kinetic energy Wk inside the TCR–associated outflow regions calculated from Equation (10) 

and magnetic energy WB inside the investigated TCRs as calculated from Equation (9) for each Cluster 

spacecraft C1–C4. For the second and third TCR only C3 observed a TCR, all other spacecraft engulfed 

the plasma flow region. The same situation appears for the fifth TCR where C2 was inside the plasma flow. 

All values are given per unit length of the reconnection line. The last line gives the ratio between WB and 

Wk of the five earthward TCRs. 

5 Conclusions 

We have shown that reconnection leads not only to the acceleration of plasma and thus, to the transport 

of kinetic plasma energy, but also to the transport of magnetic energy inside the regions of compressed 

magnetic field lines above and beneath the plasma outflow regions, i.e., inside TCRs. These TCRs prop- 

116


agate together with the plasma OR and hence, magnetic energy is removed from the initial reconnection 

site and transported along the current sheet. The amount of this magnetic energy is two times bigger than 

the kinetic energy inside the OR. This result is verified by an investigation of a series of TCRs, where the 

amount of magnetic energy is in the order of 10 10 Joule per length unit of the reconnection line. 


This work is supported by the Austrian “Fonds zur Förderung der wissenschaftlichen Forschung” under 

project P20341-N16 and by the Russian Foundation for Basic Research under grant number RFBR 07- 

05-00776a. Also acknowledged is support by the Austrian Academy of Sciences, “Verwaltungsstelle für 

Auslandsbeziehungen”. S.K. acknowledges financial support from the University Graz in form of a science 

support sponsorship (“Förderungsstipendium”). 

References 

Borälv, E., H. J. Opgenoorth, K. Kauristie, M. Lester, J.–M. Bosqued, J. P. Dewhurst, C. J. Owen, M. 

Dunlop, J. A. Slavin, A. Fazakerley, and C. Perry (2005), Correlation between ground-based observations 

of substorm signatures and magnetotail dynamics, Ann. Geophys., 23, 997–1011. 

Biernat, H. K., M. F. Heyn, and V. S. Semenov (1987), Unsteady Petschek reconnection, J. Geophys. 

Res., 92, 3392–3396. 

Kiehas, S. A., V. S. Semenov, H. K. Biernat, V. V. Ivanova, R. Nakamura, W. Baumjohann (submitted), 

Estimating the magnetic energy inside traveling compression regions, Ann. Geophys. 

Petschek, H. E. (1964), Magnetic field annihilation, in: Physics of solar flares, ed. by W. Hess, NASA 

Spec. Publ., 50, 425–440. 

Semenov, V. S., I. V. Kubyshkin, M. F. Heyn, and H. K. Biernat (1984), Temporal evolution of the 

convective plasma flow during a reconnection process, Adv. Space Res., 4, 471–474. 

Semenov, V. S., N. N. Volkonskaya, and H. K. Biernat (2000), Energy balance during bursty reconnection, 

Adv. Space Res., 26, 561–564. 

Semenov, V. S., I. V. Kubyshkin, R. P. Rijnbeek, and H. K. Biernat (2004), Analytical theory of unsteady 

Petschek–type reconnection, in Physics of Magnetic Reconnection in High–Temperature Plasmas, 

ed.: M. Ugai, 35–68, Research Signpost, Trivandrum, India. 

Slavin, J. A., E. J. Smith, B. T. Tsurutani, D. G. Sibeck, H. J. Singer, D. N. Baker, J. T. Gosling, E. W. 

Hones, and F. L. Scarf (1984), Substorm associated traveling compression regions in the distant tail 

– ISEE–3 geotail observations, Geophys. Res. Lett. 11, 657–660. 

Slavin, J. A., M. F. Smith, E. L. Mazur, D. N. Baker, E. W. Hones Jr., T. Iyemori, and E. W. Greenstadt 

(1993), ISEE 3 observations of traveling compression regions in the Earth’s magnetotail, J. Geophys. 

Res., 98, 15,425–15,446. 

Slavin, J. A., C. J. Owen, M. W. Dunlop, E. Borälv, M. B. Moldwin, D. G. Sibeck, E. Tanskanen, M. L. 

Goldstein, A. Fazakerley, A. Balogh, E. Lucek, I. Richter, H. Réme, J. M. Bosqued (2003), Cluster 

four spacecraft measurements of small traveling compression regions in the near-tail, Geophys. Res. 

Lett., 30, doi:10.1029/2003GL018438. 

117


MODULATION OF THE RIOMETER ABSORPTION AND WTISTLER- 

MODE CHORUS BY Pc5 GEOMAGNETIC PULSATIONS EXCITED BY 

THE SOLAR WIND PRESSURE OSCILLATIONS 

N. G. Kleimenova 1,2 , O. V. Kozyreva 1 , J. Manninen 3 , T. Turunen 3 

1 Institute of the Earth Physics, Moscow, Russia, e-mail: kleimen@ifz.ru; 2 Space Research 

Institute, Moscow, Russia; 3 Sodankylä Geophysical Observatory, Sodankylä, Finland 

Abstract. The case study (November 24, 2006) of simultaneous multi-points 

Scandinavian observations of pulsating energetic electron precipitation (riometer absorption), 

Pc5 range ULF geomagnetic pulsations as well as the burst of morning whistler-mode chorus 

emissions have been analysed and compared with the solar wind conditions. It was found that 

during the VLF chorus burst development (04-05 UT) there were observed two stable maxima 

(near 2 mHz and at 3-4 mHz) in geomagnetic pulsations spectra, however, the riometer 

pulsations spectra were time dependent. In the first half-hour interval, the maximum of 

pulsating riometer absorption coincided with 3-4 mHz geomagnetic pulsation maximum, but 

in the following half-hour interval - with 2 mHz ULF maximum. The spectra of the chorus 

intensity variations were relatively similar to the riometer ones. In the first discussed time 

interval, the solar wind dynamic pressure variations were turbulent in the large frequency 

range of ~1.5 – 4.0 mHz. However, in the second interval they demonstrated the quasimonochromatic 

oscillations with the clear maximum at 2.0 mHz. The same maximum was 

observed in the riometer and geomagnetic pulsation, and in VLF chorus total intensity 

variations. We interpret that as the VLF wave grow rate modulation by the compressional Pc5 

ULF waves exiting in the magnetosphere due to solar wind pressure oscillations. We conclude 

that the Pc5 pulsations can involve the simultaneous compression waves at one frequency and 

the transverse waves (FLR) at another frequency. 

Introduction 

Ground-based geomagnetic pulsations in the Pc5 frequency band (1.7 - 6.7 mHz) are typical morning 

phenomenon at auroral and subauroral latitudes. The most part of these Pc5 pulsations may be attributed to 

the field line resonance (FLR) [e.g., the extensive revue of Baker et al., 2003]. In the FLR model, 

compressional mode magnetic waves, generated by Kelvin-Helmholtz instabilities at the magnetopause, 

propagate through the magnetosphere and couple into transverse magnetic standing waves (FLR) on closed 

magnetic field lines. The cavity mode model provides a mechanism to convert these broadband 

compressional waves into monochromatic waves with the cavity eigenfrequency observed on the ground. 

Pc5 pulsations may be separated into field line resonances (FLR) and non-field line resonances (non-FLR) 

as identified by Baker et al. (2003). 

A number of ground-based and satellite observational and theoretical studies have been documented the 

particle flux modulation causing by Pc5 magnetic pulsations [e.g., Kokobun et al., 1977; Kleimenova et al., 

1997; 2005; Spanswick et al., 2005; Sarris et al., 2007]. In spite of a large body of research, the 

sophisticated treatment of the spectral features of such modulation is not being up to now performed. 

In this paper we present the results of the spectral analysis of the event of simultaneous multi-points 

ground-based observations of the Pc5-range ULF geomagnetic pulsations, pulsating energetic electron 

precipitation (riometer absorption) and the whistler-mode chorus, recorded in Scandinavia on November 24, 

2006. These data were compared with fluctuations in the solar wind and IMF. 

Observations 

In our analysis we used the ground-based 10 s sampled magnetometer data from several IMAGE 

stations located along the geomagnetic meridian of ~107-110º. The station codes and the corrected 

geomagnetic latitudes of each given station are indicated in all Figures. Beside the magnetic data we study 

the 10 s sampled 40 MHz riometer data which provide a simple means of monitoring the energetic (energy 

> 30 keV) electron precipitation via measurements of the cosmic radio noise absorption (CNA). The 

observations of VLF chorus have been carried out at Kannuslehto (KAN) station, located near SOD 

observatory. 

For our analysis we selected the event on November 24, 2006 (Fig. 1) because at this time the Pc5 

geomagnetic pulsations, pulsating CNA and the intense burst of the whistler-mode chorus were observed 

118


simultaneously in the local morning (~04-06 UT). The strong (up to 3.5 dB) riometer absorption at ~06-08 

UT resulted the chorus emission damping in the disturbed ionosphere. 

Fig. 1 The VLF chorus dynamic spectrum (top 

panel), riometer data (middle panel) and Xcomponent 

of magnetic field variations 

Fig. 2 Riometer and magnetometer data at IVA 

(red) and SOD (blue) stations 

The magnetic substorm with amplitude about 

250 nT was observed at ~02-04 UT and the 

energetic electron injection, preceded the chorus 

burst, was recorded by geostationary LANL 

satellites (not shown here). The riometer 

absorption variations and geomagnetic pulsations 

at IVA and SOD stations are show in Fig. 2 

extendedly. The riometer absorption at IVA was stronger than at SOD, located no more than 1º southward. 

One can see a good correlation between the amplitude of riometer and magnetic pulsations. 

A visible correlation between large scale (several minutes duration) chorus patches and maxima of 

pulsating riometer absorption at SOD is seen in Fig. 3. 

The amplitude dynamic spectra of magnetometer and riometers data, calculated by applying 15 min 

window, are presented in Fig. 4. One can see two bursts of pulsating particle precipitation which was much 

stronger at ABI than at IVA. These stations are located at the similar geomagnetic latitudes but IVA located 

about 7.0º to the East from ABI. The first burst with maximum between 3 and 4 mHz was observed around 

04 UT and the second one with maximum between 2 and 3 mHz – around 05 UT. Based on that, we divided 

the considered interval 04-05 UT into two half-hour parts: 0400-0430 UT and 0430-0500 UT. The dynamic 

spectra of geomagnetic pulsations manifested also two different wave bursts at all stations around 04 UT 

and 05 UT. 

The amplitude spectra of the oscillations in 

the IMF and solar wind dynamic pressure 

(arbitrary units) as well as Pc5 geomagnetic 

pulsations and pulsating riometer absorption 

over both time intervals are given in Fig. 5. 

There was a significant difference between the 

intensity of the magnetic pulsations at the 

stations, located at higher latitudes (SOR, KEV, 

IVA, SOD), and the stations, located at lower 

ones (MEK, HAN, NUR, TAR). We suppose Fig. 3 VLF chorus dynamic spectrum and 

that it is result of the plasmapause mapping at riometer data from SOD (63.8º) stations 

around Ф ~ 60º. 

Two main maxima (at ~2 mHz and at ~3.5 mHz) were observed in the spectra of magnetic pulsations 

over both time intervals. However, the riometer pulsations demonstrated only one strong spectral maximum 

119


which was different in both intervals. At 0400-0430 UT it was observed at ~3.5 mHz coinciding with the 

second spectral maximum of geomagnetic pulsation, but at 400-0430 UT the riometer spectral peak was 

observed at ~2 mHz coinciding with the first geomagnetic pulsations maximum. 

Fig. 4 Dynamic spectra of riometer (R) and magnetic (X) variations at Scandinavian stations 

In the first time interval (0400-0430 UT), the spectral maximum of geomagnetic pulsations at ~2 mHz 

slowly increased with latitude decreasing, but in the second time interval (0400-0430 UT), the spectral 

maxima of geomagnetic pulsations were stable and similar at all stations, the pulsation amplitude decreased 

with the station latitude. 

In the first time interval (Fig. 5, left panel) the solar wind dynamic pressure variations were turbulent 

with a very broadband spectral maximum at 1.5 – 3.5 mHz, however, in the second time interval (Fig. 5, 

right panel) the harmonic oscillations with the main frequency at 2.0 mHz are seen. The maximum at ~2.0 

mHz was observed as well in the IMF Bz component. 

The filtered in both spectral 

frequency (1.5–2.5 mHz and 3–4 

mHz) bands riometer and magnetic 

data are given in Fig. 6. The 180º 

phase reversal between SOR and BJN 

demonstrates the magnetopause 

location between these stations. 

Discussion 

An interesting feature of the 

presented event is the appearance of 

the single spectral maximum in 

riometer data fluctuations at ~3.5 mHz 

in the first time interval and at ~2.0 

mHz in the second one, while two 

these peaks were observed in the Pc5 

geomagnetic pulsation spectra over 

both time intervals simultaneously. 

Only one of the Pc5 pulsation maxima 

was coincided with maximum in 

riometer pulsations, but it was 

different in the different intervals. 

The spectra of VLF chorus 

intensity variations (do not shown 

here) roughly coincided with spectra 

Fig. 5 Amplitude spectra of the solar wind dynamic 

pressure (P) and IMF Bx, By, Bx components (upper 

panel), magnetic (x), and riometer (R) pulsations. 

120


of impulsive particle precipitation. The visible correlation between the large scale (several minutes) chorus 

patches and the impulsive enhancement of the riometer absorption was observed in Fig. 2 demonstrating the 

strong causal relationship between the particle precipitation and VLF chorus generation and its modulation 

by the same agent. According to the generally accepted theory by Coroniti and Kennel, (1970), these quasiperiodic 

variations of chorus intensity and CNA could be interpreted by the compressional ULF wave 

modulation of the growth 

rate of VLF emissions 

generation. 

In the first time interval 

(Fig. 5, left panel) the ~2.0 

mHz geomagnetic 

pulsations did not modulate 

the particle precipitation. 

On this basis we suppose 

that the ~2.0 mHz ULF 

waves has not involved the 

strong compressional 

component in the equatorial 

plane of the magnetosphere 

near the location of the 

chorus generation source. 

Unfortunately, we could not 

prove that fact 

experimentaly because at 

the considered time, all 

geostationary spacecrafts 

Fig. 6 Filtered riometer and magnetometer data at Scandinavian 

stations 

were located at the night-side of the magnetosphere far from the considered meridian. The observed 

geomagnetic pulsations, probably, could be by some ionosphere origin, but in such case, it is difficult to 

explain why the frequency of ~2.0 mHz spectral pick changed with the latitude. Another alternative origin 

of these geomagnetic pulsations could be the resonance of the last closed field line, which can not modulate 

the particle precipitation and VLF chorus generation at much lower 

Fig. 7 Spectra of geomagnetic 

pulsations at middle and 

equatorial stations 

L-shells. 

According to Baker et al. (2003) definition, the ULF waves 

with maximum at ~3.5 mHz, observed at 0400-0430 UT, may be 

attributed to the field line resonances (FLR) outside (but not far) of 

the plasmapause in the area of the VLF-chorus generation location. 

The observed Pc5 waves demonstrated the typical for the FLRs the 

latitude maximum at IVA (Fig. 5, left panel; Fig. 6, right panel), 

the reasonable at this latitude FLR frequency, and the phase shift 

with latitude. Spanswick et al., (2005) suggested that FLRs are 

more efficient at modulating particle precipitation than non-FLRs, 

because the magnetosphere equatorial structure of a FLR would 

much more likely have strong radial gradients that are changing in 

time. 

During the second time interval, the main spectral peak in 

particle precipitation variations was recorded at 2.0 mHz (Fig. 4, 

right panel) coinciding with this peak in the Pc5 pulsations spectra. 

The same maximum was observed simultaneously in the solar 

wind dynamic pressure variations. We assume that the 

geomagnetic pulsations, observed during the second time interval, 

represented poloidal magnetic variations excided in the 

magnetosphere by the solar wind pressure oscillations. These 

geomagnetic pulsations were recorded simultaneously at low and 

equatorial stations (Fig. 7) providing their relationship with solar 

wind pressure impulsive enhancement [Kleimenova et al., 2002]. 

ULF waves in the solar wind as direct drivers of the morning-side Pc5 pulsations in the magnetosphere 

were previously discussed by some authors [e.g., Ohtani et al., 1999; Kepko et al. 2002]. 

121


The mechanism for the enhancement and modulation of particle precipitation by the solar wind 

dynamic pressure variations was recently applied by Longden et al. (2007) to the interpretation of the 

riometer absorption variations during moderate magnetic storm. We suppose that such “classical event” we 

observed in our second time interval when the spectral maximum at 2 mHz in the fluctuations in the solar 

wind dynamic pressure, geomagnetic pulsations, energetic particle precipitation and whistler-mode chorus 

intensity was coincided. 

The ~3.5 mHz geomagnetic pulsations in the second time interval cold be the second harmonic of the 

discussed above poloidal waves with a strong compressional component. The small enhancement at this 

frequency is seen also in the spectra of the riometer data, particularly at SOD. 

Thus, we conclude that the morning Pc5 pulsations can sometimes involve simultaneously a 

compression wave at one frequency and a transverse wave (FLR) at another frequency. 

Conclusion 

For the first time, the several minutes periodicity of VLF chorus patches occurrence has been analyzed. 

A good correlation was found between the chorus patches and peaks in riometer absorption. ULF 

geomagnetic pulsations, exited due to solar wind dynamic pressure oscillation, modulated the large scale 

VLF chorus patches and particle precipitation. We suppose that these ULF pulsations have a significant 

magnetic component parallel to ambient magnetic field. We conclude that the morning Pc5 pulsations can 

sometimes involve simultaneously a compression wave at one frequency and a transverse wave (FLR) at 

another frequency. 

The simultaneous observations of VLF chorus, riometers absorption and geomagnetic pulsations may be 

used as a new opportunity to study a spatial wave structure of ULF pulsations in the magnetosphere. 

Acknowledgments. The 16-th Program of the Presidium RAS partly provided the financial support. 

References 

Baker, G.E., E.F. Donovan, and B.J. Jackel (2003), A comprehensive survey of auroral latitude Pc5 

pulsations characteristics, J. Geophys. Res., 108 (A10), doi:10.1029/2002JA009801. 

Coroniti, F.V., and C.F Kennel (1970), Electron precipitation pulsations, J. Geophys. Res., 75, 1279-1289. 

Kimura, I. (1974), Interrelation between VLF and ULF emissions, Space Sci. Rev., 16, 389-411. 

Kleimenova, N.G., O.V. Kozyreva, and H. Ranta (1997), Pc5 pulsations in geomagnetic field and riometer 

absorption in the down sector of the auroral latitudes, Geomagn.and Aeronom., 37(5), 51-56. 

Kleimenova, N.G., O.V. Kozyreva, Schott, J.J., M. Bitterly, and J. Bitterly (2002), Geomagnetic pulsations 

of Pc5-6 range at equatorial and middle latitudes, Geomagn. and Aeronom., 42(4), 468-476. 

Kleimenova, N.G., O.V. Kozyreva, J. Manninen, and A. Ranta (2005), Unusual strong quasimonochromatic 

ground geomagnetic Pc5 pulsations in the recovery phase of November 2003 

superstorm, Ann. Geophys., 23, 2621-2634. 

Kokubun, S., M. G. Kivelson, R. L. McPherron, C.T. Russell, and H.I. West (1977), OGO 5 observations of 

Pc5 waves: Particle flux modulations, J. Geophys. Res., 82, 2774-2786. 

Kremser, G., A. Korth, J. Fejer, A. B. Wilken, A. V. Gurevich , and E. Amata (1981), Observations of 

quasi-periodic flux variations of energetic ions and electrons associated with Pc5 geomagnetic 

pulsations, J. Geophys. Res., 86(A5), 3345-3356. 

Longden, N., F. Honary, A.J. Kavanagh, and J. Manninen (2007), The driving mechanisms of particle 

precipitation during the moderate geomagnetic storm of 7 January 2005, Ann. Geophys., 25, 2053-2068. 

Sarris, T. E., T. M. Loto`aniu, X. Li, and H.J. Singer (2007), Observations at geosynchronous orbit of a 

persistent Pc5 geomagnetic pulsation and energetic electron flux modulations, Ann. Geophys., 25, 

1653-1667. 

Spanswick, E., E. Donovan, and G. Baker (2005), Pc5 modulation of high energy electron precipitation: 

particle interaction regions and scattering efficiency, Ann. Geophys., 23, 1533-1542. 

Trakhtengerts, V.Yu (1995), Magnetosphere cyclotron maser: BWO generator regime, J. Geophys. Res., 

100, 17,205-17,210. 

Trakhtengerts, V.Yu., and M.J. Rycroft (2000), Whistler-electron interactions in he magnetosphere: new 

results and novel approaches, J. Atmos. Solar-Terr. Phys., 62, 1719-1733. 

122


MAGNETIC STORM EFFECTS IN THE ATMOSPHERIC ELECTRIC 

FIELD VARIATIONS 

N.G. Kleimenova 1 , O.V. Kozyreva 1 , S. Michnowski 2 , M. Kubicki 2 , 

N.N. Nikiforova 1 

1 Institute of the Earth Physics RAS, Moscow, Russia, e-mail: kleimen@ifz.ru; 2 Institute of 

Geophysics PAS, Warsaw, Poland 

Abstract. The vertical component (Ez) of the atmospheric electric field variations, measured at 

middle (obs. Swider) and polar (obs. Hornsund) latitudes under “fair-weather” conditions, have 

been analyzed. The strong effect of sharp daytime Ez increasing (negative Ez anomalies) in the 

middle latitudes was found during the main phase of the strong and moderate magnetic storms. 

The negative Ez deviation started simultaneous with the night side geomagnetic substorm 

onset. The observed effects could be interpreted as a result of the influence of the strong night 

side ionosphere conductivity increasing, caused by substorm associated particle precipitation, 

to the global electrical circuit. In the polar latitudes the Ez enhancement effects of the storm 

initial phase have been found. Sometimes the positive Ez variations have been observed during 

so called “polar substorm” development. We also found the polar ground-based Ez 

enhancement coincided with similar IMF Ey variations. 

Introduction 

According to the well established concept, the integrated worldwide thunderstorm activity is considered 

as a main source of the electric fields in the lower atmosphere. Thunderstorm activity draws current upward 

from the ground. The ionosphere disperses the current globally, and it leaks back to the surface, averaging a 

variable potential of~100 V/m at ground level under “fair weather” conditions. 

One can see in Fig. 1 that the 

magnetosphere and the ionosphere 

represent the important part of the 

global electrical circuit. Variability 

of the vertical component of the 

atmospheric electric field (Ez) near 

the Earth surface has been 

investigated in many studies. The 

daily Ez variations are created not 

only by the worldwide thunderstorm 

activity, but different solar and 

geophysical phenomena can provide 

Fig. 1 The scheme of the global electrical circuit 

some influence to Ez behavior. It 

was suggested that solar activity 

influences due to ionosphere electric 

field disturbances may significantly 

control a global electric circuit state [e.g., Sao, 1967; Apsen et al., 1988, Michnowski, 1998; Bering et al., 

1998; Rycroft et al., 2000; Frank-Kamenetsky et al., 2001; Nikiforova et al., 2003]. Although the 

ionosphere electric potential distribution and atmospheric conductivity variations depend strongly on solar 

wind change the response to them of the lower atmospheric electric field (Ez) and current (Jz) is still rather 

not known. 

The strongest manifestations of the solar wind interactions with the magnetosphere and ionosphere 

processes are especially evident at the auroral and polar latitudes. The most studies of these effects have 

been curried out at high and polar Arctic and Antarctic areas. Practically, magnetic storm influences, which 

are distinctly manifested in high latitudes, remained unknown on mid-latitude Ez variations. However, 

some anomalies in the middle latitude Ez behavior were found during the huge magnetic storm on October 

30, 2003 [Nikiforova et al., 2005] showing a possibility to find some Ez effects associated with strong 

magnetic storms. This was only one event that has to be confirmed or ignored. The aim of this paper is to 

study possible effects of magnetic storm in atmospheric electric field (Ez) disturbances at middle (obs. 

Swider) and polar (obs. Hornsund) latitudes. 

123


Data 

This study is based on the regular registrations of the vertical component of the atmospheric electric field 

(Ez) at mid-latitude Polish geophysical observatory Swider (geomagnetic coordinates: Φ=47.8º, Λ=96.8º). 

Magnetic local noon is at ~ 10 UT. The instruments and their location are reported in [Kubicki, 2001]. We 

used the 1 min sampling data averaged at 5 min intervals for reject the short period fluctuations associated 

with a local meteorological origin. 

We also present here one event of the Ez and Jz (vertical electric currents) observations at Polish polar 

station Hornsund (HOR, Ф΄=74.0º, Λ´=110.5º) at Spitsbergen archipelago during the initial phase of the 

widely discussed strong magnetic storm on July 15, 2000 (Bastille Day event). 

Only data, fulfilling the criteria of so called “fair weather” conditions lasting all 24 hours during the given 

day, have been used in our analysis. The “fair weather” conditions request the absence of rain, drizzle, 

snow, hail, fog, lower cloudiness, local and distant thunderstorms, wind velocity exceeding 6 m/c, negative 

Ez values. Such long-lasting periods are usually seldom occurred at Świder, especially in summer and 

autumn; so there are not more ~ 40-60 “fair weather” days in the year (i.e., ~12-15% of the total 

observations). 

Observations 

Middle latitudes (obs. Swider). To distinguish magnetic storm effects in atmospheric electricity it is 

very important to establish the middle latitude Ez diurnal variations under quiet geomagnetic conditions, 

observed under “fair-weather” conditions. An average ground-level electric field diurnal curve (known as 

“Carnegie curve”) with a minimum near 03-05 UT and a maximum near 18-20 UT, occurred due to 

longitudinal distribution of the global thunderstorm activity (Fig .2., right panel). The Ez data of tree 

magnetically quiet days with Kp < 2 are shown in Fig. 1 (left panel). The solid red line demonstrates the 

established average Ez values. The strong daily variations are seen with two enhancements: before local 

noon (at 06-10 UT corresponds to 08-12 MLT) and in the local evening (14-18 UT corresponds to 16-20 

MLT). One can see that the average diurnal Ez variations roughly match the Carnegie curve, but 

demonstrate many short-lasting 

differences up to 50-80 mV/ms. 

The influence of the 

worldwide thunderstorm activity 

in Asia and Africa clearly seen, 

however, the effect of American 

center is very poor. 

The strongest magnetospheric 

and ionospheric disturbances are 

usually observed during the main 

phase of a magnetic storm, thus 

we suppose that the storm main 

phase would produce some effects 

in Ez variation even in the middle 

latitudes due to significant change 

of the ionosphere conductivity 

which is an important sector of the 

global electrical circuit. In 2000- 

2004 we could found only 14 

magnetic storms, observed under 

Fig. 2 Ez variations at Swider under quiet geomagnetic 

conditions (Kp


Fig. 3 Dst-index, solar wind electric field (Em) and velocity (V), and IMF Bx, By. Bz components 

during the magnetic storm on March 30-31, 2001; the right panel - Ez observations (solid 

line) at Swider, quiet Ez (thin line); the estimated their divergence, and magnetograms from 

middle latitude station BEL and auroral latitude stations CMO and SOD. 

auroral stations College (CMO, Ф=64.7º, Λ=263º) and Sodankyla (SOD, Ф=63.8º, Λ=108º) as it is shown 

in lower part of the right panel of Fig. 3. The obs. CMO is located at opposite to obs. Swider side of the 

Earth, thus the magnetic local noon at Swider (~10 UT) approximately correspondent to the magnetic local 

midnight at CMO (~11 UT). Accurately at the time of substorms occurrence, the dayside negative Ez 

deviations from the quiet level was observed at Swider. 

Two more examples of the magnetic storm effect in mid-latitude Ez variations are presented in Fig. 4 

for October 13-14, 2000 and May 23-24, 2000 data. The strong negative estimated Ez deviations from 

magnetically quiet Ez level are clearly seen. The daytime deflection signatures of the Ez at Swider started 

simultaneously with the magnetospheric substorm onset at the night sector (obs. College - CMO). 

The similar negative Ez deviations were observed during the main phases of all 14 magnetic storms 

under consideration. These “negative” dayside Ez anomalies appeared simultaneously with night side 

substorms developing. Thus, for the first time it was found that during the main phase of a magnetic storm a 

strong daytime negative Ez deviations could be observed at middle latitudes simultaneously with magnetic 

substorm development at night side of the auroral zone. There were no local magnetic perturbations as it is 

shown by geomagnetic records at mid-latitude station Belsk (BEL). 

Polar latitudes (obs. Hornsund). In the polar region, the interaction of the solar wind and the Earth's 

magnetic field leads to polar convection enhancement driven by horizontal dawn-to-dusk electric fields 

across the polar cap. For structures larger than ~500 km, this polar cap potential drop can produce 

significant vertical electric fields at ground level [Park, 1976]. 

We present here some experimental results of the possible contribution of magnetospheric sources to 

the high latitude atmospheric electric field variations, based on the Ez and Jz observations on Polish polar 

station Hornsund (HOR, Ф΄=74.0º, Λ´=110.5º).The position of this station depending on geomagnetic 

125


Fig. 4 The same as in Fig. 3(right panel) for magnetic storms on October 13-14, 2000 and May 

23-24, 2000 

activity may be mapped or inside of the auroral oval, or in the polar cap region, i.e. under the open 

geomagnetic field lines (Fig. 5). 

Kozyreva et al. (2004) reported that the storm initial phase as well as its sudden commencement (SC), 

caused by a passage of the compression front edge of an interplanetary magnetic cloud, manifests itself 

mainly as wave magnetic disturbances at dayside polar cap latitudes. We studied a response of Ez and Jz 

variations, observed at Hornsund, to the SC and the initial phase of the large magnetic storm on July 15, 

2000. This storm was associated with 

the powerful coronal mass ejection 

(CME). The observations (Fig. 6) 

demonstrate the occurrence of the 

very strong (up to ~ 800 V/m) positive 

bursts of Ez and Jz following the 

sudden jump of the solar wind 

dynamic pressure and the IMF B 

corresponding to the bow shock 

impact (magnetic storm sudden 

commencement - SC. The positive Ez 

and Jz enhancement was observed 

Fig. 5 The location of Hornsund relatively to auroral oval under the significant cross-polar cap 

position (OVIATION data) 

potential drop. The amplitude of Ez 

126


Fig. 6 Left panel - Dst variations and IMF data from Geotail; right panel - the maps of 

ionosphere convection, cross-polar cap potential drop, and Ez and Jz data at Hornsund 

during the initial phase of the magnetic storm on July 15, 2000. 

and Jz started to decrease with the cross-polar cap potential increasing. 

Discussion 

A magnetic storm main phase is usually accompanied by high latitude geomagnetic substorms that 

manifest large magnetosphere-ionosphere disturbances seen in energetic particle precipitations and 

ionosphere potential configuration changes. These disturbances seem to be able to affect lower atmosphere 

global electric circuit changes. As a result the total resistance of the ionosphere part of the global electric 

circuit decreases [e.g., Apsen et al., 1988, Michnowski, 1998; Bering et al., 1998]. A large number of high 

latitude experimental investigations of magnetosphere effects in atmospheric electricity support this 

suggestion. According to many authors [e.g., Apsen et al., 1988; Nikiforova et al., 2003] magnetospheric 

substorms and visible auroras at high latitudes stations are accompanied by negative night side Ez 

variations. Moreover, in solar wind induced changes can be involved by more direct effects of the deep 

penetration of the interplanetary electric field into middle and low latitude ionosphere. Both factors can be 

responsible for the up to now unknown a middle latitude response of the electric field on magnetic 

substorms. 

In presented study we found the strong negative Ez disturbances at dayside middle latitude station 

Swider associated with strong magnetic storm. We suppose that the considered effect of the storm main 

phase in mid-latitude atmospheric electricity is a result of large scale change in the total conductivity of the 

global electric circuit. Another possible source of this Ez disturbances might be the penetration of the 

interplanetary electric field (Ey=V*Bz) deep into the magnetosphere [Huang et al., 2005]. 

The polar cap Ez effects of the magnetic storm initial phase might be results of the change in the 

ionosphere plasma convection due to strong solar wind dynamic pressure increasing on the front edge of 

the interplanetary magnetic cloud. However, we could not ignore an enhancement of the polar cap (zone 3) 

field aligned currents (zone 3 FACs), associated with strong increasing of the positive Bz IMF. As a 

support of that assumption could be the fact that during the previous magnetic storm SC, caused by bow 

shock with very similar solar wind dynamic pressure jump, but accompanied by negative Bz IMF, an 

enhancement of Ez and Jz at Hornsund did not observed. 

127


Summary 

For the first time there was found the effect of the main phase of a magnetic storm on the daytime middle 

latitude Ez variations being any local magnetic activity. Various strong (~100-300 V/m) deflection signatures 

of the Ez variations (negative Ez disturbances) relative to the quiet magnetic daily level have been observed 

at Swider in the daytime simultaneously with magnetospheric substorm onset at the night sector (obs. 

College). This result could be account for a significant substorm associated solar wind interplanetary electric 

field penetration from polar cap regions into the day side ionosphere influence. Such affects appear to be so 

intensive that they could be seen even in the middle and low latitude day sector of the Earth. 

During storm initial phase there was strong daytime Ez and Jz enhancement observed at polar latitudes. 

The cross polar cap potential was dropped at this time. 

References 

Apsen, A.G., Kh.D. Kanonidi, S.P. Chernishova, D.N. Chetaev, and V. M. Sheftel’ (1988), Magnetospheric 

effects in atmospheric electricity, 150 pp. M., Nauka. 

Bering, E.A., A.A. Few, and J.R. Bennnbrook (1998), The global electric circuit, Phys. Today, 51 (10), 24- 

30. 

Frank-Kamenetsky, A.V., O.A. Troshichev, G.B. Burns, and V.O. Papitashvili (2001), Variations of the 

atmospheric electric field in the near-pole region related to the interplanetary magnetic field, J. 

Geophys. Res., 106, 179-190. 

Huang, C-S., J.C Foster., and M.C. Kelley (2005) Long-duration penetration of the interplanetary electric 

field to the low-latitude during the main phase of magnetic storms, J. Geophys. Res., 110, A11309, doi: 

10.1029/2005JA011202. 

Kleimenova, N.G., S. Michnowski, N.N. Nikiforova, and O.V. Kozyreva (1995) Long-period geomagnetic 

pulsations and fluctuations of the atmospheric electric field intensity at the polar cusp latitudes, 

Geomagn. Aeron., 35(4), 469-477. 

Kleimenova, N.G., S. Michnowski, N.N. Nikiforova, and O.V. Kozyreva (1998) Variations of atmospheric 

electric field vertical component at the evening sector of polar latitudes (obs.Hornsund), Geomagn. 

Aeron., 38(6), 149-156. 

Kozyreva O.V., N.G. Kleimenova, and J.-J. Schott (2004), Geomagnetic pulsations in a storm initial phase, 

Geomagn. Aeron., 44(1), 37-46. 

Kubicki, M. (2001), Results of atmospheric electricity and meteorological observations S. Kalinowski 

geophysical observatory at Świder, Publ. Inst .Geophysics Polish Acad. Sci., D-56 (333), 3-7. 

Michnowski, S. (1998), Solar wind influences on atmospheric electricity variables in polar regions, 

J.Geophys.Res., 103(D12), 13939-13948. 

Nikiforova, N.N., N.G. Kleimenova, O.V. Kozyreva, M. Kubicki, and S. Michnowski (2003), Influence of 

auroral-latitude precipitation of energetic electrons on variations in the atmospheric electric field at 

polar latitudes (Spitsbergen Archipelago), Geomagn. Aeron., 43(4), 29-35. 

Nikiforova, N.N., N.G. Kleimenova, O.V. Kozyreva, M. Kubicki, and S. Michnowski (2005), Unusual 

atmosphere electric field variations during the main phase of the huge magnetic storm of October 30, 

2003 at the Polish mid-latitude station Swider, Geomagn.Aeron., 45, 148-152. 

Park, C.G. (1976), Solar magnetic sector effects on the vertical atmospheric electric field at Vostok, 

Antarctica, Geophys. Res. Lett., 3, 475-478. 

Rycroft, M.J., S. Israelsson, and C. Price (2000), The global atmospheric electric circuit, solar activity and 

climate change, J. Atmos. Terr. Phys., 62, 1563-1576. 

Sao, K. (1967), Correlation between solar activity and the atmospheric potential gradient in the 

Earth’s surface in the polar regions, J. Atmos. Terr. Phys., 29, 213-215. 

128


AN INFLUENCE OF THE MERIDIONAL WIND ON THE LATITUDINAL 

LOCATION OF THE ENHANCED ELECTRON DENSITY REGIONS IN 

THE NIGHT-TIME IONOSPHERIC F2-LAYER AND PLASMASPHERE OF 

THE EARTH 

M.A. Knyazeva 1 , A.A. Namgaladze 1 

1 Murmansk State Technical University, Murmansk, 183010, Russia, e-mail: 

mariknyazeva@yandex.ru, namgaladzeaa@mstu.edu.ru 

Abstract. The influence of the meridional wind velocity on the latitudinal location of the enhanced 

electron density regions (EEDR’s) has been investigated using the global numerical model of the 

Upper Atmosphere Model (UAM). We have calculated the global distributions of the ionospheric 

F2-layer critical frequency under the condition that the equatorward wind velocity is constant at 

the night-time sector. The values of the velocity were changed from 0 to 100 m/s. It has been 

shown that the latitudinal location of the EEDR’s does not coincide with the location of the 

maximum of the vertical ion velocity induced by the wind. The EEDR’s are moved to the higher 

latitudes when the equatorward wind velocity increases. It has been proposed that the horizontal 

transfer of the plasma by neutral wind is the main cause of this displacement. The ions get a 

horizontal component vector of the velocity under the collisions with the neutral particles and the 

low latitudinal part of the EEDR’s removes from middle to the lower magnetic latitude. It results 

in the EEDR’s forming at the higher latitudes. 

Introduction 

The anomalous plasma density increases in the night-time middle-latitude ionospheric F2-layer 

have been found in observed F2-layer critical frequency (f0F2), maximum electron density (NmF2) and total 

electron content (TEC) obtained by many basic methods of the ionospheric measurements such as radio 

sounding [Mikhailov et al., 2000; Richards et al., 2000], radio transmission [Bertin and Lepine, 1970; Balan et 

al., 1991], Doppler measurements [Horvath and Essex, 2000] and incoherent scatter [Richards et al., 1994; 

Richards et al., 2000]. 

The anomalous night-time middle-latitude plasma density increases appear in the form of the 

maxima on the plots of the latitude or local time dependences of f0F2, NmF2 and TEC. The night-time 

middle-latitude maxima of the TEC appear in the form of the enhanced electron density regions (EEDR’s) at 

the two-dimensional plots (maps) of the latitude-longitude or latitude-time dependences of the TEC at the 

night side [Brunini et al., 2003]. The EEDR’s are extended along the 

geomagnetic field lines to the plasmasphere [Knyazeva and 

Namgaladze, 2005] as it is seen in the experimental dependences of 

the ion densities on the L-parameter [Gringauz and Bassolo, 1990]. 

The main cause of the EEDR’s forming is the thermosphere 

wind together with the plasma flows from the plasmasphere to the 

ionosphere at the night-time [Knyazeva and Namgaladze, 2005]. The 

equatorward neutral wind drives the F2-layer plasma to the higher 

altitudes where the ion loss rate decreases. It results in the increase of 

the ionospheric F2 region plasma density. The vertical ion velocity 

induced by the meridional wind (neglecting differences between 

geographic and geomagnetic coordinates) is (Fig. 1): 

Viz ~ Vi|| ·sin I ~ Vnx·cosI·sinI, (1) 

Fig.1. The transfer of the vertical 

velocity component to the ions by 

the collisions with the neutral 

particles. 

where I – the inclination of the magnetic field B, Vnx – the meridional velocity of the neutral particles, Vi|| – 

the projection of Vnx at the magnetic field line (field-aligned ion velocity received by collision with a neutral 

particle), Viz – the projection of Vi|| at the vertical direction (axis z). 

It follows from the expression (1) that the maximum of the vertical ion velocity induced by the 

meridional wind Viz takes place at the latitudes where the maximum Vnx·cosI·sinI takes place. 

It was interesting to check if the EEDR’s position coincides with the location of the maximum of 

Viz. At this work we have presented the results of the investigation of the influence of the meridional wind 

velocity on the latitudinal location of the EEDR’s. 

129


Model calculations 

The global numerical model of the Upper Atmosphere Model (UAM) [Namgaladze et al., 1998] has 

been used in the investigation of the influence of the meridional wind velocity on the latitudinal location of 

the EEDR’s. This model describes the thermosphere, ionosphere and plasmasphere of the Earth as a single 

system by the numerical integration of the corresponding time-dependent 3D continuity, momentum and heat 

balance equations for the neutral and electron gases and equation for the electric field potential. 

The empirical model of the neutral atmosphere NRLMSISE-00 [Picone et al., 2002] has been 

integrated into the UAM. This version of the UAM allows to get the neutral gas densities and temperature 

directly from the empirical thermosphere, to calculate the pressure gradients and thus to solve the momentum 

equations for the horizontal thermospheric wind (NRLMSISE-00 wind). 

We have calculated global distributions of the ionospheric F2-layer critical frequency (f0F2) and 

the altitude-latitude distributions of the electron density in two cases: 1) the equatorward wind velocity is 

variable; 2) the equatorward wind velocity is constant at the night-time sector and equal to Vnx = 0, 10, 50 and 

100 m/s. 

Results 

1. Vnx ≠ const. 

The results of the model calculations of the latitude-longitude distributions (in the geomagnetic 

coordinates) of the ionospheric F2-layer critical frequency f0F2 (top map), meridional thermospheric wind 

velocity Vnx at the altitude 300 km (middle map) and Vnx·cosI·sinI values (bottom map) at the same altitude 

for the UT=24:00 for the night longitudinal sector (18:00-06:00 MLT) are presented in Fig. 2. The positive 

values of Vnx correspond to the northward direction. The positive values of Vnx·cosI·sinI correspond to the 

upward direction. The midnight geographic meridian, the terminator line and geographic equator are drawn at 

the maps by dashes lines. The model calculations were made for quiet geomagnetic conditions near the equinox 

(16.04.2002). 

The night-time EEDR’s are clear visible in the northern hemisphere at the geomagnetic latitudes 

~30° at the map of f0F2 distributions (left map in Fig. 2). The corresponding distribution of the meridional 

wind Vnx shows that the wind is mainly equatorward at the latitude-longitude sector where EEDR’s are 

visible (middle map in Fig. 2). The maximum of the upward vertical ion velocity induced by the meridional 

wind Viz is located at the higher latitudes (~ 55°) than the EEDR’s location because Vnx has a maximum at 

these latitudes. Thus the latitudinal location of the EEDR’s does not coincide with the location of the 

maximum of the vertical ion velocity induced by the wind Viz. In the Vnx maximum regions the EEDR’s are 

not forming because the electric fields influence dominantly on the ionospheric F2-layer electron density at 

these altitudes and latitudes forming the main ionospheric trough at night-time. 

2. Vnx = const. 

The maximum of the vertical ion velocity induced by the wind Viz takes place at those magnetic 

latitudes where the maximum cosI·sinI takes place (I = 45°) if the meridional wind velocity is constant. 

The expression cosI·sinI depends on the geomagnetic latitude by the expression: 

sin2ϕ 

sin I ⋅ cos I = 

, (2) 

1+ 

3⋅ 

sin 

2 

ϕ 

where φ – the geomagnetic latitude. It follows that the maximum of the vertical ion velocity induced by the 

wind Viz takes place at the ±27° magnetic latitude under the condition of Vnx=const. 

The latitude-longitude distributions of f0F2 for the night longitudinal sector (18:00-06:00 MLT) 

(left column) and the altitude-latitude distributions of Lg(ne, m -3 ) for the same moment UT along the 

magnetic meridian MLT=00:30 in the altitude range from 200 km to 800 km (right column) are presented in 

Fig. 3 for second case of the model calculations. The variants of the model calculations are presented topdown: 

1) Vnx= 0; 2) Vnx =10 m/s; 3) Vnx =50 m/s; 4) Vnx =100 m/s. The midnight geographic meridian, the 

terminator line and geographic equator are drawn at the maps by dashed lines. The geomagnetic field lines are 

drawn at the meridional cuts by dashed lines. 

The night-time EEDR’s are absent at the map of the distribution of f0F2 under Vnx=0 and they are 

clear visible under Vnx≠0. This fact confirms the influence of the thermospheric wind on the EEDR’s as a 

forming factor. These regions are formed at the latitudes order 30° under Vnx =10 m/s as the theory is 

predicting under the conditions that the equatorward thermospheric wind velocity is constant. The EEDR’s 

are formed at the higher latitudes when Vnx increases. The displacement of these regions to higher latitudes is 

130


Fig. 2. The calculated by using the UAM with the NRLMSISE-00 latitude-longitude distributions of the ionospheric 

F2-layer critical frequency f0F2 (MHz) (top map), the meridional thermospheric wind velocity Vnx (m/s) at the 

altitude 300 km (middle map) and Vnx·cosI·sinI values (m/s) at the same altitude (bottom map) are presented. The 

positive values of Vnx correspond to the northward direction. The positive values of the Vnx·cosI·sinI correspond 

upward direction. 

larger relatively of the latitudinal location of the maximum cosI·sinI (27°) when the meridional neutral wind 

is stronger. It follows that the latitudinal location of the EEDR’s does not coincide with the location of the 

maximum of the vertical ion velocity induced by the wind Viz as in first case when Vnx is variable. 

This effect of the meridional wind influence on the EEDR’s is visible at the meridional cuts Lg(ne, 

m -3 ) (right column in Fig.3). It is explained by the horizontal transfer of the plasma by neutral wind is the 

main cause of this displacement. The ions get a horizontal component vector of the velocity under the 

collisions with the neutral particles and the low latitudinal part of the EEDR’s removes from middle to the 

lower magnetic latitude. It results in the EEDR’s forming at the higher latitudes. 

131


Fig. 3. The calculated by using the UAM with the NRLMSISE-00 latitude-longitude distributions of the ionospheric 

F2-layer critical frequency f0F2 (MHz) (left column) and the meridional cuts of the Lg(ne, m -3 ) along the magnetic 

meridian MLT=00:30 in the altitude range from 200 km to 800 km (right column) are presented. The variants of the 

model calculations are presented top-down: 1) Vnx=0; 2) Vnx =10 m/s; 3) Vnx =50 m/s; 4) Vnx =100 m/s. 

Conclusions 

Thus the analysis of the results of the model calculations of the ionospheric F2-layer electron density 

allows making the following conclusions. 

1) It is confirmed that the main cause of the occurrence of the night-time enhanced electron density 

regions is the equatorward thermospheric wind. 

2) The latitudinal locations of the EEDR’s and maximum of the vertical ion velocity induced by the 

meridional wind does not coincide in both cases: when the meridional wind is constant and it is 

variable with the latitude. 

132


3) The EEDR’s are formed at the higher latitudes relatively of the latitudinal location of the 

maximum of the vertical ion velocity induced by the meridional wind Viz (27°) when the 

equatorward meridional wind is constant. It is explained by the horizontal transfer of the plasma to 

lower latitude by neutral wind. It results in the EEDR’s forming at the higher latitudes. 

4) The maximum Viz displaces to high latitude regions relatively of the latitudinal location of the 

EEDR’s when the meridional wind decreases toward the magnetic equator because the electric 

fields influence dominantly on the ionospheric F2-layer electron density at these altitudes and 

latitudes forming the main ionospheric trough at night-time. 

References 

Balan N., G.J. Bailey and R.B. Nair (1991), Solar and magnetic activity effects on the latitudinal variations 

of nighttime TEC enhancement. Annales Geophysicae, 9, 60-69. 

Bertin F. and J.P. Lepine (1970), Latitudinal variation of total electron content in the winter at middle 

latitudes. Radio Science, 5(6), 899–906. 

Brunini C., M.A. Van Zele, A. Meza and M. Gende (2003), Quiet and perturbed ionospheric representation 

according to the electron content from GPS signals. JGR, 108 (A2), 1056, 

doi:10.1029/2002JA009346. 

Gringauz K.I. and V.S. Bassolo (1990), The structure and properties of the Earth’s plasmasphere. The 

experimental data and problems of their interpretation. Review. Geomagnetism and Aeronomy (in 

Russian), 30(1), 1-17. 

Horvath I. and E.A. Essex (2000), Using observations from the GPS and TOPEX satellites to investigate 

night-time TEC enhancements at mid-latitudes in the southern hemisphere during a low sunspot 

number period, Journal of Atmospheric and Solar-Terrestrial Physics, 62, 371–391. 

Knyazeva М.А. and A.A. Namgaladze (2005), The mathematical modeling of the forming of the night-time 

electron density increases in the F2-layer of the quiet middle-latitude ionosphere and in the Earth’s 

plasmasphere. Proceedings of the MSTU (in Russian), 8(1), 144-155. 

Mikhailov A.V., T.Yu. Leschinskaya and M. Förster (2000), Morphology of NmF2neighttime increases in 

the Eurasian sector. Annales Geophysicae, 18, 618–628. 

Namgaladze A.A., O.V. Martynenko, M.A. Volkov, A.N. Namgaladze and R.Yu.Yurik (1998), High-latitude 

version of the global numerical model of the Earth’s upper atmosphere. Proceedings of the MSTU, 1(2), 

23-84. 

Picone J.M., A.E. Hedin, D.P. Drob and A.C. Aikin (2002), NRLMSISE-00 empirical model of the 

atmosphere: Statistical comparisons and scientific issues. JGR, 107(A12), 1468, 

doi:10.1029/2002JA009430. 

Richards P.G., M.J. Buonsanto, B.W. Reinisch, J. Holt, J.A. Fennelly, J.L. Scali, R.H. Comfort, G.A. 

Germany, J. Spann, M. Brittnacher and M.-C. Fok (2000), On the relative importance of convection 

and temperature to the behavior of the ionosphere in North America during January 6-12, 1997. JGR, 

105(A6), 12,763-12,776. 

Richards P.G., D.G. Torr, B.W. Reinisch, R.R. Gamache and P.J. Wilkinson (1994), F2 peak electron density 

at Millstone Hill and Hobart: Comparison of theory and measurement at solar maximum. JGR, 

99(A8), 15,005-15,016. 

133


ANALYTICAL MODEL OF COLLISIONLESS MAGNETIC 

RECONNECTION BASED ON THE SOLUTION OF GRAD-SHAFRANOV 

EQUATION COMPARED TO THE PIC-SIMULATION 

D. Korovinskiy 1 , V. Semenov 1 , A. Divin 1 , N. Erkaev 2,3 , H. Biernat 4,5 

1 Institute of Physics, University of Saint-Petersburg, 198504, Russia, e-mail: 

daniil.korovinskiy@gmail.com; 2 Institute of Computational Modelling, Russian Academy of 

Sciences, Siberian Branch, 660036, Krasnoyarsk, Russia; 3 Siberian Federal University, 660041, 

Krasnoyarsk, Russia; 4 Space Research Institute, Austrian Academy of Sciences, 8042, Graz, 

Austria; 5 Institute of Physics, University of Graz, A-8010, Graz, Austria 

Abstract. The Hall effect is proved to play a key role in the collisionless magnetic reconnection 

proceeding. An analytical model of steady-state magnetic reconnection in a collisionless incompressible 

plasma is developed using the electron Hall MHD approximation. It is shown that initial 

complicated system of equations may be split into a system of independent more simple equations, 

and the solution of the problem is based on the Grad-Shafranov equation for a magnetic potential. 

Results of the analytical study are further compared with the two dimensional particle-in-cell simulation 

of reconnection. It is shown that both methods demonstrate a close agreement in the electron 

current and magnetic field structures obtained. Spatial scales of the acceleration region in simulation 

and analytical study are of the same order. Such features like particles trajectories and in-plane 

electric field structure appears essentially similar in both models. 

1 Analytical study 

In the nearest vicinity of the stagnation point, at length scale of the order of lp, the proton velocities are 

small compared to the electron velocities. Hence, one may use the electron Hall MHD (EHMHD) approximation 

considering the electric current in this region as the electron current only [1] 

j ≈ −neVe, (1) 

where Ve is the electron bulk velocity. In [2] an analytical model of steady-state collisionless magnetic reconnection 

in an incompressible plasma was developed based on EHMHD approximation. We outline the model 

in next passages and review main results derived; in-depth study is provided in cited paper. 

We chose coordinate system as follows: the X-axis coincides with the magnetic field at its direction at 

infinity (in the upper semiplane), the Y -axis is directed along the X-line, and the Z-axis is perpendicular to 

both of them. We avoid the description of the EDR internal processes and consider only its size, which we 

suppose to be of the order of le in its cross section (Z direction) and ηlp along it (X direction), where η is 

a coefficient of the order of 1. Outside the EDR the plasma is supposed to be nonresistive; furthermore, it is 

assumed to be quasi–neutral and incompressible. At last, we assume homogeneity in the Y direction. 

The two-fluid description of the problem is determined by the following equations, 

ρ(Vp · ∇)Vp = −∇Pp + ne(E + 1 

c Vp × B), (2) 

E + 1 

c Ve × B = − 1 

ne ∇Pe, (3) 

∇ × B = 4πne 

(Vp − Ve), 

c 

(4) 

∇ × E = 0, (5) 

∇ · B = 0, (6) 

∇ · Vp,e = 0. (7) 

Here, Pp is the scalar proton gas pressure, Vp is the proton bulk velocity, and Pe is the scalar electron gas 

pressure. In our steady-state 2.5D case, the electric field Ey must be a constant, according to (5). So, we define 

Ey = ɛEA, (8) 

where ɛ is the reconnection rate which we assume to be small, ɛ ≪ 1, and EA = 1 

c B0VA is the Alfvén electric 

field. Here, B0 is the magnetic field value above the X-line at the upper boundary of the examined region and 

VA is the corresponding proton Alfvén velocity. 

134


To resolve system (2–7) we introduce dimensionless quantities: the magnetic field strength ˜ B = B/B0, the 

proton and electron bulk velocities ˜ Vp,e = Vp,e/VA, the electric field strength ˜ E = E/EA, the gas pressure 

˜Pp,e = Pp,e/P0, and the length scales ˜r = r/lp. Here, P0 = B2 0 /4π, and r = (x, y, z). 

Then we introduce the electric potential ˜ Φ via ˜ E = − ˜ ∇˜ Φ. Omitting the tildes, we rewrite equations (2-7) for 

normalized quantities, bearing in mind the EHMHD approximation (1), 

(Vp · ∇)Vp = −∇Pp − ∇Φ, (9) 

Ve × B = ∇Φ − ∇Pe, (10) 

∇ × B = −Ve, (11) 

∇ · B = 0, (12) 

∇ · Vp,e = 0. (13) 

Note that Φ has a linear dependence on Y coordinate, so that ∂Φ/∂y = −ɛ. Under this point of view, we can 

present Φ as a sum of two terms, Φ(x, y, z) = φ(x, z) − ɛy. Using effective potential φeff ≡ φ − Pe, we 

eliminate quantity Pe from the Ohm law (10). 

We also introduce a magnetic potential A(x, z), 

B⊥ ≡ (Bx, Bz) = ∇ × (Aey), (14) 

where ey is the unit vector and ⊥ denotes the XZ plane. 

At last, we note that accordingly to Ampère’s law (11), the out-of-plane magnetic field By is the stream function 

for the electron in-plane velocity [1], 

Ve⊥ ≡ (Vex, Vez) = −∇ × (Byey). (15) 

Paying attention to the Ohm law (10) and making use of the EHMHD approximation (1) we obtain the famous 

Grad-Shafranov equation for magnetic potential 

Vey ≡ ∆⊥A = dG(A) 

, (16) 

dA 

where ∆⊥ is the 2D Laplace operator ∆⊥ ≡ ∂2 /∂x2 + ∂2 /∂z2 , and G(A) is the unknown modelling function. 

The other equations of system (9-13) take the following form 

By(r) = (−1) k+1 ɛ 

� r 

r0 

dsfl 

|∇⊥A| + By(r0), (17) 

φeff = 1 

2 B2 y + G(A), (18) 

1 2 

Vp⊥ + Π − 

2 1 

2 |∇⊥A| 2 + G(A) = Ctr, (19) 

∇⊥ · Vp⊥ = 0, (20) 

� r 

dstr 

Vpy(r) = ɛ + Vpy(r0). (21) 

r0 Vp⊥ 

Here (17) is the equation for out-of-plane magnetic field By, where k is a quadrant number and dsfl is an 

elementary displacement along the projection of the magnetic field line onto the XZ plane; (18) is the equation 

for the effective electric potential φeff ; (19) is the Bernoulli equation for the in-plane motion of protons, where 

Π ≡ Pp + (1/2)B 2 is a total pressure and Ctr is a constant along trajectory; (20) is the continuity equation, 

where Vp⊥ is a proton in-plane velocity; and (21) is the equation for the out-of-plane proton velocity Vpy, 

where dstr is an elementary displacement along the projection of the proton trajectory onto the XZ plane. 

Scaling of the problem allows to make use of the boundary layer approximation ∂/∂x ≪ ∂/∂z. Under this 

approximation Laplace equation (16) has a following solution 

z(A) = ± 1 

� A dA 

√ 

2 A0 

′ 

� , (22) 

|G(A ′ ) − G(A0)| 

A0 ≡ A(x, 0) = 

135 

� x 

Bz(x 

0 

′ , 0)dx ′ , (23)


with the boundary condition Bz(x, 0). 

Equation (17) claims that extremum values of By are located at the separatrices of in-plane magnetic field. 

Besides, |E| ≈ |∇G(A)| and |Vey| have maximum at the separatrices as well. Using the condition of solvability 

of equation (22) we obtain estimation of extremum electric field, max |E| ∼ 10EA. As for the electron velocity 

Vey, the Ampère law yields 

max |Vey| = 1 

δ VAe, (24) 

where δ is a EDR width measured in electron skin depthes le and VAe = 

� 

mp/meVA is the electron Alfvén 

velocity. At last, proton in-plane motion obeys the Bernoulli equation (19), where total pressure is fixed by 

its distribution at the upper boundary of the EHMHD domain, so Π = Π(x) ≡ Π(x, zmax). Thus, system of 

equations (16-23) expresses the self-consistent solution of our problem based on the modelling function G(A) 

with the boundary conditions Bz(x, 0) and Π(x, zmax). We took these functions from the PIC simulation of 

reconnection and then compared our analytical solution and numerical model. 

2 PIC simulation 

The explicit particle-in-cell code P3D [3] is utilized for the simulation of 2.5D reconnection. In brief, 

P3D is electromagnetic full particle code; Boris algorithm [4] is used for the numerical solution of equation of 

motion. Electromagnetic field solver utilizes leapfrog scheme to advance fields in time. For the initial condition 

we take conventional Harris neutral current sheet [5], 

Bx = B0 tanh z 

, (25) 

λ 

n(z) = n0 cosh −2 

� � 

z 

+ nb, (26) 

λ 

with a background plasma density nb = 0.2 and half-width of the initial current sheet λ = 0.4 lp. Magnetic 

field is normalized to its maximum value in the lobes and density is normalized to its current sheet maximum. 

A small initial GEM-type perturbation [6] is added to ignite reconnection 

Ψ(x, z) = Ψ0cos 2πx 

Lx 

cos πz 

, (27) 

Lz 

where Lx = Lz = 38.4 lp are the sizes of computational box and intensity of perturbation is Ψ0 = 0.3. 

Quasistationary state was achieved at t = 15 Ω−1 p , where Ω−1 p is the inverse proton gyrofrequency, and simulation 

parameters at t = 20 were further taken as a reference to be compared with analytical study. The mass 

ratio is mp/me = 64, the temperature ratio Tp/Te = 3/2. 

Open boundary conditions for fields 

and particles 

∂Bx,y/∂x = 0, ∂Ey/∂x = 0, Ex,z = 0, Bz = 0 (28) 

∂ne,p/∂x = 0, ∂Ve,p/∂x = 0, ∂Te,p/∂t = 0 (29) 

are implemented at the exhaust boundaries to allow free outflow of plasma [7, 8]. 

Perfect electric conductor (PEC) boundary closes the simulation box at z = ±19.2. Under the boundary 

conditions adopted, no more than 15% of magnetic flux and particles escape through outflow boundary by 

t = 20. In the following section comparison of analytical model and PIC simulation is presented. 

3 Comparison of the results 

Plot of the electric current jey(z) at x = 0 is shown in Fig. 1a, where EDR is a well-recognizable region 

of domination of the electron current over the proton one. The EDR half-width δ comes up to (3/4)lp, i. e., 

δ ≈ 6le under the mass ratio used. According to estimation (24), analytical model gives max |Vey| ≈ 7VA, the 

136


1 

0.5 

a) 

0 

−4 −2 0 2 4 

−2 

−4 

0 c) 

−6 

−1 −0.8 −0.6 −0.4 −0.2 0 0.2 

3 

2 

1 

e) 

0 

0 1 2 3 4 

6 

4 

2 

0.05 

b) 

0 

0 1 2 3 4 

0.1 

d) 

0 

0 1 2 3 4 

6 

4 

2 

0 

0 5 10 

Figure 1: a) PIC simulation: jey(0, z) (thick) and jpy(0, z) (thin); b) PIC simulation: |Vey(x, 0)| (thick) 

and Vpy(x, 0) (thin); c) PIC simulation: dG/dA ≡ Vey(A); d) PIC simulation: magnetic field Bz(x, 0); e) 

analytical model: electron velocities Vex(x, 0) (thick) and proton velocities Vpx(x, 0) (thin); f) PIC simulation: 

electron velocities (thick) and proton velocities (thin). The point A = 0 on the pallet c) corresponds to the 

magnetic field separatrices. Quantity Vex at the pallet e) is undefined inside EDR, i. e., for x < 2. 

value obtained in PIC simulation is 6VA (see Fig. 1b). Electron/proton current ratio is je/jp ≈ 11 in the origin, 

it decreases moving away from the X-line. As far as EHMHD assumption is je ≫ jp, we restricted region of 

analytical model by value x = 4, where je/jp ≈ 5. Analogously, the upper boundary of the modelling region 

is restricted by value zmax = 30le. This value corresponds to zmax = 4lp in PIC simulation (mp/me = 64) 

and zmax = 0.7lp in analytical modelling (mp/me ≈ 1840). The EDR half-length reaches 2lp. PIC simulation 

provides us functions dG/dA ≡ Vey(A) and Bz(x, 0) presented in Fig. 1, pallets c) and d), respectively. The 

total pressure Π(x, zmax) turns out to be a linearly increasing but weakly varying quantity, Π(0, zmax) = 

0.61, Π(4, zmax) = 0.66. The last parameter of the analytical model is reconnection rate ɛ ≡ Ey. Its value 

obtained in simulation is 0.2. 

Electron trajectories obtained from the analytical study and PIC simulation are compared in Fig. 2, pallets 

a) and b). Magnetic field separatrix mapped by electric current is clearly visible in both cases. In fact, this is 

a classical Hall current structure [9], observed in the magnetosphere [10] and in laboratory experiments [11]. 

Electron jet in X direction is visible as well, in agreement with results of other authors [12, 13]. Dependence 

of velocity of this jet on X is plotted in Fig. 1, pallets e) and f). Analytical model undervalues electron velocity 

(approximately twice) compared to that of PIC simulation. 

Proton velocities demonstrate better agreement, with acceleration up to ≈ 1.2VA in both models, though 

at different scales. Correspondingly, proton trajectories and magnetic field structure shown in Fig. 2, pallets c) 

and d), are accurate up to spatial scales, which are of the same order. At last, electric fields Ez shown in Fig. 3 

are in good qualitative agreement as well. Localization of extremum of Ez corresponds to the jump of electric 

potential across the separatrices predicted. 

Thus, we compared essential dynamic and electromagnetic plasma parameters obtained from PIC simulation 

with corresponding analytical solution. One can see that plasma characteristics obtained are qualitatively 

identic. As for numeric values, analytical model is not precise everywhere. While some values predicted are 

137 

f)


quite accurate (e. g., max |Vey|, max |Vp|) others differ noticeably (e. g., Vex, Ez). 

0.6 

0.4 

0.2 

0 

0 1 2 3 4 

0.6 

0.4 

0.2 

0 

0 1 2 3 4 

a) 

c) 

4 

b) 

3 

2 

1 

0 

0 5 10 

4 

d) 

3 

2 

1 

0 

0 5 10 

Figure 2: Pallets a) and b): electron trajectories in XZ plane obtained in analytical model and PIC simulation, 

respectively; Pallets c) and d): proton trajectories in XZ plane (thick) and magnetic field lines (thin) obtained 

in analytical model and PIC simulation, respectively. 

0.6 

0.4 

0.2 

0 

−0.2 

−0.4 

−0.6 

0 1 2 3 4 

8 

6 

4 

2 

0 

−2 

−4 

−6 

−8 

−10 

a) 

b) 

4 

3 

2 

1 

0 

−1 

−2 

−3 

0 5 10 

Figure 3: Distribution of electric field Ez in XZ plane: analytical model (a) and PIC simulation (b). 

138 

1.5 

1 

0.5 

0 

−0.5 

−1 

−1.5 

−2


Apparently, analytical model tends to underrate the spatial scales of the process, what is likely caused by 

neglecting of electron pressure contribution adopted in the model. While outside EDR Pe is weakly varying 

quantity, indeed, situation is completely different inside EDR. Electron pressure turns there to the anisotropic 

tensor and ∇ ˆ Pe becomes the dominative in the Ohm law. This term is responsible for freezing-out of electrons 

in a thin and very stretched (∼ 10lp) layer mapping the X axis, called external EDR, where electron jet develops 

(see Fig. 2b). But this effect is completely out of the scope of our analytical study. Nevertheless, the analytical 

solution obtained demonstrates all essential Hall reconnection features and a close qualitative agreement with 

results of the PIC simulation. 

Besides, this solution claims that the powerful mechanism of electron acceleration in the X-line direction 

is required. Accordingly to the estimation (24) it must accelerate electrons up to the electron Alfvén velocity 

inside the EDR and on the separatrixes. At the downstream edge of the EDR these accelerated electrons are 

deflected by the Lorentz force in the X-direction and then get decelerated in outflow region, pulling protons. 

Acknowledgements. This work is supported by RFBR, grant N 07-05-00776-a, and by Austrian “Fonds zur 

Förderung der wissenschaftlichen Forschung” under Project P17099–N08. PIC simulations was performed by A. 

Divin in University of Maryland, USA. 

References 

[1] Biskamp, D. (2000), Magnetic reconnection in Plasmas, Cambridge University Press, Cambridge. 

[2] Korovinskiy, D. B., V. S. Semenov, N. V. Erkaev, A. V. Divin, and H. K. Biernat (2008), The 2.5-D 

analytical model of steady-state Hall magnetic reconnection, J. Geophys. Res., 113, A04205. 

[3] Zeiler, A., D. Biskamp, J. F. Drake, B. N. Rogers, M. A. Shay, and M. Scholer (2002), Three-dimensional 

particle simulations of collisionless magnetic reconnection, J. Geophys. Res., 107(A9), 1230. 

[4] Birdsall, C. K., A. B. Langdon (1991), Plasma Physics via Computer Simulation, Plasma Physics Series, 

Eds. S. Cowley, P. Stott, and H. Wilhelmsson, IOP Publ., Bristol. 

[5] Harris, E.G. (1962), On a plasma sheath separating regions of oppositely directed magnetic field, Nuovo 

Cimento, 23, 115. 

[6] Birn, J., J. F. Drake, M. A. Shay, B. N. Rogers, and R. E. Denton, M. Hesse, and M. Kuznetsova, Z. W. 

Ma, and A. Bhattacharjee, A. Otto, and P. L. Pritchett (2001), Geospace Environment Modeling (GEM) 

Magnetic Reconnection Challenge. J. Geophys. Res., 106, 3715. 

[7] Pritchett, P. L. (2001), Geospace environmental modeling magnetic reconnection challenge: simulations 

with a full particle electromagnetic code, J. Geophys. Res., 106, 3783. 

[8] Divin, A. V., M. I. Sitnov, M. Swisdak, and J. F. Drake (2007), Reconnection onset in the magnetotail: 

Particle simulations with open boundary conditions, Geophys. Res. Lett., 34, L09109. 

[9] Sonnerup, B. U. Ö. (1979), Magnetic field reconnection, in Solar System Plasma Physics., eds. L. J. 

Lanzerotti, C. F. Kennel, and E. N. Parker, 3, 46, North Holland Pub., Amsterdam. 

[10] Alexeev, I. V., C. J. Owen, A. N. Fazakerley, A. Runov, J. P. Dewhurst, A. Balong, H. Rème, B. Klecker, 

and L. Kistler (2005), Cluster observations of currents in the plasma sheet during reconnection, GRL, 32, 

L03101. 

[11] Cothran, C. D., M. Landreman, M. R. Brown, and W. H. Matthaeus (2005), Generalized Ohm’s law in a 

3D reconnection experiment Geophys. Res. Lett., 32(5), L03105. 

[12] Shay, M. A., J. F. Drake, M. Swisdak (2007), Two-scale structure of the electron dissipation region during 

collisionless magnetic reconnection, Phys. Rev. Lett., 99, 155002. 

[13] Daughton, W., J. Scudder, and H. Karimabadi (2006), Fully kinetic simulations of undriven magnetic 

reconnection with open boundary conditions, Phys. Plasmas, 13, 072101. 

139


STORM-TIME Pc5 GEOMAGNETIC PULSATIONS ANALYSIS BASED ON 

A NEW ULF-INDEX 

O.V. Kozyreva, N.G. Kleimenova 

Institute of the Earth Physics RAS, B. Gruzinskaya 10, Moscow, 123995, Russia, e-mail: 

kozyreva@ifz.ru 

Abstract. The new index of the planetary wave activity in the ultra low frequency range called as 

“ULF-index” has been applied to the statistical analysis of the intensity level of the daytime 

geomagnetic pulsations of the Pc5 range with the periods of ~3-8 min (f = 2-6 mHz) during the 

different phases both of the strong (-150 nT < Dstmin < -100 nT) and moderate (-100 nT < Dstmin < 

-50 nT) magnetic storms. It is found the most intensive geomagnetic pulsations were observed in 

the morning-noon sector of the auroral latitudes in the every storm main phase but not in the storm 

recovery phase, as this was earlier considered. It is shown that the geomagnetic pulsations, which 

are excited during and after morning substorms, introduce the basic contribution to the day ULF 

wave activity during the main phase of the magnetic storm. We found that the storm sudden 

commencement, which is characterized by a jump of the solar wind density and velocity, is 

accompanied by the sharp increasing of the ULF-index. The ULF-index level decreases in the 

storm recovery phase, however, an appearance of the separate time intervals of the negative IMF 

Bz values leads to the short-time ULF-index enhancing. 


It is known that Pc5 pulsations (frequency range 2–6 mHz) are most typical morning and daytime 

geomagnetic pulsations in the magnetosphere. Numerous satellite observations in the Earth’s magnetosphere 

also indicated that Pc5 geomagnetic pulsations at the distances of R ≥ 6–8 RE are typical daytime 

phenomenon. Numerous publications are devoted to studying the morphological characteristics and physical 

origin of generation of Pc5 pulsations. 

Generation of pulsations is of a prime importance in the processes of the energy transfer in the solar wind– 

Earth’s magnetosphere system. Many works [e.g., Antonova, 2000; Borovsky and Funsten, 2003]) indicated 

that these processes are non-stationary and turbulent. An energy is transferred most effectively during 

magnetic storms. Different magnetic storms are characterized by different levels of the wave geomagnetic 

activity. However, none of the geomagnetic index used in geophysics (Kp, Ap, AE, AL, Dst, SYM_H, PC) 

reflects the level of the wave activity. A special index should be used to estimate wave intensity. 

The first attempts to create the activity index of Pc5 geomagnetic pulsations were made at the end of the past 

century. Thus, Glassmeier [1995] proposed to use the ratio of the pulsation energy in a relatively narrow 

band to the energy in a wide band. This index was useful in studying narrowband quasi-monochromatic Pc5 

pulsations. A similar parameter, defined as a ratio of the pulsation power in the band 2–10 mHz to such a 

power at 0.2–10 mHz, was used by Posch et al. [2003] in order to study Pc5 pulsations during five magnetic 

storms. However, Posch et al. [2003] analyzed observations at stations located only in one longitudinal 

sector, which could not completely reflect wave activity on the global scale. 

O'Brien et al. [2001] used the observations at 11 stations of the INTERMAGNET network, located at L = 

3.5–7.0, in order to calculate wave activity. They calculated the Fourier spectrum of the total field vector for 

each station (all three components were taken into account) in a 2-hour sliding window in the 150–600 s 

range of periods. Then, the station where the oscillation power was maximal was selected, but the station 

local time was not taken into account in this case. As a result, nighttime oscillations in this range, which 

belong to the class of irregular Pi3 pulsations, participated in the estimation of the wave activity. In addition, 

it is sufficiently incorrect to use the total field vector because the Z field component is very sensitive to local 

geoelectric inhomogeneities. 

Since an analysis of ground-based observations at one selected observatory or at any one meridian does not 

give information about the level of wave activity on the global scale, a new ULF-index was developed in 

order to estimate the global wave activity in the dayside (0300– 1800 MLT) sector of the magnetosphere 

[Kozyreva et al., 2007]. In the English literature, it is accepted to call the frequency band of 1–10 mHz ULF 

(ultra low frequency) band; therefore, the proposed index was called the ULF index. 

The aim of the present work is to estimate the level of the daytime wave geomagnetic activity during 

different phases of strong and moderate magnetic storms applying the new ULF- index. 

140


2 Description of ULF-index 

The wave index is a proxy of global ULF activity, and 

the 1-minute data of observations at the global network 

of magnetometers in the Northern Hemisphere, 

including more than 60 stations (INTERMAGNET, 

MACCS, 210 MM, and Greenland and Russian Arctic 

coast) have been used to calculate the ground-based 

ULF index. The stations are automatically selected for 

each hour of day, depending on the specified range of 

geomagnetic latitudes, in order to calculate the hourly 

values of the ULF-index. The Fourier spectra are first 

calculated for these stations in a 1-hour window for two 

horizontal components of the geomagnetic field. Only 

the stations with the highest signal level are finally used 

to calculate the global ULF-index (the logarithm of the 

maximal oscillation amplitude during the selected hour). 

The technique for calculating the ULF-index is 

considered in more detail in [Kozyreva et al., 2007]. 

The ULF-index for the near Earth space is considered in 

a similar way. The data of the GOES geostationary 

satellites are used in this case. The data of the WIND, 

ACE, IMP-8, or 1-min OMNI data 

Fig. 1 Location of the Northern hemisphere 

observatories used for ULF-index 

calculation. 

(ftp://nssdcftp.gsfc.nasa.gov/spacecraft_data/omni/high_res_omni/monthly_1min/) are used to calculate the 

ULF-index in order to estimate the interplanetary magnetic field wave activity. The ULF-index hourly values 

are freely available via anonymous FTP Internet site (ftp://space.augsburg.edu/MACCS/ULF_index/). The 

data for each month of a year are presented as tables and figures. The ULF-index values on the Earth’s 

surface and in the near Earth and interplanetary space are completed with the data on the solar wind velocity 

(V) and density (N), IMF Bz component, and Dst index. By the present, the ULF-index has been calculated 

for the period 1991–2005, but this database is still widened and becomes more exact. 

3 Applying the ULF-index 

To analyze geomagnetic pulsations of the Pc5 type at frequencies of 2–6 mHz, we calculated the ULF wave 

index for the morning–daytime sector (0300–1500 MLT) of the auroral latitudes (Φ = 60°–70°) there were 

the strongest Pc5 pulsations observed. 

Background level of ULF-wave turbulence 

First, the background level of wave turbulence (i.e., the level of daytime ULF activity during the 

magnetically quiet period) was estimated. The days with |Dst| < 20 nT and Kp < 2 were selected in 1995– 

2001 (605 days, including 207 days in winter, 253 days in summer, and 145 days during the periods of 

vernal and autumnal equinoxes). The average value of the ULF-index under quiet conditions was 0.29 ± 

0.18. In this case the average ULF-index value in summer (0.32) was larger than in winter (0.26) and in the 

equinox (0.27). This is apparently the result of the ionospheric effect on the level of wave turbulence on the 

Earth’s surface. 

The level of daytime ULF activity during magnetic storms 

To study the level of morning–daytime ULF activity during different phases of a magnetic storm, we selected 

19 strong magnetic storms with the Dst-index varying from –150 to –100 nT at a maximum of the storm main 

phase and 37 moderate magnetic storms (-100 nT < Dstmin < -50 nT) for the period 1995–2002. The duration 

of storms was not longer than one day between the storm commencement and the main phase maximum. The 

so-called “double” storms with the main phase consisted of two minima following each other with the interval 

of several hours [e.g. Kamide et al, of 1998] were excluded. The 1-hour values of ULF-index were computed 

for each of the selected storms. Further study was carried out by the superposed epoch technique. The 

universal time when Dst-index reached minimum value during the main phase of the magnetic storm was 

used as a “zero” epoch, which corresponds to the maximum of the main phase of storm. We have analyzed the 

time interval of 48 hours for the each selected storms, i.e. 24 hours before and 24 hours after the Dst 

minimum. The results of this analysis are shown in Fig. 2 where the plots of the 1-hour ground-based ULFindex 

and the Dst index values (the bottom panel) are presented for 19 strong (left panel) and 37 moderate 

(right panel) magnetic storms, thick lines show the average value (red line) and standard deviation (±σ, blue 

lines). 

141


Fig. 2 Variations in the ground-based ULF and Dst indices during 19 

strong magnetic storms (left panel) and 37 moderate magnetic 

storms (right panel). 

It is clearly evident that the 

intensity of the day time 

geomagnetic pulsations of 

the Pc5 range grows almost 

by an order since the 

beginning of the magnetic 

storm. The greatest intensity 

of day pulsations is 

observed during the main 

phase of storm, but not in 

the recovery one, as this 

was considered earlier. One 

can note also the smallest 

deviations of the values of 

ULF-index (σ) during the 

storm main phase. The 

amplitude of daytime 

fluctuations rapidly 

decreases in the early stage 

of the magnetic storm 

recovery phase. Then, 

during the last stage of this 

phase the activity of ULF waves remains almost on the same level for a long time. The value of the standard 

deviation (σ) considerably grows at this time in comparison with a storm main phase. The behavior of the 

ULF-index for strong and moderate magnetic storms is similar, but the ULF waves are more intensive during 

the strong magnetic storms. 

Besides a ground-based ULF-index for all analyzed storms we have estimated also the storm wave activity in 

the interplanetary space and in the magnetosphere of the Earth. The 1-hour values of the ULF-index of IMF 

and magetospheric wave turbulence were calculated according to the OMNI data base and geostationary 

satellites. The analysis was carried out by the same manner as for ground-based data applying the superposed 

epoch technique. Similarly the analysis of ground observations we accepted the universal time (UT) of the 

minimum Dst-index in the main phase of each storm as the zero mark. The obtained results are shown in Fig. 

3 for 19 strong storms (left panel) and 37 moderate storms (right panel). 

Fig. 3 demonstrates that 

contrary to ground ULFindex 

behavior, there is the 

clear maximum of the wave 

activity in interplanetary 

space observed during the 

initial phase of the strong 

magnetic storms as well as 

the moderate ones. The 

level of this maximum was 

much stronger than the 

wave activity during the 

storm main phase. 

However, in the 

magnetosphere the 

maximum of the dayside 

ULF activity is observed 

Fig. 3 Variations in the interplanetary and magnetospheric ULF- index 

during 19 strong magnetic storms (left panel) and 37 moderate 

magnetic storms (right panel). 

during the storm main 

phase. The dispersion of the 

average ULF-index, that is 

difference between the 

minimum and maximum 

values of ULF-index (blue curves), or value (σ), it somewhat greater during the strong magnetic storms than 

during the moderate ones. 

142


4 Discussion 

Very many works are devoted to studying Pc5 geomagnetic pulsations; however, the nature and spatial 

features of these oscillations have been studied insufficiently. In many respects this is related to the fact that 

the class of Pc5 pulsations combines different types of oscillations with periods in the same range but with 

different generation origin. In contrast to other types of geomagnetic pulsations, Pc5 oscillations are 

characterized by not only large periods but also by huge amplitudes (~30-100 nT), reaching 300–600 nT in 

the recovery phase of the superstorms [e.g., Kleimenova and Kozyreva, 2005]. 

It is generally accepted that the Kelvin–Helmholtz instability at the magnetopause or in the entrance layers of 

the magnetosphere is the main source of Pc5 pulsations. In addition to field line resonance, Pc5 pulsations in 

the magnetosphere can be also generated due to the development of the drift–mirror instability of the ring 

current under the conditions of large β (see [Pilipenko, 1990] and references therein). These waves have the 

large azimuthal numbers (m ~ 50–100). They are mainly registered on satellites and as a rule do not observed 

on the ground. Generation of the global magnetospheric cavity mode in the Earth’s magnetosphere can be 

one more source of Pc5 pulsations [e.g., Kivelson et al., 1984]. In this case the poloidal oscillations with a 

considerable compression component in the radial direction originate in the magnetosphere. Such oscillations 

were often observed on geostationary satellites in the post noon sector of the Earth’s [e.g., Hudson et al., 

2004]. Oscillations can be also a result of a direct penetration of the waves from the solar wind [e.g., Kepko 

et al., 2002]. Thus, ULF pulsations can be resulted from the simultaneous action of different sources. 

We found (Fig. 3) that during the storm main phase the values of the ULF-index in the IMF is more than once 

smaller than in the magnetosphere (GOES data) and the estimated correlation coefficient between the ULFindex 

in the IMF and in the magnetosphere is 0.73 in the case of the strong magnetic storms and 0.67 in the 

case of the moderate storms. This suggests that the most part of ULF waves, observed on the ground, are 

generated inside of the magnetosphere and only a small part of the wave turbulence penetrates from the solar 

wind. The correlation coefficient between the ULF-index on the ground and in the magnetosphere is 0.96 in 

the case of the strong magnetic storms and 0.91 in the case of the moderate storms. By this it means that 

practically all Pc5 pulsations, observed on the ground at the auroral latitudes, are exited by a magnetosphere 

origin. 

We have applied the superposed 

epoch technique to analyzing the 

IMF and solar wind parameters 

variations of all selected storms. 

The results of this analysis are 

presented in Fig.4. In the initial 

phase of a magnetic storm there is 

observed a strong enhancement in 

variations of the solar wind 

dynamic pressure (Fig. 4) and in 

the wave turbulence in the IMF 

according to the estimated values 

of the ULF-index (IMF), as it is 

seen in Fig. 3a. In a storm initial 

phase, the ULF-index (IMF) 

maximum is much stronger than 

during a storm main phase. This 

effect is not so clearly marked in 

the ground (Fig. 2) and in the 

GOES (Fig. 3) ULF-index 

Fig. 4 The distribution of the solar wind dynamic pressure 

interplanetary, Bz component IMF and Dst index during 19 

strong magnetic storms (left panel) and 37 moderate 

magnetic storms (right panel). 

variations. Only a gradually 

increasing of the ULF-index 

values, preceded the storm main 

phase maximum, can be noticed in 

a storm initial phase. We have to 

keep in mind that the ground 

ULF-index is calculated for 

selected latitude range. In our case the ULF-index is computed for the auroral latitudes (Φ = 60°–70°). 

However, it is well established [e.g., Kozyreva et al., 2004; Kozyreva and Kleimenova, 2004, 2007] that in 

143


the storm initial phase the strongest ULF geomagnetic pulsations are observed in the dayside polar cap due to 

a direct penetration of the ULF waves from the solar wind. So, we could not expect to see this effect in the 

ground ULF-index, calculated for auroral latitudes (Φ = 60°–70°), as well as in the magnetospheric ULFindex, 

calculated applying the GOES data. 

It is known that the main phase of the magnetic storm is accompanied by the development of magnetospheric 

substorms accompanying by Pi3 irregular geomagnetic pulsations. It would seem that also the wave activity 

during the main phase of storm must be concentrated in the night sector, and during the storm recovery phase 

- in the dayside. It is well known [e.g., Afanasyeva, 1978]), that in the majority of the cases of Pc5 the 

pulsations are observed in the auroral latitudes in the early morning sector after the end of the night 

substorms. 

Baker et al, (2003) found that at the 

auroral latitudes there are two maxima 

of Pc5 occurrence: one in the morning 

and considerably weaker in the 

afternoon time. Consequently, it can be 

assumed that the basic contribution to 

the dayside (03-18 MLT) ULF-index of 

the pulsations activity consists of both 

morning and afternoon Pc5 pulsation. 

Thus, it is logical to divide up the values 

of ULF-index into two parts - morning 

(03-12 MLT) and afternoon (12-18 

MLT). As an example we analyze the 

strong magnetic storm on May 15, 1997. 

The magnetograms (X and Y 

components of magnetic field) for 

several auroral stations, located at the 

different longitudes, are given in Fig. 5. 

Fig. 5 Magnetograms of X and Y components for the several 

auroral stations on May 15, 1997; black diamonds – 

local midnight, white triangle - noon 

One can see that in the pre-midnight (MEA) and morning (NAQ) sectors there were observed the 

development of the intensive substorm accompanied by strong pulsations. 

The morning (blue) and afternoon (red) variations of the 

ULF- index during this storm are presented in detail in Fig. 

6, where the variations of the solar wind velocity (V) and 

density (N), and the Dst index are shown too. The main 

phase of this storm, as can be seen from Dst- index (Fig. 

6), began about 07 UT. During the main phase of storm 

(07-16 UT) the variations of the ULF- index demonstrated 

three maxima simultaneously before noon and after noon. 

The maps of the global scale distribution of the intensity of 

geomagnetic pulsations in the frequency band of 2-5 mHz 

(Fig. 7) were built for two stronger maxima (06-08 UT and 

14-16 UT) in the coordinates: the corrected geomagnetic 

latitude - local magnetic time (MLT). 

As can be seen in upper panel of Fig. 7, at 06-08 UT the 

most intensive pulsations were observed in two separated 

longitudinal sectors - in the evening-night (18-22 MLT) 

and in the early morning (02-08 MLT). The maximum of 

ULF- index in 14-16 UT (Fig. 6) corresponds to the 

excitation of the geomagnetic pulsations (Fig. 7, bottom 

Fig. 6 Variations of the solar wind velocity panel) which were more intensive in the morning sector 

(V) and density (N), Dst index and (03-08 MLT) than in the evening sector (16-19 MLT). 

ULF- index: blue curve – morning, red Morning geomagnetic pulsations were observed during the 

one - afternoon 

recovery phase of morning substorm at MEA (Fig. 5). 

As usual the activity of geomagnetic pulsations was higher 

in the morning than after noon. This is clearly evident in Fig. 6 by the comparison of the values of the ULFindex 

for the morning (03-12 MLT) and evening (12-18 MLT) pulsations. 

144


5 Conclusion 

The application of a new index of planetary wave activity 

(range of Pc5 of pulsations, f ~2-6 mHz) provided the great 

scope possibility for a statistical analysis of the intensity 

level of the dayside geomagnetic ULF turbulence on the 

ground as well as inside of the magnetosphere and in the 

interplanetary medium. 

The variations of the ULF- index have been studied during 

the different phases both of strong and moderate magnetic 

storms. It was first discovered, that the greatest intensity of 

day geomagnetic pulsations in the auroral latitudes is noted 

during the main phase of the magnetic storm, but not into the 

storm recovery phase, as this was considered earlier. It is 

shown that the basic contribution to the dayside ULF wave 

activity of a magnetic storm main phase provide the 

geomagnetic pulsations, excited during and after morning 

substorms. 

This work was partly supported by the Program №16 of the 

Presidium of RAS. 

Fig. 7 The maps of the spatial 

distribution of global ULF activity 

during the main phase of the 

magnetic storm on 15 May 1997 

References 

Afanasyeva L.T. (1978), Space-time distribution of geomagnetic pulsations and its dependence on the 

geomagnetic activity, Acta Geod. Geophys. Mont. Acad Sci. Hungary, 13(1/2), 239-271. 

Antonova E. E. (2000), Large Scale Magnetospheric Turbulence and the Topology of Magnetospheric 

Currents, Adv. Space Res., 26 (7/8), 1567–1570. 

Baker G.E., Donovan E.F., Jackel B.J. (2003), A comprehensive survey of auroral latitude Pc5 pulsations 

characteristics, J. Geophys. Res., 108 (A10), Doi:10.1029/2002JA009801. 

Borovsky J. E., and H. O. Funsten (2003), Role of Solar Wind Turbulence in the Coupling of the Solar Wind 

to the Earth’s Magnetosphere, J. Geophys. Res., 108A, 1246, doi:10.1029/2002JA009601. 

Glassmeier K. H. (1995), ULF Pulsations, in: Handbook of Atmospheric Electrodynamics, Ed. by H. 

Volland, CRC Press, Boca Raton, II, 463–502. 

Hudson M. K., R. E. Denton, M. R. Lessard, et al. (2004), A Study of Pc5 ULF Oscillations, Ann. Geophys., 

22, 289–302. 

Kamide Y., N. Yokoyama, W. D. Gonzalez, et al. (1998), Two Step Development of Geomagnetic Storms, J. 

Geophys. Res., 103, 6917–6921. 

Kepko L., H. E. Spenc, and H. J. Singer (2002), ULF Waves in the Solar Wind as Direct Drivers of 

Magnetosphere Pulsations, Geophys. Res. Lett., 29 (8), doi: 10.1029/2001GL014405. 

Kivelson M. G., J. Etcho, and J. G. Trotignon (1984), Global Compressional Oscillations of the Terrestrial 

Magnetosphere: The Evidence and a Model, J. Geophys. Res., 89, 9851–9856. 

Kleimenova N. G. and O. V. Kozyreva (2005), Intense Pc5 Geomagnetic Pulsations during the Recovery 

Phase of the Superstorms in October and November 2003, Geomagn. Aeron., 45 (5), 597–612. 

Kozyreva O. V. and N. G. Kleimenova (2007), Geomagnetic Pulsations and Magnetic Disturbances during 

the Initial Phase of a Strong Magnetic Storm of May 15, 2005, Geomagn. Aeron., 47 (4), 501–511. 

Kozyreva O. V., N. G. Kleimenova, and J._J. Schott (2004), Geomagnetic Pulsations at the Initial Phase of a 

Magnetic Storm, Geomagn. Aeron., 44 (1), 37–46. 

Kozyreva O. V., Kleimenova N. G. (2004), Long period polar cap geomagnetic pulsations of initial 

phase of strong magnetic storms, in: Proc. 5-th Inter. Conf. “Problems of Geocosmos”,166-169. 

Kozyreva O., V. Pilipenko, M. J. Engebretson, et al. (2007), In Search of a New ULF Wave Index: 

Comparison of Pc5 Power with Dynamics of Geostationary Relativistic Electrons, Planet. Space Sci., 55, 

755–769. 

O’Brien T. P., R. L. McPherron, D. Sornette, et al. (2001), Which Magnetic Storms Produce Relativistic 

Electrons at Geosynchronous Orbit? J. Geophys. Res., 106, 15 533–15 544. 

Pilipenko V. (1990), ULF Waves on the Ground and in Space, J. Atmos. Sol.–Terr. Phys., 63, 1193–1209. 

Posch J. L., M. J. Engebretson, V. A. Pilipenko, et al. (2003), Characterizing the Long Period ULF Response 

to Magnetic Storms, J. Geophys. Res., 108, doi: 10.1029/2002JA009386. 

145


IMPLICATIONS OF VOLCANISM AND GEOMAGNETIC FIELD 

POLARITY REVERSALS INTO THE CLIMATE VARIABILITY 

N.D. Kuznetsova, V.V. Kuznetsov 

Institute of Space Physical Research and Radio Wave Propagation, Russian Academy of Sciences, 

Far Eastern Branch, Paratunka, Kamchatka, 684034, Russia, e-mail: paratundra@mail.ru 

Abstract. Increase of volcanism just as geomagnetic field reversals and excursions implications 

into long temporal paleoclimate variability are discussed. Stratosphere volcanic fine-grained 

submicron dust is considered to be a long-living barrier to the Sun radiation input to the Earth 

surface that is borne out by the high correlation between the Earth surface temperature and the dust 

content in the ice cores of Antarctica during the last 400,000 years. The ice core dust provenance, 

its varying content in ice-core layers and properties at different climatic periods wide debated give 

us occasion to develop our concept about effect of the volcanism increase on the large temporal 

climate variability. The link between climate changes and the geomagnetic field reversals and 

excursions has no unambiguous interpretation since both climate cooling and warming are known 

to run during reversals and excursions. Considering reversals and excursions to be processes being 

accompanied by penetration of the cosmic rays particles which are governing the atmosphere 

transparency we are substantiating a consequence of the reversals and excursions impact on 

climate to be determined by a presence or absence of dust in the stratosphere. Here we attempt to 

account increase of volcanism for the geomagnetic field excursions. 

Introduction 

Discussions on links between climate changes and excursions of the geomagnetic field have conflicting 

conclusions. Taking an increasing flux of the cosmic rays particles during excursions as the governing agent 

responsible for the ionization of atmosphere air molecules the authors [1] are developing their conception of 

cosmic rays particles to provide climate cooling through intensive clouds formation which have high albedo. 

According to this hypothesis, warm periods should coincide with relative minima of GCR-flux, while 

maxima of GCR-flux should be related to periods of cold climate, which features some excursions of 

Brunhes chrone. At the same time validating the well-known climate warming during Laschamp excursion 

Svensmark [2] attributed this phenomenon to failure of the low energy cosmic rays which are mostly 

penetrating into the Earth atmosphere during excursions to drive the Earth climate. The Gothenburg 

geomagnetic field excursion (13 000–12 000 years ago) was revealed [3] to pass at the time boundary of the 

transition from the glacial period to the recent warm epoch (the Holocene). 

Taking as an example the dust concentration D in the ice cores of Antarctica and the Earth surface 

temperature T trends [4] ( Fig.1) during Gothenburg and Biwa I excursions one can see the difference in 

dust concentrations before the excursion was starting . These facts promoted our conception of changes 

Fig.1. Dust concentration D in the ice cores of Antarctica and the Earth surface temperature T trends during 

Gothenburg and Biwa I excursions. 

in optical properties of atmosphere during geomagnetic field excursions resulting from cosmic rays 

penetration into atmosphere with different aerosol content. Long temporal climate variability discussed to be 

146


governed by astronomical theory of climate proceeds from transparent atmosphere conditions. Optical 

properties of atmosphere responsible for the sun radiation transmission are mainly governed by stratosphere 

submicron solid particles emitted by volcanoes [5]. Data on explosive volcanic activity especially on 

supervolcanoes eruptions which cause a sustained stratospheric aerosol loading are invoked. 

Region study 

The more powerful is the volcanic eruption, the more intense injection of fine grain solid particles and 

sulfate aerosols into stratosphere it generates. Climate exposure to sulfate component of volcanoes is a 

cooling of some years duration. Collection mechanisms for particles in the 0.1–2 μm diameter range are 

inefficient. Experiencing extended atmospheric lifetimes these particles can have prolonged and wide 

reaching atmospheric effects. The radiative effects of particles depend strongly on size, with smaller particles 

tending to backscatter incoming short-wave solar radiation [5]. 

Fig.2 Age correlation between dust content in Antarctica ice core [4] and supervolcanoes eruptions. 

Age correlation between dust content in Antarctica ice core and supervolcanoes eruptions (Fig.2) let us to 

assume that the prolonged climate forcing of supervolcanoes eruptions is provided by stratosphere volcanic 

fine grain solid particles. 

Results 

The weaker is the intensity of the geomagnetic field the higher is the level of cosmogenic nuclides 

production by cosmic rays during their penetration into the Earth atmosphere [6,7]. 

Fig.3. Age correlation between peaks of cosmogenic nuclides 36 Cl in recorded in submarine sediments and 

ice cores and geomagnetic field excursions. Arrows point at the ages of excursions, 1 – Gothenburg, 2 – 

Mono Lake, 3 -Laschamp, 4 – Kargapolovo, 5 – Blake. 

Production of cosmogenic nuclides by cosmic rays particles interaction with air molecules is controlled 

by the intensity of the particles flux which increases during geomagnetic field excursions when the field 

147


module decreases. Hence comparing ages of the geomagnetic field excursions to these of the field intensity 

dips one can see their close correlation, see Fig.3. And it is the increasing flux of the cosmic rays particles to 

affect the optical characteristics of the Earth atmosphere during the field excursion. Taking the stratosphere 

dust content to answer the atmosphere transparency we estimated the correlation between the Earth surface 

temperature T and ice core dust D trends [4]. After T and D curves were digitized (Fig.4) with interval of 1 

thousand years we evaluated the correlation score between the curves. Here R - correlation matrix with 

diagonal cell equal to 1 and correlation coefficients are out of the main diagonal cells. P – matrix of 

correlation significance coefficients. The smaller is P, the more significant is the correlation. Taking 

confidence interval for R as 95%, we estimated R = - 0.56, P=0.0000, confidence interval (-0.62 -0.49). 

Fig.4 Correlation between the Earth surface temperature T and ice core dust D curves. 

The results suggest a high and significant correlation and a lack of time delay between two series when 

T and D vary simultaneously and in antiphase. Data of Fig.2 allowed us to relate dust peaks to explosive 

supervolcano eruptions [8] which are known to produce fine-grained submicron dust and sulfuric acid 

aerosols that can reach the upper atmosphere. These act to cool the Earth surface by backscattering incoming 

solar radiation. Fig. 5 shows that small mineral and soot inclusion into sulfate volcanic aerosol raises its mass 

absorption coefficient on some orders [9]. 

Fig.5 Optical properties of aerosol layer depending on impurities into eruption plume 

As we estimated earlier [10] the time of atmosphere cleaning from volcano dust may last about 10– 

12 Kyr. Estimating here the submicron particle lifetime we proceeded from the following facts. Firstly, 

observations do not reveal volcano dust submicron particles in ice-core layers [11] and secondly, the 

concentration of stratospheric particles between 0.045 and 1 μm in radius is several orders of magnitude 

higher than the concentration of particles above 1 μm [12]. If a stratospheric particle has r = 0.1μm, m = 10 -14 

148


g, then substituting these values into mg = eZE, where E – vertical atmosphere electric field, Е ≈ 1V/m, еZ – 

a dust particle charge, Z = 1000 one can see that this particle doesn’t precipitate in the gravitational field. 

Earlier it was considered to be the fact that solid eruptive fragments are limited to the larger size 

fractions, but it is reported that he 1986 plume of Mt. St. Augustine (Alaska) contained silicates in all 

fractions down to 0.1 mm and large explosive eruptions transport particles higher into the atmosphere, 

leading to an extended lifetime compared to equivalent lower level emissions [5]. 

Loss of geomagnetic field shielding during reversals and excursions as follows from our estimations of 

cosmic rays flux occurs during field excursions (Fig.6). Here, density (J) of the cosmic rays (CR) flux 

Fig.6. Loss of geomagnetic field shielding affecting the cosmic rays flux intensity 

as protons in relation to CR energy Е: 1 – galactic CR; 2 - Sun CR; 3 – protons flux within radiation belt; 4 – 

anomalous CR. Left scale: h –altitude the CR protons ionizing atmosphere penetrate [14]. Top scale: 

magnitude of geomagnetic field module B (module of the modern field is equal to 1) corresponding to cut off 

energy of CR protons with energy E. (B equal to 1 corresponds to Е = 10 GeV). As it is seen from the Fig.6 

the density of the cosmic rays flux raises some orders under the some-times decrease of the field module. 

The ionizing effect of the cosmic rays flux increases and its climate forcing depends on the stratosphere 

conditions. As it is shown in Fig.1 if the excursion starts in transparent atmosphere then ionizing atmosphere 

the cosmic rays flux increase generates condensation nuclei and origin of aerosols which are backscattering 

solar radiation and climate cooling arises. The dusty atmosphere conditions before the excursion are 

vanished by cosmic rays generation of condensation nuclei and the climate warming starts. 

Linking increased volcanism activity [13] and geomagnetic field excursions we operated from the hot 

Earth theory, being evolved by Kuznetsov V.V. [15]. The theory states that the geomagnetic field excursions 

are identified with phase changes at the Earth inner core boundary and this impulse quickly reaches the Earth 

surface. Considering increased volcanism activity to be generated after geodynamic impulse initiated by the 

Earth expansion or collapse it is possible to estimate a time t of the mantle substance viscous-elastic 

relaxation: t = μ/G, here μ – viscosity, а G – elasticity module. μ is estimated to fall within the range of 

1021 – 1022 Pa s and G - 109 ÷ 1010 Pa. Then t ≈ 1012 s = 30 000 years and the geomagnetic field 

excursions are 20 – 30 kyr ahead periods of increased volcanism activity. 

149


Fig.7. Link between volcanism [13] and geomagnetic field excursions. 

Fig.7 shows a link between volcanism [13] and geomagnetic field excursions. As it follows from this bottom 

part of the figure the longer is the excursion duration the higher is the volcanism activity. 

Conclusions 

During excursions and reversals when the geomagnetic cut-off action disappears and protons out of the 

destructed radiation belts add to cosmic rays flux, the flux density rises on about 4-6 orders resulting in 

stratosphere cleaning due to aerosol particles coagulating, enlarging and falling down. Transparent 

atmosphere permits solar radiation to reach the Earth surface and climate warming arises. If the excursion 

starts in transparent atmosphere conditions as modern ones the enlarged cosmic rays flux as an ionizing 

agent generates condensation nuclei and origin of aerosols which are backscattering solar radiation and 

climate cooling arises. 

Apparent link between excursions and volcanism reveals a reason for climate shifts to have rather 

terrestrial nature than astronomic one. 

References 

1. Christl, M. et al. (2004) Evidence for a link between the flux of galactic cosmic rays and Earth’s climate 

during the past 200,000 years. J. Atmosph. Solar-Terrestr. Physics. 66. 313–322 

2. Svensmark, H. (2007) Cosmoclimatology: a new theory emerges. A&G. 48. 1.18-1.24 

http://www.scribd.com/full/338170?access_key=1cowa29e3pyb2 

3. Guskova, E. G. et al. (2007) Manifestation of the Gothenburg geomagnetic field excursion in the Barents 

Sea bottom sediments. Geomagnetism and Aeronomy. 47(6). 781-786 

4. Petit, J. R. et al. (1999). Climate and atmospheric history of the past 420,000 years from the 

Vostok ice core, Antarctica . Nature. 399. 429-436 

5. Mather, T. A., Pyle, D. M. and Oppenheimer, C. (2003) Tropospheric Volcanic Aerosol in Volcanism and 

the Earth’s Atmosphere, Geophysical Monograph 139 Copyright 2003 by the American Geophysical 

Union, 189-212 

6. Baumgartner, et al. (1998) Geomagnetic Modulation of the 36Cl Flux in the GRIP Ice Core, Greenland. 

Science. 279. 1330-1332 

7. Aldahan, A. and Possnert, G. (2000) The 10Be marine record of the last 3.5 Ma. Nucl. Instr. Meth. Phys. 

Res. B. 172. 513-517. 

8. Wilson, C.J.N. (2008) Supereruptions and Supervolcanoes: processes and products. Elements. 4(1). 29-34 

150


9. Pierazzo, E. et al. (2003) Chicxulub and Climate: Radiative Perturbations of Impact-Produced S-Bearing 

Gases. Astrobiology. 3(1). 99-118 

10. Kuznetsov, V.V. and Kuznetsova, N.D. (2006) The Earth palaeoclimate response to cosmic rays 

exposure during geomagnetic field excursions, in Proceedings of Geocosmos-2006, P.112-115 

11. Narcisi, B. et al. (2005) Characteristics and sources of tephra layers in the EPICA-Dome C ice record 

(East Antarctica): Implications for past atmospheric circulation and ice core stratigraphic correlations. 

Earth Plan. Sci. Letters. 239. 253– 265 

12. Testa, J.P. et al. (1990). Collection of microparticles at high balloon altitudes in the stratosphere. Earth 

Plan. Sci. Lett. 98(3-4). 287-302 

13. Seliverstov, N.I. (2004). Gidrosphernie protsessi i tchetvertichni vulkanizm. Vestnik KRAUNTS. Seria 

Nauki o Zemle. 3. 5 – 17 

14. Akasofu, S.I, Chapmen, S. (1974) Solnechno-Zemnaya fizika. 330 pp. V.2. M. Mir 

15. Kuznetsov, V.V. (2008) Vvedenie v Fiziku Goryachei Zemli. 366 pp. Petropavlovsk-Kamchatsky 

151


CREATION OF SOLAR PROTON BELTS DURING MAGNETIC STORMS: 

COMPARISON OF TWO MODELS 

L.L. Lazutin 

Moscow State University, Scobeltsyn Institute for Nuclear Physics, 

Space Physics Division, Vorob'evy Gory, Moscow, 119992, Russia, lll@srd.sinp.msu.ru 

After strong magnetic storms enhanced fluxes of trapped proton with energy 1-20 MeV were 

registered at L=2-4. Solar cosmic rays are regarded as a source of this new proton population. 

There are two mechanisms proposed for the explanation how SCR became trapped. The first 

mechanism suggests that particles are radially injected into the inner magnetosphere at the 

beginning of the magnetic storm by the electric pulse induced by SC compression of the 

magnetosphere. By the second mechanism SCR penetrates directly to the inner magnetosphere 

during the main phase of the magnetic storm and during the recovery phase remains at the closed 

drift shells if the recovery of the magnetosphere is fast enough compared with particle magnetic 

drift period. Detailed analysis of the particle dynamics during two magnetic storms based on lowaltitude 

satellites CORONAS-F and SERVIS-1 presented in this paper shows that it is direct 

trapping during recovery phase which is responsible for the enhanced proton radiation belts 

arriving after the strong magnetic storms. 

1. INTRDUCTION 

Proton radiation belt situated on L=1.3-5 shells has been studied sufficiently well. Formation of the proton 

belt with particle energy from 0.1 to 100 MeV and spatial distribution are described by the theory of radial 

diffusion caused by the magnetic microimpulses (Parker, 1960, Tverskoy, 1965). Proton belt was regarded 

as a stable formation with certain substorm associated variations only at the outer belt boundaries. 

Nevertheless, there were several evidences of considerable proton intensity variations in the inner 

magnetosphere as well during strong magnetic bays. 

Slocum et al., [2002] found 11 events when new radiation belts appear after magnetic storms accompanied 

by solar cosmic ray events from 2000 to 2002. They claimed that one of new belts which arrive on 

November 24, 2001, was registered at least to July 2002. Lorentzen et al., [2002] found cases of solar 2-15 

MeV proton trapping during strong magnetic storms in 1998 and 2000. Solar origin of these particles follows 

from the existence of helium ions. 

First of the possible explanation of the solar proton belt formation was proposed when satellite CRRES 

registered fast increase of the energetic electrons and ions during several minutes of sudden commencement 

(SC) of the magnetic storm of March 24, 1991 [Blake et al., 1992]. It was suggested that particles were 

injected inward and accelerated by the electric field impulse induced by magnetosphere compression during 

SC [Li et al., 1993, Pavlov et al., 1993]. Although similar direct measurements with sufficient temporal 

resolution have not been repeated, model of the SC-injection became preferable if not the only one for the 

explanation of the other observation of new solar proton belt formation during magnetic storms. 

Second mechanisms of the solar proton trapping at the recovery phase of the magnetic storms was proposed 

by Lazutin et al., [2006], and Lazutin and Kuznetsov, [2007]. Radial injection was not supposed as a main 

trapping force. It was claimed that solar protons penetrate directly deep into the inner magnetosphere during 

the main phase and when penetration boundary retreats during the storm recovery phase, low energy (1-20 

MeV) protons remain at the closed drift shells due to the fast magnetosphere configuration recovery. 

It should be noted that both mechanisms are physically possible and both were observed experimentally, 

therefore our aim is not to show that one of them is erroneous, but to found which of two proposed 

mechanism really creates solar proton radiation belts. 

After short description of these mechanisms, and then analyze the details of the proton dynamics during two 

magnetic storms of October 29-31, 2003 and November 24, 2001 

2. SC-INJECTION MODEL 

The process of the Sc-injection is the same as in a classical diffusion theory of the proton belt formation 

except that in this case instead of the series of small magnetic field pulses we have only one but with large 

magnitude. The effectiveness of this mechanism depends on the particle energy. Protons shifted earthward 

152


by SC-impulse at the dayside must have magnetic drift velocity sufficient to carry them to the night side 

before the end of the impulse, otherwise its will be returned adiabatically to the starting drift shell with zero 

acceleration. Magnetic drift period may be found as: 

44 

T = (1) 

LE 

where Т in minutes and E – particle energy in MeV 

For the proton energy 1 and 5 MeV and L=4 T= 11 and 22 minutes consequently, which is exceed 

significantly typical duration of the SC (< 30s). Therefore 1-5 MeV protons cannot be directly accelerated by 

this mechanism. Kress et al., [2007] proposed a modified SC-injection of the surfing type, when protons with 

starting energy ~ 1MeV at 5Re are drifting together with the SC wave gaining energy up to 15 MeV at ~3Re. 

Presented results of the modeling sufficiently explained captured intensity of the 15 MeV, but due to the 

resonant feature of the surfing-type acceleration, it cannot explain capture of the 1 MeV protons. 

Experimental support of this work was based on SAMPEX measurements which have no low-energy proton 

channels and therefore authors do not know that enhanced 1 MeV proton flux arrived efter the strong 

magnetic storms. 

Second restriction of the effectiveness of SC-injection came from the demand of large SC amplitude to 

obtain necessary proton acceleration. The radial shift δL might be calculated using Tverskoy equation 

[Pavlov et al., 1993]: 

5 

8 h ⎛ L + L ⎞ 

max ⎜ f i 

δL 

= L − L = ⋅ ⋅ ⎟ (2) 

f i 21 Ho ⎜ 2 ⎟ 

⎝ ⎠ 

where Lf and Li are initial and final particle position, hmax, and Ho – maximal deviation and total 

magnitude of the magnetic field at the Earths surface. For example, before the SC of 29.10.2003 proton 

penetration boundary (PB) was located at L=3.7 and maximum of 1-5 MeV solar proton radiation belt was 

found at the end of the main phase of magnetic storm at L=2.4. To receive such shift one must have hmax =- 

400nT, which exceeds observed SC value more than 4 times. 

2.1 Proton radial profiles during SC. CORONAS-F 

Figure 1 presents 8 radial profiles of 14-26 NeV proton channel of CORONAS-F particle spectrometer 

MKL. CORONAS-F satellite operates from July, 30, 2001 till December, 2005 on polar circular orbit with 

an inclination of ~82.5 o . The altitude of an orbit was 500 km in an initial stage of work, and it gradually 

decreased to ~350 km at 2005. The MKL spectrometer onboard CORONAS-F satellite has two 

semiconductor detectors with thicknesses of 0.05 mm and 2.0 mm and a CsI crystal with the thickness of 1.0 

cm that was surrounded by an anti-coincidence plastic scintillator with thickness equal to 0.5 cm. The 

geometry factor was ~0.4 cm 2 sr. Electrons from 0.3 up to 12 MeV and protons from 1 up to 90 MeV in 

different energy ranges were registered [Kuznetsov et al., 2002]. 

First four profiles on Fig.1 were measured before the magnetic storm. Proton penetrates freely into the polar 

cap and quasitrapping region. The fourth profile was measured right before the SC (06.12 UT). Profile 

number five was measured 10-20 minutes after SC, but no consequences of the proton injection were found 

in this or other proton channels. Last three profiles measured during storm main phase were shifted 

earthward as usual in such conditions again without any traces of the enhanced particle intensity. 

Second example shows similar CORONAS-F measurements before and after SC on 22.49 UT magnetic 

storm 26 .11.2001. (Fig. 2). 

In this case after SC along with the earthward shift of the PB considerable increase of the proton intensity 

was registered. But again the origin of this increase was not related to the SC injection, because 

homogeneous increase was registered on all penetration regions, including the polar cap. As one can se at 

inserted box, simultaneous increases was registered in interplanetary space and it is clear, that it was caused 

by additional solar cosmic ray acceleration by the same interplanetary shock which caused SC compression 

of the magnetosphere. 

3. DIRECT TRAPPING MODEL 

During the main phase of the strong magnetic storm the penetration boundary of the solar cosmic rays 

approached toward the Earth to L=2-3. Closer to the Earth magnetic field is dipollike, while outer field lines 

are distorted and the protons are quasitrapped; their drift shells are not closed. 

153


Fig. 1. 29.10.2004. Orbits № 1-4 = 05.00 UT -6.12 UT. 

№5 =06.12-06.33 UT № 6-8 = 6.33-07.45UT. . Profile 

temporal sequence is shown from top to the bottom. Red 

color belongs to the daytime local times, blue ones belong 

to the nighttime profiles. 

Fig. 2. Radial profiles of 1-5 MeV protons measured by 

CORONAS-F before and after SC of 26.11.2001 magnetic 

storm (Lazutin, Kuznetsov, 2007). In a box measurements 

electrons and protons of MeV energy range by АСЕ. 

For the solution of the problem of creation of solar cosmic ray belt it is important to know the ratio of the 

particle magnetic drift period and the time of the magnetosphere reconfiguration. Which in turn means the 

conservation or not of the third adiabatic invariant. For the fast drifting particle recovery of the 

magnetosphere configuration vent too slow and particles enter and leave magnetosphere not mentioning 

changes, only new particles enter point moves outward according to the PB movement. For the low energy 

protons magnetosphere changes are too fast and they may remain on the closed drift shells before they are 

able to leave magnetosphere. 

There are two important differences of this mechanism and SC-injection model, namely it does not demand 

injection, it is direct trapping, and in took place not at the beginning but at the recovery phase of the 

magnetic storm. 

3.1 Effect of the double penetration boundary of the 1-5 MeV solar protons 

Complicated radial profile which we named as double PB occurs when the old low energy protons remain at 

the closed drift shells and the new low energy protons enter magnetosphere at some distance because of to 

the PB outward motion on magnetic storm recovery phase. Particle detector on board the satellite 

CORONAS-F recorded double PB for first time during magnetic storm of 29-31.10.2004 [Lazutin et al., 

2006]. It was a composition of three storms, as one can see from Fig.3. The closes PB position was registered 

at L = 2.0-2.2 at the beginning of October 30 and at the end of the same day. Both moments denote the end 

of the main phase of the second and the third magnetic storms. From the late evening of the October 30 PB 

started to move outward which was possible to follow by the measurements of three higher energy channels 

with energy range 14-90 MeV. Low energy channel 1-5 MeV shows at the same time double PB structure. 

Fig 4 shows 1-5 MeV radial profiles during two orbits (8 profiles) starting from 00 UT October 31. Double 

PB was recorded at all profiles both at the North and South and independent on the local time, except the last 

profile when the single PB recovered. The outer parts of all profiles coincide with single PB of higher energy 

protons. 

Trapped solar protons remain at L= 1.2-1.7 while PB moves outward to L= 2.7-3.5. The flux of the detected 

trapped protons at the inner PB decreases quickly which is not surprising. Low altitude satellite registered 

only precipitation particles, which input from interplanetary space stopped when PB moved outward. As 

magnetic field lines became dipollike, pith-angle distribution changes from isotropic toward trapping and for 

the satellite detector protons became invisible at the most of the orbit except those over Brazilian Magnetic 

Anomaly (BMA). In this specific orbits enhanced proton were recorded days and months after the storm. 

154


Fig. 3. Dst- index (SIM) during extremely strong 

magnetic storm of 29-31.10.2003. 

4. PROTON BELT DURING OCTOBER 27-31, 2003 MAGNETIC STORMS 

Fig. 4. The same as Fig. 1 with a double PB structure 

during the final magnetic storm recovery 

Several radial profiles over BMA are shown on Fig. 5. Two flights belong to the pre-storm days; other four 

profiles were registered during the storm at the times shown by arrows on fig 3. 

27.10.03 Radial profile is typical for the quiet time with maximum at L=3 for the 1 MeV protons. 28.10.03 

Also pre-storm time with differences created by solar protons, which occupied polar cap and quasitrapping 

region down to L=3.5-4. Proton belt maximum at the same place, L=3. 

29.10.03, ~0630 UT. Penetration boundary approached earthward to L=2.3, and proton belts situated at L=3 

disappeared because particle drift orbits became open and protons enter and leave magnetosphere without 

trapping. 

30.10.03 ~07.40 UT The middle of the recovery phase of the second magnetic storm. Penetration boundary 

at the end of the growth phase was near L=2.2 and during PB retreat new solar proton belt was created with 

maximum at L=2.4. 

30.10.03, 22-23UT. The end of the main phase of the last magnetic storm. PB approached as close as L=2. 

Previously created SCR proton belt at L=3.4 disappeared. 

31.10.03, 07 UT. During PB retreat from L=2 to L=3-3.5 new solar proton belt was created at L=2.2. This 

belt will survive at the enhanced level during one year. 

At the bottom part of the fig 5 similar profiles are shown for 14-26 MeV spectrometer channel. Only last 

SCR belt is visible at this energy while PB positions are the same as for 1-5 proton profiles. 

5. PROTON BELT DURING JULY 22-30, 2003 MAGNETIC STORMS. 

Similar analysis was performed for a chain of three magnetic storms at the end of July, 2004 using SERVIS- 

1 energetic particle measurements. It was also polar orbiter with altitude of 1000 km and therefore satellite 

contact with radiation belts was longer and more stable as compared with 

KORONAS-F. We will use results of the study of solar proton dynamics during these events presented in 

details in [Lazutin et al., 2008]. 

Three magnetic storms with a maximum Dst deviation 100, 150 and 200 nT were registered on July 22, 25 

and 27, as shown by Fig.6. Arrows indicate the moments of the proton radial profiles measured by SERVIS- 

1 spectrometer and shown on fig 7. Again we will follow proton radial profile transformation from day to 

day. 

21.07.04 Pre-storm quiet day radial profile with typical intensity and the maximum position (L=3). 

22.07.04 Measurements were done after SC, during the main phase of the first magnetic storm. There were 

no changes of the profile compared with the quiet day and no effects of the SC injections. 

23.07.04 To the end of the main phase of the first storm solar proton penetration boundary approached to 

L~3.5 and SCR intensity was at the maximum. It was the middle of the recovery phase when this profile 

was measured and one can see that low energy solar protons became trapped with maximum at L=3.7. 

24.07.04 Proton radial profile remains the same before the beginning of the main phase of the second 

magnetic storm. No traces of the injection at the beginning of this storm are present. 

155


Fig 5. Radial profiles measured by CORONAS-F spectrometer from October 27 to 30, 2003. Channels 1-5 MeV (left) and 

14-26 MeV (right) 

Fig 6 Storm-time variation during magnetic storms, July 

2004 

Fig. 7 Radial profiles of the 1.2 MeV protons, 

SERVIS-1. All profiles were taken at the same 

longitude over BMA. 

25.07.04 Important changes of the radial profiles were registered after the main phase of the second magnetic 

storm. Previously created proton belt disappeared because it was occupied by the region of the direct SCR 

penetration, the quasitrapping region. What was the fate of this trapped protons – do they escaped from the 

magnetopause into the solar wind or were lost by diffusion into the loss cone, or they survive due to the 

radial diffusion from L=3.7 to L=3.2? Anyway, new proton belt was created during the initial part of the 

recovery phase of the second storm. 

26.07.04 Before the beginning of the last magnetic storm one can see that intensity of the proton belt 

increased and maximum shifted a little earthward. That we can ascribe to the action of the recovery phase. 

27.07.04 It seems that this new (solar) proton belt was too close to the Earth to be affected by the PB motion 

during the main phase of the third magnetic storm. As was mentioned previously, there were no effects 

indicating on the particle SC injection (see Fig. 2). 

28-29.07.04 During the recovery phase of the third magnetic storm one can see an increase of the intensity 

and earthward shift of the proton belt maximum. 

It is evident from the radial profile transformation discussed above, that it was created and accelerated at the 

recovery phase of the magnetic storm, not by the SC-injection. 

6. DISCUSSION AND CONCLUSION 

Process of the solar proton capture to the proton belt at L=2-3 was confirmed by the observation during 

several magnetic storms, there are no doubts on the reality of this process. But there are different opinions on 

the mechanisms of this process. We analyzed here two models which were discussed in publications. 

156


First model of resonant particle injection into the inner magnetosphere by SC pulse was described in details 

theoretically, was registered experimentally during the magnetic storm of March 24, 1991 and accepted for 

the explanation of the poststorm increase of the proton population in radiation belt in other cases. 

There are three aspects of the SC injection model, which restrict its acceptance as a source of the solar proton 

capture. First one relates to the restriction of the energy of trapped protons which cannot be lower than ~ 15 

MeV as was discussed earlier. Second restriction comes from the demand of exceptional large magnitude of 

the SC pulse for the effective injection. And the last factor follows from the fact that even if SC injection was 

effective, there is strong probability that this new belt will be swept out when the boundary of quasitrapping 

region will move closer to the Earth during the main phase of the magnetic storm. 

The second mechanism of direct solar proton trapping during the recovery phase found confirmation by 

detailed analysis of the particle dynamics during several magnetic storms. New proton belt was found 

outward from the last position of the SCR penetration boundary, i.e. on the magnetic field lines which 

previously were at the quasitrapping region and then became dipollike, keeping protons at the closed drift 

shells. 

This mechanism has also restriction on proton energy, but different from the SC injection mechanism. Here 

exists upper limit of the trapped protons somewhere between 10 and 20 MeV. For high energy particles 

magnetosphere recovery is too slow and third adiabatic invariant conserves. 

This restriction on energy also is confirmed by the observations. 

Therefore we can conclude that from the proposed two mechanisms of the SCR capture to the radiation belt 

only the second one, mechanism of the direct trapping at the magnetic storm recovery phase effectively 

supported by the direct measurements. 

References 

Blake, J.B., Kolasinski W.A., Fillius R.W, and Mullen E.G. (1992) Injection of electrons and protons with 

energies of tens of MeV into L > 4 on 24 March 1991, Geophys. Res. Lett., 19, 821. 

Kress, B.T., M. K. Hudson, M. D. Looper, J. Albert, J. G. Lyon, C. C. Goodrich, (2007) Global MHD Test- 

Particle Simulations of >10 MeV Radiation Belt Electrons During Storm Sudden Commencement, J. 

Geophys. Res., 112, A09215, doi:10.1029/2006JA012218. 

Kuznetsov S.N., K.Kudela, S.P. Ryumin, Y.V. Gotselyuk, (2002) CORONAS-F satellite - tasks for study of 

particle acceleration, Adv. Sp. Res. 30, 223 

Lazutin L.L., Kuznetsov S.N., Podorolsky A.N. (2006) Solar proton belts in the inner magnetosphere during 

magnetic storms., In: Proceedings of the 2d International Symposium Solar Extreme Events: Fundamental 

Science and Applied Aspects, 26-30 September 2005, Nor-Amberd, Armenia, ed. by A. Chilingarian and G. 

Karapetyan, CRD, Alikhanyan Physics Institute, Yerevan, Armenia, 67 

Lazutin L. L., Kuznetsov S. N., and Podorolsky A.N. (2007) Creation and distruction of the solar proton 

belts during magnetic storms, Geomag. and aeronomy, 47(2), 187-197 

Lazutin L., E. Muravjeva, N. Hasebe, K. Sukurai and M. Hareyama, (2008) Comparative analysis of the 

energetic electron and solar proton dynamics during strong magnetic storms, Physics of Auroral 

Phenomena”, Proc. XXXI Annual Seminar, Apatity 

Li, X., Roth I., Temerin M., Wygant J.R., Hudson M.K., and Blake J.B. (1993) Simulations of the prompt 

energization and transport of radiation belt particles during the March 24, 1991 SSC, Geophys. Res. Lett., 20, 

2423. 

Looper, M. D., J. B. Blake, and R. A. Mewaldt, (2004) Response of the inner radiation belt to the violent 

Sun-Earth connection events of October–November 2003, Geophys. Res. Lett., 32, L03S06, 

doi:10.1029/2004GL021502 

Lorentzen, K.R., Mazur J.E., Loper M.E., Fennell J.F., and Blake J.B. (2002) Multisatellite observations of 

MeV ion injections during storms, J. Geophys. Res., 107, 1231 

Parker E.N. (1960) Geomagnetic fluctuations and the form of the outer zone of the Van Allen radiation belt. 

J. Geophys. Res., 65, 3117-3126 

Pavlov N.N., Tverskaya L.V., Tverskoy B.A., Chuchkov E.A., (1993) Variations of the radiation belt particle 

flux during strong magnetic storm of March 24, 1991, Geomag. and aeronomie, 33(6), 41-45 

Slocum, P.L., Lorentzen K.R., Blake J.B., Fennell J.F., Hudson M.K, Looper M.D., Masson G.M., and 

Mazur J.E., (2002) Observations of ion injections during large solar particle events, AGU Fall Meeting, 

SH61A-0501 

Tverskoy B.A. (1965) Transport and acceleration of the charged particles in the Earths magnetosphere, 

Geomag. and aeronomy, 5, 793-809 (R) 

157


SPATIAL DISTRIBUTION OF MAGNETIC STORM FIELDS 

O.I. Maksimenko, G.V. Melnik, O. Ja. Shenderovska 

Institute of Geophysics of National Academy of Sciences of Ukraine, Palladin av., 32, Kyiv 03142, 

Ukraine, e-mail: gmelnyk@igph.kiev.ua 

Introduction. 

Abstract. In this message the effect of appearance of local high-latitude areas with large 

positive values of Dst- variations in horizontal component of a geomagnetic field which can be 

connected with a ring current, namely, with its asymmetrical part generated during the main 

phase of magnetic storms is noticed. Results of representation of spatial distribution of a 

magnetic field of compound current sources of a storm in internal magnetosphere, received by 

means of calculations on empirical model of magnetic storm field Tsyganenko Т01, T04S are 

presented, and could be used at the analysis of this phenomenon (during moderate on May, 15th 

1997 and strong on April, 6-7th 2000 magnetic storms). 

In last decade the most progress in creation of magnetic storm field models has been noted. Models represented 

total and individual magnetic field of current sources generating a total magnetospheric disturbances magnetic 

field and their ground geomagnetic variations which are constantly measured on observatories of 

INTERMAGNET. Modern models of the magnetic storm field include large-scale current systems of the 

symmetric ring current (SRC), the partial ring current (PRC) which is closed by field-aligned Birkeland currents 

on an ionosphere in the region 2. 

During the intensive storms this area is located on the equatorial side of polar oval near to twilight. At once 

currents on magnetopause and cross-section currents in a magnetospheric tail (TC) are entered. They are 

supervised by parameters of solar wind plasma and interplanetary magnetic field IMF and are depending on 

inclination angle of the geodipole too. The magnetic fields of the ring current, Birkeland currents, the crosssection 

current of the near part of the magnetospheric tail, which are shielded by magnetopause and penetrating 

interplanetary fields are taken into consideration. Empirical models differ because of parameterization of current 

sources and bases of experimental data of onboard satellite measurements of the magnetic field, particles and 

their input parameters. 

The analysis of new experimental data of low-altitude satellite measurements about a spectrum and density of 

particles with involvement of kinetic model of the ring current (Comprehensive Ring Current Model – CRCM) 

and magnetosphere-ionosphere interactions models has been used for studying of morphology of dynamic 

connection between systems of the ring current and region 2 of field-aligned currents in twilight, source of which 

is the azimuthal gradient of plasma pressure in internal magnetosphere [Zheng et al., 2006]. 

However, studying of magnetic field topology on ground geomagnetic measurements continues to remain 

urgent. At the same time, experimental ground data do not allow to divide completely the contribution from 

different compound current sources of the magnetic storm field, despite of using of separate standard indexes of 

geomagnetic activity for the polar cap (PC), for auroral zone (AU, AL, AE), for middle latitudes (Kp) and lowlatitude 

areas (ASY, SYM, Dst). The last of them determine the energy characteristic of storm field and its 

asymmetry. 

Below the some results of studying of the magnetic field changes during storms with the sudden commencement 

(SC) are presented. In particular, according to INTERMAGNET observatories data local high-latitude areas with 

positive Dst-variations in afternoon sector during the main phase are displayed and the modeling calculations by 

Tsyganenko model T01, T04S are performed. [Tsyganenko, 2002; Tsyganenko et al., 2003]. 

Spatial distribution of the geomagnetic field variations during storms. 

Changes of the magnetic field during storms are characterized by Dst-variation. Here and in the further this term 

is used for definition of the magnetic field variation during the storm relative to a quiet level. As a quiet level the 

158


geomagnetic field horizontal component H (also X and Y) average value from two international magnetic quiet 

days is taken: the last before a storm and the first after it. It is considered that the magnetosphere 

a) 

b) 

Fig.1. Vectors of equivalent current during the magnetic storm main phase according to geomagnetic field 

observation by INTERMAGNET observatories: for the magnetic storm on May, 15th1997 (Dst =-115nT, 

12.40UT) a); for the strong magnetic storm on April, 6-7th 2000 (Dst =-373nT, 01UT) b). By blue color 

geomagnetic coordinates, by red – vectors of the east equivalent current are shown. 

159


a) 

b) 

Coordinates of observatories 

Station name 

ABB. 

code 

Geographic 

Lat. Long. 

Geomagnetic 

Lat. Long. 

Horsund HRN 77.00 15.55 73.88 125.99 

Tromso TRO 69.67 18.95 67.21 116.25 

Abisko ABK 68.36 18.82 66.06 114.66 

Sodankyla SOD 67.37 26.63 63.93 120.00 

Nurmijarvi NUR 60.52 24.65 57.85 113.16 

Brorfelde BFE 55.62 18.82 55.45 98.48 

Furstenfeldbruck FUR 48.17 11.28 48.38 94.61 

Fig.2. Changes of solar wind parameters: the dynamic pressure Рsw, protons thermal speed WP+; interplanetary 

magnetic field components B, Вх, Ву, Bz (WIND data); the SYMH index (WDC for Geomagnetism, Kyoto 

data); DstH on INTERMAGNET observatories in the European longitudinal sector during the magnetic storm on 

May, 15th 1997 (MC – the magnetic cloud duration) a) and during the magnetic storm on April 6-7th 2000 b). 

ring current as a basic source of Dst-variation has the asymmetry connected with RC features and also with other 

sources (ionospheric and field-aligned currents) and predetermine Dst axial asymmetry. Latitudinal dependences 

of Dst values and substorms are known in the classical case too: the maximum of the Dst amplitude is observed 

on equator and the Dst amplitude decreases polewards, amplitudes of substorms on the contrary, have a 

minimum near equator and a maximum in auroral latitudes. 

However, the behavior of Dst(H)-variation during separate magnetic storms shows essential deviations from 

described above the classical scheme. 

The picture of equivalent current vectors during Dstmin for the moderate magnetic storm on May, 15th 1997 (Dst 

=-115nT) at 12.40UT (fig.1а) and the strong magnetic storm on April, 6-7th 2000 (Dst =-323nT) at 01.00UT 

(fig.1b) have been constructed for more evident representation of distribution of the currents generate the Dst. 

160


The vectors are constructed based on orthogonality of electric and magnetic fields components according to 

observation of components X and Y by observatories of INTERMAGNET after the maximum possible 

exception of substorms. The common feature of pictures of distribution of both storm fields is global depression 

of the magnetic field with the western direction of the equivalent current vectors and with appreciable 

intensification of magnitude of the magnetic field depression and its spatial irregularity for the more intensive 

storm. The east currents of the big magnitude (hence, big positive values of the Dst-variation) at the north of the 

Europe for the magnetic storm on May, 15th 1997 are the main distinctive feature. They are observed in narrow 

area at latitudes 58-64°Ф. Weaker positive currents were observed at high latitudes (>75°Ф) above Canada and, 

probably, they reflect the effect of particles precipitation in morning sector. Duration of existence of the positive 

Dst source can be tracked according to daily changes of conditions in the near-earth environment by WIND 

satellite data (radial Bx, azimuthal By and southern Bz components of IMF, dynamic pressure Psw and speed 

WP + of the solar wind), SYM and AU indexes, and also Dst-variations at the European stations (fig. 2). Positive 

values have amplitude +350nT (ABK), +500nT (SOD), +200nT (NUR) and 100nT (LER) are attended by large 

values of AU and long-term southern component IMF during the magnetic cloud, which have caused this storm. 

They are kept in an interval 10.00 - 16.00UT, which is more than duration of substorms. The uncovered local 

high-altitude areas with big (up to 600нТл) positive values of the Dst (H)-variations, arising during the main 

phase of some magnetic storms, probably are associated with closure of the part of the ring current. That is the 

partial ring current (PRC), which is generated by particles on the open field lines. PRC is closed by field-aligned 

currents on ionospheric altitudes in polar latitudes, where the electrojets develop [Feldstein et al., 2006; 

Jaremenko et al., 2004]. Position of this ionospheric region 2 is located near equatorial border of auroral zone in 

evening sector at latitudes >65°Ф and can move to equator under storm intensification and at increase of the RC 

intensity with simultaneous moving of the region 2 center to earlier hours [Zheng et al., 2006]. 

The scheme of vectors of equivalent current for the strong storm on 6 – 7th April, 2000 with a complex 

configuration of the magnetic storm field (fig. 1b) shows the similar shift of area of east currents (positive Dst) 

up to lower latitudes 56 - 60°Ф where the border of auroral zone above Northern America is located in earlier 

afternoon sector. At the same time above the European region in night sector (fig. 2b), when the partial ring 

current was not observed, the positive Dst(H)-variations has not been noticed. The revealed features of the 

spatial distribution of the geomagnetic field disturbances during magnetic storms with the sudden 

commencement differ depending on the storms intensity and space weather. 

The strong storm on 6 – 7th April, 2000 was attended by big values of southern components IMF and the short 

peaks of SW pressure during the main and recovery phases, which can be caused by dipolarization in southern 

IMF and penetration of the field with precipitation particles at cusp latitudes under northern IMF. 

Non-uniformity of the spatial location of ground observatories, absence of additional data about the effects of 

particles precipitation complicate the explanation of the large amplitude of positive Dst(H)-variations. Using of 

the observation data of the variation magnetic field components on chains of ground system IMAGE does not 

improve interpretation of results without carrying out of the analysis of components Dst(Z) variations. 

Results of modeling calculations of the magnetic storm field. 

Using the ground geomagnetic field variations data we could not divide the contribution from each magnetic 

field of compound magnetosphere current sources in total magnetic storm field. Therefore below we shall 

consider spatial distribution of ring current (RC) magnetic field and the total magnetic storm field during the 

main phase of the storm by results of calculations with using the empirical data-based Tsyganenko model (Т01, 

T04S) for the inner magnetospheric magnetic storm field which is placed on a site 

http://geo.phys.spbu.ru/~tsyganenko/modeling.html and is easily accessible to any user. The model Т01 

represents all known magnetosphere-ionosphere electric current systems in depending on storm intensity (Dstindex) 

and conditions in the environment space. Input parameters of storm magnetic field model include an 

angle of an inclination of a geodipole, Ву, Bz IMF components and solar wind (SW) parameters and also factors 

(G1, G2) their connections with currents at calculation of magnetic field values on distance up to 10RE. 

161

90 

60 

30 

0 

-30 

-60 


-90 

0 30 60 90 120 150 180 210 240 270 300 330 360 

a) 

90 

60 

30 

0 

-30 

-60 

-90 

0 3060 90 120 150 180 210 240 270 300 330 360 

Fig.3 .Maps of longitude-latitude distribution of modeling values of the total magnetic field BzG0 a) and ring 

current magnetic field BzG4 b) at 12.40UT during the main phase of a magnetic storm on May, 15th 1997. 

a) b) c) 

Fig.4. Global distributions of the total magnetic field BzG0 a) and ring current magnetic field BzG0 b) in 

magnetosphere on distance


main phase of the storm. Elongation of negative field region boundaries in the night side with increasing of 

storm intensity is noted. Also the approaching toward the Earth for magnetopause dayside position up to 8RE 

during a strong storm on April, 6-7th 2000 is observed. The estimation of the relative contribution of the 

maximal values of RC field (BzG4) and the current in magnetosphere tail in the beginning of the storm main 

phase at 19.10UT on April, 6th 2000 and in the recovery phase 15.10UT on April, 7th 2000 has been performed. 

It reflects prevalence of RC field almost in 2 times above the magnetosphere tail current field in the recovery 

phase of the strong storm. It does not conflict with literature available data [Tsyganenko et al., 2003, Zheng et 

al., 2006). 

Conclusions. 

1. By means of the ground observations of geomagnetic variations data the area of positive values Dst (H) in 

auroral latitudes (58-64°Ф) in afternoon sector during the main phase of the storm on May, 15th 1997 

(Dst=-115nT) has been detected. It is attended by strong interplanetary meridional electric field Еу>10mV/m 

and intensive southern component of IMF (Bz


THE MODEL INTEGRATION SCHEME OF THE FRAMEWORK 

ATMOSPHERE MODEL (FRAM) 

O.V. Martynenko 

Murmansk State Technical University, Murmansk, 183010, Russia, 

e-mail: martynenkoov@mstu.edu.ru 

Abstract. This work continues the description of the Framework Atmosphere Model (FrAM), 

which is being developed on the basis of the global Upper Atmosphere Model (UAM), for the 

research of interrelation of the broad range of various processes and the phenomena in the upper 

atmosphere. Our previous publications reported about a high-level architecture of the FrAM as an 

open framework, consisting of the controlling Model Manager and the set of independent Models 

of separate atmospheric regions and processes, and about the FrAM data structure. Now we 

present the functional description of the unified model interface. Using this interface the Model 

Manager organizes the information exchange of the connected Models and controls the execution 

of the modeling process according to the task configuration prescribed by a user. 


The atmosphere is a complex natural system of many interconnecting elements. The amount of computer 

models of various atmospheric domains increased greatly in recent decades. But these stand-alone models 

use simplifying assumptions about the interaction of a particular domain with the rest of the system. For the 

reliable description and prediction of space weather events, however, it is necessary to take into account this 

interaction including feedbacks. 

Hence, it is necessary to use first-principles-based physics models in closed coupling with statistical and/or 

phenomenological models and satellite and ground-based observations. Because of the complexity of the 

system it is practically impossible to join all physical domains in a monolithic model code. 

That is why the universal framework tool is needed that would provide the simple integration of 

independently developed models of different processes and phenomena for studying of the coupling and 

inter-dependencies between them. This tool should control the data flow between the data sources and 

models; and between different models, as well, without being dependent on the internal structure and data 

processing methods of the particular model. 

Currently there are several frameworks under development in the area of geophysics (Toth et al., 2005; Hill 

et al., 2004; Allen et al., 2000; Buis et al., 2003). But most of them represent programming kits to build a 

model system from scratch. Other ones require powerful supercomputers or distributed multiprocessor 

systems for operation. 

For the present moment a simple ready-to-run instrument with moderate hardware requirements is not 

available for the common researcher. 

Our system is intended to fill this gap. Its basic structure includes the first-principles-based physics model 

UAM (Namgaladze et al., 1998), which describes the upper atmosphere, ionosphere and plasmasphere of the 

Earth as a coupled system. The already adjusted system of physical interrelations provides the researcher 

with a physical modeling environment in which he can place his own model for studying external 

interdependence of the investigated phenomena. Besides, our framework system can run on the conventional 

desktop computers, what expands the application’s scope of use. 

2. The FrAM system architecture 

Logical structure of the FrAM (with “default” set of the Models, which are inherited from the UAM) is 

presented in Fig. 1. 

The state of the modeling object (Earth upper atmosphere) during model calculation has being kept in the 

computer RAM as multi-dimensional arrays of the values of simulated physical parameters in the spatial grid 

nodes. These arrays (with attaching of some additional information about array structure and meaning of its 

content) are referenced below as Datasets (DS). The modeling simulation process in essence is the 

consecutive changing of the Datasets content in such a way as in every moment they contain the instant 

snapshot of the modeling object. 

164


Fig. 1. Logical structure of the FrAM system (including “default” set of the Models) 

The modeling calculation itself is being executed by the Models connected to the FrAM. Functionally each 

Model represents a method of obtaining the values of physical parameters in the spatial grid nodes. No one 

external object knows how the Model obtains these values – specific method is encapsulated in the Model. It 

can be the solving of some first-principles-based physics equations (as in theoretical models), or retrieving of 

values from database, or usage of some analytical synthesizing as series of polynomial, trigonometric or 

spherical functions (as in empirical models based on statistical generalization of experimental data), or even 

direct measurements of these parameters (as in real time systems). External objects only have information 

about physical meaning of this parameter (what is it) and spatial and temporal point that is attributed to 

(where and when is it). Thus every Model has being used by another system elements as "black box" 

described only in the "input – output" terms. 

The FrAM system is an open framework. It means there is a possibility to integrate additional Model blocks, 

which realise an alternative method of obtaining parameter' numerical values (e.g. first-principles-based 

models instead of statistical ones) or calculate other physical parameters of the atmosphere. 

Models can exchange data through the Manager using the standardized interface. The Manager organizes this 

data exchange: provides every Model all necessary data from other Models and receives new data calculated 

by the Model in order to transfer it to other Models. Every Model can use values of parameters provided by 

other Models. 

Another possible problem of inter-Model communication is the spatial grid difference. The FrAM system 

includes special auxiliary modules for data interpolation (or extrapolation). Formally these modules are 

designed as other Models and use the same methods of data exchange through the Manager: they get and 

return Datasets, and their internal procedure of data processing is concealed from other system modules. 

The Models' execution order can be arbitrary. The user sets it in the task configuration stage, and during the 

model run stage the Manager executes Models according to this order. 

3. Functional description of the unified model interface 

The key structure of the FrAM model interface is the Dataset object (Fig. 2) that was described in detail in 

our previous article (Martynenko et al., 2007). The universal form of data exchange between the Models is a 

passing of Datasets. The Model fills its internal arrays by return values of calculated parameters according to 

its own method and data structure. But the Model interface block can control which of these parameters to 

pass to other Models. This separation is realized by using external Dataset and selective passing of data to it. 

It allows the usage in modeling run of alternative Models of the same processes and regions (with the same 

physical parameters) in any possible combination in order to switch on/off some physical interrelations and 

feedbacks. 

All DS's during model calculation have being kept in the computer RAM, but some of them may be stored 

additionally in the disk file. These DS's may keep initial conditions for the modeling simulation, and they are 

initialized before the calculation start, or they may keep results of the simulation (final state of modeling 

object) to be processed lately. Non-stored Datasets exist only during calculation and contain intermediate 

information. 

165


Fig. 2. The Dataset object structure 

During model calculation all DS's contain the current state ("instant snapshot") of the modeling area, as it 

was indicated above. 

Hence the Dataset structure is the universal language of data exchange in the FrAM system, and the Model 

interface modules are the interpreters between this language and the internal data structure of independently 

developed Models with an additional function – censoring of the Model input and output according to 

modeling task configuration. 

In order to organize the co-operative work of Models in the FrAM system the user should create the Task 

Description File (Fig. 1). It includes two logical parts: 

1. description of the modeling World with a complete closed system of inter-relation laws of its elements; 

2. the modeling task itself – the description of external forcings (inputs) and a list of modeling results to be 

stored (outputs). 

The description of the modeling World specifies two classes of inter-connecting objects: 

1. external Datasets which are used by the Manager for data passing between the Models. The List of 

Parameters and link to the spatial Grid (Fig. 2) must be specified for every DS. 

2. the ordered list of the Model calls during the calculation cycle step. Every call description includes: 

• designation of the Model to be called with all necessary control options (directly in the Task 

Description File or as the link to external control file) and list of internal datasets of the Model 

• description of the interface tuning: which parameter of which external DS should be passed into the 

Model input and which of Model outputs must be returned into external DS's. This description is 

designed usually as the table of correspondence between the parameter numbers in external and 

internal DS's. 

An obligatory requirement to the call description language is that the Model interface module must 

understand it and tune the Model call and data transfer correctly. The call description manner of some Model 

generally can differ from other Models because every Model interface subroutine is being created 

independently during the Model integration in the FrAM (Martynenko, Knyazeva, 2008). But it's better to use 

the same manner for all Models for easy management of the whole FrAM system. 

The FrAM structure allows repeated calls of the same Model during one modeling cycle step (e. g. when 

Models use different time steps, or in case of the iterative numerical scheme, etc.). In this case every call 

should be described separately as an independent one. 

The second logical part of the Task Description File (TDF) – description of the modeling task itself – 

includes besides the list of modeling results to be stored the description of the time-variating (or not) 

physical inputs – external influences on the modeling object. Because all physics in the FrAM is 

encapsulated in the connected Models, these forcings also must be described in the specific way for every 

Model. Therefore it should be included into the call description section of TDF in order to be processed by 

the Model interface subroutine according to its internal manner. 

This work was supported by the grant № 08-05-98830 of the Russian Foundation for Basic Research. 

166


References 

Allen, G., Benger, W., Goodale, T., Hege, H.-C., Lanfermann, G., Radke, T., Seidel, E., Shalf, J., 2000. The 

Cactus code: A problem solving environment for the grid. In: 9th IEEE International Symposium on 

High-Performance Distributed Computing, pp. 25-32, IEEE Computer Society Press, Los Alamitos, 

CA. 

Buis, S., Declat, D., Gondet, E., Massart, S., Morel, T., Thual, O., 2003. PALM: A dynamic parallel coupler 

for data assimilation. Paper presented at EGS-AGU-EUG Joint Assembly, European Geophysical 

Society, Nice, France. 

Hill, C., DeLuca, C., Balaji, V., Suarez, M., da Silva, A., and the ESMF Joint Specification Team, 2004. The 

architecture of the Earth System Modeling Framework. Computing in Science and Engineering, 6, 18- 

28. 

Martynenko, O.V., M.M. Gladkikh, I.V. Artamonov, D.V. Sobolev, 2007. On usage of the object oriented 

data structure for geophysical data storage and processing. Physics of Auroral Phenomena: Proceedings 

of 30 th Annual Seminar – Apatity, 2007. – p. 171-173. 

Martynenko, O.V., M.A. Knyazeva, 2008. Model integration in the Framework Atmosphere Model (FrAM). 

Physics of Auroral Phenomena: Proceedings of 31 th Annual Seminar – Apatity, 2008. – in press. 

Namgaladze, A.A., Martynenko, O.V., Namgaladze, A.N., 1998. Global model of the upper atmosphere with 

variable latitudinal integration step. International Journal of Geomagnetism and Aeronomy, 1 (1), 53– 

58. 

Toth, G., Sokolov, I.V., Gombosi, T.I., Chesney, D.R., Clauer, C.R., De Zeeuw, D.L., Hansen, K.C., Kane, 

K.J., Manchester, W.B., Oehmke, R.C., Powell, K.G., Ridley, A.J., Roussev, I.I., Stout, Q.F., Volberg, 

O., Wolf, R.A., Sazykin, S., Chan, A., Bin Yu, Kota, J., 2005. Space Weather Modeling Framework: 

A new tool for the space science community. Journal of Geophysical Research, 110, A12226, 

doi:10.1029/2005JA011126. 

167


ANALYSIS OF CLUSTER AND IRIS RIOMETER DATA OBTAINED 

DURING EXPERIMENTS ON IONOSPHERIC MODIFICATION CARRIED 

OUT 16 FEBRUARY 2003 

A.L. Maulini 1 , A.L.Kotikov 1 , A.Gavrasov 2 , V.I. Odintsov 3 

1 Institute of Physics, St.Petersburg University, St.Petersburg, 198504, Russia, e-mail: 

maulini@geo.phys.spbu.ru; 2 Kostroma State University, Kostroma,Russia; 3 Institute of Terrestrial 

Magnetism, Ionosphere and Radio Wave Propagation (IZMIRAN), Moscow, Russia 

Abstract. This article is dedicated to one of the actively developing line of investigation in space 

plasma physics such as artificial modification of the ionosphere. Experiments carried out using 

Tromso heating facility with pump wave frequency of transmitter 4.04 MHz with square 

modulation period 10 minutes in 16 February 2003 is considered. This event was selected because 

of orbits projections of CLUSTER satellites along magnetic field lines went nearby disturbed 

region in ionosphere according to Tsyganeko model (T96). Electric, magnetic field and electron 

density data from CLUSTER satellites and IRIS imaging riometer data using wavelet, short time 

Fourier transform and spectral time analysis developed in IZMIRAN are analyzed. It is shown that 

effect is clearly observed in IRIS imaging riometer data (16 February 2003) right in the beam 

where the heating spot is. Also effect of heating is observed in CLUSTER data when satellites 

cross magnetic field lines conjugated with disturbed region. Thus it is experimentally shown that 

functioning of heating facility affects not only ionosphere but also the coupled ionosphericmagnetospheric 

interaction system. 

Introduction 

Aim of the experiment maid on 16 February 2003 by EISCAT heating facility in Tromso was the study of 

magnetospheric disturbances originated from modified ionosphere. The pump wave of 4.04 MHz had been 

used for ionospheric conductivity modification from 19:55:00 to 23:59:59 UT. The heating wave in 

eXtraordinary polarization (X-mode) and square modulation regime with 5 minutes ON and 5 minutes OFF 

cycle was employed. 

Generation of the disturbances made by enhancement of ionospheric conductivity in presence of the 

background electric field was considered theoretically by Maltsev et al. (1974), Stubbe and Kopka, (1977), 

Oguti and Hayashi (1984). Maltsev et al. (1974) have found analytical solution for some kinds of 

conductivity inhomogeneities, for more general cases numerical modeling should be used. The process can 

be described shortly as follows: in the region with enhanced conductivity electrical field can be considered as 

homogenous, at the border of the region appear field aligned currents, out of the disturbed region electric 

field diminishes as two-dimensional dipole. Disturbances of the electric field and related field-aligned 

currents propagate into magnetosphere with Alfven speed. This propagation is supposed to provide 

disturbances in coupled magnetospheric-ionospheric system much stronger than initial ones. And this work 

tries to check this supposition using different kind of experimental data. 

Satellite observations and analysis 

We used data from Cluster – satellites of European Space Agency. This is a group of four satellites 

forming a tetrahedron what make possible to measure different parameters of cosmic plasma not only from 

one point in space but from a volume. Orbits of satellites were calculated down to the ionosphere ( about 100 

km above the Earth surface) along magnetic field lines using Tsyganenko model (T96) with follows 

parameters: DST = -27, By = 2.9 nT, Bz = 2.3 nT, pressure 

of solar wind Psw = 2.5 nPa. According to calculation the 

disturbed spot at high of ionosphere has about 25 km in 

diameter. 

. 

along magnetic field lines. 

Fig.1 Results of calculation of disturbed magnetic tube 

and projection of clusters’ orbits down to the Earth surface 

168


Results of calculation of orbit projections were used to determine the time when satellites could cross the 

disturbed zone. And this times approximately are: Cluster 1 among 23:10 and 23:30 UT, Cluster 2 23:20 – 

23:40, Cluster 3 22:00 – 22:20 UT and Cluster 4 23:30 – 23:40. 

It is supposed that effect from heating can be seen in particle data and first of all in electron data from 

PEACE: Plasma Electron And Current Experiment instrument. And it is supposed that the frequency of 

modulation of heating facility 0.0017 Hz ( period 10 minutes) can be detected in the data. 

Fig. 2 Results of window fourier analysis for variations of electron density for “expected” frequency 0.0017 

Hz. Horizontal line shows approximate time of satellite crossing the heated spot. 

The window fourier analysis (Fig.2) of electron density variation data shows the time evolution of 

“expected” frequency (0.0017 Hz). The analysis is made for Cluster 1, Cluser 2, Cluser 4. For Cluser 3 the 

PEACE instrument didn’t work during considered period. It is shown that there is some amplification of 

amplitude during satellites crossing the heated tube for all satellites. There is a significant effect in Cluster 4 

in comparison with others that possibly can be explained by closer crossing by Cluster 4 to the center of spot. 

All pictures show rather complicated behavior of amplitude at 0.0017 Hz and it’s not obvious to make a 

decision. But every line has a tendency to decrease to the end of crossing the disturbed region and have a 

local maximum: Cluster 1 about 23:10, Cluster 2 – 23:35, Cluster 4 – 23:40. These local maximums perhaps 

can correspond to real satellite crossings, but it’s not so obvious however. But if so, the real disturbed zone is 

rather smaller than predicted by Fig.1, but lies within calculated boundaries that shows good coincidence 

with orbit modeling. 

Electric field data analysis 

According to supposition that heating can provide enhanced conductivity region in ionosphere which can 

produce field aligned currents analysis of duskward electric field obtained from EFW (Electric Field and 

Wave experiment) instrument was made Maulini et al (2004). 

It is clearly seen in Fig. 3 that some disturbances starts in approximately time corresponding to the 

satellites crossing the disturbed region according to orbit modeling. Line across the graphics corresponds to 

10 minute period (0.0017 Hz – frequency of transmitter). Cluster 1 figure shows set of disturbances started at 

right time, but as to period axis there is no maximum at 10 minute period. One can say that Cluster 1 doesn’t 

cross disturbed region or effect of heating is overlapped by other effect at shorter period. The most 

significant effect is in Cluster 2 data and it close to Cluster 4. According to Fig.1 they cross disturbed region 

roughly at the same time and distance. Maximum of wavelet coefficients is approximately near 10 minute 

period so it is possible to conclude that heating can provide such effect in the data. As to Cluster 3 it is seen 

from Fig.1 that it crosses the disturbed region much earlier and distantly than other and this behavior seems 

to correspond to its wavelet figure: the level of data is less than other but there is maximum in coefficient in 

vicinity of 10 minutes period line. One can conclude that it detects heating effect but near the boundary of 

disturbed zone. In contrary to Cluster 1 Cluster 3 could not be affected by some other effect at lesser period, 

but maximum at about 5 minutes is also seen at Cluster 3 wavelet figure. 

169


Fig.3 Wavelet analysis for duskward electric field for every satellite. Line shows the “expected” frequency 

0.0017 Hz. 

IRIS 

And finally the analysis of IRIS (Imaging Riometer of Ionospheric Studies) data has been done. IRIS is 

placed in Kilpisjarvi and represents 49 antennas scanning each other corresponding narrow sector of sky. 

Together they show two dimensional distribution of riometric absorption which can be calculated to different 

altitudes from 80 to 120 km. Fig.4 shows observed by IRIS part of sky at altitude of 100 km. Marked circle 

corresponds to zone being heated and coincides with 9 th ray. So we expect to see an effect from heating most 

of all in this ray data and not to see it in others not joined with 9t ray. 

Fig.4. IRIS visible part of sky at 100 km altitude. 

This part of work was done in using adaptive filter analysis based on Widrow-Hoff iterational 

algorithm. (The method was developed in IZMIRAN by V.I.Odintsov and one can be acquainted with this 

method in the article http://matlab.izmiran.ru/magdata/papers/AF_Geophys.pdf) 

170


Fig.5 IRIS spectral analysis for 0.0017Hz, 16.02.2003 

This method has been formally applied to calculations for every of IRIS beams and result of analysis is 

presented on Fig.5. It is clearly seen that there is an obvious maximum in signal level for expected frequency 

of transmitter (0.0017 Hz) right in the 9 th ray. 

Conclusions 

Different types of data and different methods have been included in analysis and these analyses show that 

the effect of heating can be seen in the level of ionosphere and orbits of Cluster. Thus it makes possible 

sounding of disturbed zone in the system of coupled ionospheric-magnetospheric interaction. But as to 

window fourier and wavelet analysis one can say that there is some effect at expected frequency, but also this 

effect exists for other frequencies and it is not so obvious that just heating is responsible for such behavior of 

parameters. So the single experiment is not enough for definite statement and other coordinated and 

combined experiments including satellite and ground based observations are needed. 

As to IRIS data and it’s analysis it seems to be rather optimistic that such a good effect appears in the 

expected zone (in 9 th beam). In Gavrasov et al.(2004) it is shown window fourier analysis of the data and it 

doesn’t show such a good effect due to very problem with noise filtering. The method applied by Odintsov is 

developed especially for very low frequency cases that are more common for geophysical research. And it 

seems to prove its value. So this method seems to be useful to try it in other data analysis. 

References 

Maltsev, Yu.P., S.V. Leontyev, W.B. Lyatsky, Pi2 pulsations as a result of evolution of an Alfven impulse 

originating in the ionosphere during a brightening of aurora. Planet. Space Sci., 24, 1519-1533, 1974. 

Stubbe, P., and Kopka, Modulation of the polar electrojet by powerful HF waves. J Geophys. Res., 82, 2319- 

2325, 1977. 

Oguti, T., and K. Hayashi, Multiple correlation between auroral and magnetic pulsations 2. Determination of 

electric currents and electric field around a pulsating auroral patch. J Geophys. Res., 89, 7467-7481, 

1984. 

Odintsov V.I., Konradov U.I., Kuksa A.A., Application of Matlab Web Server in geophysics for 

interactive adaptive data processing distrtibuted in the internet (in Russian), 1823-1835 

http://matlab.izmiran.ru/magdata/papers/AF_Geophys.pdf 

Maulini A.L., Kotikov A.L, Bosqued J-M. Spatial estimation of disturbed region in the magnetosphere 

related with ionosphere HF heating. Proceedings of the international conference “Problems of 

Geocosmos”, 204-208. 2004. 

Gavrasov A. Maulini A., Frolov A. Experiments on artificial excitation of ionosphere spent on 16 february 

2003 and 17 march 2004. Analysis of satellite and riometer data. Proceedings of student scientific 

conference “Physics and progress”, 53-59, 2007. 

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173


174


175


176


177


ON CLOSING A GAP IN SPACETIME PHYSICS 

Karl Mocnik 

A-8020 Graz, Austria, Neubaugasse 83 

Abstract. Maxwell and Michelson, the two pacemakers of Electrodynamics and Classical Optics, left us 

the best in-sights into light and space. Even though Maxwell’s proposals on how to detect the Aether were 

both ambiguous and unconsciously correct in it’s basic aim, and unsuited in their experimental promises, 

they have the absolute merit to stimulate the research on the utmost fundamental question that occupied 

Mankind long ago: Does the Aether exist or not? Continuingly, Michelson left to the world three prospects 

deserving thorough scrutiny. The first is a hint of a geometrical construction where, according to Huygens’ 

principle in conjunction with the corpuscular view, the absolute paths of the light pencils in space after 

their trips to-and-fro in his interferometer don’t exactly reunify. The second one is the actually observed 

null-result, surprisingly showing that the light rays perfectly reunify. The third fundamental is an elaborate 

proposing Aetherdrift detection by looking for a violation of the law of reflection. Nevertheless, it is 

strange to realize that just the obvious discrepancy between Michelson’s ray-optical construction and the 

experimental null-result never attracted attention of the surveyors. As a consequence the third prospect was 

dropped in the past and was envisaged again recently. 

Introduction 

We show that 

1. a positive Aetherdrift measurement is feasible by adopting an idea of Michelson and Morley proposed 

in the supplement of their historical experiment in 1887. 

2. the predominating theories on the kinematics of light propagation (Special Relativity, Lorentz’s 

“Length Contraction” hypothesis, and the “Absolute Space-Time” theory of Marinov) typically 

are travel-time-theories (TTT) and don’t explain light propagation physically but instead do interpret 

it on the grounds of hypotheses, postulates and axioms which are entirely artificial rather than 

to be developed from Euclidean geometrical fundamentals. 

3. on the grounds of Euclidean Geometry and according to the wave-train-growth-velocity theory 

(WGV) in the strict sense, the null-effect in the historical Michelson-Morley experiment isn’t at all 

a “negative result” as was purported frequently, but follows perfectly from the classical laws of 

Optics as are a) Huygens’ principle, b) Doppler’s principle; c) Bradley’s principle of the Aberration 

of light, if and only if a thorough analysis is made with a ruler and a circle. There is no use for 

quickly proposed TTT-hypotheses, postulates and axioms. 

4. Since the Space-time properties of the Michelson-interferometer has been investigated in detail 

[3], showing that according to the WGV the null-effect is a basic ingredient of the stationary 

Aether theory, it follows that neither the lengths of moving bodies do contract, nor is “the light 

speed” a constant. There isn’t any “light speed” per se, for there are two types of light speeds: a) 

the unidirectional light speed (one-way) and the echo (average) light speed (there-and-back). 

5. The unidirectional light speed is not constant but depends on the orientation with respect to the 

motional direction of the Earth in space. 

6. The echo light speed is a natural constant following from the mentioned WGV and from the principles 

of Classical Optics as a natural constant value. A separate postulation of the constancy isn’t 

longer required. 

7. The null-result in the MME has shown that a moving system separates cinematically from the preferred 

rest system of reference, however, still preserving the general conservation laws of physics. 

8. The physical separation of the moving system Σ from the rest system Σ is made obvious through 

a marvellous co-operation of two basic principles, namely the Doppler-principle and the Aberration 

principle. As the Doppler wave field propagates in the rest space, a related wave-train pattern 

arises which is shifted by the aberration-angle in the moving system, preserving an invariant geometrical 

size. It’s central feature is the “growth-velocity of the wave-train” (WGV) which correspond 

to each other in both in the rest system and in the inertial system, accomplishing the cinematic 

link between both. 

9. Though the travel time of the front wave and the expansion time of the wave-train are identical, 

the paths they cover aren’t in general identical. 

178


On the Elements of Physical Reality 

In the past presentation we have shown [1] that the length contraction doesn’t and didn’t exist. Length 

contraction is the remedy against another hypothesis put forward by violating both the basic rules of Euclidean 

Geometry and the basic principles of Classical Optics. This hypothesis is called the positive “Aetherdrift-effect” 

in the Michelson interferometer (MI) expected to observe in the past. 

If carefully analysing the MI it shows that the null-effect is both necessary and sufficient to prove nothing 

more and nothing less than the existence of the preferred system of reference which was called “Stationary 

Aether” by Maxwell and others. 

Thus, the notions “Electromagnetic field” and “Aether” are interchangeable. They aren’t only notions 

without real content but are physical realities which can be detected indirectly, firstly, by the MI through the 

positive null-effect-observation, and secondly, by the evidence of the violation of the law of reflection proposed 

by Michelson and Morley. 

In the supplementary section of the historical paper [2] on Aetherdrift, Michelson presented several suggestions 

how else to measure the motional velocity of the Earth without resorting to astronomical means. 

One among them takes advantage of the most original feature he recognized when analyzing the aberration 

of light taking place after the reflection on a mirror inclined 45° with respect to the motional direction of the 

Earth (x-Axis). Interestingly, this feature comprises a surplus aberration-effect of the second order in v / c , 

and is subject of an experimental test envisaged herewith. This suggestion fell into oblivion simply because 

Lorentz’s “length-contraction” rendered it’s investigation meaningless through the argument of a perfect 

masking of the expected angular surplus-aberration angle. 

Recently, Euclidean analysis showed [1,3] that the “length-contraction” isn’t necessarily an element of 

physical reality. Thus, the mentioned argument against the proposal of Michelson and Morley fails to be true. 

Upgrading the Deduction of the Surplus-Aberration 

In their original paper Michelson and Morley treated the special case (45°), herewith neglecting the full 

potential of the method. For this reason, the general case has been considered, Fig.1. Let us start with a parallel 

light beam the width of which is D that hits the mirror AC inclined under an angle ζ with respect to 

the x-axis. The upper element B of the wave front D = AB has to cover the path E = BC = D / tanζ 

�at the 

speed c, in order to hit the mirror at rest in the Aether. If, however, the mirror moves at the speed v along the 

x-axis the upper wave front element B has to cover an additional path s = CC’ in order to meet the mirror. 

The direction of the reflected ray in the Aether system (angle φ) follows from Huygens’ principle according 

to which the reflected lower element A of the wave front covers an identical path AD = BC´ 

in the rest system, 

where DC ´ becomes the reflected wave front when leaving the translating mirror. 

D 

Fig. 1: Trajectory of the absolute light path according to the law of 

reflection when a mirror AC moves in the “Aether”. 

From the relation ( E + s) 

/ c = s / v 

B C C´ 

(put v / c = ε ) it is 

s = ε ⋅ E /( 1− 

ε ) . Consequently, the angle ζ alters and becomes ζ ´ , 

D φ ζ ζ ´ 

then it is tanζ ´ = ( 1− 

ε ) tanζ 

. From Fig.1 it isφ = 90° − 2ζ 

. 

x 

As a result, the total aberration angleφ , after a little calculation, 

A v 

2 2 

is sinφ 

= 2( 

ζ −ζ 

´) = ε ⋅sin 

2ζ 

+ 3⋅ 

ε sin ζ ⋅sin 

2ζ 

. The first order 

component ε ⋅ sin 2ζ 

cancels out within the inertial system of 

reference and isn’t observed at all if the light source is attached to the inertial system of the observer. Hence, 

2 2 2 

he only observes the second order component of the aberration which is Ψ = kε 

= 3⋅ 

ε ⋅sin 

ζ ⋅sin 

2ζ 

��as 

a 

function of the incidence angle μ = 90 −ζ 

, indicating that in the moving system the law of reflection seems to 

2 

be violated in this special case of optical arrangement. The coefficient k = 3⋅ 

cos μ ⋅sin 

2μ 

at μ �= 45° is 3/2, 

in contrast to ½ in the abbreviated calculation of Michelson and Morley, and is subject of an experimental 

test just going on. 

179


Either TTT or WGV theory? 

Exclusively all theories on spacetime forthcoming hitherto are “travel-time-theories” (TTT). As such, 

Lorentz’s theory of 1886 [4] is known to be “classical”, but in fact it is the contrary of it: it is simply an arbitrary 

forecast, initiated by an insufficient use of geometry. A theory proposed recently [1,3] starts from 

Euclidean Geometry, and is a wave-train-growth-velocity theory (WGV). The TTT and the WGV are in general 

incompatible with each other insofar as the former is based on the so-called “Galilean-Velocity- 

Subtraction-Operation” (GVO), whilst the latter is based on the Co-linear-Velocity Subtraction Operation 

(CVO), the theoretical difference being a subject to be settled experimentally. In one respect the WGV has 

been experimentally confirmed already long ago through the observation of the null-effect, and was explained 

without using additional hypotheses or postulates [1,3]. In another respect that concerns the reflection 

of light neither the TTT nor WGV has been tested experimentally, as yet. 

Imagine a light beam incident orthogonally on a mirror attached at the upper extremity of a measuring rod 

AB inclined to the x-axis under an angle i , and moving at the speed v < c , where v / c = ε . At the inclination 

angles i = 0°, 90°, 180°, 270° of the rod, the TTT and the WGV predict the same, namely: the returning light 

beam is reciprocal, i. e. the light comes back along the same trajectory as it has propagated out. At these angles 

the TTT and the WGV are indiscernible from each other, as they imply zero lateral deflection of the 

reflected light beam. However, at angles other than these the TTT predicts a lateral deviation of the reflected 

light beam, whilst the WGV doesn’t. 

Approach according to the TTT 

Huygens’ principle is an unexpected subtle means. It permits a sharp decision between the mentioned 

theories. If μ is the angle of incidence of a light ray AM ´ on the meanwhile the space point X ´ passing 

mirror X ´M´ 

in the moving system, and if i is the inclination angle between the light beam and the x-coordinate 

(direction of motion of bar A ´M´ 

), then in the moving system the law of reflection is violated [5]. 

During the time interval when the wave propagates from A to M the bar AM moves to the position 

A ´M´ 

(Fig.) where the wave front arrives at the advanced 

n 

L 

n 

/ R 

K 

mirror inclined under the angle μ to the bar and attached 

to it’s upper extremity M , at the advanced space point 

M ´ . Supposed that the bar and the mirror would in this 

μ 

Ψ 

ω 

κ 

κ 

T 

α 

moment stop motion along the x-axis, then M´ L would 

be the trajectory of the reflected wave front. The 

reflection law would then remain intact. Because of the 

wf motion of the bar together with the mirror one doesn’t 

2μ-i β 

l M´ M´´ 

μ μ-i 

α 

x 

know at the moment where the trajectory of the reflected 

wave front is located. One does only know with certainty 

that during the common motion of the bar together with 

w v 

the mirror from A ´ to A " the reflected wave just arrives 

η i X´ X´´ 

A v A´ A´´ 

Huygens’ circle H-C (radius M´ A ). The not reflected 

wave front, if imagined to be infinitesimal small, would 

Huygens-Circle H-C 

arrive at H-C in the space point T und would leave the 

Fig. 2 

mirror which has to be imagined to be larger, in the space 

point K . Consequently, M´ K were the “virtual mirror” 

along which the individual elements of the wave front are reflected, whilst the bar together with the mirror 

move from M ´ to M " . Thus, KR is the actual wave front of the reflected wave which is a tangent through 

the space point K and touches H-C. Also M´ R is the new trajectory of the wave reflected in the space point 

M ´ . If one adopts the standpoint of an observer who together with the bar approaches M " he observes the 

apparent trajectory to be identical with the direction M" R which deviates by the angle Ψ from the line n 

oriented parallel to M´ L . 

Thus, it is tanΨ = [ LR − M´ 

M" 

⋅sin( 

2μ 

− i)] 

/ [ LM´ + M´ 

M" 

⋅cos( 

2μ 

− i)] 

Because of the smallness of Ψ


According to the sine law it is M ´ K / cos( μ − i) 

= ε / cos( μ + κ −α 

) = 1 / cosκ 

. Finally, cos κ , sin κ , sin 2κ 

, 

cos 2κ 

, sin ω , sin Ψ have to be expressed through the given notions i , μ and ε = v / c . 

It follows: 

2 

2 2 2 2 

cosκ 

= (sin μ ⋅ 1− 

( ε sin i) − ε sin i cos μ) 

/ 1− 

2⋅ 

ε cos μ cos( μ − i) 

1− 

( ε sin i) 

+ ε (cos μ − sin i) 

2 

2 2 2 2 

sinκ 

= (cos μ ⋅ 1− 

( ε sin i) − ε cosi 

cos μ) 

/ 1− 

2⋅ 


1− 

( ε sin i) 


sin 2μ 

− 2ε 

⋅cosμ 

sin( i + μ) 

⋅ 1− 

( ε sini) 

+ ε (cos μ ⋅sin 

2i 

− sin i ⋅sin 

2μ) 

sin 2κ 

= 

2 2 2 2 

1− 

2⋅ 

ε cosμ 

cos( μ − i) 

1− 

( ε sini) 


− cos2μ 

− 2ε 

⋅cos 

μ cos( i + μ) 

⋅ 1− 

( ε sini) 

+ ε ( −cos 

μ ⋅cos2i 

− sin i ⋅cos2μ 

) 

cos2κ 

= 

2 2 2 2 

1− 

2⋅ 


1− 

( ε sini) 


2 

2 

sinω 

= sin( 2κ 

+ 2μ 

−α 

) = sin 2κ 

⋅[cos2μ 

⋅ 1− 

( ε sin i ) + ε sin isin 

2μ] 

+ cos 2κ 

⋅[sin 

2μ 

⋅ 1− 

( ε sin i) 

+ ε sin i cos 2μ] 

, 

and one arrives at the general expression 

2 

2 

Ψ ~ sinω 

−ε 

sin( 2μ 

− i) = ( v / c) 

cos2μ 

⋅sin( 

2μ 

− 2i) 

, which by putting μ = 0 leads to Ψ( 

o) = −( 

v / c) 

sin 2i 

. 

This formula shows that the Lorentzian, or, TTT-approach proposes a violation of the law of reflection even 

in the case of orthogonal incidence of light on a mirror attached to the measuring rod. 

Approach according to the WGV 

Provided that an observer moves in space together with a light source, WGV implies two independent 

wave-trains [6], the first one propagating in a Dopplerean manner in the Aether, following the trajectory of a 

“null-effect-ellipse” and being unobservable to the moving observer, whilst the other one is cinematically 

caught by the aberration of light and, thus, propagates in the moving system itself, actually observed by the 

moving observer and behaving such as though light were subject of a perfect “dragging along” together with 

the inertial system. Thus, in this specific case of orthogonal incidence on a mirror the law of reflection, according 

to the WGV, is perfectly preserved. 

Discussion 

The alternative experiment on “Aetherdrift” proposed by Michelson and Morley in 1887 has the potential 

to settle the question whether or not Lorentz’s two hypotheses, firstly the hypothesis of “Aetherdrift” in the 

MME, and secondly the “length contraction” (which depend on each other) either do both co-exist together 

physically or have to be dismissed altogether. The “orthogonal incidence reflection experiment” proposed 

above in order to check whether light incident at 0° on a mirror suffers a violation of the law of reflection or 

not, has the potential to settle the question whether or not the “Galilean” (TTT) prediction of Aetherdrift in 

the Michelson-interferometer experiment of 1887 is a physical element of reality, or is ruled out through the 

null-effect-prediction by the CVO in the sense of the WGV which entirely avoids introduction of artificial 

hypotheses and postulates. If the present experiment on the test of the 45° reflection law violation be positive, 

then and only then the conclusion can be drawn that there isn’t any physical length-contraction. As a 

consequence the GVO together with all TTT would fail to become elements of physical reality. 

Literature 

[1] Proceeding of the International Conference “Problems of Geocosmos”, St. Petersburg, “Coronation of Maxwell’s Aether”, 

p. 246-251; 2002; ISBN 5-7997-0463-0. 

[2] Michelson, A. A, Morley, EW, American Journal of Science, 134, p. 33, 1887. 

[3] Mocnik, K., PM - Praxis der Mathematik im Unterricht, 4/40, 165-67, Köln 1998. Mocnik, K.: The Unnoticed 

Discovery. How Michelson was misled by the Aether”, 2. edition, Graz, 2002, 254 pages, ISBN 3-901805-99. Močnik, K., 

Didaktik der Mathematik, 36. Konferenz, Klagenfurt, „Rätselhafte Geschwindigkeitsvektoren”, 339-342, 2002; 

[4] Lorentz, H. A., De l’influence du movement de la Terre sur les phenomènes lumineuses, Archives Néerlandaises 21, 

pp.103-176, 1886. 

[5] Mocnik, K., Didaktik der Mathematik, 38. Konferenz, Augsburg, 2004 „Die Örter und das Huygenssche Prinzip”, 

385-388. 

[6] Mocnik, K., Didaktik der Mathematik., 37. Konferenz., Dortmund, 2003 „Weg-Zeit-Diagramme verstehen versus Schnelldenker”, 

445-448. 

181 

2 

2 

2 

2 

2 

2 

2 

2


INVESTIGATION OF THE SCATTERING OF VLF FIELD AT A THREE- 

DIMENSIONAL IONOSPHERIC IRREGULARITY, ASSOCIATED WITH 

RED SPRITES 

E.V. Moskaleva 1 , O.V. Soloviev 2 

Institute of Radiophysics, St.Petersburg University, St.Petersburg, 198504, Russia, e-mail: 

1 moelvi@niirf.spbu.ru; 2 soloviev@OS1121.spb.edu 

Abstract. The paper is devoted to the mathematical simulation of the Trimpi effect to obtain the 

tendencies of the electromagnetic field behavior in the presence of such phenomenon as sprites. 

The simulation is based on the studies of VLF field diffraction at a three-dimensional irregularity 

in the lower ionosphere. To solve the problem of the vertical electric dipole field in the Earthionosphere 

waveguide with a local irregularity at the upper wall an original method based on the 

integral equations theory is applied in this paper. The irregularity is chosen in the form of a finite 

by height cylinder without any limitations on the shape and dimensions of its cross-section. The 

model does not take into account fine structure of the sprites. In this paper the numerical 

simulation is performed in terms of the vertical electrical component of the electromagnetic field 

unlike our previous papers considering the attenuation function of the Hertz vector. One can draw 

the same conclusions, as for investigation of the attenuation function. The calculation of the 

attenuation function is more compact and occupied less CPU time. Above conclusions are: 1) not 

only the forward scatter of the field but the backscatter as well are observed; 2) the irregularity 

impact depends on the propagation path orientation relative to the geomagnetic field, on the 

underlying surface properties, and the irregularity location and its geometric dimensions; 3) the 

computed field variations are of a significant character and can be detected experimentally. 

The scientific community pays a great attention to studies of the phenomena related to thunderstorm activity. 

It became clear relatively recently that many of these phenomena are accompanied by local changes in the 

properties of the lower ionosphere (electron concentration and collision frequency). These changes should 

influence the propagation of VLF signals. Due to that, the Trimpi effect may be interpreted as a result of the 

scatter of the electromagnetic field propagating in the wavequide Earth—ionosphere at a local irregularity in 

the lower ionosphere. The goal of this paper is a mathematical simulation of the Trimpi effect which is a 

short-time variation in the amplitude and phase of VLF signal caused by appearance of a local threedimensional 

perturbation in the lower ionosphere. The Trimpi effect related to sprites, what can be also 

considered as three-dimensional irregularities of the propagation medium, attracts increased interest 

especially recently [Rodger, 2003]. Sprites are rather rare phenomena and it is still impossible to reproduce 

them in laboratory, so for their studies all possible methods should be attracted including the VLF remote 

sounding method observing and studying variations in the fields of permanently operating VLF transmitters. 

Sprites or “Cloud—ionosphere discharges” was discovered in 1989. Sprites are light flashes 

observed over the thunderstorm clouds. It is interesting that for a human eye these flashes look not only red 

but rose, orange, even green. Their study appeared to be a rather complicated problem due to their low 

optical brightness and short lifetime equal to tens of milliseconds. Probably that is why their observations are 

registered only at night. By their appearance sprites may be subdivided to the following types: having the 

shape like a carrot, column and jele-fish [Rodger, 1999]. Their occurrence is usually related to strong (>50 

kA) lightning discharges between a cloud and the surface of positive polarity (+CG). Sprites are generated at 

a height of about 50 km, that is, approximately by 30 km above the thunderstorm cloud. Their upper 

boundary is located at a height of about 90 km over the Earth’s surface. The horizontal diameter of sprites (in 

the case when there are not less than two “posts”) is 25-50 km [Rodger, 1999]. The frequency of sprite 

generation is rather low. Over the entire globe, lightning discharges occur 50--100 times per minute, but only 

a few are accompanied by sprites. The causes of this are, first, the fact that the lightning discharges of the 

positive polarity occur much more seldom than the discharges of negative polarity (10% «+CG» and 90% 

«-CG»). Second, all sprites are related to strong positive discharges, whereas only in rare cases strong 

positive discharges are accompanied by these phenomena. Appearance of sprites has been detected in various 

climatic conditions both over the land and seas. The information about other phenomenon related to the 

thunderstorm activity one can found in following paper [Rodger, 1999]. 

Many authors paid attention to studies of the Trimpi effect. A fairly detailed review of these studies 

was presented by Soloviev and Hayakawa [2002] who analyzed various methods of solution of the three- 

182


dimensional problems in the radio wave propagation theory. As far as we know from the publications, 

currently nothing cardinally new can be added to the list presented earlier. This paper presents a development 

of the studies begun by Soloviev and Hayakawa [2002]. The influence of the geomagnetic field in the 

problem of diffraction at a three-dimensional irregularity was considered in our paper [Moskaleva and 

Soloviev, 2006]. The investigation was performed in terms of attenuation function of the Hertz vector. In this 

paper the numerical simulation is performed in terms of the vertical electrical component of the 

electromagnetic field. It could be useful for estimation of the waiting variations of the experimental data. 

This influence in the considered frequency range is most strongly manifested at night when all sprites 

described in publications were optically observed. 

In this paper to solve the 

problem on the field of a vertical electric 

dipole in the Earth—ionosphere 

waveguide having a local irregularity at 

the upper wall, an original method based 

on the integral equations theory 

[Soloviev and Agapov, 1997] is applied. 

The irregularity is chosen in the form of 

a finite by height cylinder without any 

limitations on the shape and dimensions 

of its cross-section. Though in 

publications there are indications to a 

Figure 1. Geometry of the problem. 

presence of a fine structure of the 

sprites, this model does not take into 

account such structure, but models a 

sprite as a scattering volume. It is evident that using VLF electromagnetic field with a wavelength of the 

order of 15 km (for a frequency of 20 kHz) one can not resolve the fine structure of a sprite. The scatter from 

the system of close-located “posts” would not differ from the scatter at the whole cylinder. 

3 

The properties of the waveguide space D ∈ R limited by the waveguide walls and surfaces of the 

model irregularity coincide with the properties of the vacuum, its dielectric and magnetic permeability and 

wave number being ε 0 , μ 0 , and k , respectively (see Figure 1). For determination of the values of the 

parameters of the inhomogeneous impedance model of the waveguide channel Earth--ionosphere, we 

attracted known from publications [Orlov et al., 2000] vertical profiles of the concentration N e ( z) 

and 

effective collision frequency ν e ( z) 

of electrons. 

Using the second Green formula one can obtain an expression for the unknown electrical Hertz 

vector vertical component Π ( r, ϕ, 

z ) in any point of the D region via the integral over the irregularity surface 

S p ∪ Sl 

: 

r r 

r r ikε 

r ⎡ 

r r 

( ) ( ) ( ) ( ) ( ) ( ) ⎤ 

0 

∂ Π 0 R, 

R′ 

Π R = Π 0 R + ∫∫Π R′ 

⎢δ 

p r, 

ϕ Π 0 R, 

R′ 

− ⎥ dS′ 

+ 

P0 

⎢⎣ 

i k ∂ z′ 

S 

⎥⎦ 

p 

r 

r r 

ε ∂ Π( 

R′ 

) ⎡ r r ∂ Π 

( ) ( ′ ) ⎤ 

0 

1 0 R, 

R 

+ ∫∫ ⎢Π 

0 R, 

R′ 

− 

⎥ dSl′ 

, 

P0 

∂ n′ 

⎢⎣ 

ikδ 

∂ ′ 

S 

l n ⎥⎦ 

l 

r 

r 

where R ( r, 

ϕ, 

z) 

∉ S p , Sl 

denotes the observational point, R ′ ( r′ 

, ϕ′ 

, z′ 

) ∈ S p , Sl 

corresponds to the integration 

point, n′ is the normal directed outside the wave volume, ( R) r 

Π 0 is the field of the initial source in a regular 

r r 

waveguide with a thickness of h and homogeneous walls with the impedances δ g and δ i , and Π 0 ( R , R′ 

) is 

the Green function. 

If the vertical component of the Hertz vector is known, the vertical component of the electric field 

may be calculated by the formula: 

2 2 2 

Ez ( r, 

ϕ, z) 

= ( k + ∂ ∂z 

) Π( 

r, 

ϕ, 

z) 

. 

Using the method of construction of an approximate solution of equation described in detail by 

Soloviev [1998] we obtain the expression for the attenuation function of the vertical electrical component of 

the electromagnetic field 

183


r 

r r 

где G u() 

v , 

V 

r r r exp ( ) ( ) ( − ikr) 

∂W 

( R′ 

) ⎡ r r 1 ∂W 

( ) ( R R′ 

) ⎤ 

0 , 

R V R + 

W R, 

R′ 

− 

dS′ 

+ 

= 0 

2π 

∫∫ 

Sl 

δn′ 

Figure 2. Amplitude of the vertical electrical 

component of the electromagnetic field for the nighttime 

period. Black and red curves correspond to a 

regular waveguide and a waveguide with local 

irregularity. 

+ 

kr 

2π 

2 

γ 

∫ 

p 

exp 

i3π 4 

iπ 

4 

[ v] 

= e f ( 0, 

v) 

w( 

e p) 

+ f ( 0, 

v) 

⎢ 

⎢⎣ 

0 

δ 

[ ikr( 

ch( 

u) 

−1) 

] G[ 

u() 

v , v] 

( ( ) ) 

[ () ] ⎥ 1 ⎡ f u v , v ⎤ 

π ⎢ − , 

p ⎣ ch u v 2 ⎦ 

l 

ik ∂ n′ 

( ) ( ) ⎟ ⎟ 

x 

2 ⎛ ⎞ 

−x 

= ⎜ 2i 

2 

w x e 1+ 

⎜ ∫ exp t dt , p = 2kr sh[ 

u( 

v) 

2] 

, u , v - the ecliptic coordinates of the surface z = z p . 

⎝ π 0 ⎠ 

r P r r 

0 

P r r r 

( 0) 

0 

exp 

Ez ( R) 

= W( 

R) 

, E z ( R) 

= W0 

( R, 

R′ 

) , ( ) ( ikr) 

r r r exp( 

ikr ) r r 

1 

W R = V( 

R) 

, W 0 ( R, 

R′ 

) = V0 

( R, 

R′ 

) . 

2πε 0 

2π 

ε 0 

r 

r1 

To solve equation the numerical-analytical method of semi-inversion [Soloviev and Agapov, 1997] is 

applied. It combines the direct inversion of the dominant part of the integral operator of the problem 

(Volterra operator) with the iterative process by which the remaining part of the integral operator is inverted 

through successive approximations. 

As a result of the performed calculations, a series of tendencies in the behavior of the amplitude and 

phase of the vertical component of the electric field E z at the presence of a local irregularity at the upper 

wall of the Earth-ionosphere waveguide is found. It was assumed at calculations that the source and receiver 

are located on the Earth’s surface: z z = 0 . The frequency of the source was chosen to be f = 20 kHz. 

= t 

The impedances of the base S p and side surface S l of the irregularity cylinder were chosen equal to 

−2 

2 

δ = 0, 

5⋅ 

( 1+ 

i) 

⋅10 

and = ( 1− i) 

⋅10 

p 

l 

dv , 

δ , respectively [Soloviev and Hayakawa, 2002]. The dimensions of 

2 

2 

the cross-section of the cylinder (described by the formula [ ( x ) a ] + [ ( y − y ) b ] = 1 

⎥ 

⎥⎦ 

x − p p 

p p ), its height p 

and location relative to the propagation path (shown in the figures by arrows) determined by the coordinates 

of the ellipse center p x and y p were varied. Along the path 0 < x ≤ 1500 km the amplitude and phase of the 

E z were calculated for the cases of various path orientation relative to the geomagnetic field vector, 

properties of the underlying surface, and location and geometric dimensions of the irregularity ( p a , b p and 

z p ). 

Figure 3. Phase of the attenuation function for E z. 

Black curve corresponds to a regular waveguide, red 

curve - waveguide with local irregularity. 

Figure 2 and Figure 3 show the amplitudes and phases of the vertical electrical component of the 

electromagnetic field E z and its attenuation function for the nighttime period. The distance from the source 

to the receiver in kilometers is shown at the x axis. The underlying surface is sea water with a relative 

dielectric permeability of ε = 81 and conductivity of σ = 4 S m -1 . The radio wave propagation direction is 

m 

184 

l 

z ,


chosen along the South—North line (the azimuth is A z = 0 ). The following parameters of the irregularity are 

chosen: a p = bp 

= 20 km and z p = 20 km. The irregularity is put directly over the signal propagation path 

( y p = 0) 

in the region of the minimum of the attenuation function amplitude at the regular path ( x p = 800 

km). At such choice of the coordinates, the effects related to the presence of the irregularity are best 

pronounced [Moskaleva and Soloviev, 2006]. 

No graphs of the amplitude and phase of the vertical electrical component of the electromagnetic 

field E z for the daytime are presented in the paper. Soloviev and Hayakawa [2002] showed that such 

irregularities weakly distort the field in the daytime Earth—ionosphere waveguide. Moreover, the sprites 

modeled here are observed mainly at night. 

Below we consider the perturbation of the amplitude of the vertical component of the electric field 

E z : the difference in the E z amplitude values in the undisturbed and disturbed by a three-dimensional 

irregularity cases. There exists an influence of the irregularity on the behavior of the attenuation function 

phase, but it is less important than the influence on the amplitude behavior. Since the graphs showing the 

phase changes are not such visual as the graphs showing the amplitude changes, below the former are not 

presented. 

Figure 4. Perturbation of the amplitude (E z disturb – 

E z unpert ). Black curve corresponds to the case when 

the geomagnetic field is not taken into account and red 

curve corresponds to the magnetic azimuth of the 

propagation path Az=0. 

Figure 5. Perturbation of the amplitude E z in cases of 

various wave propagation path orientations relative to 

the geomagnetic field . 

Figure 4 shows the curves of amplitude disturbances corresponding to the cases when the 

geomagnetic field is and is not taken into account. The curves differ considerably from each other, so one 

may conclude that taking into account of the magnetic field is important. One can see in Figure 4 and the 

following figures the presence of not only forward 

scatter but backscatter as well. 

The perturbations in the amplitude E z 

illustrating the influence of the irregularity on the 

field as a function of the propagation direction relative 

the magnetic azimuth of the path are shown in Figure 

5. The strongest difference is seen between the field 

behavior at the paths with the azimuth A z 

0 

= 90 and 

A z 

0 

= −90 

, the former and the latter azimuths 

corresponding to the eastward and westward 

Figure 6. Influence of the underlying surface properties 

propagation, respectively. 

The influence of the underlying surface 

properties is shown in Figure 6. The curves are shown 

corresponding to the following underlying surfaces: 

on perturbation of the amplitude Ez. wet soil ( ε m = 20 , σ = 0, 

01 S m -1 ) and sea water 

( ε m = 81, 

σ = 4 S m -1 ). The figure shows the graph calculated at the value of the propagation path magnetic 

azimuth A = 0 . It is worth noting that stronger influence of the irregularity is observed if a see is the 

z 

185


underlying surface than if waves propagate over a land. At other orientation of the wave propagation path, 

the character of the amplitude perturbations is the same. 

Figure 7. Perturbation of the amplitude E z at various 

dimensions of the base of the irregularity cylinder. 

Figure 9. Perturbation of the amplitude E z at a shift of 

the irregularity location in the direction lateral to the 

propagation path. 

Figure 8. Influence of the cylinder vertical dimension 

on the amplitude E z. 

Figure 7 and Figure 8 show the influence of the geometric dimensions of the irregularity on the 

attenuation function amplitude. Figure 7 shows curves corresponding to various values of the semi-axes of 

the cylinder base of the irregularity. The large and small semi-axes of ellipse are taken to be equal ( a p = bp 

) 

and to have values of 10 km, 20 km, and 40 km. 

The influence of the cylinder height z p (10 km, 20 km, and 40 km) is shown in Figure 8. The 

values of the impedances of the base and side wall of the cylinder stayed fixed. Comparing the curves one 

can conclude that taking into account of the possibility of a descent (assent) of the local region of the 

waveguide upper wall relative to the level of the regular ionosphere plays an important role in the study of 

the irregularity impact on radio wave propagation. 

Figure 10. Perturbation of the amplitude E z at various 

location of the irregularity. 

Figure 9 illustrates the fact that the influence of the irregularity on the field in the waveguide 

depends also on the location of the irregularity relative to the radio wave propagation path. Figure 9 shows 

the curves corresponding to the distance of the cylinder axis from the path line equal to y p = 0 , 20 , and 50 

km for a p = bp 

= 20 km and x p = 800 km. Perturbations of the amplitude Ez for y p = 0 and y p = 50 km 

differ more than 10 times that may be explain in the terms of the Fresnel’s zone. It should be noted here that 

for the considered propagation path the lateral dimension of the first Fresnel’s zone on the ionosphere 

surface, the small semi-axis of the latter is ~53 km. 

The position of the observer influences considerably the estimate of the changes caused by the 

presence of the irregularity. A shift in the coordinates of the observational point actually corresponds to a 

186


shift in the irregularity location along and across the radio wave propagation path. The same shift in the 

direction lateral to the path would cause much stronger changes in the irregularity impact than a shift along 

the path. This dependence is shown in Figure 10. 

The performed studies make is possible to conclude on the degree of the influence of the local 

irregularity on the wave propagation. On the base of the numerical simulation performed in terms of the Ez 

one can draw the same conclusions, as for investigation of the attenuation function of the Hertz vector. But 

the calculation of the attenuation function of the Hertz vector (performed in previous papers) is more 

compact and occupied less CPU time. Above conclusions are: 1)Not only the forward scatter of the field but 

the backscatter as well are observed; 2) The irregularity impact depends on - the propagation path orientation 

relative to the geomagnetic field, - the underlying surface properties, - the irregularity location, - geometric 

dimensions of the irregularity; 3) The computed field variations are of a significant character and can be 

detected experimentally. 

References: 

Moskaleva, E.V., and O.V. Soloviev (2006), Scattering of VLF field at a three-dimensional ionospheric 

irregularity: Investigation and application to the Trimpi problem, International. J. Geomagn. And 

Aeronomy, vol. 6, GI3001. 

Orlov, A.B., A.E. Pronin, and A.N. Uvarov (2000), The electron density of lower ionosphere profile 

modeling according to the VLF propagation data, Problems of Diffraction and Propagation (in Russian), 

28, 83. 

Rodger, C.J. (1999), Red sprites, upward lighting, and VLF perturbations, Reviews of Geophys., 37, 317. 

Rodger, C.J. (2003), Subionospheric VLF perturbation associated with lighting discharges, J. Atmos. Terr. 

Phys., 65, 591. 

Soloviev, O.V., and V.V. Agapov (1997), An asymptotic three-dimensional technique to study radio wave 

propagation in the presence of a localized perturbation of environment, Radio Sci., 32(2), 515. 

Soloviev, O.V. (1998), Low frequency radio wave propagation in the Earth-ionosphere waveguide perturbed 

by a large-scale three-dimensional irregularity, Radiophysics (in Russian), 41(5), 588. 

Soloviev, O.V., and M. Hayakawa (2002), Three-dimensional subionospheric VLF field diffraction by a 

truncated highly conducting cylinder and its application to Trimpi effect problem, Radio Science, 37(5), 

1079. 

187


SUB-RELATIVISTIC ELECTRON PRECIPITATION AT HIGH 

LATITUDES: LOW-ALTITUDE SATELLITES OBSERVATIONS 

I.N. Myagkova, E.E. Antonova, S.N. Kuznetsov , Yu.I. Denisov, 

B. V. Marjin, M.O. Riazantseva 

Skobeltsyn Institute of Nuclear Physics, Moscow State University, 119191, Moscow, Russia, 

e-mail: irina@srd.sinp.msu.ru 

Introduction. 

Abstract. The precipitation of electrons with the energies more than 300 keV to the pole of 

external radiation belt is studied. Results of observations of CORONAS-F satellite are used. 

Low altitude (350-500 km) CORONAS-F satellite was launched into a circular orbit with an 

inclination of ~82.5 o and with an initial altitude of about 500 km on July 31, 2001. It operated 

until December 12, 2005 with a final altitude of about 350 km. Its orbital period (� 1.5 hours) 

corresponds to about 15 circuits per day. Charged particles in different energy ranges (protons 

with energy 1-90 MeV, electrons 0.3-12 MeV) were measured by semiconductor and plastic 

scintillator telescopes. Localized electron precipitations were observed to the pole from the 

external boundary of the external radiation belt. It is shown, that such kind of precipitations can 

be observed for about a half of polar crossings. The most of them were observed during 

southward Bz component of interplanetary magnetic field. Results of observations are compared 

with data of auroral satellite Meteor-3M. The nature of observed phenomena is discussed. 

Outer radiation belt is carefully analyzed from the moment of its discovery. However, the 

processes of acceleration of relativistic electrons forming the outer radiation belt are not proper studied till 

now. Outer radiation belt is filled as a rule by large particle fluxes during recovery phases of magnetic 

storms. The dynamics of such filling and article losses is greatly variable. Radial distribution of the main 

peaks of relativistic electrons is comparatively well known (Kuznetsov and Tverskaya, 2007). At the same 

time, small-scale features of such distribution are not studied well. In this paper we present the results of 

the preliminary simultaneous analysis of observations of relativistic electrons on CORONAS-F satellite and 

plasma sheet particles on Meteor-3M satellite and try to show that an additional comparably stable peak of 

relativistic electron precipitation can appear at auroral oval latitudes. We also discuss the possible 

explanations of the observed phenomena. 

Experiments. 

CORONAS-F 

Russian solar space observatory CORONAS-F was launched into a circular orbit with an inclination 

of ~82.5 o and with an initial altitude of about 500 km on July 31, 2001. It operated until December 12, 2005 

with a final altitude of about 350 km. Its orbital period equal � 1.5 hours corresponds to about 15 circuits 

per day. Charged particles in different energy ranges (protons with energy 1-90 MeV, electrons 0.3-12 

MeV) were measured by semiconductor and plastic scintillator telescopes. The devices were developed by 

the Skobeltsyn Institute of Nuclear Physics, Moscow State University (Kuznetsov et al., 2002). Due to the 

low circular polar orbit of the CORONAS-F satellite fluxes of solar protons and electrons were measured by 

the MKL-device on board CORONAS-F experiment only in the south and north polar caps (areas of open 

magnetic field lines) during 15-20 minute intervals every ~45 minutes. 

Meteor-3M 

The satellite Meteor-3M was launched on December 10, 2001 into the orbit with altitude ~ 1000 km 

and inclination ~ 99,6�. Its time of circulation was ~105 min (Marjin et al., 2004). The scientific 

information was collected from Febriary 19, 2002 till June 12, 2005. Presented data were obtained with the 

help of the device MSGI-5EI. MSGI-5EI measures the fluxes of protons and electrons with energies 0.1-10 

keV in 50 energy channels and the integral flux of electrons with energies >40 keV. Comparison of 

188


Meteor-3M observations with the predictions of OVATION model of auroral oval (see Marjin et al., 2006; 

Riazantseva et al.,2006) demonstrate the possibility of using Meteor-3M data for the identification of the 

position of auroral oval. Results of CORONAS-F observations are analyzed together with the simultaneous 

data of auroral satellite Meteor-3M to identify the localization of high energy electron precipitation (auroral 

oval or polar cap). 

Data analysis. 

412 crossings of polar region at altitude 400-450 km were analyzed (CORONAS-F data). Small 

increases of electron precipitations at L>8 to the pole from the polar boundary of the outer radiation belt 

were observed in 248 of them. The time periods where selected when it was no solar electrons in the polar 

caps. 

The examples of electron precipitations at high latitudes in the northern hemisphere are presented 

in Fig. 1. Time dependence of electron flux with the energy 300-600 keV is shown by blue line, 0.6-1.5 

MeV – by green one. L-shell value (Mac-Illvain parameter) is shown by lilac line. We can see that there 

are no electron precipitations in the southern polar region in this time interval. Red arrows mark the 

electron precipitations and show studied peaks of relativistic electrons. It is possible to see that electron 

precipitations were detected in both energy ranges. 

Figure 1. Examples of electron precipitations at high latitudes during 15 September, 2003. 

189


More detailed example of electron precipitations observed at high latitudes at this time in the 

southern polar region during 20 September is presented in Fig. 2 (top panel). It is possible to see that the 

next southern polar cap (1.5 hour later), shown at he bottom panel, does not contain any electron 

precipitations. The integral flux of electrons with the energies > 500 keV (light blue) is presented in 

addition to 300-600 (dark blue) and 0.6-1.5 MeV (lilac) in Fig. 2. We can see that for al three energy 

ranges the electron precipitations in polar regions are clearly selected. 

Figure 2. The example of intensive electron precipitation at high latitudes during 20 September, 

2003 (top panel) and the next crossing of polar region (1.5 hour later) without any electron 

precipitations. 

190


We investigated 16 days during 2003 and 2004 years – four days in each month July, September, 

December 2003 and April 2004. We should notice that significant seasonal variations of the observed 

effect cannot be selected. 

It is important that significant part of analyzed electron precipitation were observed during 2 and 

some of them 3 consecutive crossings of polar regions. Such phenomena were observed during rather quiet 

geomagnetic conditions. This means that observed structure can exist more than 4.5 hours. Fig. 3 shows 

examples of such three consecutive crossings of polar region obtained 5-6 April 2004 and 15-16 July 2003 

The intensity of electron fluxes with the energy 300-600 keV at different L-shells changes not very greatly. 

It is possible to see the L-position of precipitation peaks are practically the same for both cases. Therefore, 

these structures are rather stable. The geomagnetic disturbances during these time intervals were moderate 

– during 4-5 April 2004 Kp index was 4-5 and during 15-16 July 2003 – 4-6, the IMF Bz was southward 

and changed its sign during July 2003. 

Figure 3. The example of consecutive electron precipitation at high latitudes during 4-5 April 2004 

and 15-16 July 2003. 

191


We have the opportunity to compare 61 polar crossings with electron precipitations observed 

during December 2003 and January 2004 on board CORONAS-F with auroral oval position in accordance 

with Meteor-3M data. The time of observations, coordinates and MLT-sectors were suitable for lawful 

comparison for 25 of them. The position of only one of electron precipitations can be identified as polar 

cap, the other 24 ones are situated in polar oval or near its boundary. 

Figure 4. The example of comparison of electron precipitation at high latitudes and METEOR-3M 

data during 1 January 2004. 

The example of such comparison is shown on Fig. 4. The top and middle panels of figure 4 show 

the time dependence of intensity of 300-600 keV electrons (blue line) measured on board CORONAS-F 

satellite, L-shell value (red stroke-dashed and line) and the MLT variations (violet dashed line) during 

the time period of measurements. The bottom panel of figure 4 the Meteor-3M data obtained January 1, 

2004 presented. The presented data of Meteor-3M satellite contains the values of particle fluxes with 

energy 0.1–10 keV. Every flight gives four auroral oval boundaries crossing for each hemisphere to 

192


determine the auroral oval position. The values of universal time (UT), magnetic local time (MLT), 

Invariant latitude (ILAT) and L-shell (L) are signed under the bottom panel of figure 4. Colors mean the 

logarithm of electron flux intensity, cm -2 s- 1 sr. One can see that electron precipitation observed by 

CORONAS-F (noted by an arrow) was situated near the boundary of polar oval. 

Discussion and conclusion. 

1. Peaks of precipitations of electrons with the energy >300 keV were observed by polar lowaltitude 

satellite CORONAS-F to the pole from the outer radiation belt boundary during for more than a 

half crossings of polar region (L>8) in about 60% of crossings. 

2. Part of analyzed electron precipitations were observed during 2 and 3 consecutive crossings of 

polar region. It is possible to suggest that observed structure can exist more than 3 and 4.5 hours. 

3. Practically all of observed electron precipitation in agreement with the METEOR-3M satellite 

data were situated in polar oval or at its boundary. 

Two possible explanations of observed phenomena can be suggested. First traditional connects 

observed features of polar outer radiation belt boundary with filling of loss come due to pitch-angle 

diffusion. Such filling can be inhomogeneous and have definite radial dependence. Second not so 

traditional one is the appearance of localized quasistationary regions of quasitrapping due to magnetic field 

distortion. Radial distribution of plasma pressure in the high latitude magnetosphere can be quite 

inhomogeneous (see, for example, Antonova, 2004; Kozelova et al., 2008). Eastward directed transverse 

current can be formed producing current loops. Magnetic field is decreased inside the loop and plasma 

pressure is increased. Local plasma traps can appear in such a case. Both suggested explanations requires 

the additional verifications with will be done in the future works. 

REFRRENCIES 

Antonova, E.E. (2004), Magnetostatic equilibrium and current systems in the Earth’s magnetosphere. Adv. 

Space Res., 33, 752-760. 

Kozelova, T. V., L. L. Lazutin, and B. V. Kozelov (2008), Total ion pressure changes with L shell in the 

nightside inner magnetosphere, J. Geophys. Res., 113, A07211, doi:10.1029/2007JA012799. 

Kuznetsov S.V., and Tverskaya,L.V. (2007), Radiation belts, Models of Space, V. I, ed. M.I. Panasyik, 

Moscow, 518-546, (In Russian). 

Kuznetzov, S.N., Kudela, K., Ryumin, S.P., Gotselyuk, Yu.V. (2002), CORONAS-F satellite - tasks for 

study of particle acceleration, Adv. Space Res, 30, 1857-1863. 

Marjin B. V., M. V. Teltsov, M. O. Riazantseva, E. E. Antonova, V. V. Khoteenkov, M. A. Saveliev, V.M. 

Feigin (2004), Meteor-3M No 1 particle observations: Initial results, in: Proc. of the 5th International 

Conference Problems of Geocosmos St. Petersburg,(Petrodvorets, May 24-28, 2004), 92-95. 

Marjin B.V, M.O. Riazantseva, E.E. Antonova, V.V. Khoteenkov, I.L. Ovchinnikov, M.A. Saveliev, V.M. 

Feigin (2006), Comparison of Meteor-3M observations of auroral oval position with Ovation model, 

in: Proc. of 6-th International Conference Problem of Geocosmos, (St. Peterburg, Russia, 23-27 May, 

2006), 139-142. 

Riazantseva M.O., E.E. Antonova, B.V. Marjin, V.V. Hoteenkov, I.L. Ovchinnikov (2006), Auroral oval 

boundary observations by Meteor 3M satellite, in: Proc. of 8-th International Conference on Substorms 

(ICS8), (Banff, Canada, 26-30 April, 2006), 259-262. 

193


HIGH LATITUDE MAGNETOSPHERE DYNAMICS DURING MAGNETIC 

STORMS: ENERGETIC PARTICLE DATA FROM LOW-ALTITUDE 

SATELLITES AND GLOBAL MAGNETOSPHERIC MODELING 

I.N. Myagkova, V.V. Kalegaev, S. Yu. Bobrovnikov, 

S.P. Likhachev, D.A. Parunakian 

Skobeltsyn Institute of Nuclear Physics, Moscow State University, 119991, Moscow, Russia, 

e-mail: irina@srd.sinp.msu.ru 

Abstract. Experimental data obtained during magnetic storms by low-altitude satellites permit to 

investigate the high latitude Earth’s magnetosphere structure and dynamics. We have studied the 

variations of the solar energetic particles penetration boundary measured by CORONAS-F and 

“Universitetskiy-Tatiana” satellites during magnetic storm on 15-17 May 2005 (Dstmin=-263 nT). 

It was obtained that on 15 May 2005 the penetration boundary was shifted to the low latitudes in 

the evening sectors of MLT up to 51 degree. Solar energetic particle penetration boundaries have 

been compared with those calculated by the model of magnetospheric magnetic field. It was 

shown that during May 2005 event both solar particle penetration boundary obtained from 

measurements and calculated polar cap boundary are shifted to the lower latitudes in accordance 

with geomagnetic activity enhancement. 

Introduction 

Solar energetic particles (SEP) events are very important source of radiation damage in the near- 

Earth space. So SEP detection in near-Earth space in the experiments on board low-altitude polar satellites, 

studies of their dynamics and spectral characteristics and the variations of the SEP penetration boundaries in 

the Earth’s magnetosphere during the magnetic storms are very important for space weather questions. 

Some CORONAS-F and “Universitetskiy-Tatiana” satellites results of such studies for November 2001, 

October-November 2003 and November 2004 solar extreme events have been published in (e.g. Panasyuk et 

al., 2004, Yermolaev et al., 2005, Kuznetsov et al., 2005, Myagkova et al., 2006, Sadovnichy et al., 2007). It 

was obtained, that SEP penetration boundary during magnetic storm maximums shifts deep to the low 

latitudes. In this paper we will study the dynamics of SEP penetration boundaries during magnetic storm on 

15 May 2005 on the base of experimental data from CORONAS-F and “Universitetskiy-Tatiana” satellites 

and magnetospheric magnetic field modeling. 

Energetic particle fluxes measurements onboard CORONAS-F and Universitetsky-Tatiana Satellites 

One of the scientific goals of the SCR-experiment (Solar Cosmic Rays) on board Russian observatory 

CORONAS-F (Complex ORbital Observations in the Near-Earth space of the Activity of the Sun) was the 

study of the solar energetic particles ( SEP) penetration boundary variations and SEP events influence on the 

Earth’s magnetosphere. CORONAS-F was launched to the polar orbit with the inclination 82.5 o , initial 

altitude about 500 km and was operated until December 12, 2005. Its orbital period was 94.8 min. Charged 

particles in different energy ranges (protons with energy 1-90 MeV, electrons 0.3-12 MeV) were 

measured by semiconductor and plastic scintillator detectors (Kuznetsov et al., 2002). 

Space Scientific and Education project of Lomonosov Moscow State University "MSU-250" was 

timed to its 250-th anniversary (http://cosmos.msu.ru). “Universitetskiy-Tatiana” satellite was launched to 

the orbit with the inclination 83 o , initial altitude about 1000 km on January 20, 2005 (during the most 

powerful SEP event of 2005) and was operated until March 8, 2007. The scientific task of this satellite is 

monitoring of radiation conditions near the Earth. In this work the data about proton with energies 2-100 

MeV, obtained by semiconductor detector (1000 mkm Si) and scintillation detector (CsJ(Tl) 15×20 mm) 

were used (Sadovnichy et al., 2007). 

194


The magnetic storm on 15-17 May 2005 

The magnetic storm was produced by fast CME reaching the Earth's magnetosphere at ~3UT on 15 

May 2005. Plasma density at shock front approached 18 cm -3 , bulk velocity was about 1000 km/sec. After 

inretplanetary magnetic field (IMF) southward turning the magnetic storm develops with peak Dst about - 

260 nT. Strong auroral activity with AL


Figure 2. SEP penetration boundary variations during geomagnetic storms in May 

2005. Dst-variation is shown by solid line. 

Because the proton flux on the penetration boundary does not fall down abruptly, it is possible to apply 

different criteria to the analysis of the penetration boundary position. Along with (Kuznetsov et al., 2002), 

we have used the traditional for Skobeltsyn Institute of Nuclear Physics Lomonosov Moscow State 

University criterion - twice below the maximum of the SEP flux. The values of penetration boundary 

obtained during the morning MLT are marked as open symbols, during evening MLT – as closed ones. The 

time variation of the Dst index is also shown in Figure 1 for comparison. We can see that penetration 

boundary variations correlate with Dst in accordance with (Panasyuk et al., 2004, Kuznetsov et al., 2005). 

The dashed line on the Fig. 2 represents the distance to the inner edge of the magnetospheric tail 

current – projection of the equatorward boundary of the auroral oval at midnight to the geomagnetic equator. 

This distance was obtained on the base of magnetic field calculations by paraboloid model of the Earth's 

magnetosphere (Alexeev et al., 2001). We can see that during storm maximum penetration boundary lies 

below the auroral oval in the region of trapped particles, while during recovery phase it shifts to the higher 

latitudes. Obviously, during magnetic storm main phase there exist the additional mechanisms transporting 

energetic particles from solar wind to magnetosphere on the closed L-shells. 

During storm maximum SEP approached latitudes corresponding L-shells about 2.5. It is accepted that 

SEP fluxes are measured in the region of open field lines, but latitudes with L=2.5 can be hardly associated 

with open magnetic field flux tube. It is interesting to compare the obtained results with those obtained from 

the other experimental sources or model calculations. Figure 3 represents auroral oval observed by IMAGE 

WIC instrument at 06:25:31 15 May 2005 (data from http://workshops.jhuapl.edu/s1/science.html), and SEP 

penetration boundary cross-sections by CORONAS-F satellite pass through the polar cap measured at 6.42 

UT and 6.72 UT. These time moments correspond to the storm main phase. Electric field equipotentials in 

the polar cap calculated by mapping of electric potential from the magnetopause along the open field lines 

are shown by pink lines. They fill the area that can be associated with polar cap. We can see that SEP 

penetration boundary lies on the latitudes lower than not only the polar cap but also than whole auroral oval. 

The experimental data and the results of calculations in four time moments before the storm, during 

storm maximum and during recovery phase are presented in the Table 1. The values of the proton flux with 

the energy 1-5 MeV, magnetic local time (MLT), geographic latitude and longitude (LAT) (LON), magnetic 

latitude and longitude (MLAT), (MLON), experimental and calculated L-shell values are shown. The Lcoordinate 

of the ionospheric point is often considered as the distance to its projection to geomagnetic 

equator along the magnetic field line. 

196


Figure 3. Auroral oval and SEP penetration boundary cross-sections 

The Earth's internal magnetic field model was used to calculate L coordinate. However the 

magnetospheric currents can significantly change the equatorial footprint location. The last column of the 

Table 1 represents the distance to the equatorial footprint of the magnetic field line mapped from ionosphere 

to the equatorial plane by paraboloid model of the magnetospheric magnetic field (Alexeev et al., 2001). The 

"real" L , values differ from "classical" significantly, depending on longitude and MLT. Figure 4 shows the 

magnetic field lines calculated by IGRF (green line) and paraboloid (red line) models at 6:43 UT 15.5.2005. 

We can see that magnetospheric currents shift magnetic field lines to the night side. From the other hand, we 

can see from the Table 1 that during all the chosen time moment penetration boundary lies on the closed 

magnetic field lines, though before the storm and during recovery this is region adjacent to polar cap, while 

during storm main phase this is region of trapped radiation. 

Table. 1. 

MM HH Jp 1-5 

MeV 

MLT LAT LON MLAT MLOM L(exp) L(calc) 

BEFORE THE STORM 

14 5 21.2487 430.0 15.979 55.195 -76.813 66.469 -10.03 6.29 6.04 

14 5 21.4749 706.9 3.011 69.539 68.219 60.125 152.00 5.45 4.06 

15 5 0.3263 920.5 14.985 61.305 -120.219 66.984 -71.14 6.98 6.1 

15 5 0.5331 622.6 3.849 67.945 23.781 64.672 118.81 5.66 5.4 

MAIN PHASE 

15 5 6.4348 97.9 15.716 62.867 148.594 53.297 -151.72 3.44 2.8 

15 5 6.7274 174.6 3.08 46.82 -58.781 57.953 14.28 3.28 3.5 

RECOVERY PHASE 

16 5 3.7991 19.9 15.018 65.117 -172.125 60.633 -123.03 4.63 4.2 

16 5 4.0287 26.5 3.615 59.758 -25.078 66.578 63.078 4.47 6.2 

197


Figure 4. The calculated magnetic field lines from the 

CORONAS-F crossings of penetration boundary during 

storm maximum. 

Magnetospheric magnetic field changes during magnetic storm and L-values variations reflect 

the magnetic field changes during magnetic storm. Fig. 5 shows the magnetic field structure at different 

moments of magnetic storm development (UT 21.2487 14.05.2005; UT 0.3263 15.05.2005; UT 6.4348 

15.05.2005; UT 3.7991 16.05.2005). The solar wind and IMF changes influence the magnetic field 

changes, which reveal themselves in the SEP penetration boundary variations as represented in the 

Fig. 2. 

Figure 5. Magnetospheric response on solar wind variations during magnetic storm 15-17 May 

2005. 

198


Discussion and conclusion. 

Low polar orbits of the CORONAS-F and Universitetskiy-Tatiana satellites give the opportunity to 

measure the fluxes of solar protons and determine their penetration boundaries in the south and north highlatitude 

ionosphere, which commonly associated with polar caps (areas of open magnetic field lines). Results 

of combined experimental data analysis and magnetic field modeling show that SEP penetration boundary 

lies in the region of closed magnetic field lines. During magnetic storm main phase it belongs even to the 

region of trapped particles, while during more quiet periods (storm recovery or initial phases) penetration 

boundary is located at auroral latitudes. Due to magnetic field model limitations it is difficult to determine 

whether SEP penetration boundary lies on the open or on closed field lines. 

High energy solar particle penetration in the polar caps during the main phase of magnetic storms is 

an important source of radiation danger in the near-Earth space, especially for low-altitude satellites. The 

size of the proton penetration area depends on proton energy and on geomagnetic conditions (e.g. Leske et 

al., 2001). Our study has demonstrated that both the intensity of energetic solar particles and location of the 

boundaries of solar particle penetration in the Earth’s magnetosphere are very important for the estimation of 

possible SEP-related damage. The results of more detailed calculations and their verifications with will be 

presented in the future works. 

Acknowledgement 

This study was supported by RFBR grant No 06-05-64508. 

REFERENCES 

Alexeev I.I., Kalegaev V.V., Belenkaya E.S., Bobrovnikov S.Yu., Feldstein Ya.I., Gromova L.I. (2001), The 

Model Description of Magnetospheric Magnetic Field in the Course of Magnetic Storm on January 9-12, 

1997, J. Geophys. Res, 106, A11, 25,683-25,694. 

Kuznetzov, S.N., Kudela, K., Ryumin, S.P., Gotselyuk, Yu.V. (2002), CORONAS-F satellite – tasks for 

study of particle acceleration, Adv. Space Res, 30, 1857–1863. 

Kuznetsov, S. N., Myagkova, I.N., Yushkov B. Yu. (2005), Dynamics of the Boundary of Solar Electron 

Penetration into the Earth’s Magnetosphere in November 2001, Geomagnetizm & Aeronomy. 45, 2, 

151-155. 

Leske R.A., Mewaldt R.A., Stone E.C., von Rosenvinge T.T. (2001), Observations of geomagnetic cutoff 

variations during solar energetic particle events and implications for the radiation environment at the 

Space Station, J. Geophys. Res, 106, A12, 30,011. 

Myagkova, I.N., Kuznetsov, S.N., Panasyuk, M.I. et al. (2006), Solar Flares, Solar Energetic Particle Events 

and their influence on near-Earth environment in May 2005 as observed by CORONAS-F and 

Universitetskiy-Tatiana spacecrafts, Sun and Geosphere, 1, 2, 32-36. 

Panasyuk, M. I., Kuznetsov, S. N., Lazutin, L. L., Avdyushin S. I. et al. (2004), Magnetic Storms in 

October 2003, Cosmic Research, 42, 5, 489-534. 

Sadovnichy, V.A., Panasyuk, M.I., Bobrovnikov, S.Yu., et al. (2007), First Results of Investigating the 

Space Environment onboard the Universitetskii-Tatyana Satellite, Cosmic Res., 45, 273–286. 

Yermolaev, Yu. I., Zelenyi, L. M., Zastenker, G. N. et al. (2005) A Year Later: Solar, Heliospheric, and 

Magnetospheric Disturbances in November 2004, Geomagnetism and Aeronomy, 45, 681-719. 

199


ON A CLOSE RELATION BETWEEN THE STATIONARY SOLAR WIND 

VELOCITIES AND THE SOLAR MAGNETIC FIELDS 

K. I. Nikolskaya 

Pushkov Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation, Russian 

Academy of Sci., Russia, 142190, Troitsk of Moscow region, IZMIRAN; 

e-mail: knikol@izmiran.troitsk.ru 

Abstract. The purpose of this paper is to elucidate a possible role of the solar magnetic field in 

the formation of the stationary solar wind (SW). An analysis of the SW proton velocities 

measured by Ulysses for the period of ~1.5 activity cycle in combination with SW speed IPSobservations 

as well as the XUV corona images and solar magnetic field data has been 

performed. The main result of this study is the finding of inverse relation between the SW speeds 

and solar magnetic field strengths: the stronger the closed magnetic fields the slower the solar 

wind and vice versa, that points to direct interactions of the solar wind plasma flows with solar 

magnetic fields. Thus, solar magnetic fields are responsible not only for the solar corona 

formation via plasma trapping and heating but also for the SW velocity ranging. A few examples 

of SW velocity – solar magnetic field connection are presented. 

Introduction 

A goal of this paper is to present results of a study of the relationship between the solar wind) velocities in 

the inner and outer heliosphere and the magnetic events on the Sun by the way of the analysis of the SW 

velocity behavior in different phases of activity cycles. An analysis has been carried out of SW velocity data 

for the outer heliosphere taken from Ulysses’ archive and those for inner heliosphere deduced from IPS 

observations and taken from literature. 

Designated to probe the extra-ecliptic outer heliosphere space-craft Ulysses after passage by Jupiter in 

February1992 climbed to high southerly latitudes until it reached -80.2° on September 12, 1994. It then 

proceeded to fly northward reaching perihelion near the ecliptic plane in March 12, 1995, and peak northern 

latitude at +80.2° on July 31, 1995. Hitherto Ulysses has made nearly 3 rotations over the Sun: the first and 

third rotations – around the activity minimum and the second one – within the maximum. SW parameters 

including the proton velocities and densities were measured by the device SWOOPS on board Ulysses 

(device SWOOPS – Solar Wind Observations Over Poles of the Sun). IPS observations in south and north 

high latitude heliosphere were performed with the stations EISCAT (North Finland) and VLBA (USA) 

in1994 and 1995 when Ulysses passed from south to North Pole on its first orbit. In addition, XUV solar disk 

images by Yohkoh and EIT/SOHO, full disk magnetograms (NSO/Kitt Peak and MDI/SOHO) and coronal 

hole (CH) maps (NSO/KP, USA) taken from internet-archive were utilized too. 

Solar wind velocities in the activity cycles No. 22-23 

Coupling between the stationary SW velocity and solar magnetic fields (MF) is very well seen in the Fig.1 

where SW speed latitudinal distribution are represented for low activity phase of 22-th cycle (left panel) and 

high activity phase of 23-th cycle, for the first and second Ulysses’ rotations around the Sun. Pictures of the 

SW velocity distribution over latitudes on the left and right panels in Fig.1 are completely different. Left 

panel that is referred to the quiet Sun epoch reveals stable SW speeds within 700–800 km/s at all 

heliographic latitudes beyond streamer belt and mainly slow SW inside it (≤±20° of latitude) with isolated 

high speed peaks caused by low latitude coronal holes. Contrary, as right panel shows, the heliosphere of the 

active Sun epoch was dominated by the slow solar wind except for the regions over the North Pole where the 

coronal hole situated, and irregular high velocity peaks over middle- and low-latitude coronal holes. 

The second Ulysses’ flight in the quiet Sun epoch (during declining phase of the 23-th cycle) took place on 

the third space-craft orbit with passages over solar South and North Poles in ~ 2007 January and December 

200


respectively. Latitudinal distribution of SW velocity was similar to that in Fig.1 left panel but with shorter 

south and north 700–800 km/s tracks and twice wider streamer belt (~ ±40° instead of ~ ±20° in Fig.1). 

Figure 1: Daily averaged solar wind proton velocities measured by Ulysses/SWOOPS in the outer 

heliosphere versus heliographic latitudes in polar co-ordinates are represented for the first (left upper 

panel) and second (right upper panel) space-craft rotations around the Sun. Three concentric circles on both 

graphs correspond to SW proton velocities 1000, 750 and 500 km/s. Heliographic latitudes are given in 

degrees ±45° and ±90° for the north and south heliosphere. An arrow on the outer circle in right lower 

sector of the left scheme shows the direction of Ulysses’ orbital travel. Heliocentric distance of the spacecraft 

varies within each rotation around the Sun from r ≈ 5AU in aphelion through r ≈ 2AU over the poles 

till 1.24AU – in perihelion. Numbers over north and below south solar poles denote the times of SC flight 

over the solar polar zones. All data are given from the internet archive. On the bottom of Fig.1 there is a 

graph of the solar activity in smoothed averaged monthly spot numbers versus time in years. 

Figure 2: SW flow velocities versus heliocentric distances in the inner (r


In Fig.2 there are presented SW flow velocities versus heliocentric distances in the inner (r


active corona structures and therefore had sharp boundary mainly at +70° of latitude. On the other hand, as it 

is seen on the monitoring, Ulysses entered the CH and left it at ~70° of heliographic latitude. CH maps refer 

to the heliocentric distance r ~ 1RSUN, whereas monitoring has been performed on r ~ 2 AU. Thus, CH 

angular dimensions are the same on r ~ 1RSUN and r ~ 2 AU that evidence for the radial direction of the SW 

extension. The latter means that SW flows are detected in heliosphere on the same latitudes from which they 

leave the Sun. 

In turn, we can conclude that SW streams with uniform velocities 700–800 km/s are emanated from the 

whole quiet Sun except for the regions within the streamer belt. Results of the identification of the solar 

regions responsible for the various SW speeds are displayed in Table 1. 

SW 

velocity 

Fast SW 

700–800 km/s 

Fast SW 

500–750 km/s 

Slow SW 

< 500 km/s 

Solar corona structure - 

SW velocity coupling 

TABLE 1. 

Only polar coronal holes (Te < 1MK) and 

background corona (Te ≤ 1MK) of the 

quiet Sun. 

Middle- and low-latitude isolated recurrent 

and short-living CHs of the high 

activity epoch and single low latitude 

CHs of the declining activity epoch. 

Active regions – hot, dense, bright 

coronal loops (1.5 MK≤ Te ≤ 3.0 MK) 

The streamer belt in any activity phase. 

Solar magnetic field types - 

SW velocity coupling 

Open polar MF and weak (500 G), closed magnetic 

fields of the active regions; 

High magnetic loops over neutral line 

of the global magnetic field of the Sun. 

The next relationship “solar magnetic fields – corona – solar wind velocity” emerges from the Table1: 

Open and weak 

(500G) 

→ 

→ 

Cold (Te ≤ 1 MK) and 

weak corona or 

coronal holes 

Hot (1.5MK≤Te ≤ 3.0MK), 

dense and bright coronal 

loops 

→ 

→ 

Fast solar wind 

with uniform speeds 

700 – 800 km/s 

Slow solar wind 


Figure 4: SW velocity and density variations during Ulysses traveling over solar North Pole and its 

surrounding (40°→ 80°→ 40° heliographic latitude) in maximum activity between 01.07.2001 - 01.07.2002. 

Above the CH maps (from Kitt Peak NSO, USA – archive) and two EUV FeXV (SOHO/EIT) solar disk 

images (for 2001.07.30 and 2002.05.02) are displayed to illustrate a connections of VSW and DSW variations 

– with the polar CH. 

In Fig.4 a difference in a character of SW velocity and density variations inside of polar CH - and beyond it 

is very well seen. This polar CH, as a feature of the high activity epoch, was sharply restricted by the coronal 

active regions as it is seen in it FeXV images in Fig.4. Unlike the polar CH interior with small and short time 

SW velocity variations (700-800 km/s), outside of it SW displays recurrent high velocity peaks ranging 

within 350 – 800 km/s with period ~ 25 days (=solar Carrington rotation period for Ulysses). Such deep and 

sharp SW velocity and plasma density inverse variations are typical for the isolated recurrent CH of the high 

activity epoch. Indeed, as it is seen in Fig.3, CH on the North solar Pole had a narrow tail stretched over 

latitude and occurred over more than one year. This CH tail with its open magnetic field was identified as a 

cause of SW velocity and density oscillations in the Fig.4. recorded by Ulysses on the heliocentric distances 

~1.6 AU in the left side, ~2 AU over the North Pole and ~ 4 AU in the right part of monitoring respectively. 

Figure 5: Another example of the results of direct interaction of the high velocity SW streams with 

meridionally elongated activity complex developed quickly on one side of the Sun from small low latitude 

active region in minimum of the 22-th cycle .A famous recurrent coronal hole “Elephant trunk” (1996.07– 

10) was connected with this complex. In the left part of graph area the XR- image (Yohkoh) of the opposite 

side of the Sun free of any activity is placed. An active complex is no more than 60–70° wide in longitude, 

that is ~ 1/6 of the solar rotation. 

204


In the final part of Ulysses’ first orbit between heliographic latitudes +40° and ecliptic (at 0°) left edge of the 

velocity track reveal typical for the activity minimum SW speeds within 700–800 km/s till latitude of ~33°. 

From this point the recurrent velocity drops appear due to influence of the magnetic complex. These drops 

became dipper as SC approached to the center of magnetic activity. 

Thus the solar wind streams carry information on the solar magnetic fields through which they go away, in 

form of velocity and plasma density variations resulted from the direct interactions of the plasma outflows 

with solar magnetic fields. 

Conclusion 

The main conclusions of the study presented are the following: 

• the solar wind streams with uniform velocity 700–800 km/s is exclusively a phenomenon of the 

background Sun, that is Sun of low activity epoch when closed magnetic fields on it are either absent 

or very weak; 

• the solar magnetic fields are not only responsible for the corona formation and heating but also 

control the stationary solar wind velocity, both through plasma flow - the magnetic field interaction; 

• there is inverse coupling between the SW speeds and solar magnetic field strengths: the stronger the 

closed magnetic fields the slower the solar wind and vice versa that points to SW plasma 

deceleration in the magnetic field structures; 

• SW plasma – solar magnetic fields interactions occur inside of the source surface where solar 

magnetic fields of different types are located. 

This work has been made under support of RFFI grant No.08-02-00070. 

References 

Gosling et al. (1995), The band of solar variability at low heliographic latitudes near solar activity minimum: 

Plasma results from the Ulysses rapid latitude scan, Geophys. Res. Lett., 22, 3329–3332. 

Grall, R.R., W.A. Coles, Klinglesmith M.T. et al. (1996), Rapid acceleration of the polar solar wind, Letters 

to Nature, Nature, 379, 429–431. 

Nikolskaya, K.I. (2007), Solar wind and magnetic fields of the Sun, in: Proc.XIth Pulk. Intern.Conf. On the 

Solar Physics “Physical Nature of the Solar Activity and Prediction of its Geophysical Effects” (Pulkovo, 

Russia, 2–7 July 2007), ed. By A. Stepanov, A. Solovyev, V. Zaitsev. Publ. GAO RAN, 277–280. 

Offman, L., L.M. Davila, W.A. Coles et al. (1997), IPS observations of the solar wind velocity and the 

acceleration mechanism, in: Proc. the31st ESLAB Symposium on Correlated Phenomena at the Sun, 

heliosphere and in Geospace (Noordwijk, the Netherlans, 22–25 September 1997), ed. by E. Wilson, ESA 

Publications Division ESTEC, Noordwijk, the Netherlands. 

Woo, R., and S.R. Habbal (1997), Extension of coronal structure into interplanetary space, Geophys. Res. 

Lett., 24, 1159–1162. 

Woo, R., and S.R. Habbal (1999a), Radial evolution of density structure in the solar corona, Geophys. Res. 

Lett., 26, 1793–1796. 

Woo, R., and S.R. Habbal (1999b), Imprint of the Sun on the solar wind, Astrophys. J., 510, L69–L72. 

Woo, R., and S.R. Habbal (2000), Connecting the Sun and the solar wind: Source regions of the fast wind 

observed in interplanetary space, J. Geophys. Res., 105, 12667–12674. 

205


SINP SPACE MONITORING DATA CENTER PORTAL 

Parunakian D.A. 1 , Kalegaev V.V. 2 , Bobrovnikov S.Yu. 2 , Barinova W.O. 2 

1 

Moscow State University Skobeltsyn Institute of Nuclear Physics 119991, Russia, 

e-mail: rumith@srd.sinp.msu.ru; 

2 

Moscow State University Skobeltsyn Institute of Nuclear Physics 

Abstract. The space monitoring data center contains multiple features that allow quick retrieval of 

data received from a wide range of Russian and Western spacecraft, visualization of the said data and 

also has some analytical capabilities. The portal also provides access to the results of automated 

services such as the quasi real time magnetopause standoff distance monitor, detailed descriptions of 

existing and prospective space experiments, processed data on coronal holes and solar flares, and 

online models such as the paraboloid model of the magnetosphere and the COSRAD model. 

The space monitoring data center (SMDC) has been designed to provide researchers a unified interface for data 

retrieval, visualization and analysis, development and testing of new models as well as publishing their work. 

Below we give brief descriptions on the most important features of the SMDC portal currently implemented. 

Data of space experiments collected at SINP 

Historically, the wide selection of datasets based on results produced by SINP experiments has been fragmented 

and stored on multiple servers and sometimes even PCs of particular researchers [1]. These datasets include 

experimental data on fluxes of energetic electrons and protons (E>40 keV), gamma- and X-rays measured at 

altitudes lower than 1000km aboard Russian satellites and orbital stations. Measurements available cover the 

period from 1979 through this day, which enables the study of variations of near-Earth radiation in the duration 

of almost two cycles of solar activity. Data received from high inclination satellites enables investigation of 

particles trapped in the radiation belts, as well as radiation fluxes above the belts and in the polar regions of the 

Earth's magnetosphere. In addition to data obtained during SINP's own space experiments, additional data from 

OMNI and COHO (NASA/NSSDC ) archives describing solar wind conditions since 1963 is available. This 

allows conducting research of the Earth's magnetosphere response on solar wind driving. 

The main goal of SMDC is to unite all these datasets into a single online information system. Table 1 

contains information on the type and amount of data currently available at the SMDC (http://smdc.sinp.msu.ru). 

Table 1. Overview of space experiment data collected at SINP 

Project Time interval Physical experiment 

Flux of gamma-rays (50keV 

Amount of data 

Coronas-I SKL 03.1994 - 04.1995 - 200MeV), electrons, 

protons, nuclei 

Flux of X-rays (15-100keV). 

387Mb 

Coronas-F SPR-N 08.2001 - 12.2005 

Data on x-ray polarisation in 

1.2Gb 

20-40, 40-60 and 60- 

100keV intervals 

Flux of gamma-rays (50keV 

Coronas-F SKL 08.2001 - 06.2005 - 200MeV), electrons, 

protons, nuclei 

4.5Gb 

206


Table 1. (Continuation) 

Project Time interval Physical experiment Amount of data 

Meteor-3M 01.2002 - 12.2003 

Tatyana 02.2005 - 02.2007 

Cosmos 1686 02.1986 - 12.1986 

MIR orbital station – 

radiation experiment 

(Ryabina) 

MIR orbital station – 

gamma experiment (Grif) 

11.1990 - 06.2000 

Differential spectra of 

electron and ion (proton) 

components of corpuscular 

radiation in Earth's 

magnetosphere 

Flux of charged particles in 

Earth's magnetosphere 





6Gb 

430Mb 

150Mb 

70Mb 

10.1995 - 06.1997 Flux of gamma and X-rays 1.5Gb 

Prognoz-9 06.1983 - 03.1984 Flux of gamma and X-rays 20Mb 

User can build his request to the comprehensive database we possess with just a few clicks using our data forms. 

First, the user has to select the spacecraft he is interested in. Then, the time interval and the channels to retrieve 

must be selected. After that, the user has to select the representation of the data that he needs. 

Figure 1. Example of data retrieval form. 

Data retrieved can be provided as text, graphic or as an archive. The visual representation allows to graphically 

preview the data to determine whether or not it is actually of interest in the context of a particular problem. The 

textual representation usually serves error catching, value confirmation and debugging purposes, since it dumps 

a portion of the data table directly into the user's web interface. The archived representation is useful for 

retrieving large amounts of data for subsequent client-side processing. Data visualization is performed by our inhouse 

software project Qlook [7]. 

207


In order to assist researchers attempting to develop their own software for processing spacecraft telemetry data, 

we provide FTP access to communication session files for most SINP space experiments. Currently, telemetry 

data for Universitetsky-Tatyana is already available; we are planning to deploy data for Coronas-F/I, Mir station, 

Prognos-9 and other spacecrafts in the nearest future. 

Supplemental information 

Besides spacecraft data and telemetry, SMDC also contains processed and analyzed datasets. They have been 

built based on space experiment data available at SMDC as well as at other data centers. 

Magnetic Storms catalogue. We have analyzed data produced by the OMNI project to detect magnetic 

storms and to separate them from the general data flow. Only magnetic storms with Dst less than -70 nT have 

been selected in the 1998-2003 time interval. Data on these magnetic storms includes interplanetary magnetic 

field components, solar wind bulk velocity, proton density, Dst and AL indices. There's also a Dst threshold 

selector which allows to view only storms during which Dst index reaches a particular value. 

Solar flares. It is well known that the Sun is the most energetic particle accelerator in the Solar system, 

producing ions of up to tens of GeV and electrons of up to tens of MeV. The information regarding peak gamma 

emission energy obtained by the SONG experiment allows us to estimate the flux and spectra of charged 

particles accelerated in the Solar atmosphere. The CORONAS-F duty cycle of solar flare detection lasted 

approximately 40% of its total flight time as a consequence of its orbital parameters; thus many major flares that 

occurred since August 14, 2001 till September 12, 2005 were not observed. Yet, 9 flares with HXR emission 

have been detected by CORONAS-F during 2004 and 23 ones during 2005. Data on HXR and gamma fluxes 

produced by solar flares and detected by SONG (CORONAS-F) experiment [2004-2005] is available at SMDC. 

APEV database. This tool provides access to time profiles of the key geomagnetic and solar wind 

parameters and solar event maps. APEV database has been initially developed by by Alexei Dmitriev, Andrey 

Zhukov and Igor Veselovsky [2]. 

Coronal holes database. This tool provides access to a large catalogue of solar imagery automatically 

processed [3] to detect and measure coronal holes (CH), as well as their numeric characteristics. Solar images 

are taken from SOHO/EIT measurements data bases. CH area is measured in relative units, where total area of 

the Sun equals one unit. Minimal significant area is 0.002 relative units. Average intensity is calculated after 

filtering and histogram scaling into the range from 0 to 255. Calculation is performed not taking into account 

correction for spherical shape of the Sun. This tool is based on an earlier work by J. Shugai and SOHO/EIT 

consortium. 

Magnetopause crossings. It has been demonstrated [4] that the shape of the Earth's magnetosphere 

depends upon the IMF orientation, while remaining self-similar for variations in solar wind dynamic pressure. 

Data set of 1821 magnetopause crossings has been processed and matched with simultaneously observed hourly 

averages of solar wind dynamic pressure and IMF Bz. The data set used includes data collected from IMP 

1/2/3/4/6/8, Explorer-33, Prognos 7/8/10, ISEE 1/2, IRM spacecraft. SMDC portal provides full access to this 

data set, which covers the time period from 07.08.1968 through 21.02.1979. 

208


Models 

Paraboloid model of the Earth's magnetosphere. Dynamic paraboloid model (A2000) allows to 

calculate the magnetic field of magnetospheric large scale current systems during quiet and disturbed periods 

[5]. Magnetic field variations are determined by input parameters depending on conditions in space. Distinct 

sources of the magnetospheric magnetic field can be individually taken into account or ignored. The IMF 

penetrated into the magnetosphere as well as field-aligned currents magnetic field are included in the total 

magnetospheric magnetic field. SMDC portal provides both online access to the model and its source code so 

users can run it elsewhere. 

COSRAD model. The COSRAD model (developed by N.V. Kuznetsov) is intended to forecast the 

radiation environment onboard near-Earth elliptic orbiting satellites in the open space as well as behind 

aluminum shielding. It can calculate the following parameters: 

1. The energy spectra of particles of radiation belts, galactic and solar cosmic rays. 

2. LET (Linear Energy Transfer) spectra in Si of heavy charged nuclei. 

3. Absorbed dose in Si and equivalent dose in tissue-eqiuvalent matter. 

4. Single event effects in integral chips. 

Real-time services 

The general objective of SMDC is to build reliable forecast of key magnetospheric parameters and 

analysis of current geophysical and radiation conditions in the near-Earth space. High-performance computers, 

relational databases and engineering models of space environment should be used for such analysis. One of the 

first examples of such activity is the magnetopause stand-off distance monitor. 

This automated service calculates in real time the magnetopause stand-off distance (geocentric distance 

to the magnetopause subsolar point, Rss) in the framework of Kuznetsov-Suvorova model: Rss = 8.6*(1 + 

0.407*exp( - (|Bz| - Bz) 2 /(200*p0.15 ))*p-0.19 ) [6], where Bz [nT] (interplanetary magnetic field z-component 

is GSM coordinates) and P [nPa] (solar wind dynamic pressure) are measured by ACE spacecraft. ACE is 

located in L1 point where solar and terrestrial gravitation forces are balanced. ACE measures solar wind 

parameters and delivers data to the Earth, that allows to provide short-term forecast of magnetopause location 

approximately 40min prior solar wind approaching terrestrial magnetosphere. 

Other resources 

Links directory. The SMDC portal has a section dedicated to keeping an up-to-date directory of 

hyperlinks to space physics related websites, journals, data sources, model sites, and a wealth of other 

information. This section also contains links to manuals and user guides for software routinely used by our 

visitors. 

Details on prospective SINP experiments. We highlight most of the space physics related projects 

currently under development by SINP and in collaborations. At the moment of this writing, information is 

available on RELEC, InterHelios, Nucleon, TUS and Coronas Photon experiments. We provide an overview of 

each experiment's instruments, participants, related publications and contacts of researchers responsible 

participating in the corresponding experiments. 

209


Conclusions 

Space monitoring data center collects data on the radiation conditions in the Earth's environment measured by 

Russian and Western spacecrafts during approximately the last 20 years. The interactive services provide access 

to a database of energetic particle fluxes, X-ray and gamma fluxes, magnetospheric plasma and magnetic field 

parameters. The future development of SMDC portal involves real-time data processing allowing fast and 

reliable analysis of radiation and geomagnetic conditions in the near-Earth space. 

Acknowledgement 

This study was supported by RFBR grant No 06-05-64508. 

References 

1. Kalegaev V.V., Alexeev I.I., Bobrovnikov S.Yu., Dmitriev A.V., BAFIZ project and space physics 

information systems in SINP MSU, SINP MSU Preprint 2000-28-632, 2000 (in Russian) 

2. Panasenko O., Veselovsky I.S., Dmitriev A.V., Zhukov A.N. Solar origins of intense geomagnetic 

storms in 2002 as seen by the CORONAS-F satellite. Advances in Space Research, 2005. 

3. Persiantsev I.G., Ryazanov A.Y., Shugai J.S. The automatic processing and analysis of solar image 

sequences. Pattern Recognition and Image Analysis, 2006 

4. Sibeck D. G., R. E. Lopez, and E. C. Roelof, Solar Wind Control of the Magnetopause Shape, Location, 

and Motion. J. Geophys. Res, 5489, 1991 

5. Alexeev I.I.. Kalegaev V.V., Belenkaya E.S., Bobrovnikov S.Yu., Feldstein Ya.I., Gromova L.I., The 

Model Description of Magnetospheric Magnetic Field in the Course of Magnetic Storm on January 9-12, 

1997, J. Geophys. Res., 106, 25683, 2001 

6. Kuznetsov S.N., Suvorova A.V. An Empirical Model of the Magnetopause for Broad Ranges of Solar 

Wind Pressure and and BzIMF. Polar Cap Boundary Phenomena, Proceedings of the NATO Advanced 

Study Institute, Longyearbyen, Svalbard, Norway, 4-13 June 1997 

7. Barinova W.O., Parunakian D.A., Kalegaev V.V. Qlook 2.0: scientific measurements data visualization 

system. Proceedings of Scientific Service in the Internet 2007 (in Russian) 

210


FORMATION OF LOCAL ATMOSPHERIC ELECTRIC FIELD UNDER 

THE INFLUENCE OF IONIZATION FACTORS 

E.A. Ponomarev 1 , N.V. Cherneva 2 , P.P. Firstov 3 

1 Institute of Solar-Terrestrial Physics SB RAS, Irkutsk, Russia; 2 Institute of Cosmophysical 

Research and Radio Wave Propagation FEB RAS, Kamchatka, 684034, Russia, e-mail: 

nina@ikir.kamchatka.ru ; 3 Institute of Volcanology and Seismology FEB RAS, Russia, 

Petropavlovsk-Kamchatskiy 

Abstract. The influence of different ionization factors on the formation of local atmospheric 

electric field (AEF) in the near-ground layer is considered in the present work. Estimations of 

change of AEF strength (EZ) due to conductivity variations under the influence of radon and 

cosmic ray intensity are presented. It is shown that atmospheric conductivity changes due to 

ionization under the influence of radon emanations and it is determined by excalation and 

turbulent diffusion of the near-ground layer, while cosmic ray intensity affects to the conductivity 

of the near-ground layer under the influence of change of ion recombination state. The decrease of 

atmospheric conductivity, determined by cosmic ray flux, decreases EZ whereas the decrease of 

radon sink leads to EZ increase. The valuation of influence of light conditions on AEF value due to 

the change of relative concentration of heavy and light ions under the influence of 

photodetachment and photoattachment processes is given. This process may, evidently, explain the 

morning maximum for the days with fair weather conditions in diurnal EZ variation. It is shown, 

that the effect of “spread current” potential from auroral electrojet region to mid latitudes during 

geomagnetic disturbances may contribute AEF variations is about 5%. 

Introduction 

The high sensitivity of an electrical field of an atmosphere (EFA) to the most various natural factors 

has determined low selectivity of monitoring systems based on the use of EFA. There was a 

problem of research and classification of the factors forming an electrical field of an atmosphere in 

the observation point. Today it is known, at a qualitative level, that EFA is determined, basically, 

by radon concentration in near ground layer, intensity of cosmic rays, light exposure of an 

atmosphere, managing photoionization processes, influencing on balance of heavy and easy ions in 

an atmosphere, variations of the electrosphere potential. The generalized scheme of causeconsequence 

relations EFA under influence of some natural processes is given in Fig.1. 

Fig.1. The scheme of processes of formation of an electrical field of an atmosphere in the presence of the factors 

determining its size in near ground layer. The letters R22 and R21 mark areas of modulation of atmosphere 

resistance under action of the ionizator qR (radon) and qC (cosmic rays). It is supposed that the action of stick 

and unstuck processes are both in area R22, and in area R21, that is symbolized by an index n in a circle. The 

situation of areas R22 and R21 at heights is shown on the insertion h22 и h21 (not in scale). 

211


The features of seasonal course EFA. 

On the basis of the data received at observatory “Paratunka” during 1998-2008 at a qualitative level 

the connection Ez of EFA with a flow radon to near ground layer of the atmosphere is shown. 

In the area of observatory “Paratunka negative daily average T is keeping about 5 months from 

November to May. These months are conditionally named "winter". In winter months the sharp 

fluctuations T up to 15 o C, caused by arrival of warm cyclones, with trajectories taking place 

through water area of Pacific Ocean, are observed which are accompanied by fluctuations P with 

amplitude up to 25 gPa. During negative daily average temperatures (November - April) the arrival 

of cyclones from southern directions is accompanied by significant reduction Ez EFA at the 

expense of increase of a flow Rn under influence of strong fall of atmospheric pressure and sharp 

warming up on 10-15 o . 

Tropical cyclones, which come on Kamchatka from a southwest direction, influence on all 

parameters of the bottom atmosphere [3]. As the example the cyclonic activity was considered in 

details, when two cyclones has approached to peninsula Kamchatka at once, the trajectories are 

shown in Fig. 2-a. 

Fig. 2. Trajectory of the cyclones which have arisen in water area of Pacific Ocean 8 and January 9, 2002 - (a); 

azimuth distribution of lighting discharges and epicenters of cyclones - (b); distance from epicenters of 

cyclones up to observatory “Paratunka”" - (c). Dynamics of an atmospheref parameters during passage of a 

southern cyclone: P - atmospheric pressure, T - temperature of air - (d); quantity of atmospherics at one 

o'clock (e); intensity EFA, instant and time-averaged meanings - (f); volumetric activity Rn, 1-point PRT, 2 – 

point GLL (F). 

Azimuth distribution of atmospherics is shown by points in Fig. 2-b from January 8 to January 16, 

2002 according to the data VLF direction finder. The situation of cyclone epicenters are marked by 

the rhombuses in fig 2-a. It is visible in comparison of Fig. 2-b and 2-c, that at the approach of a 

cyclone to the place of registration the quantity of atmospherics is increased. In the period from 

January 10 to January 12 the cyclone epicenter has approached up to 50 kms to the observatory 

“Paratunka”. 

In Fig. 2-d where dynamics of meteorological sizes is shown, the cyclones have brought significant 

quantity of heat. Atmospheric pressure of January 10, since 14 hours sharply began to fall, and 

212


temperature of air – to grow. The difference of pressure has made 30 gPa, and temperature (-15 o -2 o ) 

14 o C , and precipitations as sleet have begun to drop out at the end of January 12 , that has resulted 

to strong disturbances both VLF - radiation (Fig. 2 -e), and Ez EFA (Fig. 2-f). 

Dynamics of ground Rn on two points, located near the observatory, is shown in Fig. 2-g. It is 

visible, that VA Rn in the zone of aeration at both points has increased synchronously in 4 times 

from 2 up to 8 kBk/m 3 . Such powerful increase of the flow Rn to an atmosphere is caused by 

"exhausting" effect of fall of pressure and increase of permeability of mountain breeds under action 

of temperature increase. In one’s turn the increased flow radon to the near ground layer, obviously, 

has resulted to the increase of its ionization and conductivity, that has resulted to the fall of Ez EFA. 

The coefficient of correlation between Rn and Ez has made -0.43, at 0.3 for 95 % for a level of 

confidence. 

There is the interaction of geogas with atmospheric air on border of porous environment and 

atmosphere. Air enters to pores at increase of atmospheric pressure and "compresses " the geogas, 

and at reduction – air and a part of geogas leaves from pores. So on the average, "the evacuation" of 

geogas to an atmosphere occurs for the period of change of atmospheric pressure [4, 5]. 

The connection between a seasonal dependence Ez, capacity of a snow cover and temperature at 

observatory “Paratunka” was analysed. Decadely average data of snow cover heights and 

temperatures of air were used. It is visible in Fig. 3, that the maximum of capacity of snow cover 

falls at the branch of recession of the seasonal course Ez with maximal coefficient of correlation 

rmax = 0.73 (at r = 0.49, for 95 % of a level of confidence) at shift per 50 day. While the minimum of 

a seasonal course of temperature almost coincides with a maximum Ez, at shift per 10 day rmax = - 

0.67 (r = - 0.42 for 95 % of a level of confidence). It specifies, that the seasonal courses Ez and 

temperature of air are in antiphase, that, apparently, is connected with the increase of a flow Rn to 

an atmosphere in summer at the expense of increase of permeability of the top ground layer, and the 

snow cover influences little on dynamics Ez. 

Fig.3. Height of a snow cover and seasonal course of intensity EFA and temperature of air: 1-intensity EFA, 

2-height of snow cover, 3-temperature of air. 

Influence of Forbush-reduction on EFA 

The influence of Forbush-reduction on dynamics Ez EFA is shown for days with conditions of fair 

weather (CGW). The reduction galactic cosmic rays (GCR) on 3-10% results in essential reduction 

Ez EFA on 20 - 80 %. 

High-altitude distribution of the source of ionization, connected with cosmic rays, is more stable, 

than distribution ionizator in near ground layer. Nevertheless, there is one type of the variation of 

intensity and spectrum of cosmic rays, which essentially has an effect for the value of near ground 

EFA. It is so-called Forbush - effect. As shown in Fig. 7, the decrease of Ez magnitude is 

synchronously with Forbush-reduction of GCR and is sometimes shown convincingly enough. 

213


21 cases were chosen for the analysis. Unfortunately, practically in all cases time CGW on 

Kamchatka has appeared less than time of restoration Ez, which, as was shown on the data of 

observatory "Nagycenk", makes 5 days [2, 6]. Most typical curve, showing Forbush-reduction of 

intensity GCR simultaneously with reduction of Ez, are shown in Fig. 4-a. The results of data 

analysis show, that the reduction of Ez begins practically simultaneously with the beginning of 

Forbush-reduction, the delay of a variation of the signal Ez concerning Forbush-reduction does not 

exceed two hours. The speeds of reduction of sizes of intensity of a flow GCR and EFA practically 

coincide. 

Fig.4. Most typical curve Forbush- reduction GCR and variation Ez, registered on observatory 

“Paratunka”- (a); connection between Forbush-reduction in GCR and reduction Ez on the 

observatory “Paratunka” data (b). 

For 18 cases, when the reduction galactic cosmic rays and Ez were fixed very precisely, the 

functional connection Ez(%) =f (N, %) was investigated. The dependence y=9.64x−0.72 (Fig. 4 b) 

was received, from which it is visible, that the reduction Ez on 3-10% results in essential reduction 

Ez EFA on 20 -80 %. 

The features of daily course EFA 

In view of the geographical situation of the peninsula Kamchatka the feature of daily course Ez 

EFA is maximum at 18-20 hours, which is formed under the action both UT - variation, and sunrise. 

It is necessary to note, that the zone time of observatory “Paratunka” outstrips time UT at 12 hours 

and, thus, maximum of Ez meanings during the greater period of year is to morning hours 

coinciding with sun-rise. The attempt of allocation of a UT-variation on observatory “Paratunka" 

was made in report [1]. The found out maximum of meanings Ez had on 19 - 20 hours UT, that was 

connected with UT-variations. However it became obvious at detailed elaboration, that the 

maximum in daily variations changes from 18 to 21 hours UT seasonally, that, apparently, specifies 

influence both UT - variations, and terminator on a maximum of a daily course for observatory 

“Paratunka". 

The quiet days were chosen with the purpose of the division influence of the effect UT - variation 

and morning terminator, into a daily course Ez for the period 1998 - 2006, when there were no 

sharp fluctuations. The general number of the chosen days were 203 days: March - 48, April - 46, 

May - 35, June -42, July - 32. Curves were constructed by the method of imposing of epoch, which 

were normalized on the maximal meaning, and time of the sun-rise (on the data 

214


"Kamchatka Hydrometer Service") was chosen as a zero point. The root-mean-square deviation did 

not surpass 14 %. As it is visible in Fig. 5 and, with some portion of conditionality, it is possible to 

allocate two maxima. 

In March they almost merge in one with relative amplitude 40 %, and in June – July they form two 

maxima separated on 1.5 hour and amplitude ~ 20 %. 

The average course Ez at the moment of the sun-rise, received by a method of imposing of epoch in 

203 cases of fair weather, chosen for spring-summer months 2004 and 2005, is shown in Fig. 5 b. 

As the beginning of epoch the sun-rise hour is chosen. It is visible, that in a two-hour interval after 

the beginning of epoch the smooth maximum as the size some percents is observed. 

The experimental confirmations of influence nonequipotential of the electrosphere on a variations 

Ez are received. 

Fig.5. Allocation morning terminator on a background of UT - variation in EFA on observatory 

“Paratunka " - (à); allocation of sun-rise effect in EFA by a method of imposing of epoch 

The example of allocation of "ionospheric" variation of the electrical field of an atmosphere by a 

method of imposing of epoch for 37 geomagnetic bays is given in Fig. 5 c. The beginning of a bay 

is taken as zero epoch. The cases about local midnight are selected. At average size of an electrical 

field ~ 120-140 v/m it is about 5 % - the value leaving for statistical errors of a method and, it is 

basically detected. 

Conclusions: 

1. On the basis of long-term numbers of the data, the seasonal dependence Ez EFA from a flow 

radon into near ground layer of the atmosphere is shown. During negative daily average 

temperatures (November - April) the arrival of cyclones from southern directions is accompanied 

by significant reduction Ez EFA at the expense of increase of a flow Rn under influence of fall of 

atmospheric pressure and sharp getting warmer on 10-15 o . 

2. In view of the geographical situation of a peninsula Kamchatka the feature of daily course Ez 

EFA is maximum at 18-20 hours, which is formed under action both UT - variation, and sun-rise 

effect (morning terminator). 

215


3. The influence of Forbush-reduction on dynamics Ez EFA is shown for days with conditions of 

fair weather. The reduction of GCR on 3-10% results in essential reduction of Ez EFA on 20 - 

80 %. 

References: 

1. Buzevich A.V., Cherneva N. V., Ponomarev E.A. Observations of many years and morphology 

of the variations of electrical field Ez in Kamchatka. Coll. of reports III int. conf. ”Solar-Terr. 

Relations and Electromagnetic Precursors”. P-Kamchatsky. 2004. P.155-160. 

2. Cherneva N. V., Kuznetsov V. V. Forbush-reduction and effects of terminator in atmospheric 

electrical field of Kamchatka. Int. Baikal school on fundamental physics “Astrophysics and 

Physics of near Earth space environment”. Irkutsk. 2005. Pt I. P.37-40. 

3. Kuznetsov V. V., Cherneva N. V., Druzhin G. I. Influence of Cyclones on the Atmospheric 

Electric Field of Kamchatka. ISSN 1028-334X, Doklady Earth Sciences. 2007. Vol. 412, №. 1. 

P. 147–150. 

4. Firstov P.P., Cherneva N. V., Ponomarev E.A., Buzevich A.V. Under ground radon and 

intensity of electrical field of atmosphere in the area of Petropavlovsk-Kamchatsky. Vestnik 

KRAUNSCH. Science of Earth. 2006. №1. P.102-109. 

5. Firstov P. P., Ponomarev E. A., Cherneva N. V., Buzevich A. V. and Malysheva O. P. On the 

Effects of Air Pressure Variations on Radon Exhalation into the Atmosphere. Journal of 

Volcanology and Seismology. 2007. V.1, № 6. P. 397. 

6. Märcz F. Short-term changes in atmospheric electricity associated with Forbush decreases. J. 

Atm. Solar-Terr. Physics. 1997. V. 59. N. 9. P. 975-982. 

216


OBSERVATIONAL SIGNATURES OF CONSECUTIVE RECONNECTION 

PULSES 

S. Posratschnig 1 , V. S. Semenov 2 , M. F. Heyn 1 , I. V. Kubyshkin 2 , S. A. Kiehas 3 

1 Institute of Theoretical and Computational Physics, Technische Universität Graz, Petersgasse 16, 

A-8010 Graz, Austria, e-mail: posse@sbox.tugraz.at; 2 St. Petersburg State University, 

Petrodvoretz, 198504 Russia; 3 Space Research Institute, Austrian Academy of Sciences, 

Schmiedlstraße 6, A-8042 Graz, Austria 


Abstract. We investigate model data produced by several close reconnection pulses. It is shown 

that a series of such pulses tends to induce a clear trend in the time-evolution of x- and zcomponents 

of both, the magnetic field (Bx, Bz) and plasma velocity (vx, vz). Such signatures with 

a typical trend in time during pulse propagation occur only for moderate distances of the observer 

with respect to the current layer. In all other cases relatively close to the current layer, the observer 

will see the direct effect of every single pulse onto the behaviour of the in detail measured 

magnetic field and plasma velocity. On the other hand, far away, all pulses will join and will look 

like one single pulse in the observational data. 

For the interaction between the solar wind and the Earth’s magnetosphere the reconnection process is in 

general very important. Petschek proposed in his work in 1964 a steady-state reconnection model as a 

possible explanation for this. It can be shown that a local dissipative electric field is generated in the 

diffusion region and produces the decay of a tangential discontinuity. In detail, the current sheet breaks into a 

thin boundary layer given by a system of nonlinear magnetohydrodynamic (MHD) waves. It collects plasma 

from the near flux tubes and accelerates the plasma to Alfvénic speed vA. This kind of shock structure 

propagates then outward along the current sheet away from the diffusion region (Figure 1). 

Fig. 1: Time-dependent Petschek-reconnection after Semenov et al. (2004) and Ivanova 

et al. (2007) in the switch-off phase. Heated and accelerated plasma is enclosed by the 

shocks (S-). The magnetic field lines are connected via shocks. The dotted line represents 

the separatrix which confines the flux tube. 

The magnetic field lines above and below the current sheet, which are initially antiparallel directed, are 

connected via the shocks, which form the outflow region (OR), illustrated by the grey areas in Figure 1. The 

surrounding area is then called the inflow region (IR), and the plasma flow has always the direction from IR 

into OR. 

We know that nature is never ideal, and so reconnection appears often in form of an unsteady and patchy 

behaviour of impulsive character. Nevertheless, if we suppose a series of several pulses, we observe that the 

average reconnection flux can increase nearly linear like for steady-state reconnection with 

∂F 

E = ≈ const 

c ∂t 

1 * 

. 

Here E* stands for the electric reconnection field and F is the magnetic flux per unit length along the X-line. 

If the time duration of the reconnection pulse is many Alfvén times, impulsive reconnection will look similar 

to a quasi steady-state reconnection. 

217


In this paper we start with Petschek-like reconnection for a chain of pulses, and we investigate the trend in 

the magnetic field and velocity components. The tangential components are, in this case, “trivial”, because 

they are not connected to the pulses. So we put our attention on the normal components. There exist two 

different regimes: a flux dominated (FD) and a shape dominated (SD). The shape dominated part shows the 

influence of the temporarily growing OR. Figure 2 shows the constant linear growth of the shocks and the 

separatrix which is the border of the flux tube surrounding the shocks. 

Fig. 2: Details of the shape of a series of impulsive multi pulses (in the first quadrant) 

which propagate in the x direction through space and the magnetic field line geometry 

influenced by it (thick red line the shocks; thick blue line separatix). 

2. Model and calculations 

From the ideal MHD equations and the Rankine-Hugoniot jump relations for an incompressible plasma with 

�� 

2004). The current sheet, based on a 2D geometry, is a tangential discontinuity, which separates two 

incompressible plasmas with oppositely oriented magnetic fields which are undisturbed and stationary at the 

beginning. Inside the diffusion region, the electric field E * (t) which is assumed to be much less than the 

Alfvénic electric field EA, is an arbitrary function of time 

* 1 

E B v = E , 


( 1) 

c * ⎛ x ⎞ 

Bz 

( t, 

x, 

0) 

FP = E ⎜ 

⎜t 

− ⎟ , 

vA 

⎝ vA 

⎠ 

( 1) 

v ⎛ ⎞ 

A * x 

vz 

( t, 

x, 

0) 

FP = − E ⎜ 

⎜t 

− ⎟ , 

EA 

⎝ vA 

⎠ 

and a shape dominated part (SP) 

( 1) 

c * ⎛ x ⎞ c * ⎛ x ⎞ 

Bz ( t, 

x, 

0) 

SP = E ⎜ 

⎜t 

− ⎟ − xE ' ⎜ 

⎜t 

− ⎟ , 

2 

vA 

⎝ vA 

⎠ vA 

⎝ vA 

⎠ 

( 1) 

x * ⎛ x ⎞ 

vz ( t, 

x, 

0) 

SP = E ' ⎜ 

⎜t 

− ⎟ . 

EA 

⎝ vA 

⎠ 

All these expressions are valid for x > 0. For x < 0 the magnetic field can be continued as an odd function 

and the velocity as an even function. 

All calculations are done using the time scale T0, the time duration of the pulse, vAT0 = L0, as a typical length 

of reconnection line (X-line), B0, the initial magnetic field where vA is Alfvénic velocity and F0 = vAB0T0 the 

magnetic flux per unit length. 

3. Results and discussion 

The reconnection inducing electric field E * (t) can be chosen as an arbitrary function of time. We directly get 

Petschek steady-state solution, if E * is constant. 

For modelling the pulses we define for each pulse the same function 

* 

2 

E ( t) 

= ε sin ( π ⋅t 

), 0 ≤ t < 1 

* 

E ( t) 

= 0, 

�� * |/|EA| = 0.1. 

t > 1. 

In all pictures, z defines the height of the observer above the current layer. Here we have put z = 1.2, because 

this is the intermediate distance where signatures of steady-state reconnection appear as shown in 

Posratschnig et al., 2008. 

��x (blue) and Bz (green) for a typical 

three pulse case. Also shown is the splitting of the results into FP and SP. The dotted lines 

describe the trend in time for the significant central part. 

219


Fig. 5: Velocity components (above for the complete Poisson integral, below for FP and 

SP) for the three pulse case. The dotted lines are the trend in time for the significant 

central part even here. 

Figures 4 and 5 show that the flux is more or less constant in the central part, so the trend starts to disappear 

for Bz and vz. On the other hand, the shape dominated part has a strong slope in the trend because the growth 

of the shocks in time is caused by the fact that all the plasma is collected inside the OR. 

Fig. 6: Magnetic field components (above for the complete Poisson integral, below for FP 

and SP) for a case with seven pulses. The dotted lines describe the trend in time for the 

significant central part. 

220


Also in Figures 6 and 7 we observe a clear trend in the normal components. In order to obtain trend lines we 

restrict the interval to the central part of the function. There we expect steady-state reconnection, because 

there the electric field E * in average is practically constant as a consequence of the linear growth of the flux. 

Fig. 7: Velocity components (above for the complete Poisson integral, below for FP and 

SP) for seven pulses. The dotted lines are the trend in time for the significant central part 

even here. 

Thus, we are lead to the conclusion that the whole mechanism cannot be explained just by reconnection. 

Also, the growing of OR has a major influence. 

Fig. 8: Time series with three pulses of Bz, observed by four Cluster satellites. 

In order to substantiate our supposition, we searched through satellite data. It is very intricate to identify a 

series of reconnection pulses. We did not find clear multi pulse reconnection events with coexistent trends in 

the x and z components, i.e. have negative and positive slopes at the same time. Figure 8 is a good example 

for three pulses, observed by Cluster satellites during a series of nightside flux transfer events on September 

8 th in 2002. The data have been investigated in detail in Sergeev et al., 2005 and in Kiehas et al., 2008. In 

221


these data, the trend of the z component of the magnetic field actually shows a positive slope in agreement 

with our prediction. 

4. Conclusion 

a) We find for the case of intermediate distances z ~ 1.2 vAT0 from the current layer, that the profile of 

the signatures for the multi pulse case are dominated by the shock shape rather than the reconnected 

flux. 

b) A closer look on the differences in the components shows, that Bz and vx typically have an increasing 

trend characteristics in time, and Bx and vz behave vice versa. 

c) It is difficult to find multi pulse reconnection events in satellite data which have the suggested 

upward trend in Bz and a coexistent downward trend in Bx. Nevertheless the search for such events is 

still going on. 

Acknowledgements. S.P. acknowledges the ''KUWI'' funding by the Technische Universität Graz, office for 

''International Relations and Mobility Programs'', for a scientific stay at the St.Petersburg State University, 

department of geophysics. 

V.S.S. acknowledges the financial support from the Technische Universität Graz and the hospitality of the 

''Institute of Theoretical and Computational Physics'' during a scientific visit to Graz. His work is supported 

by the RFBR grants No. 07-05-00776a. 

References: 

Biernat, H. K., M. F. Heyn, and V. S. Semenov (1987), Unsteady Petschek reconnection, J. Geophys. Res., 

92, 3392. 

Ivanova, V. V., V. S. Semenov, T. Penz, I. B. Ivanov, V. A. Sergeev, M. F. Heyn, C. J. Farrugia, H. K. 

Biernat, R. Nakamura, and W. Baumjohann (2007), Reconstruction of reconnection rate from Cluster 

measurements: Methodes improvements, J. Geophys. Res., 112, A10226. 

Kiehas, S. A., V. S. Semenov, T. Penz, H. K. Biernat, and R. Nakamura (2008), Determination of 

reconnected flux via remote sensing, Adv. Space Res., vol.41, N 8, pp.1292-1297. 

Petschek, H. E. (1964), Magnetic field annihilation, Physics of solar flares, edited by W. N. Hess, pp. 425- 

440, NASA Spec. Publ., 50. 

Posratschnig, S., V. S. Semenov, I. V. Kubyshkin, and M. F. Heyn (2008), Model study of transition from 

impulsive to steady-state reconnection, Proceedings of the 31 st annual seminar "Physics of Auroral 

Phenomena" in Apatity. 

Semenov V. S., M. F. Heyn, and I. B. Ivanov (2004), Magnetic reconnection with space and time varying 

reconnection rates in a compressible plasma, Phys. Plasmas, 11, 62-70. 

222


GLOBAL SIMULATIONS: WHAT DO THEY TELL ABOUT 

THE LARGE-SCALE MAGNETOSPHERIC DYNAMICS 

Tuija I. Pulkkinen 1 , Minna Palmroth 1 , Katerina Andreeova 1 , Tiera Laitinen 2 

Introduction 

1 Finnish Meteorological Institute, POBox 503, FI-00101 Helsinki, Finland 

2 Swedish Institute of Space Physics, POBox 537, SE-751 21 Uppsala, Sweden 

Abstract. Quantitative methods have been developed to evaluate energy transport across the bow 

shock to the magnetosheath and into the magnetosphere in global magnetohydrodynamic 

simulations of the solar wind – magnetosphere – ionosphere system. A series of simulation runs 

are used to identify the most important factors controlling the energy transport from the solar wind 

into the magnetosphere and ionosphere. Analysis of these results have brought new aspects that 

complement the earlier observational results: (1) The energy input through the magnetopause is 

delayed with respect to changes in the IMF orientation, which is seen as a delayed response in 

both tail dynamics and ionospheric energy dissipation. (2) The solar wind clock angle modulates 

the energy input, but the solar wind speed has a larger effect than that suggested by the empirical 

epsilon-parameter. (3) The solar wind density has a minor role in ionospheric parameters, but does 

affect the magnetotail dynamics and transport properties. Similarly, methods have been developed 

to examine disturbance propagation in the magnetosphere at times of shock interactions. The 

simulations confirm the observational result that the propagation speed is higher in the magnetosphere 

than in the solar wind. Furthermore, the simulations are used to examine the routes of 

fastest propagation in the magnetosphere. Several simulation results are reviewed and compared 

with recent observational analyses. 

Energy circulation from the solar wind through the magnetosphere – ionosphere system is a key topic for 

magnetospheric physics, not only because of the importance of understanding the basics of the Sun-Earth 

system, but also for its practical significance for space weather. The coupling is for the most part governed 

by magnetic reconnection, which at the dayside magnetopause allows energy input into the magnetosphere, 

and in the nightside heats the plasma sheet and creates flows both out of the magnetosphere and toward the 

inner magnetosphere and ionosphere. Thus, the most critical parameter controlling the coupling process is 

the Y-component of the solar wind electric field (E = –V×B), which in a simple geometrical construction is 

the electric field imposed along the (dayside) reconnection line. 

Global magnetohydrodynamic (MHD) simulations have been developed to model the temporal evolution of 

the large-scale plasma dynamics in the coupled solar wind – magnetosphere – ionosphere system (Janhunen 

et al., 1996). These models in their present state are far from perfect, and describe neither multicomponent 

plasma processes nor small-scale phenomena correctly. However, they do give a comprehensive description 

of the dynamics, within the MHD limitations, as dictated by the boundary conditions in the solar wind (e.g., 

Lyon et al., 2004). As especially the inner magnetosphere involves many plasma components and processes 

not described by MHD, the role of the large-scale simulations from the space weather point of view is to 

provide an outer boundary condition for the inner magnetosphere based on the driving solar wind. 

GUMICS-4 global MHD simulation 

The GUMICS-4 global magnetohydrodynamic (MHD) simulation solves the ideal MHD equations in 

conservative form in a simulation box extending from 32 RE upstream of the Earth to –224 RE in the tailward 

direction and ±64 Re in the directions perpendicular to the Sun-Earth line (Janhunen, 1996). The inner 

boundary is a spherical shell with a radius of 3.7 RE, which maps along the dipole field to 60° latitude. Solar 

wind density, temperature, velocity, and interplanetary magnetic field (IMF) are given as boundary conditions 

along the sunward boundary while supersonic outflow conditions are applied on the other boundaries of 

223


the simulation box. The MHD part is coupled to an electrostatic model of the ionospheric potential at an 

altitude of 110 km. The ionospheric potential equation is solved by using the field-aligned currents from the 

magnetosphere as a source for the horizontal ionospheric currents. The ionospheric potential is then mapped 

to the inner shell of the magnetosphere, where it is used as a boundary condition for the MHD domain. 

Two series of idealized simulation runs were driven by artificial solar wind and interplanetary magnetic field 

time series. In the four “IMF rotation runs” (Palmroth et al., 2006) the IMF clock angle was rotated from 0 to 

360° during six hours. Two values of dynamic pressure (P = 2 and 8 nPa) and IMF magnitude (B = 5 and 10 

nT) were used. In the four “pressure enhancement runs” (Laitinen et al., 2007) the solar wind dynamic 

pressure was first increased linearly from 1 nPa to 10 nPa during 90 minutes, held constant for 30 min, and 

then decreased linearly back to 1 nPa during another 90 min. During the remaining hour of simulation time 

the pressure was held constant at the minimum value. The four simulations were run for two different values 

of the IMF clock angle, θ = 18° and θ = 162°. In two runs the pressure was increased by enhancing density 

while keeping the velocity constant, in the other two the pressure increase was done through increasing the 

solar wind speed while keeping the density constant. To study the information propagation, a double shock 

event in the solar wind on Nov 9, 2002, was run with the observed solar wind and IMF parameters. 

Energy transfer from the solar wind into the magnetosphere 

Several earlier works describe the solar wind energy coupling with the magnetosphere – ionosphere system. 

While it is well understood that the southward IMF component is key for the coupling and that high solar 

wind speed enhances magnetospheric activity, the scatter in the statistics is large and it has been difficult to 

find the best coupling function that would adequately address the entire system. The most used coupling 

functions are the solar wind electric field EY and the ε-parameter related to the incident Poynting flux. 

Recent observational statistics show that even for the same solar wind EY, the magnetospheric response can 

vary: The left panel of Figure 1 shows three superposed epoch analyses conducted on sets of stormtime 

substorms, sawtooth events, and steady magnetospheric convection (SMC) events. The events were selected 

based on standard criteria that are reported in the literature. For each data set, pairs of subsets were formed 

that consisted of events that had roughly equal driving electric field. Comparing storms and sawtooth events 

shows that, for the same EY, the storms caused a larger AL response in the ionosphere. Comparison of 

sawtooth and SMC events similarly showed that sawtooth events were associated with higher AL than the 

SMC events. More detailed analysis of the solar wind parameters showed that the storms were driven by the 

highest solar wind speed, while the solar wind speed during the SMC events was lowest. The conclusion 

from these comparisons is that for the same level of driving EY, higher solar wind speed causes higher 

activity in the ionosphere (Pulkkinen et al., 2007). 

In the global MHD simulation, the energy input from the solar wind into the magnetosphere can either be 

evaluated from direct integration of the total energy flux through the magnetospheric boundary (Palmroth et 

al., 2003) or by evaluating the energy conversion surface density as a measure of the energy conversion from 

magnetic to plasma energy at the magnetopause. The integral of that quantity over the boundary surface then 

gives the total amount of magnetic energy to plasma energy by reconnection (Laitinen et al., 2006). 

Examination of the X-line location and orientation, energy conversion at the boundary, and energy input 

through the boundary shows that the X-line controls the energy conversion and input locations and 

intensities (Pulkkinen et al., 2008). Furthermore, it was shown that when the IMF changes, the energy input 

changes with a delay, while the energy input change creates an almost simultaneous change in dissipation in 

the magnetotail and ionosphere. Thus, it would seem that the time lag between solar wind change and 

magnetospheric response is incident already at the magnetospheric boundary (Pulkkinen et al., 2006). The 

energy input dependence on solar wind parameters confirms the observationals above: the solar wind speed 

plays a larger role than EY alone. The solar wind density affects especially flux generation tailward of the 

cusp. The right panel of Figure 1 shows a composite of the 8 simulation runs, showing the conversion of 

magnetic to plasma energy in the top and plasma to magnetic energy in the middle panel. The driving solar 

wind and IMF parameters are shown in the bottom panel(s). The left panels show the “IMF rotation runs”, 

while the right panels show the “pressure runs”. The top panels reflect the tendency of high velocity to create 

highest energy conversion rates, while the middle panel shows the effects of high density for the flux 

generation (or flux compression which also leads to an increase magnetic energy) tailward of the cusp. 

224


Figure 1. (Left) Observational results. Superposed epoch analyses of stormtime substorms, sawtooth events, 

and steady convection events. Figures show subsets where the driving solar wind is almost the same for the 

two sets compared. Panels from top to bottom show the solar wind electric field, negative of the AL index, 

and the solar wind speed. Stormtime substorms are shown in red, sawtooth events in green, and SMC events 

in blue. Note that the sawtooth event subsets are different in the two comparisons. (Right) Simulation results. 

Eight simulation runs using artificial solar wind input. Left panels show IMF rotation runs, with IMF BZ 

changing as indicated in the bottom panel. In runs shown in red P = 8 nPa, and in blue P = 2 nPa. Right 

panels show runs where the pressure was enhanced either by increasing density (blue) or solar wind speed 

(red). The top panels show energy conversion from magnetic to plasma energy (top) and from plasma to 

magnetic energy (middle). The bottom panels show the solar wind density and speed. 

Signal propagation in the magnetosphere 

Interplanetary shock encounters with the magnetosphere offer a unique opportunity to follow a discontinuity 

propagation in the solar wind – magnetosphere – ionosphere system. Observationally, this has only recently 

become feasible with the multitude of satellites that we now have available in different regions of the system. 

Even so, the results include large uncertainties concerning the paths of information propagation, caused by 

large gaps between observations in any particular event. 

Recent observational statistical analysis suggests that the shock propagation speeds inside the magnetosphere 

are larger than those in the ambient solar wind, and that the speeds are larger for events with high dynamic 

pressure (Andreeova et al., 2008). Furthermore, there is evidence that the propagation speeds increase from 

dayside to nightside, indicating an acceleration process during the passage through the magnetosphere. 

Figure 2 shows a double interplanetary shock event studied by Andreeova and Prech (2007). Observations 

from two locations in the solar wind and from the dayside and nightside magnetotail allow evaluation of the 

shock speed both in the solar wind, in the dayside magnetosphere, and in the nightside magnetotail. In the 

solar wind, the shock was observed as a jump in the total magnetic field, solar wind speed and density. In the 

magnetosphere, the shock signatures vary depending on the spacecraft location: at some locations the main 

effect was a compression of the magnetic field, while at other locations the dominant effect was an increase 

in plasma density. The leftmost panel in Figure 2 shows the satellite locations in the magnetosphere. 

The right panel of Figure 2 shows global MHD simulation results of the same event. The panels show time 

series from artificial satellites located along the Sun-Earth line such that they intersect the Polar spacecraft. 

This representation allows us to examine the timing of the disturbance propagation along the Sun-Earth line 

225


and compare the results with the actual measurements. The results confirm the compression of the magnetic 

field especially visible in the dayside magnetosphere. In the nightside, the magnetic field signal is weak both 

in observations and in the simulation. The density enhancement in the simulation dayside magnetosheath (X 

= 12 RE) is large, unfortunately there are no density measurements available from the dayside magnetosphere. 

In the nightside, the simulation shows larger density variations than were observed, especially during 

the second shock arrival. However, Cluster observed strong density enhancement highlighting the sensitivity 

to the observation location. In short, the simulation shows propagation speeds that are consistent with those 

observed, within the (rather large) error bars, which indicates that the general features of information 

propagation can be studied using the MHD simulation (Andreeova et al., 2008). 

Figure 2. Double shock event on Nov 9, 2002. (Left) Satellite locations in the solar wind and magnetosphere. 

(Middle) Observations of total magnetic field and plasma density from Geotail, GOES-8, GOES-10, 

Polar and Cluster. (Right) GUMICS-4 global MHD simulation results of the event. Top three panels show 

total magnetic field, bottom three panels plasma density. Each curve is time series from a point along a line 

extending from X = 12 RE in the dayside to X = –6 RE in the nightside tail (shown red in the left panel). In 

each block, the panel marked “solar wind” shows results between X = 9...12 RE, panel marked “dayside” 

results between X = 1...8 RE, and panel marked “nightside” results for X = 0...–6 RE. The simulation curve 

closest to the observation location is plotted in black. 

Discussion 

Simulation 

results 

In this short paper, we have shown (1) that in the large scale, the global MHD simulations produce results 

that are consistent with observations, and (2) that the global simulations provide an added value to the 

observational analyses by providing a means to examine the system in a global sense. Energy circulation and 

information propagation are key issues in magnetospheric research, and significant advances can be made by 

careful combination of simulation and observational results. 

Examination of the processes at the magnetopause show that the X-line orientation follows the IMF 

orientation with a slight delay. From there on, the X-line orientation controls the energy conversion and input 

locations. Figure 3 shows a two-dimensional representation of the magnetopause for two different IMF 

orientations. The black dots in the left panels mark the X-line location, while the color coding in the center 

226


panel show the energy conversion and in the right panel the energy input into the magentosphere. The 

locations of the energy conversion are clearly dependent on the IMF and X-line orientation. The similarity of 

the two color plots indicates that the two completely independent ways to determine the energy transfer are 

consistent with each other, which increases the reliability of our analysis. 

Figure 3. The Earth’s magnetopause as viewed from the direction of the Sun. Two IMF clock angles are 

shown: 60° (top) and 300° (bottom). Location of the X-line (left), energy conversion (center, red indicting 

energy conversion from plasma to magnetic energy, blue from magnetic to plasma energy), and energy input 

(right, blue colors showing energy input to the magnetosphere, red colors showing energy out from the 

magnetosphere). The concentric circles show the intersection of the magnetopause with the planes X = 0 

(inner) and X = –30 RE (outer). 

Information propagation in the magnetosphere is depicted in Figure 4 illustrating the discontinuity arrival 

during the shock event discussed above. The color coding shows the magnetic field time difference (at onemin 

resolution) after the first shock arrival. In the equatorial plane, the shock propagates along the tail flanks, 

reaching the nightside magnetotail within a few minutes arriving at the tail center last. The propagation is 

fast along the magnetopause, while in the high-latitude lobes the disturbance propagates at about the same 

speed as along the equatorial regions. 

Comparing the observations, the time series from the simulation at artificial satellite locations and the 

surface plots in Figure 4 illustrate the power of the simulations when interpreting observational results: Even 

in this very well-documented event, the observations give only a glimpse of the total dynamics. After 

favorable point comparisons, the simulation can provide a much more complete picture that can reveal the 

causal relationships as well as the governing physical processes. 

In conclusion, both artificial solar wind input and time-series of real solar wind events can be used to run 

global MHD simulations to gain understanding of the large-scale magnetospheric processes. The idealized 

events provide enhanced understanding of the underlying processes, while the event studies provide a global 

context for the point measurements. 

Several efforts are underway to develop the solar, solar wind, and magnetospheric models to a level where 

they can reliably be used to forecast and monitor space weather events (e.g., Hughes and Hudson, 2004; Toth 

et al., 2007). While these groups have done intensive studies of actual space weather events, our approach 

has been to concentrate on studying “easier” cases with often artificial solar wind input. The artificial events 

and new analysis methods have allowed us to examine the energy input from the solar wind, through the 

magnetosheath and magnetopause into the magnetosphere, magnetotail, and finally the ionosphere. 

Similarly, we have started to examine information propagation in the magnetosphere, using shock events as 

clear-cut examples of a single change easily tractable in the magnetosphere. In the future, these studies will 

be complemented with actual event studies. 

227


Figure 4. Interaction of the shock with the magnetosphere. Magnetic field temporal changes in the 

magnetosphere are shown in color coding following the shock arrival. The top panel shows the equatorial 

plane, the bottom panel shows the noon-midnight meridian. 

References 

Andreeova, K., and L. Prech, Propagation of interplanetary shocks into the Earth’s magnetosphere, Adv. 

Space Res., 40, 1871, 2007. 

Andreeova, K., T. Pulkkinen, T. Laitinen, L. Prech, Shock propagation in the magnetosphere: Observations 

and MHD simulations compared, J. Geophys. Res.,113, A09224, doi:10.1029/2008JA013350, 2008. 

Hughes, W. J. and M. K. Hudson, Towards an integrated model of the space weather system, Journal of 

Atmospheric and Solar-Terrestrial Physics, Volume 66, 1241-1242, 2004. 

Janhunen, P., H. E. J. Koskinen, and T. I. Pulkkinen, A new global ionosphere-magnetosphere coupling 

simulation utilizing locally varying time step, in: Third International Conference on Substorms (ICS-3), 

ESA-SP 389, p. 205, 1996. 

Laitinen, T. V., P. Janhunen, T. I. Pulkkinen, M. Palmroth, and H. E. J. Koskinen, On the characterization 

of magnetic reconnection in MHD simulations, Ann. Geophys., 24, 3059-3069, 2006. 

Laitinen, T. V., M. Palmroth, T. I. Pulkkinen, P. Janhunen, and H. E. J. Koskinen, Continuous reconnection 

line and pressure-dependent energy conversion on the magnetopause in a global MHD model, J. 

Geophys. Res., 112, A11201, doi:10.1029/2007JA012352. 

Lyon, J. G., J. A. Fedder, and C. M. Mobarry, The Lyon-Fedder-Mobarry (LFM) global MHD magnetospheric 

simulation code, J. Atmos. Solar-Terr. Phys., 66, 15-16, 1333, 2004. 

Palmroth, M., T. I. Pulkkinen, P. Janhunen, and C.-C. Wu, Stormtime energy transfer in global MHD 

simulation, J. Geophys. Res., 108, (A1), 1048, doi:101029/2002JA009446, 2003. 

Palmroth, M., P. Janhunen, and T. I. Pulkkinen, Hysteresis in the solar wind power input into the 

magnetosphere, Geophys. Res. Lett., 33, L03107, doi:10.1029/2005GL025188, 2006. 

Pulkkinen, T. I., M. Palmroth, E. I. Tanskanen, P. Janhunen, H. E. J. Koskinen, and T. V. Laitinen, New 

interpretation of magnetospheric energy circulation, Geophys. Res. Lett., 33, L07101, 

doi:10.1029/2005GL025457, 2006. 

Pulkkinen, T. I., N. Partamies, R. L. McPherron, M. Henderson, G. D. Reeves, M. F. Thomsen, and H. J. 

Singer, Comparative statistical analysis of stormtime activations and sawtooth events, Geophys. Res., 

112, A01205, doi:10.1029/2006JA012024, 2007. 

Pulkkinen, T. I., M. Palmroth, and T. V. Laitinen, Energy as a tracer of magnetospheric processes: Global 

MHD simulation results, J. Atmos. Terr. Phys.,70 (2008) 687–707. 

Toth, G., D. L. De Zeeuw, T. I. Gombosi, W. B. Manchester, A. J. Ridley, I. V. Sokolov, I. I. Roussev, Sun 

to Thermosphere Simulation of the 28-30 October 2003 Storm with the Space Weather Modeling 

Framework. Space Weather Journal, 5 S06003, 2007. 

228


ON A COMBINED INFLUENCE OF LONG-TERM SOLAR ACTIVITY 

VARIATIONS AND GEOMAGNETIC DIPOLE CHANGES ON CLIMATE 

CHANGE 

O.M.Raspopov 1,3 , V.A.Dergachev 2 , E.G.Guskova 1 

1St.Petersburg Filial of Pushkov Institute of Terrestrial Magnetism, Ionosphere, and Radiowave 

Propagation of RAS, St.-Petersburg, Russia, oleg@or6074.spb.edu; 

2 Ioffe Physico-Technical Institute of RAS, St.-Petersburg, Russia, v.dergachev@mail.ioffe.ru; 

3 Polar Geophysical Institute of Kola SC of RAS, Murmansk, Russia 

Abstract. The influence of variations in galactic cosmic rays (GCR) on climate change has been 

analyzed for the time intervals of thousands and tens of thousands of years. It has been shown that in 

the last millennium quasi-two-hundred-year variations in the GCR intensity (variations in the 

cosmogenic 14 C isotope concentration in dated tree rings) modulated by solar cyclicity (the ~210-year 

cycle) correlated well with climate change (temperature and precipitation variations). The correlation 

coefficient between variations in GCR and climate parameters for different regions of the Earth has 

been found to range from 0.58 to 0.95. Analysis of variability in the concentration of the cosmogenic 

10 Be isotope (that also reflects the GCR flux variability) in Greenland ice for the time interval from 

20,000 to 50,000 years ago has revealed that the 10 Be concentration is modulated by the quasi-twohundred-year 

solar cycle. Comparison of variations in the cosmogenic 10 Be isotope concentration with 

changes in the magnitude of the virtual axial dipole moment (VADM) of the geomagnetic field has 

shown that the envelope of the 10 Be concentration amplitude correlates well with the VADM 

variations. Thus, it can be concluded that long-term solar activity and geomagnetic dipole variations 

exert a combined influence on the GCR fluxes that enter the Earth’s atmosphere and affect the 

climate. A decrease in the geomagnetic dipole leads to an enhancement of the total GCR flux on the 

one hand and an increase in the depth of modulation of the GCR fluxes caused by solar activity 

variability on the other hand. 


The problem of the influence of variable cosmic ray fluxes on atmospheric processes and meteorological and 

climatic parameters has been intensely studied in recent years [Pudovkin and Raspopov, 1992; Pudovkin, 

2004; Dergachev et al., 2006, 2007; Raspopov et al., 2007, 2008]. Major attention has been paid to the effect 

of solar activity on amplitude modulation of the galactic cosmic ray fluxes (GCR) entering the atmosphere. 

However, there also exists another geophysical factor that affects the amplitude modulation of GCR fluxes 

and thus exerts influence on climate parameters. This is the magnitude of the geomagnetic dipole. The 

geomagnetic field is a peculiar umbrella that prevents GCR penetration into the magnetosphere. The fact of 

amplitude modulation of GCR fluxes in the atmosphere caused by variations in the geomagnetic dipole is 

evidenced by experimental data on the concentration of cosmogenic 10 Be isotope in the terrestrial archives 

whose production in the atmosphere occurs under the influence of cosmic rays [Masarik and Beer, 1999]. 

The time scale of these variations is thousands and tens of thousands of years, while variations in solar 

activity have a much smaller scale. 

The goal of our paper is to consider a combined effect of long-term variations in solar activity and changes 

in the geomagnetic dipole on climate. 

2 Data used 

To analyze the climate change caused by long-term solar activity variations and changes in the geomagnetic 

dipole, we used the data on the concentrations of cosmogenic 14 C and 10 Be isotopes and stable 18 O isotope in 

the terrestrial archives (ice caps of Greenland and Antarctica, bottom sediments) and also on summer 

temperatures and precipitations reconstructed from variations in ring widths of different species of juniper in 

Tien Shan and Tibetan Plateau and ring widths of Fitzroya cupressoides in Chile. 

229


2.1 Data on solar activity 

To analyze solar activity variations, data on the 14 C variations in tree rings for the last 8,000 years [Stuiver at 

al., 1998] and also measurements of the 10 Be concentration in Greenland ice for the time interval from 50,000 

to 25,000 years ago [Masarik and Beer, 1999] were used. 

2.2 Data on changes in the geomagnetic dipole 

Changes in the geomagnetic dipole were analyzed by using data on changes in the dipole moment M for the 

last 40,000 years [Lehman et al., 1996] and palaeomagnetic high-resolution data (SAPIS-8) on changes in M 

for the last 100,000 years obtained at the continental edge of the Antarctic peninsula (65 O S, 78 O W) [Sagnotti 

et al., 2001] were used. 

2.3 Data on climate change 

To analyze the influence of long-term solar activity variations on climate, we used data on ~200-year solar 

activity cyclicity (de Vries cycle) in the time interval of the last 1,000 years and also the 1,229-year 

chronology around 50,000 years ago. For these intervals, data on annual variations in tree ring widths are 

available. For the last millennium, data on variations in ring widths of juniper Junipedrus turkestanica from 

two regions of Tien Shan [Maksimov and Grebenyuk, 1972; Esper at al., 2003; Mukhamedshin and Sarbaev, 

1988] and juniper Sabina przewalskii growing on the Tibetan Plateau [Shao et al., 2005] are available. The 

growth of Junipedrus turkestanica was found to be affected by summer temperatures and independent of 

precipitations. The radial growth of Sabina przewalskii was governed by the amount of precipitations. 

For the time interval around 50,000 years ago, a floating 1,229-year chronology developed from subfossil 

stumps of Fitzroya cupressoides from the mid-latitude region of Chile has been reported [Roig et al., 2001]. 

The trees were buried by a landslide and were well preserved. Analysis of variations in the ring widths of 

living trees of this species showed that their radial growth was governed by summer temperatures. 

To analyze the intercorrelation between climate change and changes in the magnitude of the geomagnetic 

dipole, the data of the concentration of stable oxygen 18 O isotope in Greenland ice for the time interval of 

40,000 years [Grootes and Stuiver, 1997] and in the Antarctic ice for the time interval to 100,000 years [Steig 

et al., 2000] were used. Variations in the relative 18 O isotope concentration give information on relative 

temperature variations [Souchez, 1997]. 

3 Results of analysis and discussion 

To examine the interrelation between changes in the geomagnetic dipole and temperature oscillations in the 

past, a cross-correlation analysis of the curves (series) characterizing these variations was carried out. Fig. 1a 

and 1b show changes in the Earth’s dipole [Lehman et al., 1996] and variations in the 18 O concentration 

[Grootes and Stuiver, 1997] in Greenland ice for the time interval from 39,900 to 3,400 years ago, 

respectively. Fig. 1c gives estimates of the cross-correlation function between changes in the Earth’s magnetic 

moment and 18 O concentration (temperature). The correlation coefficient between these series was found to be 

rather high and equal to 0.71. 

It is evident from Fig. 1 that there is a similarity between the curves shown in Fig. 1a and 1b and Fig.1d 

and 1e, respectively, and the high correlation coefficients (Fig. 1c and 1f) for the curves plotted 

independently indicate that a relation between variations in temperature and intensity of the cosmic ray 

fluxes modulated by the geomagnetic field does exist. 

Let us now consider the interrelation between climate change and ~200-year solar cyclicity. Fig. 2 shows 

results of wavelet transformation (Morlet basis) in the range of 100-300-year periods of solar activity ( 14 C) 

(a), variations in summer temperatures in three regions of Tien Shan (b), and variations in precipitations on 

the Tibetan Plateau in the same range of periods (c) for the last millennium. The variations in summer 

temperatures and precipitations were reconstructed from variations in tree ring widths of the junipers 

mentioned in Section 2.3. As one can see from Fig.2, the behavior of climate characteristics correlates well 

with the ~200-year solar activity variations. The correlation coefficients between the series of solar activity 

and climate parameters shown in Fig. 2 were found to be 0.94, 0.78, and 0.84. This indicates that the 200-year 

solar cyclicity strongly affects climate parameters. 

230

а 

b 

c 


Years, BP 

Fig. 1 (a) changes in the Earth’s dipole moment [Lehman et al., 1996]; (b) variations in the 18 O concentration 

[Grootes and Stuiver, 1997] in Greenland ice for the time interval from 39,900 to 3,400 years ago; (c) cross- 

correlation function between changes in the Earth’s magnetic moment and variations in the 18 O concentration; 

(d) changes in palaeointensity of the Earth’s magnetic field (SAPIS-80) reconstructed by using sediment cores 

from the Antarctic peninsula for the last 100,000 years [Sagnotti et al., 2001]; (e) variations in 18 O 

concentration in ice cores from the Taylor Dome station, Antarctica [Steig et al., 2000]; (f) cross-correlation 

function between the series presented in Fig. (d) and (e). 

231 

Fig. 2 (a) results of wavelet 

transformation (Morlet basis) in the 

range of solar activity periods of 

100-300 years ( 14 C), (b) variations 

in summer temperatures in three 

regions of Tien Shan, and (c) 

variations in precipitations on the 

Tibetan Plateau in the same range of 

periods for the last millennium. 

d 

e 

f

a 


Fig. 3 (a) 208-year variations in the 10 Be concentration in cores from Greenland glaciers; (b) results of 

spectral analysis of variations in ring widths of Fitzroya cupressoides buried by a landslide around 50,000 

years ago in Chile 

Fig. 4 Simulated rate of production of 10 Be in the atmosphere in the case of changes in the geomagnetic 

dipole and variations in solar activity [Masarik and Beer, 1999]. The measure of solar activity in the figure in 

coefficient Φ which is zero in the absence of disturbances and equals 1,000 at a high solar activity. The limits 

of variations in the geomagnetic dipole M in the graph are taken to be from 0 to 2, where 1 is the modern 

value of the geomagnetic dipole. 

By examining cores of Greenland ice with the aim of tracing variations in the 10 Be concentration, 

Masarik and Beer (1999) revealed the 208-year solar cycle in the time interval from 50,000 to 25,000 years 

ago. They found that the amplitude of these variations was modulated by changes in the geomagnetic field 

intensity (Fig.3a). The efficiency of the effect of the ~200-year solar cycle during this time interval is 

confirmed by spectral analysis of the variations in tree ring widths of Fitzroya cupressoides buried by a 

landslide around 50,000 years ago in Chile. Fig. 3b shows results of spectral analysis of the variations in ring 

widths of the trees mentioned above. The spectrum clearly exhibits the quasi-two-hundred-year climatic cycle 

and also other solar cycles, i.e., 80-90 years (Gleissberg cycle) and 23 years (Hale cycle). This result, together 

with the data on the quasi-two-hundred-year solar cycle around 50,000 years ago shown in Fig.3a, points to a 

232 

b


combined influence of the geomagnetic field intensity and solar activity on climate during the time intervals 

from hundreds to tens of thousands of years. 

The experimental result obtained is in good agreement with the simulated global pattern of the rate of 

production of 10 Be in the atmosphere in the case of varying magnitude of geomagnetic dipole and solar 

activity (Fig. 4) [Masarik and Beer, 1999]. In Fig. 4 the measure of the solar activity is coefficient Φ which is 

zero in the absence of disturbances and equals 1000 at a high solar activity. The limits of changes in the 

geomagnetic dipole in the graph are from 0 to 2. The rage of production of 10 Be equal to 1 corresponds to the 

modern magnitude of the geomagnetic field (M = 1) and its average disturbance (Φ = 550). As one can see 

from the graph, in the limits of the given M and Φ the intensity of the integral cosmic ray flux in the 

atmosphere can vary by an order of magnitude. A decisive factor in the enhancement of the SCR flux in the 

atmosphere is a decrease of the geomagnetic dipole by a factor of 2 and more and a low solar activity. 

4 Conclusions 

Experimental data and simulation have shown that changes in the geomagnetic dipole magnitude and longterm 

variations in solar activity exert a combined effect on climate change and, hence, confirm the idea of the 

influence of cosmic ray fluxes on climate change. 

The work was supported by the Presidium of RAS (Program “Environmental Change and Climate”), 

Presidium of St.-Petersburg Science Centre of RAS and Russian Foundation for Basic Research (Projects 06- 

04-48792a, 06-02-16268a, 06-04-64200a). 

References 

Dergachev V.A., P.B. Dmitriev., O.M. Raspopov, and H. Jungner (2006), Variations in cosmic ray fluxes 

modulated by solar and Earth’s magnetic fields and climate change. Part 1. Time interval to 10,000- 

12,000 years ago (Holocene), Geomagnetism and.Aeronomy., 46(1), 123-134.. 

Dergachev V.A., P.B. Dmitriev, O.M.Raspopov, and H. Jungner (2007), Variations in cosmic ray fluxes 

modulated by solar and Earth’s magnetic fields and climate change. Part 2. Time interval from 

~10,000 to ~100,000 years ago (between the warm period of the Holocene and Eemian interglacial 

period), Geomagnetism and.Aeronomy, 47(1), 116-125. 

Maksimov E.B., and A.K. Grebenyuk (1972), Variability in the climate conditions of the high-mountain 

zone of the Zeravshansk range for the last 800 years. Izvestiya Akademii Nauk SSSR, Geographical ser., 

No. 2, 105-106. 

Pudovkin M.I., and O.M. Raspopov (1992), Mechanism of influence of solar activity on the state of the 

lower atmosphere and meteoparameters, Geomagnetism and .Aeronomy, 3(1), 1-22. 

Grootes P.M. and M. Stuiver (1997), Oxygen 18/16 variability in Greenland snow and ice with 10 -3 to 10 5 - 

year time resolution, J Geoph. Res., 102, 26.455-26470. 

Esper, J., S.G. Shiyatov, V.S. Mazepa, R.J.S. Wilson, D.A. Graybill, and G. Funkhouser (2003), 

Temperature-sensitive Tien Shan tree ring chronologies show multi-centennial growth trends. Climate 

Dynamics, 21, 699-706. 

Lehman B., C. Laj, C. Kissel, A. Mazaud, M. Paterne, and L. Labeyrie (1996), Relative changes of the 

geomagnetic field intensity during the last 280 kyr from piston cores in the Azores area. Phys. Earth 

Planet. Sci., 93, 269-284. 

Pudovkin M.I. (2004), Influence of solar activity on the lower atmosphere state. International Journal of 

Geomagnetism and Aeronomy. V.5. GI2007, doi:10.1029/2003GI000060. 

Raspopov O.M., V.A. Dergachev, A.V. Kuzmin, O.V. Kozyreva, M.G. Ogurtsov, T. Kolström, and E. 

Lopatin E (2007), Regional tropospheric responses to long-term solar activity variations. Advances in 

Space Research, 40, 1167-1172. 

Raspopov O.M., V.A. Dergachev, J. Esper , O.V. Kozyreva, D. Frank, M.G. Ogurtsov, T. Kolström, X. Shao 

(2008), The influence of the de Vries (~200-year) solar cycle on climate variations: results from the 

Central Asian Mountains and their global link. Palaeogeography, Palaeoclimatology, Palaeoecology, 

259, 6-16. 

Roig F.A., C. Le-Quesne, J.A. Boninsegna, K.R. Briffa, F. Lara, Grudd., P.D.Jones, and C. Villagran. 

(2001), Nature, 410, 567-570. 

233


Masarik J. and J. Beer (1999) Simulation of particle fluxes and cosmogenic nuclide production in the Earth’s 

Atmosphere, J. Geoph. Res., 104D, 12099-12111. 

Mukhamedshin R.D. and S.K. Sarbaev (1988), Champion of longevity, Kaynar, Alma-Ata (in Russian) 

Sagnotti L., P. Macri, A. Camerlenghi, and M. Rebesco (2001), Environmental magnetism of Antarctic Late 

Pleistocene sediments and interhemispheric correlation of climatic events, Earth Planet. Sci. Lett., 192, 

65-80. 

Shao X., E. Liang, L. Huang, and L. Wang (2005), 1437-year precipitation history from Qilian juniper in 

the northeastern Qinghai-Tibetan Plateau, PAGES NEWS, 13(2), 14-15. 

Souchez R. (1997), The buildup of the ice sheet in central Greenland, J. Geoph. Res. 102, 26,317-26,323. 

Steig E.J. D.L. Morse, E.D. Wadington. M. Stuiver, P.M. Grootes, P.A. Mayevski, M.S. Twickler, and 

S.I.Whitlow (2000), Wisconsinan and Holocene climate history from an ice core at Taylor Dome, 

Western Ross Embayment, Antarctica, Geografica Annaler, 82A(2-3), 213-235.. 

Stuiver, M., R.J. Raimer, and T.F.Braziunas (1998), High-precision radiocarbon age calibration for 

terrestrial and marine samples, Radiocarbon, 40(3), 1127-1151. 

234


SOLAR ACTIVITY, COSMIC RAYS AND CLIMATE CHANGE 

(ON THE 75TH ANNIVERSARY 

AND IN MEMORY OF PROF. M.I. PUDOVKIN ) 

O.M. Raspopov 1,3 , S.V. Veretenenko 2 

1 St.Petersburg Filial of Pushkov Institute of Terrestrial Magnetism, Ionosphere and Radiowave Propagation 

of RAS, St.Petersburg, 191023, Russia, e-mail: oleg@or6074.spb.edu; 2 Ioffe Physico-Technical Institute 

RAS, St.Petersburg, 194021, Russia; 3 Polar Geophysical Institute of Kola Scientific Centre of RAS, 

Murmansk, Russia 


Abstract. A review of the research activity of M.I.Pudovkin, his co-workers and followers in 

solving the problem of the solar activity influence on atmospheric processes and climate change is 

presented, the roles of cosmic ray variations and changes in cloudiness are emphasized. The 

problems that still remain unresolved in this field are outlined. 

M.I. Pudovkin was an outstanding scientist-geophysicist famous for remarkable achievements in solarterrestrial 

physics. He was a founder of a scientific school at St.Petersburg (Leningrad) State University. 

Under his guidance about 50 candidate and doctor theses were defended. The team formed by Prof. 

Pudovkin still occupies one of leading positions in this area of science in Russia. It is the first at 

St.Petersburg University by the citation indexes of the works [Krivovichev, 2008]. 

M.I. Pudovkin’s scientific interests were extremely versatile. The subjects of his investigations were 

magnetic storms and substorms, ionospheric disturbances, auroral processes, the formation and dynamics of 

the radiation belts, simulation of the structure and dynamics of the magnetosphere, boundary processes 

associated with the solar wind - magnetosphere coupling, the structure and dynamics of the solar wind, etc. 

Considerable attention was given to the study of the influence of solar activity on the processes in the lower 

atmosphere and climate parameters. The goal of this paper is to briefly review the main achievements of 

M.I.Pudovkin and his team in the investigations of this problem. 

2. Influence of solar activity and cosmic ray variations on the lower atmosphere state and climate 

parameters in the studies of M.I. Pudovkin and his followers 

The first paper devoted to this subject was published by M.I. Pudovkin in “Geomagnetism and 

Aeronomy” in 1989. Its title was “Manifestation of solar and magnetic activity cycles in the air temperature 

variation in Leningrad” [Pudovkin and Lubchich, 1989]. The most popular concept in the interpretation of 

the solar activity – climate links at that time was “the Sun – solar wind – magnetosphere – ionosphere – a 

trigger mechanism of atmospheric disturbances”. The main problem in this interpretation was a considerable 

difference between the energies of the processes in the magnetosphere-ionosphere and the lower atmosphere. 

The energy of atmospheric processes exceeds the energy of the magnetosphere-ionosphere ones by a factor 

of 10 3 -10 4 [Pudovkin and Raspopov, 1992; Pudovkin and Babushkina, 1992a]. Pudovkin put forward the 

hypothesis that there had to be an agent related to solar activity and able to affect directly the lower 

atmosphere by changing its thermal state. There were two candidates: the first was variations in solar 

irradiance, including the ultra-violet part of the spectrum, and the second was variations in the cosmic rays 

(CR), with the intensity modulated by solar activity, which affect optical parameters of the atmosphere 

(aerosol concentration etc.), cloud cover and the global electric circuit. 

The �10-year data of satellite observations (NIMBUS 7, SMM etc.) of the total solar irradiance (TSI) 

available to the moment the paper was published indicated that the solar irradiance changed only slightly 

(�0.1 % of the mean TSI) during the 11-year solar cycle (Fig.1) [Frölich and Lean, 2004]. For this reason 

M.I.Pudovkin came to the conclusion that cosmic rays, both solar and galactic, could be the main agent 

transferring the solar activity influence to the lower atmosphere. So, right from the start, M.I.Pudovkin and 

his co-workers began to develop this concept, looking for experimental data confirming the idea of cosmic 

ray effects on the atmospheric processes. The first paper of Pudovkin and Lubchich [1989] also reported the 

�11-yr and �22-yr periodicities coinciding with the main solar cycles revealed in the near-ground 

temperature in Leningrad. It is known that the 22-yr solar magnetic cycle manifests itself very weakly in the 

sunspot number variations, but it is pronounced in the geomagnetic activity and galactic cosmic ray (GCR) 

235


Fig.1. Results of total solar irradiance measurements at the different satellites [Frölich and Lean, 2004]. The arrow 

indicates the year of the first publication by M.I. Pudovkin on the problem of solar-climate relationships. 

variations. By now the 22-yr periodicity has been revealed in the concentration of cosmogenic 10 Ве isotope 

in Greenland ice cores [Veretenenko et al., 2005] whose production in the atmosphere is due to cosmic rays. 

Thus, the result obtained by M.I. Pudovkin in 1989 is confirmed by modern data. 

In further investigations M.I. Pudovkin and 

his co-workers focused attention on the atmosphere 

response during sharp decreases of CR fluxes 

associated with geomagnetic storms (Forbushdecreases 

of GCR) and also during the CR increases 

– solar proton events (SPE). New important results 

were obtained in the studies of variations in the 

zonal circulation in the lower atmosphere at middle 

latitudes [Pudovkin and Babushkina, 1992a]. It was 

found that an intensification of zonal circulation 

took place due to the CR increases (SPE), whereas 

its weakening was observed during decreases of CR 

fluxes (Forbush-decreases of GCR) (see Fig.2 

according to [Veretenenko and Pudovkin, 1993; 

Pudovkin and Veretenenko, 1996]). The energy 

necessary for the changes in the atmospheric 

circulation to occur was estimated to be ~5.10 26 – 

2.10 27 ergs [Pudovkin and Babushkina, 1992a; 

Pudovkin and Raspopov, 1992]. 

The study of meridional profiles of zonal 

atmospheric pressure during intense geomagnetic 

disturbances, including periods of SPE and Forbushdecreases 

of GCR (Fig.3), revealed that the observed 

variations in zonal circulation were due to the 

�� 2.0 

1.0 

0.0 

-1.0 

-2.0 

-3.0 

3.0 

2.0 

1.0 

0.0 

-1.0 

-2.0 

-3.0 

-6 -4 -2 0 2 4 6 8 10 

�t, day 

1 

2 

Forbush-decreases of GCR 

N=33 

Solar Cosmic Ray bursts 

E > 90 MeV (N=27) 

E < 90 MeV (N=29) 

�t, day 

-6 -4 -2 0 2 4 6 8 10 

Fig.2. Superposed epoch analysis of the variations of the 

zonal circulation indices ��10 3 (� is angular velocity 

of the zonal flow at middle latitudes, � is the angular 

velocity of the Earth’s rotation) associated with cosmic 

ray variations. Moment �t=0 corresponds to the day of 

the event onset; N is the number of events. 

atmospheric processes at subpolar and polar latitudes (� > 55�N), i.e., they were characterized by a 

latitudinal dependence [Pudovkin and Babushkina, 1992a]. The latitudinal dependence of the zonal pressure 

spoke in favor of the hypothesis that CR variations were the most probable link between solar activity and 

the lower atmosphere. Later studies of short-period effects of CR variations in meteorological characteristics 

236


Fig.3 Meridional profiles of zonal pressure at different stages 

of geomagnetic disturbances (N =19). Moment �t=0 corresponds 

to the day of the disturbance onset: curve 1� �t= –1 

day (flare effect); curve 2 – �t= +4 days (Forbush-decrease 

effect); curves 3 and 4 – �t= –4 and –5 days (quiet days). 

of the high-latitude atmosphere (Sodankylä 

station, Finland) carried out by Pudovkin’s 

team confirmed once more an important role of 

the variations in cosmic ray fluxes associated 

with solar activity in the disturbances of 

tropospheric circulation [Pudovkin et al., 1996, 

1997]. Note that by now the correlations 

between the atmospheric circulation and CR 

flux variations have been revealed not only at a 

short time scale, but also for the ~200-yr solar 

periodicity (de Vries cycle) [Meeker and 

Mayewski, 2002; Delmonte et al., 2005; 

Raspopov et al., 2007]. 

The next step in the studies of the CR 

influence on the lower atmosphere carried out 

by M.I.Pudovkin and his colleagues was 

analysis of variations in the atmospheric 

transparency during Forbush-decreases of GCR, 

for which the actionometric data of groundbased 

stations were used. It was shown that 

during these events a significant increase in the 

atmosphere transparency took place in auroral and subauroral zones and caused an increase in the solar 

radiation input by �10-13% at these latitudes [Pudovkin and Veretenenko, 1992; Pudovkin and Babushkina, 

1992b]. According to the quantitative estimates, the additional income of solar energy to the lower 

atmosphere during the period of a Forbush-decrease of GCR may reach �10 27 ergs. This value exceeds the 

energy coming to the magnetosphere from the solar wind (~10 23 ergs/day) by a factor of 10 3 -10 4 , and it is 

comparable to the energy necessary for the changes in the zonal circulation associated with solar activity 

phenomena. According to Pudovkin’s ideas, the changes in the atmosphere transparency associated with 

Forbush-decreases of GCR, solar cosmic ray bursts, and intense geomagnetic disturbances and, hence, the 

changes in the amount of the solar energy coming to the lower atmosphere must give rise to variations in the 

atmospheric temperature and pressure. Simulation of possible changes in the high-latitude temperature and 

pressure due to the transparency variations associated with solar cosmic ray bursts was carried out by 

Pudovkin and Morozova [1997, 1998]. 

The most remarkable achievement of 

M.I.Pudovkin and his team was establishment of 

the relationships between variability of cosmic ray 

fluxes and cloud cover formation. It was found that 

the total cloud cover decreased in the auroral and 

subauroral zones during Forbush-decreases of 

GCR [Veretenenko and Pudovkin, 1994; Pudovkin 

and Veretenenko, 1995]. Variations in the cloud 

amount averaged over the ground-based 

actinometric stations of Russia in the latitudinal 

belts � � 65-68�N and 60-64�N are shown in Fig.4 

for the period including the development of GCR 

Forbush-decreases. It can be seen that a rather 

sharp decrease in the cloud cover (on the average, 

by 5-8% of the total sky area relative to the 

undisturbed level) occurs on the +1/+2 day after 

the event onset. The total cloudiness variations 

associated with Forbush-decreases of GCR were 

revealed at all the stations involved, the frequency 

of occurrence of clear-sky days at some stations 

was found to increase by a factor of 2 during these 

events (Fig.5). Thus, the conclusion was made that 

a decrease in the GCR fluxes resulted in a 

decreasing cloudiness, mainly at the latitudes that 

Fig.4. Mean variations of the total cloud amount (in per cent 

of total sky area) averaged over the stations in the auroral 

(��65-68�N) and subauroral (��60-64�N) zones during Forbush-decreases 

of GCR. Moment �t=0 corresponds to the 

day of Forbush-decrease onset: curve 1 – winter events 

(number of events N=42); curve 2 – summer events (N=21). 

237


Fig.5. Frequencies of occurrence f (%) of clear sky 

days (i.e. days with the total cloud amount n � 20% 

of total sky area) during Forbush-decreases of GCR 

at the stations in the latitudinal belt ��60-64�N: 

curve 1 – Okhotsk, curve 2 – Oimyakon, curve 3 – 

Vanavara, curve 4 – Voeykovo, curve 5 – Yakutsk, 

curve 6 – Aleksandrovskoe. 

Further studies of the total solar radiation 

input to the lower atmosphere during Forbushdecreases 

of GCR confirmed that cosmic rays 

affected the cloud cover state. The total radiation 

fluxes are defined as the sum of both direct radiation 

coming directly from the Sun’s disk and the 

scattered radiation coming from the remaining area 

of the sky. Both the total and direct radiation 

decrease as the cloudiness increases. A statistically 

significant increase in the daily sums of the total 

radiation that provides evidence for a cloud cover 

decrease was detected at the stations at the latitudes 

� >60�N in the first days after the Forbush-decrease 

onsets [Veretenenko and Pudovkin, 1997]. It was 

found that the changes in the solar radiation input 

could reach 2�10 5 �5�10 5 J/m 2 (Fig.7). Thus, not only 

the CR effects on the cloudiness state were 

confirmed on the basis of new experimental data, but 

also quantitative estimates of changes in the solar 

radiation input were obtained. 

The influence of GCR on the cloud cover state 

and the total solar radiation input were considered 

for the 11-year solar cycle as well [Veretenenko and 

Pudovkin, 1999]. A negative correlation between the 

half-year sums of the total radiation and GCR 

intensity, which pointed to an increase in the cloud 

could be reached by cosmic particles with the energies 

from about several hundred MeV to several GeV. The 

variations in the cloud cover during the bursts of 

energetic solar cosmic rays, i.e., those associated with the 

increases of CR fluxes, were analyzed in the next paper 

[Veretenenko and Pudovkin, 1996]. The results of this 

study are shown in Fig.6 for four stations in the 

latitudinal belt 61�-69�N, the zero moment �t = 0 

corresponding to the day of the SCR burst onset. One can 

see that the SCR increase is accompanied by increasing 

cloud cover at all the stations under study. The effect was 

found to grow with increasing latitude. 

238 

Fig.6. Variations of cloud cover associated with SCR 

bursts (Е > 90 MeV). Moment �t=0 corresponds to the 

day of the burst onset: 

a) Mean variations of cloud amount (in per cent of 

total sky area) at the high-latitude stations: curve 1 – 

Kotelny island (�=69.3�, N=15); curve 2 – Chetyrekhstolbovy 

island (�=64.6�, N=18); curve 3 – 

Olenek (�=62.8�, N=30); curve 4 – Verkhoyansk 

(�=61.3�, N=40). 

b) The amplitude of SCR effects �n/ n ( n is the mean 

level of cloud amount before the event onset, �n is the 

deviation from the mean level) vs. geomagnetic 

latitude of the stations.


cover with increasing GCR at solar activity minima, 

was revealed at high-latitudinal stations both during 

cold and warm periods. In addition, it was shown 

that the flare activity of the Sun as well as the 

auroral activity could also exert a considerable 

influence on the cloudiness state and the solar 

radiation input. The changes in the solar radiation 

input in the 11-year solar cycles were found to 

amount to �4-6%, so they could be regarded as a 

possible energy source of long-term disturbances of 

the atmospheric circulation associated with solar 

activity. 

In later years M.I. Pudovkin and his group 

concentrated their attention on analysis of regional 

climatic responses to solar activity phenomena in the 

North Atlantic region and Central Europe 

[Morozova et al., 2002]. 

Thus, M.I. Pudovkin and his group carried out 

thorough complex investigations that indicated that 

cosmic ray fluxes exerted a considerable influence 

on the processes in the lower atmosphere. The 

experimental data were supported by the quantitative 

estimates that showed that the changes in the solar 

radiation in the lower atmosphere due to the CR 

variations provided a sufficient amount of energy for 

intensification of dynamic processes. 

It is important to note that the first papers of 

Pudovkin and Veretenenko [1994, 1995] devoted to 

the correlation between the cloud cover and GCR 

variability were published 2 and 3 years before the 

paper of Svensmark and Friis-Christensen [1997] on 

a possible influence of GCR fluxes on cloudiness 

state appeared. Thus, the priority of Pudovkin’s 

group in these investigations is evident though these 

groups of investigators used different data: Pudovkin 

and Veretenenko employed ground-based 

observations of the cloud cover and solar radiation 

input, while Svensmark and Friis-Christensen used 

satellite data. 

total radiation changes ��Q��10 5 J/m 2 �day 

7.0 

5.0 

3.0 

1.0 

-1.0 

-3.0 

-5.0 

-7.0 

3.0 

1.0 

-1.0 

-3.0 

-5.0 

4.0 

2.0 

0.0 

-2.0 

-4.0 

Okhotsk 

N=42 

-6 -4 -2 0 2 4 6 

Oimyakon 

N=43 

-6 -4 -2 0 2 4 6 

Yakutsk 

N=43 

-6 -4 -2 0 2 4 6 

�t, days 

Fig.7. Mean variations of the daily sums of total 

radiation �(�Q) at the stations in the latitudinal belt 

� = 60-64�N during Forbush-decreases of GCR. 

Moment �t=0 corresponds to the day of the Forbushdecreases 

onset. 

However, in using satellite data for estimation of the cloud cover response to solar activity the Russian 

scientists were also the first. Dmitriev and Govorov [1972] and Dmitriev and Lomakina [1977] used satellite 

data to consider the cloud cover dynamics after solar flares. Dmitriev and Lomakina [1977] traced the 

changes in the cloudiness associated with solar flares above four regions of the USA in the latitudinal range 

25�-50�N and longitudinal range 65�-130�W and revealed an increase in the cloud cover after solar flares. 

On the basis of these data, Pudovkin and Raspopov [1992] supposed that the cosmic ray variability could 

result in the cloud cover variability. 

In their first publication Svensmark and Friis-Christensen [1997] cited the paper by Pudovkin and 

Veretenenko [1995] in Journal of Atmospheric and Terrestrial Physics. However, to our great surprise, on 

page 70 in a new book by Svensmark and Calder “The Chilling Stars. A New Theory of Climate Change” 

published in 2007 one can read: “Svensmark thought that the supply of cosmic rays that the Sun admits to 

the Solar System might help to control the Earth’s cloudiness. More cosmic rays, more clouds. Scientist in 

Russia had flirted with opposite idea, that cosmic rays might reduce cloudiness”. This means that 

distorted information is given to the reader about the results obtained by M.I. Pudovkin and his team. 

Moreover, on the next page Svensmark and Calder write:”The clouds obeyed the cosmic rays closely. By the 

norms of climate science the correlation was exceptionally good, and Svensmark and Friis-Christensen were 

astonished that no one had noticed such obvious linkage before. Afraid of being beaten to the 

announcement of the discovery by other scientists, they rushed to complete a scientific paper. It went off at 

239


the end of February 1996 to the journal 

Science in Washigton DC”. It is astonishing 

that the book gives such an incorrect 

information: the fact that the paper on the 

relation between cosmic rays and cloudiness 

was published by Pudovkin and Veretenenko 

several years earlier than the paper of 

Svensmark and Friis-Christensen is a 

convincing proof that the situation is different. 

It is interesting to note that the idea to 

consider links between the cloud cover and 

cosmic ray variations was prompted to 

Svensmark by Russian scientists. N. Calder, 

one of the authors of the book mentioned 

above, writes in his earlier book “The Magic 

Sun” published in 1997 and devoted to the 

scientists of Danish Meteorological Institute 

K. Lassen, E. Friis-Christensen and H. 

Svensmark [Calder, 1997]: “A chance remark 

in May 1995 switched Svensmark on to 

cosmic rays. A colleague had attended a 

seminar at the institute arranged by Friis- 

Christensen in connection with visit by two 

Russian scientists, and told Svensmark what 

he had heard. The Russian had suggested 

that cosmic rays could alter the 

transparency of the air by provoking 

chemical action, and perhaps by affecting 

cloud formation (page 125)”. In other words, 

at the seminar in Danish Meteorological 

Institute in 1995 the Russian scientists spoke 

about a possible relationship between the 

cloud cover variations and cosmic ray fluxes. 

This was a meeting in the framework of the 

joint project supported by the European 

Commission INTAS-93-3248-ext “Effects on 

stratospheric ozone and terrestrial climate of 

varying solar activity”, and the Russian 

scientists participating in the project and at the 

seminar were Prof. O.M.Raspopov and Dr. 

O.I. Shumilov. At this seminar they presented 

a figure (see Fig.8) demonstrating the satellite 

data on cloud cover variations according to Dmitriev and Lomakina [1977] and also the data on the 

development of Forbush-decreases of GCR after solar flares and changes in the atmospheric transparency at 

subauroral latitudes during intense geomagnetic disturbances according to Pudovkin and Veretenenko 

[1992]. Thus, the problem of the influence of cosmic ray fluxes on the cloud cover was formulated by the 

Russian scientists at the seminar. The Russian scientists suggested that Danish and Russian colleagues carry 

out a joint study of this problem. The answer was very specific: in two years Svensmark and Friis- 

Christensen published a paper on the influence of GCR fluxes on cloudiness [Svensmark and Friis- 

Christensen, 1997]. 

3. Conclusions 

Fig.8. Top: curve 1 – mean changes of the cloud cover over 4 

regions of USA after solar flares according to the satellite data 

[Dmitriev and Lomakina, 1977]; curve 2 – variations of the 

atmospheric transparency in the subauroral zone during the 

solar flares and the following intense magnetic storms averaged 

over 27 events [Pudovkin and Veretenenko, 1992]. Moment 

�t=0 corresponds to the day of the magnetic storm onset and 

�t= –2 corresponds to the day of solar flare. 

Bottom: curves 1 and 2 – the cosmic ray variations averaged 

over the same events in the auroral zone (Apatity) and at 

middle latitudes (Moscow), respectively; curve 3 – mean 

values of geomagnetic �К р -index. 

To summarize, M.I.Pudovkin and his group made valuable contributions into the solution of a large 

number of problems concerned with the influence of solar activity and cosmic ray variations on the structure 

and dynamics of the lower atmosphere and climate parameters. They obtained pioneering results on changes 

in the cloud cover, atmospheric circulation, and other atmospheric processes under the influence of cosmic 

ray fluxes. 

240


It is also important to outline here the problems that require close attention in developing the ideas of 

M.I.Pudovkin and his team. First of all, there is still no quantitative theory explaining the physical 

mechanism of the influence of cosmic ray fluxes on atmospheric processes. Only first steps in this direction 

have been made (see, e.g., the review by M.I.Pudovkin [2004]). 

Another important direction of research relies on the understanding of the fact that the global influence 

of cosmic rays (or irradiance variations) on atmospheric processes is realized through the atmosphere-ocean 

climatic system characterized by internal processes. This means that the response of the system can have a 

nonlinear character, a regional structure and dynamics. Analysis of the experimental data on the long-term 

solar activity variations and the results obtained in simulation of the temperature response of the atmosphereocean 

system to solar irradiance variations confirms this statement [Raspopov et al., 2007; 2008; Waple et 

al., 2002]. 

The nonlinear character of the atmosphere-ocean system response to external forcing must result in the 

variability of the atmospheric circulation corresponding to the solar activity variability. In particular, it can 

manifest itself in the dynamics of cyclonic activity. The results of analysis of specific features of cyclone 

development in the North-Atlantic region [Veretenenko et al., 2007; Veretenenko and Thejll, 2008] support 

this idea. 

The research efforts of the followers of M.I. Pudovkin are directed to the solution of the problems 

mentioned above. 

References 

Calder, N. (1997), The Magic Sun, 311 pp., Pilkington Press, London, UK. 

Delmonte, B., J.R Petit, G. Krinner, et al. (2005), Ice core evidence for secular variability and 200-year 

dipolar oscillations in atmospheric circulation over East Antarctica during the Holocene, Climate 

dynamics, 24(6), 641-654. 

Dmitriev, A.A,. and D.V. Govorov (1972), Relations of physical and heliophysical experiments, Proceedings 

of Arctic and Antarctic Research Institute, 311, 132-137 (in Russian). 

Dmitriev, A.A., and E.Yu. Lomakina (1977), Cloudiness and cosmic X-rays, in: “Effects of solar activity in 

the lower atmosphere”, ed. by L.R. Rakipova, Hydrometeoizdat, Leningrad, 70-77 (in Russian). 

Frölich, C., and J. Lean (2004), Solar radiative output and its variability: evidence and mechanism, 

Astronomy and Astrophysics Review, 12(4), 273-320. 

Krivovichev, S.V. (2008), Saint-Petersburg University in the mirror of Web of Science, St.Petersburg 

University, 3, 44-46 (in Russian). 

Meeker, L. D., and P.A. Mayewski (2002), A 1400-year high-resolution record of atmospheric circulation 

over the North Atlantic and Asia, The Holocene, 12(3), 257-266. 

Morozova, A.L., M.I. Pudovkin, and P. Thejll (2002), Variations of atmospheric pressure during solar proton 

events and Forbush-decreases for different latitudinal and synoptic zones, International Journal of 

Geomagnetism and aeronomy, 3(2), 181-189. 

Pudovkin, M.I. (2004), Influence of solar activity on the lower atmosphere state, International Journal of 

Geomagnetism and Aeronomy, 5(2), GI2007. doi: 10.1029/2003GI000060. 

Pudovkin, M.I., and S.V. Babushkina (1992a), The influence of solar flares and disturbances of the 

interplanetary medium on the atmospheric circulation, Journal of Atmospheric and Terrestrial Physics, 

54(7/8), 841-846. 

Pudovkin, M.I., and S.V. Babushkina (1992b), Atmospheric transparency variations associated with 

geomagnetic disturbances, Journal of Atmospheric and Terrestrial Physics, 54(9), 1135-1138. 

Pudovkin, M.I., and A.A. Lubchich (1989), Manifestation of solar and magnetic activity cycles in the air 

temperature variation in Leningrad, Geomagnetism and aeronomy, 29(3), 359-363 (in Russian). 

Pudovkin, M.I., and A.L. Morozova (1997), Time evolution of the temperature altitudinal profile in the 

lower atmosphere during solar proton events, Journal of Atmospheric and Solar-Terrestrial Physics, 

59(17), 2159-2166. 

Pudovkin, M.I., and A.L. Morozova (1998), Time variation of atmospheric pressure and circulation 

associated with temperature changes during solar proton events, Journal of Atmospheric and Solar- 

Terrestrial Physics, 60(18), 1729-1737. 

Pudovkin, M.I., and O.M. Raspopov (1992), A mechanism of solar activity influence on the state of the 

lower atmosphere and meteoparameters, Geomagnetism and aeronomy, 32(5), 1-9 (in Russian). 

Pudovkin, M.I., and S.V. Veretenenko (1992), Influence of geomagnetic disturbances on intensity of direct 

solar radiation, Geomagnetism and aeronomy, 32(1), 148-150 (in Russian). 

241


Pudovkin, M.I., and S.V. Veretenenko (1995), Cloudiness decreases associated with Forbush-decreases in 

galactic cosmic rays, Journal of Atmospheric and Terrestrial Physics, 57(11), 1349-1355. 

Pudovkin, M.I., and S.V. Veretenenko (1996), Variations of the cosmic rays as one of the possible links 

between the solar activity and the lower atmosphere, Advances in Space Research, 17(11), 161-164. 

Pudovkin, M.I., S.V. Veretenenko, R. Pellinen, and E. Kyrö (1996), Cosmic ray variation effects in the 

temperature of the high-latitude atmosphere, Advances in Space Research, 17(11), 165-168. 

Pudovkin, M.I., S.V. Veretenenko, R. Pellinen, and E. Kyrö (1997), Meteorological characteristic changes in 

the high-latitudinal atmosphere associated with Forbush-decreases of the galactic cosmic rays, Advances 

in Space Research, 20(6), 1169-1172. 

Raspopov, O.M., V.A. Dergachev, A.V. Kuzmin et al. (2007), Regional tropospheric responses to long-term 

solar activity variations, Advances in Space Research, 40(7), 1167-1172. 

Raspopov, O.M., V.A. Dergachev, J. Esper, et al. (2008), The influence of the de Vries (~200-year) solar 

cycle on climate variations: results from the Central Asian Mountains and their global link, 

Palaeogeography, Palaeoclimatology, Palaeoecology, 259, 6-16. 

Svensmark, H., and N. Calder (2007), The Chilling Stars. A New Theory of Climate Change, 246 pp., Totem 

Books, USA. 

Svensmark, H., and E. Friis-Christensen (1997), Variations of cosmic ray flux and global cloud coverage – a 

missing link in solar-climate relationships, Journal of Atmospheric and Solar-Terrestrial Physics, 59(11), 

1225-1232. 

Veretenenko, S.V., V.A. Dergachev, and P.B. Dmitriyev (2005), Long-term variations of the surface 

pressure in the North Atlantic and possible associations with solar activity and galactic cosmic rays, 

Advances in Space Research, 35(3), 484-490. 

Veretenenko, S.V., V.A. Dergachev, and P.B. Dmitriyev (2007) Solar activity and cosmic ray variations as a 

factor of intensity of cyclonic processes at midlatitudes, Geomagnetism and aeronomy, 47(6), 399-406 (in 

Russian). 

Veretenenko, S.V., and M.I. Pudovkin (1993), Effects of cosmic ray variations in the lower atmosphere 

circulation, Geomagnetism and aeronomy, 33(6), 35-40 (in Russian). 

Veretenenko, S.V., and M.I. Pudovkin (1994), Effects of Forbush-decreases of galactic cosmic rays in the 

variations of total cloudiness, Geomagnetism and aeronomy, 34(4), 38-44 (in Russian). 

Veretenenko, S.V. and M.I. Pudovkin (1996), Variations of total cloudiness during the bursts of solar cosmic 

rays, Geomagnetism and aeronomy, 36(1), 153-156 (in Russian). 

Veretenenko, S.V., and M.I. Pudovkin (1997), Effects of the galactic cosmic ray variations on the solar 

radiation input in the lower atmosphere, Journal of Atmospheric and Solar-Terrestrial Physics, 59(14), 

1739-1746. 

Veretenenko, S.V., and M.I. Pudovkin (1999), Variations of solar radiation input to the lower atmosphere 

associated with different helio/geophysical factors, Journal of Atmospheric and Solar-Terrestrial Physics, 

61(7), 521-529. 

Veretenenko, S.V., and P. Thejll (2008), Solar proton events and evolution of cyclones in the North Atlantic, 

Geomagnetism and aeronomy, 48(4), 542-553 (in Russian). 

Waple, F.M., M.E. Mann, and R.S. Bradly (2002), Long-term pattern of solar irradiation forcing in Model 

experiments and proxy based surface temperature reconstruction, Climate Dynamics, 18, 563-778. 

242


MAGNETOSHEATH TURBULENCE AND THE LOW LATITUDE BOUNDARY 

LAYER FORMATION 

S.S. Rossolenko 1 , E.E.Antonova 1,2 , I.P. Kirpichev 2,1 , Yu.I. Yermolaev 2 , 

N.N. Shevyrev 2 , O.M. Chugunova 2 

1 Skobeltsyn Institute of Nuclear Physics Moscow State University, Moscow, 119991, Russia, e-mail: 

sv_ross@ mail.ru; 2 Space Research Institute RAS, Moscow, Russia 

Abstract. Results of the study of low latitude boundary layer (LLBL) properties are presented. Data, 

obtained on high apogee satellites, are used. Intervals of multi satellite observations are selected when one 

satellite was inside the magnetosheath and the other crossed magnetopause and measured plasma 

parameters in LLBL. Amplitudes of magnetic field fluctuations in the magnetosheath are compared with 

the values of magnetic field inside the magnetosphere. Such values are determined for case studies using 

observations inside the magnetosphere and results of model calculations. It is shown, that amplitudes of 

magnetosheath magnetic field fluctuations are comparable with the values of magnetic field inside the 

magnetosphere in the near cusp regions. The role of magnetosheath turbulence in LLBL formation is 

discussed. It is shown that it is difficult to select the dependence of LLBL thickness on the angle between 

the interplanetary magnetic field and the normal to the bow shock. 


The low latitude boundary layer (LLBL) is the region just earthward of the magnetopause where the 

magnetosheath-like and magnetosphere-like plasmas coexist. The solution of the problem of LLBL formation is 

connected with the study of mass, momentum and energy transfer between the magnetosheath and the 

magnetosphere. LLBL is formed due to process of interaction between the turbulent solar wind and the Earth’s 

magnetic field. The condition of stress balance on the magnetopause is not proper studied until now. Therefore, 

the problem of the magnetosheath plasma penetration through the magnetopause has no definite solution. 

Changes in the observed LLBL properties are commonly explained as a result of changes in the conditions of 

magnetosheath plasma penetration through the magnetopause when the interplanetary magnetic field (IMF) has 

different values and orientations. However, the processes inside the magnetosphere can also influence to the 

LLBL properties observed (Antonova, 2005). 

In this paper we examine the results of simultaneous THEMIS satellites observations of LLBL, solar wind 

and magnetosheath plasma for the event 8 November 2008 and try to show that fluctuations of magnetic field in 

the magnetosheath can be the important factor of magnetosheath plasma penetration inside the magnetosphere. 

We also analyze the dependence of LLBL thickness on the angle between the interplanetary magnetic field 

vector and the normal to the bow shock on the base of INTERBALL/Tail satellite observations. 

2. Results of THEMIS observations 

We use data obtained by the THEMIS multi satellite experiment. The plasma spectrograms for ions and 

electrons are computed on the basis of the Electrostatic Analyzers (ESA) measurements 

(http://cdaweb.gsfc.nasa.gov/). ESA measure the flux of thermal particles in a 360° field of view over the energy 

range from ~3 eV to 30 keV. The magnetic field data are obtained from the Flux Gate Magnetometer (FGM). 

Fig.1 shows the coordinates of THEMIS satellites A, B and C. The satellite A crossed the magnetosheath, LLBL 

and entered the magnetosphere at 00.06 UT on 8 November 2008. The satellite B was in the solar wind, the 

satellite C crossed the magnetosheath. 

The electron ESA spectrograms from A (panel 1), B (panel 2) and C (panel 3)-satellites for the discussed 

period of time are presented on Fig.2. 

Fig.3 presents the results of ESA observations on the THEMIS-A satellite. The upper panel shows the ion 

spectrogram. Next panel shows the electron spectrogram. The intensity of the colors on the spectrograms is 

color-coded according to the logarithm of the measured count rate per sample as shown by the color bar on the 

243


right of the figures. Satellite THEMIS_A crossed the magnetosheath, LLBL and then plasma sheet from 01.00 

till 03.00 UT on 28 November 2008. Satellite was in magnetosheath till 01.45 UT, from 01.10 till 01.37 UT and 

from 01.45 till 01.57 UT it crossed LLBL. The analysis of distribution functions shows the simultaneous 

presence of magnetosheath and plasma sheet particles from 01.15 till 01.27 UT and at 01.48-01.57 UT at Z ≈ 3 

RE which means low latitude boundary layer crossing. The satellite entered the magnetosphere, crossing the 

magnetopause several times during mentioned time intervals. The analysis of LLBL crossing gives the 

possibility to select particle jet structures. 

Figure 1.A,B,C THEMIS satellite coordinates for the event 8 November 2008. 

Figure 2. Electron spectrograms for simultaneous LLBL, magnetosheath and solar wind observations on 

THEMIS-satellites. 

Fig. 4 shows THEMIS-B measurements of the IMF BX, BY and BZ components in GSM coordinate system 8 

November 2008. Solar wind magnetic field was oriented northward till 01.50 UT. Then IMF BZ changed its 

orientation to southward with the value ~ - 2 nT. 

Fig. 5 shows the results of THEMIS-C observations of magnetic field components BX, BY, BZ in GSM 

coordinate system. It is possible to see typical for the magnetosheath magnetic field fluctuations. 

We can see analyzing Fig. 4 that solar wind conditions are comparatively stable: fluctuations of magnetic 

field do not exceed 4 nT. Simultaneous variations of magnetosheath magnetic field are ~20 nT (see Fig.5). 

244


Figure 3. Results of ESA THEMIS-A observations 8 November 2008. 

Figure 4. Interplanetary magnetic field components in accordance with THEMIS-B data. 

3. Results of the analysis 

Fig. 6 shows magnetic field line configuration in the plane Y=0 determined in accordance with Ts-96 model 

(Tsyganenko, 1995) for solar wind parameters corresponding to the results of THEMIS measurements (BY= 1 

nT, BZ= 1 nT, nsw=13 cm -3 , Vsw=305 km/s). Magnetic field distribution along magnetic field line has minima 

positioned far from the equatorial plane. Values of magnetic field in minima constitute from 4.3 till 32.5 nT. 

Such values of magnetic field in the near cusp regions take place during modeling using different models of 

magnetic field in the magnetosphere and well corresponds to the data of observations. 

It is possible to see comparing values of magnetic field in the magnetosheath in accordance with the results of 

conducted analysis and taking into account data of multiple magnetic field measurements inside the 

magnetosphere near cusp, that the amplitudes of magnetic field fluctuations in the magnetosheath can be larger 

than values of magnetic field in the near cusp regions and in LLBL on the magnetospheric flanks. 

245


Magnetopause position as it is well known is determined by the condition of plasma and magnetic field 

pressure balance. Magnetic field in the magnetosheath and its fluctuations obviously is the important factor 

determining the conditions of plasma penetration inside the magnetosphere when the value of magnetic field 

under the magnetopause is comparable with the value of magnetic field in the magnetosheath. 

Figure 5. Magnetosheath plasma parameters in accordance with THEMIS-C data 

Figure 6. Magnetic field line configuration in the day-night plane in accordance with Tsyganenko-96 model 

under solar wind parameters BY=1 nT, BZ= 1 nT, nsw=13 cm -3 , Vsw=305 km/s 

246


4. Bow shock types and the ΘBn angle 

To clarify the role of magnetic field fluctuations of the magnetosheath in LLBL formation we analyze the 

dependence of LLBL thickness on the angle between the interplanetary magnetic field vector and the normal to 

the bow shock ΘBn as the properties of magnetosheath magnetic field fluctuations is determined by this angle. 

ΘBn determines the conditions of solar wind particle motion through the bow shock and the magnetic field 

variations in the magnetosheath. The reflected from the bow shock front solar wind particles and the high energy 

magnetosphere and magnetosheath particles, leaked through the bow shock reel in the magnetic field lines and 

can flow far with the solar wind flow if the bow shock orientation is quasiparallel (ΘBn < 45°) (Fuselier, 1994). 

The reflected particles, rotating around the magnetic field lines, have no possibility to leave the front, the 

oscillations are generated on the bow shock surface or behind it if the bow shock orientation is 

quasiperpendicular (ΘBn > 45°) and the magnetic field is oriented nearly tangent to the bow shock. 

Figure 7. The dependence of time in LLBL crossing on the ΘBn angle. 

Variations of the ion flow and the magnetic field in magnetosheath decrease with the growth of the ΘBn angle 

at the nearby bow shock (see, for example, Shevyrev et al., 2005). The fluctuations of plasma and magnetic field 

parameters in magnetosheath behind the quasiparallel bow shock exceed the fluctuations behind the 

quasiperpendicular bow shock. We supposed that the pressure balance at the magnetopause should be more often 

disturbed behind the quasiparallel bow shock because of the high level of plasma parameters and magnetic field 

fluctuations. These conditions can lead to LLBL plasma jets formation. We have made an assumption that the 

LLBL thickness increases if the bow shock is quasiparallel (ΘBn < 45°). 

We have estimated the ΘBn angle during several LLBL INTERBALL/Tail intersections (Yermolaev et al.,, 

1997; Klimov et al., 1997; Sauvaud et al., 1997). The plasma flow lines was found for each case. The plasma 

flow lines distribution was evaluated using Spriter magnetosheath model. The found plasma flow line was 

prolonged to the bow shock where the position of the normal to the bow shock and the ΘBn angle were 

estimated, using the IMF orientation and the time of plasma flow from the bow shock to the satellite position. 

Mitchell et al. (1987) show that LLBL thickness can be estimated using the time of LLBL crossing by satellite. 

The time of LLBL crossing was estimated for a number of cases. Fig. 7 presents the dependence of time of 

LLBL crossing from the ΘBn angle. Pink colored points are the LLBL tail intersections and the black points – the 

dayside LLBL intersections. The dayside LLBL is usually thinner than LLBL in the tail region, what is possible 

to see analysing Fig.7. We take into account the difference between the tail and dayside LLBL thickness. 

Analysis of Fig. 7 shows that no dependence of LLBL thickness on the ΘBn angle cannot be selected. 

247


5. Discussion 

The absence of the dependence of LLBL thickness on the ΘBn angle can be explained with the separation of 

the processes responding to the plasma penetration and LLBL formation, The LLBL is formed due to the 

magnetosheath particle penetration inside the magnetosphere in the near cusp regions where the level of 

fluctuations of plasma parameters and magnetic field is high (Rossolenko et al., 2007). At the same time the 

thickness of the LLBL can be determined by the processes inside the magnetosphere such as particle flow in 

YGSM direction (Antonova Е.Е., 2005) in the conditions of pressure balance. Such processes can dominate in 

LLBL thickness formation which explain the absence of finite dependence on Fig. 7. It is necessary to mention 

that the processes of plasma structure motion in the magnetosheath and the plasma penetration inside the LLBL 

are not well studied till now. We have to note that the number of analyzed cases is not big enough to make any 

final conclusions. 


The conducted analysis of the results of simultaneous observations on satellites of THEMIS-project supports 

the results obtained earlier on the existence of high level of fluctuations of parameters of plasma and magnetic 

field in the magnetosheath under comparatively stable solar wind conditions. This finding requires the creation 

of a new models of LLBL formation. The amplitude of magnetic field fluctuations in the magnetosheath can 

exceed the value of the magnetic field under magnetopause in the near cusp region. That is why the existence of 

such fluctuations is necessary to take into account in the analysis of the processes of magnetopause formation 

and particle penetration through the magnetopause. 

The investigation of the dependence of LLBL thickness on the ΘBn angle on the base of INTERBAL/Tail data 

push to the assumption that the formation of the LLBL thickness doesn’t depend on the processes in 

magnetosheath in the near cusp region. The processes inside the magnetosphere can determine the formation of 

the thick LLBL. 

References 

Antonova E.E. (2005), The structure of the magnetospheric boundary layers and the magnetospheric turbulence, 

Planet. Space Sci. 53(1), 161–168. 

Fuselier S.A.(1994), Suprathermal ions upstream and downstream from the Earth's bow shock, Solar Wind 

Sources of Magnetospheric Ultra-Low-Frequency Waves, Geophys. Monogr., 81, 107. 

Klimov D.I., Romanova S., Amata E., et al. (1997), ASPI experiment: measurements of fields and waves on 

board the INTERBALL-1 spacecraft, Annales Geophysicae, 15(5), 514-527. 

Mitchell, D., Kutchenko, F., Williams, D., Eastmann, T., Frank, L., Russel, C. (1987), An extended 

study of the low-latitude boundary layer on the dawn and dusk flanks of the magnetosphere, J. 

Geophys. Res. 92(A7), 7394-7404. 

Rossolenko S.S., E.E.. Antonova, Yu.I. Yermolaev, M.I. Verigin, I.P. Kirpichev, N.L. Borodkova., and E.Yu. 

Budnik (2007), Magnetosheath turbulence and low latitude boundary layer, WDS’07 Proceedings of 

Contributed Papers, Part 2, 50–56. 

Sauvaud J.-A., P. Koperski, T. Beutier, H.Barthe, C.Aoustin, J.J. Thocaven, J. Rouzaud, E. Penou, O. 

Vaisberg, and N. Borodkova (1997), The INTERBALL-Tail electron experiment: Initial results on the lowlatitude 

boundary layer of the dawn magnetosphere. Ann. Geophys. 15(5), 587-595. 

Shevyrev N.N., and G.N. Zastenker (2005), Some features of the plasma flow in the magnetosheath behind 

quasi-parallel and quasi-perpendicular bow shocks, Planetary and Space Science, 53. 95-102. 

Tsyganenko N. A. (1995), Modeling the Earth's magnetospheric magnetic field confined within a realistic 

magnetopause, J. Geophys. Res. , 100(A4), 5599-5612. 

Yermolaev Yu.I., A.O. Fedorov, O.L. Vaisberg., V.M. Balebanov, Yu.A Obod., R Jimenez., J. Fleites, I. 

Llera, and A.N. Omelchenko (1997), Ion distribution dynamics near the Earth's bow shock: First 

measurements with 2-D ion energy spectrometer CORALL on INTERBALL-Tail Probe satellite. Ann. 

Geophysicae, 15(5), 533-541. 

248


INTERACTION OF OBLIQUE INTERPLANETARY SHOCKS WITH THE 

BOW SHOCK 

A.A. Samsonov 1 , Z. Němeček 2 , J. ˇSafránková 2 , L. Pˇrech 2 

1 Physical Faculty, St. Petersburg State University, 198504, Russia, e-mail: 

samsonov@geo.phys.spbu.ru; 2 Charles University, Prague, Czech Republic 

Abstract. This is first work where propagation of oblique interplanetary shocks from the solar wind 

through the magnetosheath is investigated by a three-dimensional MHD simulation. The oblique 

shocks are characterized by a normal diverged from the Sun-Earth line; they are usually driven by 

corotating interaction regions. We simulate variations in the dusk (quasi-perpendicular) and dawn 

(quasi-parallel) magnetosheath after propagation of an artificial shock and show a real event with 

an oblique shock observed by Themis and Cluster spacecraft. We find that MHD variations in the 

magnetosheath for the oblique interaction are generally similar to those for the direct interaction (i.e. 

when the shock normal is along the Sun-Earth line) that has been studied previously. However values 

of plasma and magnetic field parameters are different on the dawn and dusk sides, and consequently 

the pressure pulse magnitudes affecting the opposite magnetopause flanks are different too. 


Interplanetary shock (IS) observed as a simultaneous steep increase of the solar wind dynamic pressure and 

magnetic field magnitude compresses the Earth’s magnetosphere and results in sudden impulses in magnetic 

field observations. Most strong ISs connected with coronal mass ejection (CME) occur during solar maximum. 

Another type of ISs dominated near solar minimum is often observed as recurrent events with periodicity about 

27 days. These shocks are explained by interaction of the fast stream emanating from a coronal hole with the 

low-speed stream associated with the heliosperic current sheet. The fast stream compresses the slow solar wind, 

creating a corotating interaction region (CIR) [see review Pizzo, 1985]. 

Using spacecraft observations of ISs near 1 AU, it was found that the shock normals of CME-generated 

shocks have a scattered distribution (in a few tens of degrees) with a maximum at the Sun-Earth line [e.g. Chao 

and Lepping, 1974]. The normals of CIR-generated shocks near 1 AU are assumed to lay in the heliospheric 

equatorial plane, and a mean angle between the normals and the Sun-Earth line is about 45 degrees [ref. Pizzo, 

1991]. Such oblique shocks strike the Earth’s magnetopause first on the dusk (more often) or dawn flank, 

rather then near the subsolar point. In this work, we present results of a new MHD simulation to understand 

difference of the magnetospheric impact of the oblique shocks from the impact of the direct shocks studied in 

several previous works [e.g. Samsonov et al., 2006; Samsonov et al., 2007]. 

Interaction of a forward fast IS with the bow shock was theoretically studied by Grib and Pushkar (2006). 

They obtained solutions of the Rankine-Hugoniot (R-H) relations on the both flanks and showed a spatial 

density distribution in the magnetosheath after the interaction. Assuming that the IS normal has a duskward 

component (the angle to the solar wind velocity is 40 degrees), the ratio of the mean densities from the dawn to 

dusk flanks was found to be equal to 1.16. The authors assumed that this difference may explain a statistically 

observed dawn-dusk assymmetry in the magnetosheath density profiles [Paularena et al., 2001; Němeček et al., 

2002], however the last is a controversial point because the ISs occur too rarely to make a real input in the 

statistical profiles. 

Pˇrech et al. (2008) studied an event when the oblique shock (with the angle between the shock normal and 

the Sun-Earth line in the equatorial plane equal to about 41 o ) was observed by Themis in the magnetosheath and 

by several spacecraft upstream of the bow shock. They found a deceleration of the shock in the magnetosheath 

and generation of a new discontinuity characterized by an increase of the magnetic field and plasma density 

and by a drop of temperature. These results agree with those obtained previously from the MHD simulations 

in the case of an IS strictly aligned with the Sun-Earth line [Samsonov et al., 2006]. In particular, Samsonov 

et al. (2006) predicted a discontinuity at the Sun-Earth line consisted from the combination of a forward slow 

expansion wave, a contact discontinuity, and a reversed slow shock. The three discontinuities propagate from 

the bow shock to the magnetopause with velocities nearly equal to the bulk flow speed, therefore they can not 

be separated both in the 3-D simulations and in observations. The above-mentioned variations of the MHD 

parameters observed by Pˇrech et al. (2008) are obtained as a combination of variations through the three 

discontinuities. Similar discontinuities in the magnetosheath measurements from Interball and Geotail were 

found by ˇSafránková et al. (2007) after the interaction between non-oblique ISs and the bow shock. 

249


2 Numerical model 

A numerical 3-D MHD model has been developed to study plasma flow around the Earth’s magnetopause 

[Samsonov and Pudovkin, 1998; Samsonov, 2007]. In this model, the magnetopause is assumed to be an 

impenetrable parabolic obstacle in the case when the magnetopause reconnection does not influence the magnetosheath 

flow. The outer solar wind boundary is placed upstream of the bow shock. The fast IS is imposed as 

an abrupt increase of the plasma density from 5.0 to 14.2 cm −3 and an increase of the magnetic field magnitude 

from 5.0 to 14.2 nT. The solar wind velocity before the IS is equal to 400 km/s and directed along the X axis 

(the Sun-Earth line). The angle between the shock normal and the X axis is 41 degrees. Both the shock normal 

and the interplanetary magnetic field lay in the XY plane. The normal is directed dawnward, while the magnetic 

field is directed duskward, and the angle between them equals 86 degrees. According to the R-H conditions, 

the dawnward velocity downstream of the IS is equal to 94 km/s, the earthward Vx component equals 504.9 

km/s. 

At the beginning, we have found a quasi-stationary solution using the time-relaxation method. Then the 

oblique IS has been launched at the outer boundary. A self-consistent solution of the MHD equations determines 

its interaction with the bow shock, then the propagation of resulted discontinuities through the magnetosheath 

has been studied. 

3 Results of simulation 

Figure 1 shows temporal profiles of the density, velocity, temperature and magnetic field magnitude both 

in the dusk (left plate) and dawn (right plate) magnetosheath flanks at two points, closer to the magnetopause 

(red lines) and closer to the bow shock (blue lines). First observed variation at every point is the forward fast 

shock transmitted through bow shock. Second variation is actually a compound discontinuity (CD) with a 

smooth increase of the density and magnetic field magnitude and a clear decrease of the temperature. A similar 

discontinuity was predicted early in the MHD simulation with a direct IS and observed by several spacecraft in 

the magnetosheath (see references in Introduction). 

According to the previous studies, the velocity does not change through the CD or, more precisely, it may 

change insignificantly due to a weak slow shock/expansion wave. The same is predicted there in the dusk 

magnetosheath, on the flank where the IS strikes first the bow shock. However the situation may be different 

on the opposite flank. Note that the dawn magnetosheath in this case is downstream of the quasi-parallel bow 

shock. This explains why the initial magnetic field there is weaker than in the dusk magnetosheath downstream 

of the quasi-perpendicular bow shock. Moreover, the |B| increases just a little through the IS on the dawn side. 

The second variation in the outer dawn magnetosheath seems to be a modified CD. It follows the IS with 

a time lag about 40 sec (compare with 30 sec in the dusk magnetosheath). This discontinuity is characterized 

by a clear increase of the density and magnetic field magnitude and by a drop of the velocity and temperature. 

Consequently the CD on this flank may consist from a different combination of the MHD discontinuities than 

the CD in the dusk magnetosheath. We intend to continue this study in the future. 

In the simulation, we assume the magnetopause to be an immovable impenetrable obstacle. Although this 

assumption is unrealistic, results of our simulations reproduce well observed features in the magnetosheath 

(ˇSafránková et al., 2007). Both our local magnetosheath model used in this work and the global MHD BATS- 

R-US model (Samsonov et al., 2007) predict generation of a reflected fast shock (RFS) propagating outward 

from the inner numerical boundary. Observed electric field pulses in the magnetosphere and the inward-outward 

bow shock motion after the IS arrival confirm indirectly formation of the reflected shock. The RFS appears in 

this model when the IS has reached the inner boundary, and it is observed in the inner dusk magnetosheath about 

74 sec later the coming IS. A short solar wind passage follows the IS and CD in the outer dusk magnetosheath. 

The bow shock moves inward after the interaction with the IS, and this inward motion continues until the new 

interaction of the bow shock with the reflected shock. After that the bow shock moves outward and a new 

discontinuity seems to reflect back into the magnetosheath. 

Clear signatures of the RFS (see Figure 1) are a strong increase of the density, temperature, and |B| and 

a decrease of the |V |. In the dawn magnetosheath, these signatures are not clearly observed as well as we do 

not see the inward-outward bow shock motion at the symmetrical point in the outer magnetosheath. Contours 

250


Figure 1: Temporal profiles at fixed points in the XY (equatorial) plane. On the left side, the points are in the 

dusk magnetosheath: (x,y)=(6.0,12.0) shown by red color and (6.7,13.3) shown by blue color. On the right 

side, the two points are symmetrical with respect to the XZ (meridional) plane. An imaginary observer on both 

flanks registers an interplanetary shock (IS) and a compound discontinuity (CD). However a reflected fast shock 

(RFS) or a solar wind passage (SW) are predicted only in the dusk magnetosheath. 

of the MHD parameters in the XY plane (not shown) confirm that the normal of the reflected shock is nearly 

aligned with the normal of the coming IS. 

4 Observations in the magnetosheath 

Propagation of an oblique IS through the magnetosheath was studied by Pˇrech et al. (2008) using recent 

Themis data. The oblique shock was identified in the supersonic solar wind by ACE, Wind, SOHO, and Cluster 

(near the bow shock). The orientation of the shock normal is similar to that used in the present simulation 

(i.e. Nx ≈ Ny < 0). Themis A, B, C, and D were in the dusk dayside magnetosheath, whereas Themis 

E was in the magnetosphere prior the IS arrival. All Themis, including Themis E, observed the IS related 

discontinuity. Several minutes later the IS arrival, Themis B, C, and D observed the bow shock crossing, while 

Themis E crossed the magnetopause after ≈ 20 sec. The compound discontinuity with anti-phase variations 

of the density and temperature was registered by all Themis where the plasma measurements were available. 

Figure 2 shows the magnetic field magnitude, the density, the temperature, and the Vx velocity observed by 

Themis C during 10 minutes interval. 

Themis C registered the IS at 0822:36 UT, having the GSE coordinates (6.5, 11.3, -3.1) RE. The CD was 

observed there 70 sec later. The clear signatures of this discontinuity are increase of the density and decrease 

of the temperature. The fluctuated magnetic field also increases, while the velocity varies insufficiently. Using 

251


B t [nT] 

n [cm -3 n [cm ] 

-3 ] 

T [eV] 

v X GSE [km/s] 

35 

30 

25 

20 

15 

10 

200 

150 

100 

50 

0 

120 

100 

80 

60 

40 

20 

-100 

-150 

-200 

-250 

-300 

THEMIS-C 07-May-2007 

0821 0824 0827 0830 

UT 

Figure 2: Observation of the oblique shock in the magnetosheath from Themis C (from Pˇrech et al., 2008). The 

vertical lines show the times of the IS (solid), the CD (dashed) and bow shock (dotted) crossings. 

multi-point observations, Pˇrech et al. (2008) determined the propagation velocity of the CD which equals 105 

km/s in the Earth frame. This is close to the flow velocity along the shock normal. 

5 Conclusion 

Using results of the numerical MHD simulation, we study interaction of the oblique IS with the bow shock. 

We compare these new results with those obtained previously for the IS aligned with the Sun-Earth line. Similar 

to the previous studies, a discontinuity with anti-phase variations of the density and temperature follows 

the IS front in the magnetosheath. This compound discontinuity in the dusk magnetosheath downstream of the 

quasi-perpendicular bow shock (near the point of collision between the IS and bow shock) changes the MHD 

parameters (increasing the density and |B| and decreasing the temperature), like as it was predicted previously 

near the Sun-Earth line for the interaction between the bow shock and a direct IS. On the opposite magnetosheath 

flank, downstream of the quasi-parallel bow shock, a similar discontinuity following the IS is found 

but the variations of parameters are different. In particular, the results show a decrease of the flow velocity 

which is not observed on the dusk side. 

In this paper, we are not ready to separate the MHD discontinuities which form the compound discontinuity. 

But according to Grib and Pushkar (2006), several combinations will appear in addition to the above-mentioned 

252


combination of the slow expansion wave, contact discontinuity, and reversed slow shock. These combinations 

may include both forward and reversed Alfven waves. If velocities of some waves/discontinuities are sufficiently 

different from the flow velocity, one would observe more than one discontinuity following the IS in the 

magnetosheath. 

References 

Chao, J. K., and R. P. Lepping (1974), A Correlative Study of ssc’s, Interplanetary Shocks, and Solar 

Activity. J. Geophys. Res., 79, 1799–1807. 

Grib, S. A., and E. A. Pushkar (2006), Asymmetry of Nonlinear Interactions of Solar MHD Discontinuities 

with the Bow Shock. Geomagnetism and aeronomy, 46, 442-448. 

Němeček, Z., J. ˇSafránková, G. N. Zastenker, P. Piˇsoft, and K. I. Paularena (2002), Spatial distribution 

of the magnetosheath ion flux. Adv. Space Res., 30, 2751-2756. 

Paularena, K. I., J. D. Richardson, M. A. Kolpak, C. R. Jackson, and G. L. Siscoe (2001), 

A dawn-dusk density asymmetry in Earth’s magnetosheath. J. Geophys. Res., 106, 25377-25394, 

doi:10.1029/2000JA000177. 

Pizzo, V. J. (1985), Interplanetary shocks on the large scale: A retrospective on the last decade’s theoretical 

efforts. In: ”Collisionless shocks in the heliosphere: Reviews of current research” ed. by B. T. Tsurutani 

and R. G. Stone, AGU Press, Washington D.C., Monograph. 35, 51-68. 

Pizzo, V. J. (1991), The evolution of corotating stream fronts near the ecliptic plane in the inner solar 

system. II - Three-dimensional tilted-dipole fronts. J. Geophys. Res., 96, 5405–5420. 

Pˇrech, L., Z. Němeček, and J. ˇSafránková (2008), Response of magnetospheric boundaries to the interplanetary 

shock: Themis contribution. Geophys. Res. Lett., 35, doi:10.1029/2008GL033593. 

ˇSafránková, J., Z. Němeček, L. Pˇrech, A. A. Samsonov, A. Koval, and K. Andréeová (2007), Modification 

of interplanetary shocks near the bow shock and through the magnetosheath. J. Geophys. Res., 112, 

A08212, doi:10.1029/2007JA012503. 

Samsonov, A. A., and M. I. Pudovkin (1998), Ideal anisotropic plasma flow around a sphere in the 

CGL-approach. Geomagnetism and aeronomy, 38, 50-57. 

Samsonov, A. A., Z. Němeček, and J. ˇSafránková (2006), Numerical MHD modeling of 

propagation of interplanetary shock through the magnetosheath. J. Geophys. Res., 111, A08210, 

doi:10.1029/2005JA011537. 

Samsonov, A. A. (2007), Specific Features of Magnetic Barrier Formation Near the Magnetopause. 

Geomagnetism and Aeronomy, 47, 316-324. 

Samsonov A. A., D. G. Sibeck, J. Imber (2007), MHD simulation for the interaction of an interplanetary 

shock with the Earth’s magnetosphere. J. Geophys. Res., 112, A12220, doi:10.1029/2007JA012627. 

253


ANALITICAL INVESTIGATION OF 3D IMPULSIVE MAGNETIC 

RECCONECTION USING GREEN FUNCTION IN FRAME OF 

INCOMPRESSIBLE MHD APPROXIMATION 

Y. L. Sasunov, V. S. Semenov 

Saint Petersburg, St. Petersburg University, 198504 Russia, jurasl2006@mail.ru 

Abstract. Magnetic reconnection is the universal plasma process which is responsible for solar 

flares, magnetospheric substorms and solar wind – magnetosphere coupling. Petschek-type 

reconnection [1] is distinguished from other models of reconnection such as tearing instability or 

Sweet-Parker regime, with a local generation of reconnection electric field along the X-line. The 3D 

time-dependent Green function corresponding to the delta-like behavior of the electric field, is found 

and investigated for the general current sheet geometry with skewed reconnecting fields and 

tangential velocities in the frame of an incompressible plasma model. Distributions of the magnetic 

field and velocity components are obtained for different moments in time. The wave fronts produced 

by a sharp pulse of reconnection are studied. 


For the interaction between the solar wind and the Earth’s magnetosphere the reconnection process is in 

general very important. Petschek proposed in his work in 1964 a steady-state reconnection model as a 

possible explanation for this. It can be shown that a local dissipative electric field is generated in the diffusion 

region and produces the decay of a tangential discontinuity. In detail, the current sheet breaks into a thin 

boundary layer given by a system of nonlinear magnetohydrodynamic (MHD) waves. It collects plasma from 

the near flux tubes and accelerates the plasma to Alfv´enic speed Va. This kind of shock structure propagates 

then outward along the current sheet away from the diffusion region. Heated and accelerated plasma is 

enclosed by the shocks (S−). The magnetic field lines are connected via shocks. The magnetic field lines 

above and below the current sheet, which are initially antiparallel directed, are connected via the shocks, 

which form the outflow region (OR). The surrounding area is then called the inflow region (IR), and the 

plasma flow has always the direction from IR into OR. We know that nature is never ideal, and so 

reconnection appears often in form of an unsteady and patchy behaviour of impulsive character. 

2. Model and calculation 

Here we present the solution of a problem about 3D time-dependent magnetic reconnection in incompressible 

plasma. We consider a two-dimensional infinitely thin current layer (tangential discontinuity) which is 

located in plane ХY (Fig.1). Initial configurations of the magnetic fields are laying in plane ХУ: 

Ba = (Bax, Bay, 0) - above the current layer, and Bb = (Bbx, Bby, 0) - under the current layer, hence vectors 

of magnetic field and plasma velocity do not have a normal component in z-direction. Initial magnetic field 

has the jump B r 

Δ = Bb Ba 

r r − across the tangential discontinuity, so there is a surface current 

r c r r 

I = [ ΔB× 

n], 

4π 

where n r is the normal vector to the current layer. 

Reconnection starts with a decrease of plasma conductivity σ inside a small diffusion region due to 

development of some kind of turbulence which leads to occurrence of dissipative electric field 

* 

E y ( t, 

y) 

= j / σ . Usually the reconnection electric field E y 

* is much less than the alfvénic field 

EA = VAB0 

/ c , where Bo is the characteristic initial magnetic field, Va is the alfvénic velocity, and c is the 

speed of light. Therefore there is a small parameter in our problem 

and the following scaling 

* 

E y 

ε =


x , Vx, 

Bx, 

y, 

Vy 

, By 

~ 1. 

This means that the tangential components of V and B are of the order of 1, whereas the normal components 

are O (ε ) . 

Fig.1: Geometry of the current sheet. 

For calculation of all disturbances outside the diffusion region, we use the ideal MHD equations for 

incompressible plasma 

r 

r r 

∂V 

r r ( B∇) 

B 

ρ + ρ( 

V∇) 

V = −∇P 

+ , 

∂t 

4π 

r 

∂B 

r r 

= rot[ 

V × B] 

, 

∂t 

divB = 0 

r 

, 

divV = 0 

r 

. 

The problem of reconnection is nonlinear one which is difficult to solve, but it is possible to find an 

n 

n 

n 

asymptotic solution with respect to the small parameter ε : V = ∑ Vnε 

, P = ∑ Pnε 

, B = ∑ Bnε 

. 

n= 

0 

n= 

0 

n= 

0 

The appearance of reconnection electric field in the diffusion region leads to a decay of initial tangential 

discontinuity into pair of a slow shocks which bounded an outflow region (OR) with accelerated plasma. The 

surrounding area is called inflow region (IR) (Fig. 2). The shapes of shocks as well as the plasma velocity and 

magnetic field in the ORs are unknown from the very beginning, and they have to be found from the MHD 

equations (5-8) and the following jump relations 

{ B n} 

= 0 , 

{ ( V D ) } = 0 

ρ n − n , 

⎧ 

1 ⎫ 

⎨ρ 

( Vn 

− Dn 

) Vt 

− BnBt 

⎬ = 0 , 

⎩ 

4π 

⎭ 

( V D ) B − B V = . 

{ } 0 

n − n t n t 

Note that in the system of these equations, equation of energy is absent for the incompressible plasma, which 

essentially simplifies the problem. 

The scaling allows to find first the main tangential components of V and B, and then small normal 

components. It turns out that for homogeneous initial magnetic fields Ba and Bb, the magnetic field and 

velocity inside the ORs are also homogeneous (i.e. constant). They easily can be found from the jump 

relations (see [2]) 

Bax 

+ Bbx 

Bx = + ( Vax 

−Vbx) 

4πρ 

, 

2 

Vax 

+ Vbx 

( Bax 

− Bbx 

) 

Vx 

= + , 

2 2 4πρ 

Bay 

+ Bby 

By = + ( Vay 

−Vby 

) 4πρ 

, 

2 

255


V 

y 

Vay 

+ Vby 

( Bay 

− Bby 

) 

= + . 

2 2 4πρ 

It is interesting to note that these tangential components inside the OR do not depend on reconnection electric 

field Ey. In particular this means that in the zero-order with respect to ε plasma is accelerated at the slow 

shocks to approximately alfvénic velocity independently of reconnection rate. 

The unknown shape of the slow shocks, which arises during reconnection, can be mathematically expressed 

as z =ε ⋅ f ( x, 

y, 

t) 

. It is convenient to introduce the displacement vector ξ ( t, 

x, 

y, 

z) 

(see [3]) 

ξ r r r ⎛ ∂ ⎞ 

V 1 = ⎜ + ( V0∇) 

⎟ ; ξ 

⎝ ∂t 

⎠ 

r r r 

B 1 = ( B0∇) 

. 

The general solution of reconnection problems in term f , ξ is z 

f 

x Wy 

−ξ z = Φ( 

t − , y − x) 

, 

W W 

x 

B 

B 

where 

x 

y 

W x = Vx 

± , W y = Vy 

± are the components of the deHoffman-Teller velocity. 

4πρ 

4πρ 

The functions Ф are different in three areas (in the IR above the current layer (a), in the IR under the current 

layer (b), and inside the OR(i), see (Fig.2)) which gives relations (see [4]) 

= Φ 

+ ξ = Φ + 

fa + 

a a 

+ 

i ξi 

− 

− 

fb = Φ b + ξ b = Φ i + ξ . i 

+ + − − 

Eliminating ξ between these equations we have i 

ξ az −ξbz 

= Φ i −Φ 

a + Φ b −Φ 

i , which means that the width of 

OR is defined by the Ф functions only. 

Fig.2: Positions of functions Ф at plane XZ. The red line shows the surface of slow shocks. The blue 

lines depict the magnetic field lines. 

It can be shown that the functions Ф is expressed via reconnection electric field as follows 

Φ 

j 

k 

( y, 

t) 

= 

c 

B 

t 

∫ 

xk 0 

, 

x 

cEzk 

E* 

( τ, y − ( t −τ)) 

dτ 

. 

B 

Where the indices k = (a,b,i) and j = (+,-) correspond to different regions depicted in Fig.2 (see [4]). 

The perturbations to the initial magnetic field in the inflow regions can be obtained from the linearized system 

of MHD equations in terms of the displacement vector. 

256 

xk

Since ( ξ ) = 0 

r 


div the perturbation of the total pressure is satisfied to the Laplace equation(see [4]). In order to 

solve the initial value problem, it is convenient to perform a Laplace transformation with respect to time t 

∞ 

∫ 

0 

−pt 

ξ ( p) 

= ξ( 

t) 

e ∂t 

, 

and a Fourier transformation with respect to the coordinates x and y 

ξ ( k , k ) = ξ( 

x, 

y) 

e 

x 

y 

+∞ +∞ 

∫∫ 

−∞−∞ 

ikx 

x+ 

ikyy 

dxdy. 

After all transformations we can obtain equations for the z-component of the displacement vector. 

The solution for pressure is: 

p 

t → 

∂ ∂ ∂ 

, →−ik 

, x →−ik 

, y 

∂ ∂x 

∂y 

2 

∂ P 2 2 

− ( k + k ) P = 0 

2 

x y , 

∂z 

2 ∂P 

a 

(( p−ikxV 

ax−ikyV 

ay) 

+ ( kxBax+ 

kyBay) 

) ξaz= 

− 

∂z 

2 ∂P 

b 

(( p−ikxV 

bx−ikyV 

by) 

+ ( kxBbx+ 

kyBby) 

) ξbz= 

− 

∂z 

2 , 

2 . 

− k z 

P = A( 

k, 

p) 

e , z > 0 

a 

k z 

Pb 

= B( 

k, 

p) 

e , z < 0 

Since Pa=Pb for z=0, we conclude that A(k,p)=B(k,p). This leads to the equation for z-components of the 

displacement vector 

L1( k, 

p) 

ξ az = −L2 

( k, 

p) 

ξ , bz 

where 

2 

2 

L 1( k, 

p) 

= (( p−ikxV 

ax−ikyV 

ay) 

+ ( kxBax+ 

kyBay) 

) , 

2 

2 

L 2( k, 

p) 

= (( p−ikxV 

bx−ikyV 

by) 

+ ( kxBbx+ 

kyBby) 

) . 

We can rewrite the equation (24) in terms of the Laplace- and Fourier transformations as follows 

+ 

− 

− 

ξ −ξ 

= Φ ( , k , p) 

−Φ 

a( 

k , k , p) 

+ Φ b( 

k , k , p) 

−Φ 

i( 

k , k , p) 

≡Q( 

k , k , p), 

az 

bz 

+ 

i kx y 

x y 

x y 

x y 

x y 

and obtain the solution of the reconnection problem in the Laplace-Fouriere space 

L2( 

k, 

p) 

ξ az( 

kx, ky, 

p) 

= 

Q( 

k, 

p) 

, 

L1( 

k, 

p) 

+ L2( 

k, 

p) 

L1( 

k, 

p) 

ξ bz( 

kx, ky, 

p) 

= − 

Q( 

k, 

p) 

. 

L( 

k, 

p) 

+ L ( k, 

p) 

1 

2 

To return back to space (t, x,y) we have to perform three integrations with respect to (p, kx, ky). For the 

arbitrary reconnection electric field this is rather difficult problem. The final equation for calculation is 

∞ 

1 L1 

t 

ξaz ( t, 

x, 

y, 

z) 

= α ∂α 

2 

π ∫ Q( 

, t, 

x, 

y, 

z) 

2 , 

2 L + L 

M 

−∞ 

1 

2 2 

2 

L 1= 

( 1−isα 

( Vax+ 

Bax) 

−is( 

Vay+ 

Bay)) 

+ s ( αBax+ 

Bay) 

, 

2 2 

2 

L 2= 

( 1−isα 

( Vbx+ 

Bbx) 

−is( 

Vby+ 

Bby)) 

+ s ( αBbx+ 

Bby) 

, 

257 

2


t 

s = 

M 

, M = z 

2 

α + 1 + i( 

xα 

+ y) 

+ a, 

Vax 

+ Bax 

1 

Vbx− 

Bbx 

1 

Q = 

− 

− 

B1x 

−isE1z 

isα( 

Vax+ 

Bax) 

+ is( 

Vay+ 

Bay) 

−1 

B1x 

−isE1z 

isα( 

Vbx− 

Bbx) 

+ is( 

Vby− 

Bby) 

−1 

Vax 

+ Bax 

1 

Vbx− 

Bbx 

1 

− 

+ 

. 

Bax−isEazisα( 

Vax+ 

Bax) 

+ is( 

Vay+ 

Bay) 

−1 

Bbx−isEbzisα( 

Vbx− 

Bbx) 

+ is( 

Vby− 

Bby) 

−1 

The z-component of the displacement vector can be used to obtain the z-components of plasma velocity and 

magnetic field from the equations. To get the x- and y-components of the displacement vector we have to 

change the kern of the integral (41) as follows 

3. Results and discussion 

ξ x ( t, s, 

α, 

z) 

= −i 

2 

α + 1 

ξ z ( t, 

s, 

α, 

z) 

, 

α 

ξ ( , s, 

α, 

z) 

= −i 

2 

α + 1ξ 

( t, 

s, 

α, 

z) 

. 

y 

t z 

To simplify the calculations we can now specify the electric field as follows 

2 

* 

a 

E ( t, 

y) 

= δ ( t) 

, 

2 2 

a + y 

where δ (t) 

is the delta function and a is a parameter. 

We obtain then finally the x- and y- and z-components of plasma velocity and magnetic field. To illustrate the 

method we calculate time variations of magnetic field and plasma velocity observed by satellites located at 

x=3, z=0.9, and different values of y for initial magnetic fields Ba=(1,1,0), Bb=(-2,1,0) depicted in Fig. 3. 

The variation of the z-component of magnetic field has clear bipolar structure which is signature of FTE (flux 

transfer event). The Bx-component reaches its maximum value when the shock passed below the observer 

which can be interpreted as TCR (travelling compression region). The By variation also has bipolar character 

(+-) for y>2 and (-+) for y


z 

2 

1 

0 

-1 

-2 

10 

y 

0 

-10 -6 

-4 

-2 

x 

0 

2 

4 

6 

y 

10 

8 

6 

4 

2 

0 

-2 

-4 

-6 

-8 

-10 

-6 -4 -2 0 

x 

2 4 6 

(a) (b) 

Fig.4: Structure of shock waves and tangential discontinuities(a) and projection all disturbances on the 

current sheet(b) produced by a pulse of reconnection. 

4. Conclusion 

The Green function for a delta-like reconnection rate is obtained for a 3D configuration in the frame of an 

incompressible plasma model. 

The developed method allows us to calculate the disturbances of the magnetic field and the plasma velocity in 

the surrounding media due to impulsive reconnection events. 

This analytical solution of three-dimensional time dependent reconnection in incompressible plasma with 

moving shocks is present. In this model it is assumed that all dissipative processes, which are responsible for 

reconnection, are localized in an idealized reconnection line of finite length and can be taken into account by 

specifying a time and space varying reconnection rate. 

We have shown that even for our simple model it is possible to reproduce the main features of reconnection 

such as BBF (accelerated plasma flows), FTE, TCR and others. Moreover the variations in By components of 

magnetic field and velocity can be used to estimate the effective length of the reconnection line. 

References: 

1. Petschek H. E., Magnetic field annihilation, Physics of Solar Flares, edited by W. N. Hess, NASA 

Spec.Publ.,SP50,pp.425-440, 1964. 

2. Semenov V. S., Heyn M. F., and Ivanov I. B., Magnetic reconnection with space and time varying 

reconnection rates in a compressible plasma, Phys. Plasma 11, pp 62-70 2004. 

3. Priest E., Forbesr T., Magnetic Reconnection, Cambridge University Press 2000. 

4. Heyn, M. F. and Semenov V. S., Rapid reconnection in compressible plasma, Phys. Plasma 3(7), 2725 

1996. 

5. Biernat, H. K., Heyn M. F., and Semenov V. S., Unsteady Petschek reconnection, J. Geophys. Res., 92, 

3392, 1987. 

6. Sasunov Y.L., Semenov V. S., Analytical investigation of 3D impulse magnetic reconnection in the 

frame of incompressible plasma using Green function, Proceedings of the XXXI Annual Seminar 

“Physics of Auroral Phenomena”, Apatity, pp.92-95, 2008. 

259 

1.8 

1.6 

1.4 

1.2 

1 

0.8 

0.6 

0.4 

0.2 

0


THE STRUCTURALLY ADEQUATE MODEL OF MAGNETOSPHERIC 

PROCESSES 85-08 

Introduction 

P.A. Sedykh, E. A. Ponomarev , V.D. Urbanovich, O.V. Mager 

Institute of Solar-Terrestrial Physics, 

Siberian Branch of the Russian Academy of Sciences, Lermontov str., 126 a, 

p/o box 291, Irkutsk, 664033, Russia; e-mail: pvlsd@iszf.irk.ru 

Abstract. The structurally adequate model of magnetospheric disturbances consists of the 

following modules: A. Bow shock as a source of power for magnetospheric processes. B. 

Generation of magnetospheric convection. C. Plasma pressure distribution in the magnetosphere 

and electron-proton precipitations into the ionosphere. D. Magnetosphere-ionosphere coupling. 

Field-aligned currents. 

Essentially, each module presented in an analytical form is a model of a particular process 

described in physical terms. It has input and output for coupling with other modules. When 

combined, the modules comprise a single large physically adequate model describing a 

phenomenon in such a way that we understand its essence and contribution of each of the physical 

processes into the overall picture. 

According to their tasks, models are divided into two types. The first type models task is the maximally 

accurate description of the outcome parameters relation with the income ones. Such models are created as a 

combination of the regression equations, which coefficients present the model’s content. The coefficients are 

determined on the basis of the teaching samples, for which are known the income and outcome parameters. 

Such models correctly reflecting the system functions should be named as functionally adequate (FAM). The 

other type of models has in its basis the physics equations, which describe the real physical processes 

happening in the system. They more or less can form the physical structure of the object. That’s why they 

should be called as structurally adequate models (SAM). Models of the first and also of the second types can 

be formed from the blocks (modules). Each block (module) describes the structural element or the process. 

The blocks should be related with each other. The outcome of the previous block is the income for the next 

one. So, we have a difficult nature system – geomagnetosphere. The one review of the detailed «anatomy» of 

the magnetosphere is enough to understand that such complicated structure should have also the complicated 

functions. So it appeared to be. The most common appearance of it is the magnetosphere response to the 

disturbance of plasma density, velocity of solar wind and magnitude of the magnetic field in solar wind. At 

the present time there are created several functionally adequate models, which describe well the 

magnetosphere behavior, if the incoming parameters are located in the frames of provided teaching samples. 

With the structurally adequate models the case is facing another way. It is as follows. If the FAM cannot 

base on the knowledge of the certain physical processes and can be constructed only in formal, then for the 

SAM the giving of the real physical mechanisms is the work content. Here the case is not in the use of 

physics equations for the description or not. The case is in the use of the equations for the processes, which 

are in the system, but not of their «substitutes». 

Bow shock as a source of power for magnetospheric processes 

The solar wind undergoes the greatest change of its parameters during the passage through the bow shock 

front. Indeed, the magnetic field tangential component and magnetic energy density increase by factors of 

almost 4 and approximately 15, respectively, at the bow point when the front is crossed. The physical 

essence of this process consists in that the Earth in the solar wind stream disturbs this stream, which is 

supersonic for the Earth. This means that the bow shock front is formed, upstream of which the solar wind 

plasma is not disturbed and new scales of a change in the values appear downstream (a front thickness is the 

minimal of these scales). In describing the bow shock, we followed [Whang, 1987; Ponomarev et al., 2006 a, 

b]. A jump of the magnetic field tangential component at front crossing means that the front carries a current. 

The surface density of this current composed of two components is [Ponomarev et al., 2006, b]: 

Jl=-c(σ-1)B0τ/4π, Jτ=c(σ–1)B0l/4π, (1). 

266


Figure 1. Fragment of the Bow Shock (BS), of the Transition 

Layer (TL) or magnetosheath, magnetopause (MP). Location of 

the orthogonal coordinate system with the origin in the Earth’s 

center (axis x is directed towards the sun, axis y is directed 

from dawn to dusk and axis z is directed towards the 

geographic north) and location of auxiliary coordinate system 

(r, φ, ψ) and local coordinate system (l, n, τ). 

The bow shock front will be approximated by a paraboloid of rotation with a focus at the Earth's center (fig. 

1). The front equation has the form: 

r = yg/(1+ cos φ) = yg/2cos(φ/2) (2) 

where φ is the angle between the X axis directed toward the Sun and the radius vector r, and yg is the 

distance from the origin along the Y axis to the intersection with the surface of a paraboloid. Any section a 

paraboloid of rotation by the M plane passing the X axis will be parabola. Let us introduce an auxiliary 

coordinate system l, τ, n. In this system n will be the normal to the parabola at a certain point and will lie in 

our plane, l will be the tangent at the same point and will also lie in the M plane, and τ will complete this 

system to the orthogonal coordinate system. The surface currents have been written in these coordinates. It is 

evident that: div J = -jn. From this it follows that 

jln = -c[B0τcos 3 (φ/2) ∂σ/∂φ]/2πyg (3) 

where В0τ is the IMF tangential component. In the equatorial plane, this is simply Вz, σ(φ)=В1τ/B0τ,, i.e., 

σ(φ)is equal to the ratio of the strength of the magnetic field tangential components before and behind the 

bow shock front. The dependence of this quantity on coordinates was studied in [Ponomarev et al., 2006 a, 

b]. With increasing distance from the bow point, the coefficient σ(φ) decreases (tending to unity at infinity), 

and this means that the current could become divergent and that the current component normal to the front 

appears, which will close outside the front, e.g., through the body of the magnetosphere or within the 

magnetosheath. Such a situation is actually observed. This problem was considered in detail in [Ponomarev 

et al., 2006 a, b] and includes many interesting details, but we are interested in the conceptual aspect. Let us 

consider the situation in more detail but in a simplified case. It is clear that the current direction depends on 

the sign of the tangential component. For the current flowing along the front in the equatorial plane, IMF Bz 

is the tangential component. At Bz < 0, the dawn-dusk current will correspond to the current closing through 

the magnetosphere. Since the magnetic field together with plasma will sweep over the bow shock front, the 

electric field (which can be easily estimated) will appear in the front coordinate system. The electric field 

component directed along the E1 front is defined as: 

El = VnB0τ/c (4) 

Taking into account that the element of length of the parabola is dl= yg/2cos 3 (φ/2)dφ, and dФg/dl = -El, Vn = 

V0 cos(φ/2) and B0τ are independent of φ, we find the bow shock front potential: Фg= -(V0B0τ/c) tg(φ/2)⋅yg , 

(5). It has been demonstrated [Ponomarev et al., 2006 a, b] that the corresponding electric field is always 

directed against the current so that the bow shock front is the generator of electric power. Almost a half of 

the SW kinetic energy is transformed into this power; consequently, the problems of energetic character do 

not arise in this case. Ponomarev et al. [Ponomarev et al., 2006 a, b] considered the problem of the 

magnetopause potential and find the explicit expression for this potential: Фm = (a/b)⋅Φg , (6), where a is an 

almost constant quantity. It is evident that Фg changes its sign at a change of the B0τ sign. The electric 

current depends on the Bz sign and is directed from dawn to dusk only at Bz < 0. However, this current 

cannot change its direction in the body of the magnetosphere since the plasma pressure gradients remained 

unchanged, corresponding to the previous current direction. Consequently, the external current really does 

not fall into the magnetosphere at Bz > 0. The previous internal current, which will be always spent on the 

maintenance of ionospheric processes and will gradually decay, will continue circulating in the 

magnetosphere. Thus, the magnetosphere becomes energetically isolated at Bz > 0. We used the expression 

for Фm(φ) as a boundary condition for solving the boundary-value problem of finding the potential within the 

magnetosphere. Ponomarev et al. [Ponomarev et al., 2006 a, b] obtained the known expressions for this 

potential. 

267


Generation of convection in the magnetosphere 

The electric field along the bow shock front and the potential depend on the solar wind velocity normal 

component and on the IMF tangential component and are defined by the formulas (4) and (5). The 

magnetopause potential Фm (expression (6)) is determined from the conditions of balance of the matter 

coming through the shock front and outgoing from the magnetosheath through the magnetopause and space 

between the bow shock front and magnetopause [Ponomarev et al., 2006 a, b]. This potential differs from Фg 

only in a multiplier. If we assume that the flux tubes are equipotential, the motion of the plasma tube content 

completely depends on the motion of the tube equatorial trace [Ponomarev, 1985]. Thus, it is sufficient to 

determine the potential distribution in the equatorial plane within the boundaries, one of which 

(magnetopause) is represented by parabola with the parameter ym and the other, by a circle of radius rp. The 

problem is solved in parabolic coordinates [Ponomarev et al., 2006 a, b] where the Laplace operator seems to 

be the simplest [Madelung, E, 1960]. The solution is sought in the form of expansion into the series in terms 

of orthogonal functions in a standard way. The obtained result is also standard. The character of electric field 

distribution over the dawn-dusk meridian quite corresponds to the classical distribution obtained in 

[Heppner, 1977] (fig. 2). The significance of this result consists in that the convective electric field (taking 

into account corotation) was for the first time obtained from the main principles. The power source for 

maintaining convection was specified, and the boundary conditions at the magnetopause were obtained from 

the solution of the general problem rather than were specified proceeding from intuitive considerations. 

а 

б 

-E 

+E 

60° 70° 80° 90° 80° 70° 60° 

Figure 2. The character of the electric field 

distribution along the dawn-dusk meridian: (a) data 

obtained in [Heppner, 1977], and (b) our calculated 

values. 

The problem of determining the power coming in this case into the magnetosphere is solved as if 

automatically because j and E are known. We should merely integrate the product of these quantities over 

the volume of the magnetospheric cavity. By the way, we also obtain a standard value of ~3·10 18 erg/s for 

average conditions (Bz = -2 nT, V0 = 450 km/s). Finally, we note that the energy flux into the magnetosphere 

is closely related to the current through the magnetosphere by the relationship: S = jФ – с/4π curl(ФB). 

Plasma pressure distribution in the magnetosphere and electron-proton precipitations into the 

ionosphere 

Particles (and energy) can escape from the magnetospheric plasma into the atmosphere through open ends of 

flux tubes. This type of loss can be very substantial and should be taken into account. The first consequences 

of such loss were studied by C.F. Kennel [Kennel, 1969]. We present the set of equations describing the 

magnetospheric plasma: 

dni /dt + ni divVi = - ni/τi ni = n0i(U0/U)exp(-∫dt/τi) (7) 

dpi /dt + γpidivVi = - pi/τi pi = p0i(U0/U) γ exp(-∫dt/τi) (8) 

∇p = [jxB]/c E = - [VxB]/c p = pe + pp (9) 

si = cv(γ-1)∫dt/τi ∫dt/τ = ∫dR/VRτ = ∫Rdλ/Vλτ (10) 

Here i = e, p is the index of electrons or protons; ni is the particle number density; pi is the pressure of given 

particles; t is the current time; U is the plasma tube volume (by plasma tube we mean the plasma content of a 

magnetic flux tube); E is the electric field strength; B is the magnetic field strength; Vi is the electric drift 

velocity of the corresponding plasma component; V = Ve + Vp is the drift velocity of plasma as a whole; cv 

is heat capacity at a constant volume, and j is the electric current density. Hereafter, we will do so if no 

special assumptions are made. The condition of quasineutrality, i.e., (np - ne)/(np + ne)


detail in [Ponomarev, 1985; Ponomarev, Sedykh, 2006]. The applicability of this set was analyzed, and the 

definitions of τ were given in the same work. The process of magnetic flux tube depletion due to particle 

escape into the loss cone is superposed on the above process; then, the gas pressure is defined as 

[Ponomarev, 1985; Ponomarev, Sedykh, 2006]: 

0 

20 

3 

(11) 

⎛ L∞ 

⎞ ⎛ 5 dr ⎞ 

p = ⎜ ⎟ ⎜ 

⎜− 

∫ ⎟ 

g pg 

exp 

⎝ L ⎠ ⎝ 3 Vrτ 

⎠ 

It is evident that dt =dR/VR =R0dλ/Vλ , Δt = ∫dt is the transport time, i.e., the time over which the flux tube 

will move from the boundary to the given point on the flux line; and VR and Vλ are the radial and azimuthal 

components of convection velocity. Thus (11) indicates how gas pressure changes when plasma moves along 

the convection line at a velocity V = (VR 2 + Vλ 2 ) 1/2 . Specifying the initial pressure p0 at the boundary L = L∞, 

we can find the resultant pressure at any point on the flux line. In such a way, the field of pressures in the 

entire magnetosphere is calculated (Fig. 3a). Several characteristic details are observed when we consider 

this three-dimensional plot. First of all, this is the general shape resembling amphitheatre. The crest maximal 

height is almost at the zero meridian, and the amplitude decreases in both opposite directions. 

(e) (f) (g) 

Figure 3. Gas pressure relief 

(calculated values) under the 

nonstationary boundary conditions: (a) 

t = 0 s, (b) t = 1000 s, (c) t = 2800 s, 

(d) t = 4500 s; e), f), g) profiles and 

values (calculated) of plasma pressure 

in the magnetosphere. 

The amphitheatre represents an oval, the contour of which maximally approaches the center from the inside. 

It is clear that this figure will resemble the auroral oval in the projection onto the ionosphere. The situation 

changes principally when the boundary conditions are dependent on time (fig. 3b-d). The solution structure is 

so that p0(t) can be considered as an input signal multiplied by the transfer function: p(t`)= G(t) A(L). 

According to [Ponomarev, 1985], the flux density of precipitating electrons at the level of the ionosphere 

will be: 

j׀׀ е =B I ∫ndl/Bτ. The time variation in precipitation during a model substorm is shown in fig. 4. 

The magnetosphere-ionosphere coupling. Field-aligned currents 

Figure 4. Contour lines of the intensity of 

the precipitating electron flux density for 

the nonstationary boundary conditions: (a) 

t = 0 s, (b) t = 1000 s, (c) t = 2800 s, and 

(d) t=4500 s. The precipitation intensity 

sharply increases at t = 2800 s, which 

corresponds to breakup. 

We can obtain from the set of equations (7-10) the relationship very important for the physics of the 

Earth's magnetosphere: V·∇p = E·j, (12). The hydrodynamic and electrodynamic quantities are in the left 

269


and right sides of this equation, respectively. The physical sense of this expression is clear. If gas moves 

toward increasing pressure, then Ej >0. We have an electric power consumer: MHD compressor. If plasma 

flows toward decreasing pressure, gas kinetic forces can do the work over electric forces. Knowing plasma 

pressure distribution, we can easily determine the locations of the MHD compressor and MHD generators in 

the magnetosphere. MHD generators were at least three. The first generator is located at the inner boundary 

of the plasma sheet. This generator operates on a radial gas pressure gradient ∇rp; two other generators 

operate on longitudinal gradients ∇λp (for more detail, see [Ponomarev, 1985; Ponomarev, Sedykh, 2006]). 

Generators feed the Birkeland-Bostrom (BB) current systems of the first and second types. Here we note that 

actually physically substantiated sources of power for electrojets were for the first time proposed in 

[Ponomarev, 1985]. The electric scheme of electroject connection was proposed in the same work (Fig. 5). 

Figure 5. Schematic spatial location 

of the magnetospheric-ionospheric 

currents: (a) the system of feeding 

the meridional currents, (b) the 

system of feeding the latitudinal 

currents, and (c) the equivalent 

scheme of the magnetosphericionospheric 

current circuit. 

This scheme was based not only on the formula (12) but also on the expression for the field-aligned currents 

[Ponomarev, 1985] (see fig. 6): 

jll = cB I {[∇pg×∇pB]⋅B/pB B 3 l 

∫ 

}dl (13) 

0 

where В I is the magnetic field strength in the ionosphere, the integral is taken over the entire flux tube from 

the equator to the ionosphere, and рВ is the magnetic pressure. The expression for jll is well-known 

Vasyliunas-Tverskoy’s expression for FAC. It is clear that the integrand in (13) is proportional to the sine of 

the angle between the contour lines pg=const and pB= const. In a dipole approximation, lines of equal 

magnetic pressure are concentric circles, and isobars follow plasma pressure relief contour lines. It is clear 

that in this case the field-aligned currents are concentrated on an amphitheatre crest and vanish and change 

the sign at the crest top point. In the case shown in fig. 5, we have only the current corresponding to the BB 

loop of the first type. In this case only westward current is observed in the ionosphere. The BB loop of the 

second type with short sections of meridional currents in the ionosphere originates at a more complicated 

pressure configuration. 

a) b) c) 

60 60 

70 

80 

1 2 

70 

80 

60 

70 

80 

Figure 6. Results of calculations of the 

field-aligned currents as divergence of 

the magnetospheric bulk currents; 

(resulted from the convergence of the 

contour lines of the gas and magnetic 

pressures): (a) t = 0 s, (b) t = 1000 s, and 

(c) t = 2800 s. (1) and (2) the zones of 

inflowing and outflowing currents. 

The second amphitheatre and a specific corridor between the amphitheatre and the main crest appear in Fig. 

3b. The cross section of this spatial pattern along any intermediate contour line is represented by plasma 

corridors (channels of MHD-generators). The field-aligned currents are directed oppositely on both sides of 

the corridor. Since the sign of the pg gradient changed and that of the pB gradient remained unchanged, the 

double "curtain" of field-aligned currents is formed, which is a characteristic feature of auroral electrojet 

feeding. The geometry of these electrojets corresponds to that of the BB current loop of the second type. We 

270


have considered in [Sedykh, Ponomarev, 2002; Sedykh et al., 2004] the important but particular case of the 

ionosphere-magnetosphere coupling in the region of auroral electrojets. 

Conclusions 

We managed to generally describe magnetospheric processes and phenomena since used the new 

constructive conception based on the C.F. Kennel assumption [Kennel, 1969] that pitch-angle diffusion of 

electrons and protons and convection of plasma are the main processes of magnetospheric physics. 

Input: solar wind 

parameters before the 

bow shock front (VSW, 

Bz, By, ρSW…..) 

Picture of 

particle 

precipitation 

into the 

ionosphere 

Spatio-temporal 

picture of fieldaligned 

current 

(FAC) in the 

ionosphere 

Satellite 

data of 

Pg(t,xij) 

Satellite 

data 

Current in the bow shock 

front. Courses of potential 

as a function of ϕ along the 

bow shock front and on the 

magnetopause. 

Distribution of 

plasma pressure 

in the 

magnetosphere 

Energy flux into the 


Distribution of electric 

field 

20 

⎛ L ⎞ 3 

0 ∞ ⎛ 5 dr ⎞ 

p = ⎜ ⎟ ⎜ − ∫ ⎟ 

g p g exp 

⎝ L ⎠ ⎝ 3 V rτ 

⎠ 

p(t`)= G(t) A(L) 

Satellite 

data of 

E 

Energy 

parame- 

Spatio-temporal 

Distribution of 

ters of 

MIC 

picture of FAC 

from the 

magnetosphere into 

the ionosphere 

bulk current in 

the 

magnetosphere 

Module in the form of rhombus is only for correcting 

data (not obligatory, only additional data for calibration 

{correction} of the main parameters). 

Figure 7. The simplified scheme of the structurally adequate model of magnetospheric processes. 

Apart from its cognitive value, the model (fig. 7) will be useful for predicting the response of the 

magnetosphere to extreme situations absent from the teaching sample of empiric models, as well as for 

compatibility between various empiric models predicting magnetospheric disturbances and determination of 

the limits of their applicability. 

Acknowledgment. The work was done within the framework of the grant MK-3697.2008.5. 

References 

Heppner, J.P. (1977), Empirical Models of High-Latitude Electric Fields. J. Geophys. Res., 82, N7, 1115– 

1125. 

Kennel, C.F. (1969), Consequence of a magnetospheric plasma. Rev. Geophys., 7, N 1-2, 379-419. 

Madelung, E. (1960), Mathematical Apparatus in Physics, Gosud. Izd. Fiz.-Mat. Lit., Moscow., pp 24-48, (in 

Russian). 

Ponomarev, E.A. (1985), Mechanism of magnetospheric substorms. Moscow: Nauka., pp 157, (in Russian). 

Ponomarev, E.A., Sedykh, P.A. (2006), How can we solve the problem of substorms? (Review). 

Geomagnetism and aeronomy. Pleiades Publishing Inc., 46, N4, 560-575. 

Ponomarev, E.A., Sedykh, P.A., Urbanovich, V.D. (2006), Generation of electric field in the magnetosphere, 

caused by processes in the bow shock. J. Atmos. and Sol. Terr. Phys. Elsevier Science, 68, 679-684, (a). 

Ponomarev, E.A., Sedykh, P.A., Urbanovich, V.D. (2006), Bow shock as a power source for magnetospheric 

processes. J. Atmos. and Sol. Terr. Phys. Elsevier Science, 68, 685-690, (b). 

Sedykh, P.A., Ponomarev, E.A. (2002), The magnetosphere-ionosphere coupling in the region of auroral 

electrojets. Geomagnetism and aeronomy. Pleiades Publishing Inc., 42, N5, 613-618. 

Sedykh, P.A., Ponomarev, E.A., Mager, O.V. (2004), Concerning the compatibility of field-aligned currents. 

Proc. of 7-th Intern. Conf. on Substorms. Levi, Finland. March 22-26, 2004, pp. 111-115. 

Whang, Y.C. (1987), Slow shocks and their transition to fast shocks in the inner solar wind. J. Geophys. 

Res., 92. N5, 4349-4356. 

271

Introduction 

ON THE NATURE OF PLASMA INHOMOGENEITIES IN THE 

MAGNETOSPHERE 

P.A. Sedykh, E. A. Ponomarev 

Institute of Solar-Terrestrial Physics, 

Siberian Branch of the Russian Academy of Sciences, Lermontov str., 126 a, 

p/o box 291, Irkutsk, 664033, Russia; e-mail: pvlsd@iszf.irk.ru 

Abstract. In this paper it is shown that the existence of spatial inhomogeneity of convection 

velocity and its sudden change in time can create in combine action the spatial - temporal 

formation which looks like inhomogeneity of plasma density (pressure), moving at convection 

speed (in the direction of the Earth) or at Alfven speed towards the magnetotail. We show that the 

structure appears on the magnetosphere night side at the distance of 10-20 Earth radii, because of 

peculiarities of the electric field of convection. Plasmoids observed during geomagnetic 

disturbances moving towards the magnetospheric tail, approximately at Alfven speed, are Alfven 

resonances. Even though mechanisms of generation of both convecting, and Alfven wave 

perturbations are similar, conditions of excitation of the latter are harder. Therefore, not all 

substorms will be accompanied by generation of plasmoids. And may be intensive, but short 

pulses of south IMF Bz-component can generate plasmoids, but not create auroral break up of a 

substorm. 

The substorm “break up” nature is of prime importance for magnetospheric physics. The “break up” 

shows up as a sudden amplification of electron precipitations and electric currents in the night-time region of 

auroral oval near the Harang discontinuity. The amplification rapidly covers the whole night-time region of 

the oval. Akasofu [1971] affirmed that the half-sum of disturbance propagation velocity to the west and east 

is approximately equal to the convection velocity projection onto the ionosphere, i.e. there is a connection 

between the break up and the convection in the magnetosphere. 

Generation of plasma inhomogeneities in the geomagnetosphere 

It is known that the combined action of convection and strong pitch-angle diffusion of electrons and protons 

is responsible for the formation of gas pressure distribution in the magnetosphere [Kennel, 1969; Ponomarev, 

1985], that is, steady bulk currents. The divergence of these bulk currents brings about a spatial distribution 

of field-aligned currents, i.e. magnetospheric sources of ionospheric current systems. It is known 

[Ponomarev, 1985] that the contents of the magnetic flux tube (MFT) to be referred to as the plasma tube 

(PT) throughout the text, transfers from one MFT to another in the convection process without surplus and 

deficiency in the case where the field lines of the magnetic flux tube are equipotential ones. This idealization 

is quite realistic everywhere apart from polar auroras. Then, as the PT drifting toward the Earth in a dipole 

field, its volume decreases in proportion to L -4 , and the situation is the reverse for density, while pressure 

increases in proportion to ~L 20/3 . However, the process of adiabatic compression is attended by the processes 

of PT depletion due to pitch-angle diffusion into the loss cone. This process is described by the factor ~exp(- 

∫dt/τ) = exp(-∫dr/Vrτ) = exp(-∫rdυ/Vυτ). Thus gas pressure has a maximum on each line of convection. In 

accordance with the equation for pg [Ponomarev, 1985], we have: 

p 


g 

20 

⎛ L ⎞ 3 ⎛ ⎞ 

∞ 5 dr 

= p ⎜ ⎟ ⎜ 

⎜− 

∫ ⎟ 

g ( t) 

exp 

⎝ L ⎠ ⎝ 3 Vrτ 

⎠ 

0 (1) 

Here pg is gas pressure, L is the L-coordinate, r = LRe is the distance to the Earth (Re being the Earth’s 

radius), Vr and Vυ are the radial and azimuthal components of the convection velocity of the equatorial trace 

of the plasma tube, respectively, and τ is the characteristic time of PT depletion due to pitch-angle 

diffusion(fig.1). 

M.I. Pudovkin called the time of the plasma tube passage from the boundary L∞ to the observation point L as 

“transport time” [Pudovkin, Semenov, 1985]. Obviously it is not longer than the period between the reversal 

of the Bz-component sign of the interplanetary magnetic field (IMF) and the substorm commencement 

260


80 

80 

80 

70 

70 

70 

60 

60 

60 

8 

0 

Figure 1. Gas pressure relief (calculated values) under the nonstationary boundary 

conditions and contour lines of the intensity of the precipitating electron flux density for the 

nonstationary boundary conditions. 

(45-60 min). During this time, the plasma tube covers the distance of L∞-L with average velocity of 

(сE/4B0)L∞ 4 /(L∞ - L) ~(cE/4B0) L∞ 3 while drifting; the time of this process is T= 4B0R0(L∞-L) 2 /cEL∞ 4 . Given 

T = 3000s, В0 = 0.5, R0 = 6.37 10 8 cm, Е = 3 ·10 -8 CGSE, we derive L∞ value ≥ 10.86, if L ≤ 5.43. Thus the 

plasma tube should start from the L-shell 10-12 to be found on the L-shell of the auroral oval midposition. 

M.I. Pudovkin considers reconnection region to be situated on the L-shell 10-12 [Pudovkin, Semenov, 1985]. 

There were many unsuccessful attempts to find physical processes (microscopic processes) accompanying 

the reconnection (i.e. existence of strong plasma turbulence implying quasi-collisional regime) in this region. 

What is there at these distances on the Earth night side? 

The magnetic field empirical model of Mead-Fairfield [Mead, Fairfield, 1975] is based on generalization 

results of observations and does not contain artificial corrections of hypothetical character. Fig. 2 shows 

significant depression of the magnetic field on the magnetosphere night side at L ~ 12-15. All figures 

demonstrating the magnetic field distribution in [Mead, Fairfield, 1975] distinctly show this effect, though 

authors consider it to be an artifact. 

80 

80 

7 

0 

70 

70 

6 

0 

60 

60 

80 

80 

80 

70 

70 

70 

60 

60 

60 

Figure 2. The magnetic field empirical model of 

Mead-Fairfield [Mead, Fairfield, 1975]. 

261 

8 

0 

80 

80 

7 

0 

70 

70 

6 

0 

60 

60


There should be balance between the magnetic and gas pressure; consequently, the region of the magnetic 

depression should coincide with that of the increased gas pressure. Region of the gas pressure increase in 

one-dimensional flow under study is also the region of an increased plasma density and low convection 

velocity. How make plasma density (pressure) inhomogeneities move at the electric drift velocity? The main 

problem here is to “get” inhomogeneity into the convective stream. As pressure and density in the 

magnetosphere are related by the adiabatic equation, we will interpret the equation: 

n’(x,t) = n∞(x-V0t) (x∞/x) 4 exp(-∫dx/Vxτ), (2), 

that is an analogue of (1). Hereafter, x is the distance along the axis X in Earth radii Re, V is the convection 

velocity in Re/s. 

Consider one-dimensional case. Let us suppose spatial density inhomogeneity: n’(x,t.) = n0A(t)R(x), (3), 

where A (t) is the time function, R(x) is the x-coordinate function. Let A(t) and R(x) be a(ω) and r(k), 

respectively: A(t) = (1/2π)∫a(ω) exp(-iωt)dω and R(x) = (1/2π)∫r(k) exp(-ikx)dk, (4). 

It is necessary that ω = kV0 for frequency and spatial oscillations form the wave moving at V0 phase velocity. 

Then: 

n’/n0 = (x0 /2π) {∫a(kV0)r(k) exp(-ik(V0t + x)) dk} (5). 

Thus “resonance” adjoint oscillations with ω = kV0 (waves moving at the convection velocity) “get” into the 

convection stream. The product a(kV0)r(k) should not be small inside the integration interval (i.e., curves 

a(kV0) and r(k) should coincide) for the generation process of such oscillations to be effective. According to 

the “resonance” ω = kV0, spatial inhomogeneity dimension is 1; consequently, the adjoint period of temporal 

oscillations should be 1/V0. The period of temporal oscillations is 3 ·10 3 s (about an hour) at l ~ 6·10 9 cm (i.e., 

10 Earth radii) and the convection velocity 2·10 6 cm/s. Resonance can appear at the convection velocity as 

well as at the Alfven velocity VA. The Earth-directed higher inhomogeneity of the magnetic field results in 

certain excitement conditions of the Alfven wave moving towards the Earth. These conditions are harder 

than those of the wave moving towards the magnetotail. Besides, the Alfven velocity is higher than the 

convection one; therefore frequency range is higher. If “convective waves” resonate with variations of IMF 

Bz-component with the period of about an hour, Alfven waves resonate with Bz-component (IMF) variations 

(period of 5-10 min), i.e. with steep fronts. 

Plasmoids moving towards the magnetotail at the Alfven velocity during the geomagnetic disturbance are 

most probably Alfven resonances. Generation mechanisms of both convective and Alfven wave disturbances 

are similar, but excitement conditions of the latter are harder. That is why just some substorms involve 

plasmoid generation. Probably, these are intensive narrow (short) pulses of the south IMF Bz-component that 

may generate only plasmoids. The A(t) certain form is specified by variation of the Bz-component and solar 

wind velocity. Though this dependence is variable, it can be characterized by a rapid increase (modulo) and 

more gradual decrease. Let us approximate it by the function: 

A(t) = t0 (t + t0) /(t 2 + t0 2 ), t ≥ 0 (6). 

The R(x) function describing the “bunch” of plasma density (of plasma pressure) in the region of the 

magnetic field decrease can also be approximated by a simple function: 

R(x) = x0 [(x* – x) + x0]/[(x* – x) 2 + x0 2 ] (7). 

Functions (6) and (7) present disturbances of a certain initial state; density variations should be considered in 

reference to it: n∞ = ng + n’(x,t). 

Certain form of approximating functions is an arbitrarily chosen (to make the Fourier transform operation 

easier). Parameters of approximating functions are deduced from generalized observation data. Recall that 

x


[Ponomarev, 1985]) for V0. We can specify the tube average velocity at the segment between the L-shell 1 

and L-shell 2 for the stable electric and dipole geomagnetic field: 

= cE/B0 L 3 эфф, где L 3 эфф = L1 2 L2 2 /(L1 + L2) 

If the segment is not long, substitution of Lef for the least value from {L1L2} will not result in mistake. Thus 

the convection velocity will be considered coordinate-independent in the region of the wedge formation. 

Equation (10) consists of four parameters V0, t0, x0 and x*. Let us determine them using problem situation. 

From (6) it follows that tm = t0, where tm is the moment of the time-disturbance maximum. Hereafter we will 

consider t to be t = 1.8·10 3 s (half of an hour), V0 to be constant value equal to 1.8 ·10 -3 RE/s or 1.15·10 6 

cm·s -1 This magnitude corresponds to the electric field of ~25 mV/m in the ionosphere in latitude of ~ 68°, 

i.e. to a typical electric-field value in the medium-disturbed auroral ionosphere. Given transport time of 45 

minutes (time between the change of the Bz-component sign and the break up), let us determine distance 

from L=5 to the start point, where the wedge motion of about 5 Earth radii started 40-45 minutes before. The 

distance L=5 corresponds to the geomagnetic latitude of 64°, where we can observe the extreme equatorial 

point of the auroral oval night side at moderate disturbances. In this case the start-point coordinate, where the 

plasma packet “tip” started its motion, is x* = -10. Finally, from (8): x0 = (x*- xr (2) )/(√2- 1). 

Given x* = -10, xr (2) = -13, x0 is -7.25. 

Fig. 3 demonstrates hand-specified density distribution in the magnetic-field depression region as (7) (the 

static wedge). Also, fig. 3 shows density distribution, derived from (10), for 3 sequential instants of time t = 

0 s, 560 s and 1120 s. The said arguments explain formation of the space-time traveling disturbance, which 

results from interaction of spatial and temporal oscillations. There are many such disturbances, but 

significant are those with the phase velocity close to the convection one (“resonance” disturbances). If 

hydrodynamical flow decelerates, the plasma pressure bunch appears. In this case the only one cause of 

negative anomaly is that of the electric convection field. 

6.414 

F0() x 

Gx () 

F1() x 

F2() x 

1.862 

7 

6 

5 

4 

3 

2 

1 

0 5 10 15 20 

0 x 

Figure 3. Static wedge [G(x)] and dynamic wedge (plasma packet) in moving to the Earth [ F0,1,2(x)]. 

The magnetospheric electric field depends on the solar wind parameters. The bow shock (BS) front is the 

main converter of the kinetic energy of the solar wind into the electromagnetic and gas-kinetic energy of the 

transition layer and magnetospheric processes [Ponomarev et al., 2006, (b)]. Potential of the BS front can be 

defined from the electric field integration at the front using continuity of a normal component of the solar 

wind velocity and the IMF tangential component [Ponomarev et al., 2006, (a)]: 

Ub = -(VsB0/c) yb(by 2 +bz 2 ) 1/2 tgφ/2 sin(ψ-ψ0) 

where VS is the solar wind velocity, B0 is the IMF intensity modulus, c is the velocity of light, bx and by are 

unit vectors of the solar-magnetospheric coordinate system, φ is the angle between the axis X and the vector 

directed from the coordinate origin to this front point. The front is approximated by the paraboloid of 

263 

20


rotation with yb parameter (yb/2 is the distance from the coordinate origin to the “nose” (“head”) BS-front 

point). Finally, tgψ = y/z, tgψ0 = by/bz. 

The magnetosphere is also approximated by the paraboloid of rotation with yg parameter. Solution of the 

Laplace equation in parabolic coordinates yields potential [Ponomarev et al., 2006, (a)]: 

Ug = [(au +b/u)(cv+d/v) + U02 J1(ku) I1(kv)}sin(ψ – ψ0)] (11) 

where u and v are parabolic coordinates, J1 and J2 are Bessel functions, 

u =(r +x) 1/2 = (2r) 1/2 cosφ/2, v =(r-x) 1/2 = (2r) 1/2 sinφ/2, r = (x 2 +y 2 +z 2 ) 1/2 . Hereafter distances will be measured 

in Earth-radius units in the Cartesian coordinate system (unless otherwise specified). The k value is chosen in 

such a way that the second summand of the potential (11) is nil in the magnetopause [Ponomarev et al., 

2006, (a)]. 

In this case k = 3.83(yg) -1/2 , where yg is the magnetosphere half-width (with the guess value of 20 Earth radii) 

along the Dawn-Dusk meridian. Note that the distance from the Earth to the subsolar magnetosphere point is 

yg/2. 

Electric potential for the magnetosphere in the XY plain at by = 0 (without considering the corotation field) 

can be written as Ug=[-A(VsB0z/c)y+ U02 J1(ku) I1(kv)] z=0, (12), 

where A is a certain numerical coefficient calculated from conditions of the substance balance (substance 

coming through the BS front and going along the transition layer). It is the constant magnitude under steady 

conditions [Ponomarev et al., 2006, (a)]. 

Y-differentiation of (12) yields y-component Еу D of the electric field for the Dawn-Dusk meridian: 

Ey D = E01 + E02[J1(Sx)/Sx] (13) 

where E01 = -AVsB0z/c, E02= -U02k 2 , Sx = k(2x) 1/2 . V0 is velocity, Bz is a vertical component of the 

interplanetary magnetic field; U02 is found using boundary conditions. 

Time dependence of the electric field is expressed by time-dependent solar wind parameters V0 and B0z of 

the component E01. Time dependence of the E02 electric field is unknown. Let us suppose that it is equal for 

E01 and E02. Then: 

Eу D = E01 [1 + G J1(1.21√x)/√x] (14) 

Here G = E02/1.21E01=const, E01 depends only on time (fig. 4). In the case of one-dimensional steady flow 

for yg = 20: 

n’ = /V =n0V0/V = D/[1 + GJ1(1.21√x) /√x] (15) 

where n’ is the density disturbed value, n0 is an undisturbed value of the plasma density, is a time- and 

space-averaged value of the particle flux under undisturbed conditions, D is the function of t. Equation (15) 

corresponds to (1) and (2) from the physical point of view. Structure of these expressions is similar to that of 

(1): it is a product of two functions, one of which is time-dependent, while the second is X coordinatedependent. 

Figure 4. A profile of electric field Ey as a 

function of L-shell parameter: 

Ey(L) = 1+ J1(1.21√L)/1.21√L. 

3.5 

3.365 

Nx () 

Qx () 

3 

2.5 

2 

1.693 

1.5 

0 5 10 15 20 25 

0 x 

25 

Figure 5. Comparison of two curves. Solid 

line - accordingly to the function, 

describing by (7); dot line - accordingly to 

the expression (15). 

Fig. 5 depicts equiscaled curves that represent function described by (7) (continuous curve) and (15) 

(discontinuous curve). Value xm 0 for (7) is -18, and the (7) maximum coincides with that of (15). Parameters 

264


of D and G for (15) are 0.981 and 2.43, respectively. In this case both curves correlate well. The first curve is 

obtained on the assumption that the magnetic field depression should correspond to the density hump (with 

its maximum at the field minimum), and hump spatial characteristics should be connected with substorm 

development by delay time. The second curve is based on electric field properties resulting from the 

magnetosphere parabolic model. It turns out that they can be put in the same form by a simple coefficient 

fitting. The curve (7) maximum position (-13) should be changed (-18 RE), the G-coefficient value is 2.43. 

Conclusions 

Physical meaning of this coincidence is that the electric field theory [Ponomarev et al., 2006,(a),(b); 

Ponomarev, Sedykh, 2006] forecasts electric field peculiarity along the magnetotail axis with the minimum 

at L ~ 18, in the magnetic field depression region. This anomaly is associated with the negative anomaly of 

the convection velocity, positive anomalies of the density and the gas pressure. The latter should result in the 

magnetic field depression observed in the model MF-75 exactly in this region. The most important is that 

interaction between the spatial inhomogeneity of density and the temporal oscillation of the same density 

results in the plasma pressure inhomogeneity moving at the convection velocity towards the Earth (fig.6). 

0.2 

0.192 

V0() x 

V1() x 

V2() x 

− 0.158 

0.1 

0 

0.1 

0.2 

5 10 15 20 25 30 

5 x 

30 

Figure 6. Moving of a plasma package. 

It is shown above that, according to generalized observation data, the magnetic pressure and related to it gas 

pressure positive anomaly on the Earth night side at L ~ 12-15 can be a source of pressure inhomogeneities 

moving from the magnetotail towards the Earth at the convection velocity. The convection electric field 

model obtained for the magnetosphere parabolic model is shown to have field depression with moderate 

disturbance on the magnetosphere night side at L=18. The plasma packet is a necessary and sufficient 

condition for the substorm “break up” appearance [Ponomarev, 1985; Ponomarev, Sedykh, 2006]. 

Acknowledgment. The work was done within the framework of the grant MK-3697.2008.5. 

References 

Akasofu S.I. (1971), Polar and magnetospheric substorms. M.:Mir. 317, (in Russian). 

Kennel C.F. (1969), Consequences of magnetospheric plasma. Rev. Geophys. V. 7, P. 379-419. 

Mead G.D., Fairfield D.H. (1975), A quantitative magnetospheric model derived from spacecraft 

magnetometer data. J. of Geophys. Res. 80, No 4, p. 523 – 534. 

Ponomarev E.A. (1985), Magnetospheric substorm mechanisms. M.: «Nauka», 157, (in Russian). 

Ponomarev E.A., Sedykh P.A. (2006), How can we solve the substorm problem (Review). Geomagnetism 

and aeronomy. Vol. 46, №4, P.530-544. 

Ponomarev E.A., Sedykh P.A., Urbanovich V.D. (2006), Generation of electric field in the magnetosphere, 

caused by processes in the bow shock. J. Atmos. and Sol. Terr. Phys. Vol. 68, P. 679-684, (a). 

Ponomarev E.A., Sedykh P.A., Urbanovich V.D. (2006), Bow shock as a power source for magnetospheric 

processes. J. Atmos. and Sol. Terr. Phys. Vol. 68, P.685-690, (b). 

Pudovkin M.I., Semenov V.S. (1985), Theory of reconnection and interaction between the Solar wind and 

the Earth magnetosphere. M. Nauka, P. 128, (in Russian). 

265


STANDARD DATA-BASED MAGNETOSPHERE MODELS TUNING FOR 

THEMIS PROJECT 

Introduction 

I. G. Shevchenko 1 , V. A. Sergeev 1 , M. V. Kubyshkina 1 , V. Angelopoulos 2 


ishevchenko@geo.phys.spbu.ru, 2 University of California, Los Angeles, USA 

Abstract. Empirical magnetosphere models have been used for years since enough amount of 

data was obtained from satellite (in situ) measurements. Nevertheless modern models still have 

some serious deficiencies: they represent average magnetosphere conditions and may strongly 

differ from configuration at any particular time; they rely on solar wind parameters which may be 

unavailable or time-shifted inappropriately. Another problem is the estimation of data error given 

by certain model, which cannot be easily calculated because one has nothing to compare the 

model results with. In order to achieve better tracing of space events to Earth's surface we've 

developed a tool for routine tuning of existing standard data-based magnetosphere models. The 

tool uses as an input only THEMIS spacecraft magnetic measurements which have a reasonably 

good magnetosphere coverage. Also we tested the addition of the magnetic and plasma 

measurements from other spacecraft to increase the coverage and to stabilize the solution. In this 

article we present the results of some tests of these tuned model. The processed data are available 

to the world scientific community at http://geo.phys.spbu.ru/themis/MODELS_PUBLIC. 

Nowadays Tsyganenko’s T96 and T01 magnetosphere models [1, 2] are de-facto standard models used for 

space event modeling, tracing along magnetic field lines. Nevertheless these models have a number of well 

known deficiencies caused by different factors: model inner structure (functions) are just approximations; the 

data set used for functions constructing and coefficients search may not have an optimal coverage; model 

input parameters; could not be easily and precisely measured. For example, because of an oversimplified 

approximation for the ring current, the model field in the inner magnetosphere in T96 model was found 

generally overstretched, especially during strongly disturbed conditions. It is also unable to replicate the 

strong dawn-dusk asymmetry of the inner magnetosphere during stormy periods [2]. The more recent T01 

model includes a number of improvements, e.g. model ring current includes both axisymmetric and partial 

components making it possible to represent strongly asymmetric disturbances during storm times. Also it 

includes some magnetosphere state history (taking into account the solar wind variations during an hour 

preceeding the modeling event). However it made model more complicated and harder to tune and sharpened 

input parameters problem. 

The input parameter problem in the standard models is a problem of accurate characterization of the real 

conditions affecting the magnetotail (i.e. solar wind parameters near the subsolar magnetopause) which 

suffer from errors in propagating the data from the (often distant) measurement point, which needs to take 

into account the character of discontinuities, their tilts etc. 

A further more disadvantage of any empirical model is that they are built on the basis of big data set, 

therefore, they represent statistically averaged data instead of representing the instant magnetosphere 

configuration – which may include small but still very important components of the system such as thin 

current sheets and large local magnetic field gradients. 

THEMIS (The History of Events and Macroscale Interaction during Substorms) is an international space 

scientific project consisting of two parts launched in February 2007. The Earth-based part consists of two 

dozens ground observatories located throughout Canada and Alaska. The space part includes five identical 

spacecraft with near-equatorial orbits and apogees at 10-12 RE (three spacecraft), 18RE and 25 RE (during 

tail stage of the mission). Satellites line up once every four days along the equator (major conjunction) and 

take observations synchronized with the ground observatories. The primary objectives of the mission are to 

establish when and where substorms begin, determine how the individual components of the substorm 

interact, determine how substorms power the aurora, and identify how local current disruption mechanisms 

couple to the more global substorm phenomena. Thus the knowledge of the connection along the magnetic 

272


field lines between these two separate parts is crucial for this project. Practically it means a need to achieve 

the most accurate tracing of space events (spacecraft measurements) to Earth's surface at any instant of time, 

that is to use the most accurate magnetosphere model or, at least, to warn when the standard mapping 

procedure becomes inaccurate. 

Taking into account the abovementioned problems of existing magnetosphere models we propose a different 

approach to increase the mapping accuracy – to tune standard magnetosphere model for every single moment 

of time by adapting the model to better represent the magnetic field observed by THEMIS spacecraft. 

Method 

We selected Tsyganenko T96 model as a basic model and developed a number of model versions numbered 

with increasing complexity (see Table 1). Common for all tuning procedures is that they do not treat input 

variable as SW parameters, but as free parameters, varying which we search for the best fit of the model to 

the magnetic field observed by the THEMIS spacecraft. Complexity is added by including more observed 

data to the fitting functional (such as solar wind tilt angle, pressure in the lobes etc.) and/or more data 

sources (e.g. GOES spacecraft data). This approach helps us partially solve problems mentioned in the 

previous section. Refusing to use the propagated SW data we save the model from inaccuracies inherent in 

the propagation procedures. Selecting the best fitting model by observed data makes selected model “less 

averaged” (comparing to the model which would be selected by input parameters, which were chosen 

processing huge amounts of data). Surely we cannot get rid of model inner structure problems, but as an 

extreme measure we can modify it (it should be done with the great care because some unphysical solutions 

may be obtained). More details about these improvements listed in Table 1 may be read in [3]. 

Version Input data Parameters varied Usage Deficiences 

AM-01 B field observations at 

Themis P1..P5 

AM-02 level 01 input data + B field 

from other SC (Goes etc) in 

nearby MLT sector + plasma 

pressure at Themis P1&P2 

(lobe pressure) 

AM_03 level 02 input data+ plasma 

pressure at P1..P5 + isotropic 

boundaries 

T96 parmod(1:4) routine calculations, 

5min step, 

http://geo.phys.spbu.ru/ 

themis/ 

T96 parmod (1,2,4) + neutral 

sheet tilt in XZ plane 

(nonradial SW, flapping etc) 

intensity of RC, tail current + 

NS tilt in XZ plane + 

additional thin current sheet 

major conjunction 

periods 

fixed NS 

tilt, fixed 

CS 

thickness 

fixed CS 

thickness 

only selected substorms too many 

variable 

(choice?) 

In this paper we concentrate on the first level improvement (AM_01) which implies that the model selection 

should be based solely on the observed magnetic fields, rather than on the solar wind information. This is 

possible because of unique wide coverage and favorable distribution of the THEMIS spacecraft in the 

equatorial magnetotail. The fitting to the observed field is done by varying all four model input parameters 

(i.e. interpreted as free, formal parameters) to minimize the functional 

F= Σi=1,..,3Σj=1,..,5wj(Bij-Bij`) 2 

where Bij is the magnetic field measured at the location of j-th spacecraft (j=1,…,5), Bij` - the field 

calculated from the model at this location (i = 1,…,3 is magnetic field component), wj – weight of spacecraft 

273


data depending on its position (relative to other spacecraft, Earth, magnetopause) and varying from 0 to 1. 

Using the weights one can flexibly exclude the spacecraft observations near perigee (here, at r < 5Re), 

decrease the contribution to the model from closely-spaced-spacecraft and get a quantitative indicator how 

many useful data we have to tune the model- all done with the same computation scheme. 

We used simple search in two stages which works with adequate speed and brings desired results. On the 

first stage parameter range is divided into ten parts for Pd and Bz and into five parts for Dst and By. Selection 

of different intervals number for different parameters is due to various parameters influence on resulting 

magnetic field. Search ranges are selected according to most often observed in reality parameter values: Pd - 

(0.1; 10), Bz – (-10; 10), Dst – (-80; 20), By – (-10; 10). Its obvious that dynamic pressure, for example, may 

have extreme values, such as 20nPa, but possibility of such an event is very small and it is not reasonable to 

widen search range in such a way. Additionally one should remember that model built on statistically 

averaged data will build bad magnetosphere model if input parameters are strongly non-standard. On the 

second stage we select areas around solution found on first stage and perform more accurate second search 

with steps 0.1, 0.4, 2.0, 2.0 for Pd, Bz, Dst and By, accordingly. 

The code was intensively tested on synthetic data, and later used for routine computations during the tail 

season of 2008. Here we show the testing results and what we have learned from massive application of 

AM01 procedure. 

Figure 1. Results of testing using synthetic 

data: solar wind parameters (thin line) and 

reconstructed model parameters obtained 

after the tuning procedure (thick line). At X 

axes the time in hours is shown. 

Testing and routine procession results 

a. Testing on synthetic data. To test the AM-01 algorithm 

performance and evaluate the mapping difference (here - a 

difference between footprint latitudes calculated with 

standard model and with the tuned one) we formed a synthetic 

data set, using pre-calculated spacecraft orbits for 4 days of 

February 2007 and tagging them with solar wind data for 

corresponding days of 2001, which included both quiet and 

severely disturbed periods. We used standard T01 model to 

calculate ‘spacecraft data’ based on these ‘solar wind data’. 

Then we tuned the AM01 model to fit these calculated data in 

the best way. After that we traced spacecraft positions to the 

Earth surface in one hour intervals using both standard and 

tuned models and compared their results. The results shown 

in Fig.1 indicate that the fitting procedure usually catch well 

the input parameters (Pd,By, Dst) used in the direct solution, 

although there are large variations in the reconstructed 

parameters and reconstructed IMF Bz does not look so good. 

However, the comparison between the initial and 

reconstructed magnetic fields in Figure 2 shows a pretty good 

agreement, indicating that reconstructed magnetic 

configurations are very similar. The difference in the initial 

and reconstructed input parameters (e.g. Bz) can be partly 

attributed to difference between T01 and T96 models. We 

recall that reproducing the input parameters is not our goal, 

but rather the accurate reconstruction of the magnetic 

configuration. The lesson learned from these comparisons 

indicate to us that the fitting function F in this problem may 

have a few comparable deep minima in the parameter space 

which correspond to the similar magnetic configurations. 

Another lesson is that even in this ‘close to ideal’ 

reconstruction experiment the average difference between 

projections, the ‘mapping difference’, is approx 0.6 degrees 

CGLAT. We reckon that this ‘mapping difference’ reflects 

major part of real mapping difference because we suppose 

274


that difference model and real magnetosphere are of the same order. 

Figure 2. Testing the synthetic data set. Comparison of Bx magnetic field component at THEMIS 

spacecraft p1, p2, p3, p5 taken as input for solving the inverse problem (thin line) with its values 

reconstructed using the tuned model. Periods of time marked with grey indicate SC apogee. 

b. Example of routine procession of the real data. Figure 3 represents results of routine procession of real 

THEMIS data we performed at January-March 2008. AE index and spacecraft footpoints latitude (in 

corrected geomagnetic coordinates) are shown for 2 nd 

and 6 th of February 2008. Red line corresponds to 

latitude obtained from tuned model, blue – standard one, based on solar wind data. Gaps in data correspond 

to periods when spacecraft was near perigee, out of magnetosphere or total function weight was smaller than 

3. As one can see latitude difference is much bigger and it strongly fluctuates during disturbed day. 

Figure 3. Mapping results examples. Disturbed (on the left hand side) and quiet (on the right hand side) 

days are shown. Grey boxes show low-weight regions. Gaps in data may be caused by spacecraft position. 

275


We found that ‘mapping difference’ is of the same order as for synthetic tests. Also we noted that big 

‘mapping difference’ may be used as an indicator of models applicability: standard and tuned models differ 

dramatically when ‘mapping difference’ is much greater than its average value and magnetosphere looks 

unrealistic (e.g. current sheet thickness is overestimated). Thus these situations yield furthermore modeling 

and investigation. 

c. Test on independent observations (GEOTAIL). 

Another test was performed using real THEMIS data including orbits and magnetic field measurements. 12 

hours intervals around major conjunction events were selected from January-March 2008. Then only those of 

them were selected, which correspond with GEOTAIL spacecraft being located at the night side, at distance 

at least 5 Earth radii. We compared GEOTAIL magnetic field measurements with those predicted by 

standard and tuned models and examined ‘mapping difference’ to see if results differ from synthetic tests. 

Field comparison let us know if the model works adequately in real situation and test how it represents 

magnetic field in the inner magnetosphere. 

The comparison confirmed results of the previous tests: magnetic field was reconstructed very well despite 

of big model differences (differences between input parameters); average mapping difference was less than a 

degree CGLAT and could rose up to several degrees (possibly during high activity periods). 

d. Dependence of the mapping difference on the AE index. 

We noticed that mapping difference rises during high activity periods and decided to test if there is a relation 

between model “mapping difference” and AE index. Here we understand ‘mapping difference’ as absolute 

difference between corrected geomagnetic latitudes of spacecraft footpoints calculated using both standard 

and tuned models. The whole number of twelve hour intervals around major conjunction events (during 

January-March 2008) was selected to process. We processed these intervals with 15-minutes resolution. As 

soon as quite wide scattering was found in AE data we propose averaged results, i.e. we have split all AE 

range in several intervals each including approximately the same number of measurements and averaged all 

“mapping differences” in each of them. In Fig. 4 X-axis corresponds to these intervals numbers: 1 

corresponds to average AE approximately equal to 30 nT, 2 – 50 nT, 3 – 80 nT, 4 – 130 nT, 5 – 210 nT, 6 – 

360 nT. As one can see there is a dependence on AE index showing that error slightly increases with growth 

of AE. Nevertheless, big dispersion makes it useless to look for precise mathematical rule. 

Figure 4. Dependence of mapping difference dCGLat on AE index. “Mapping difference” value in 

CGLAT degrees at the Y axis. X axis shows AE index interval number. 1 corresponds to average AE ~ 30 

nT, 2 – 50 nT, 3 – 80 nT, 4 – 130 nT, 5 – 210 nT, 6 – 360 nT. 

276


Summary 

Results of tests we performed to analyze AM-01 model shows that there are great means of tuning existing 

models to achieve better accuracy but even minor changes require much attention to the results obtained. We 

found that mapping difference order is approx. half a degree during calm periods and may reach values of 

several degrees during disturbed ones. АМ-01 model is not the very accurate mapping tool because of its 

rigidity and simplicity of realization but it let us estimate error order and it is just a starting point for model 

tuning. Difference between its results and results of standard model should be used as an indicator of 

situations which require more detailed modeling using more data and variables (such as current sheet 

thickness and its tilt angle), particularly АМ-02 and АМ-03 models. Merit of АМ-01 model is its speed and 

also continuity and homogeneity of modeling results – that is very important for statistical studies. 

Acknowledgements. This work was supported by CRDF grant 2861 as well as RFBR grants 07-05-91109 

and 07-02-91703 and Intergeophysics program. 

References 

1. Tsyganenko, N. A., Modeling the Earth’s magnetospheric magnetic field confined within a realistic 

magnetopause, J. Geophys. Res., Vol. 100, 5599, 1995. 

2. Tsyganenko, N. A., A model of the near magnetosphere with a dawn-dusk asymmetry 2. Parameterization 

and fitting to observations, J. Geophys. Res., Vol. 107, No. A8, 10.1029/2001JA000220, 2002 

3. Kubyshkina, M., V.Sergeev, N. Tsyganenko, V.Angelopoulos, Toward adapted time dependent 

magnetospheric models: a simple approach based on tuning the standard model, J. Geophys. Res., 

submitted, 2008 

4. THEMIS website, http://themis.ssl.berkeley.edu/overview.shtml, last available: 13 September 2008 

277


FLAPPING-STRUCTURES AND BURSTY BULK FLOWS IN THE 

MAGNETOTAIL NEUTRAL SHEET FROM MHD MODELING RESULTS 

AND FROM THEMIS MULTI-SPACECRAFT OBSERVATIONS 

D.A. Sormakov 1 , V.A.Sergeev 1 , V.Angelopoulos 2 , A.V. Runov 2 


dima@geo.phys.spbu.ru; 2 University of California, Los Angeles, USA 

Abstract. Flapping-structures (kink-like deformations of the magnetotail neutral sheet) have been 

investigated based on 3D MHD modeling results (using OpenGGCM code at Community 

Coordinated Modeling Center in Greenbelt). Modeling results confirm their presence in the 

magnetotail in association with bursty bulk flows (BBFs), although the BBF does not provide a 

sufficient condition for flapping generation. Duration of flapping structures were of about 2-20 

minutes. In some cases, the flapping-structure moved across the tail (being extended in X 

direction), which was probably associated with the cross-tail motion of the BBF. 

We also compare the modeling results with first observations of flapping structures at 10-30 

RE in the magnetotail by THEMIS spacecraft. We confirm the kink geometry of individual 

structures having several RE scale along X and few RE across tail. We found that the life-time of 

some structures extended along X exceed 5 min. Most of flapping structures were observed at low 

magnetic activity and in some events fast plasma flows have not been registered. 

Introduction 

Investigation of the magnetotail current sheet and its instabilities is necessary for understanding of physical 

processes occurring in the plasma sheet, including plasma transport, energy transformation and necessary 

initial conditions for the explosive phase of a substorm. Even in the earliest spacecraft measurements near 

the tail current sheet, the fast changes of the magnetic field Bx-component sign have been noticed, that 

occurred due to up-down motions of the current sheet, they were named as flapping motions. A source of 

such fluctuations was thought to be the solar wind, whose fluctuations could provide the large-scale motions, 

analogous to the flag waving in a wind and propagating antisunward in the tail. However, in recent studies at 

4 spacecraft system CLUSTER [Runov et.al 2005], it has been shown on the small statistics that fluctuations 

propagate from the center current sheet to its flanks (the average speed of propagation ~80 km/s, the spatial 

sizes by different estimations was 1-2 RE on Y gsm and the same on Z gsm), which contradicts to the largescale 

flag-wave-like motions. The conclusion followed that the sporadic source of fluctuations is situated in 

the middle part of the tail current sheet and, possibly, is connected to the reconnection in the magnetotail. 

There is one more phenomenon generated by the reconnection, this is the bursty bulk flows (BBF, on the 

satellite data it looks as an increase Vx-components of plasma speed to hundreds km/s) [Angelopoulos et al. 

1992]. Recent statistical studies of fast flows and flapping based on GEOTAIL spacecraft observations 

[Sergeev et al. 2006] have shown a similarity between spatial occurrence distributions of these two 

phenomena, although without local one-to-one correspondence. Establishing is there is any connection 

between these two phenomena would be an important issue to investigate. 

Till now the flapping is still a poorly studied phenomenon. Its general picture and origin are not known 

in details. The previous studies by single spacecrafts and by spacecraft system Cluster, with small separation 

between the spacecraft, haven't allowed to establish spatial scale and life time of the flapping structure. In 

our work we investigate this phenomenon using two different methods. First one is the 3D MHD modeling 

which may allow to address the overall structure and scale of the flapping corrugations, as well as its 

relationship to the fast flows. Second, we use observations made by the new 5 spacecraft system THEMIS, 

which sometimes allow the radial alignment with a large separation of spacecraft along the Xgsm axis, with 

possibility of azimuthal separation of other spacecraft, to estimate its spatial scale and the life-time. 

MHD results 

We used opportunity of 3d MHD modeling of the magnetosphere provided by the computer center CCMC 

(Community Coordinated Modeling Center, http://ccmc.gsfc.nasa.gov). The UCLA code OpenGGCM 

(Geospace General Circulation Model) [Raeder 2003] was used. The box size for this run was [24,-350] RE 

for X and ±48 RE for Y and Z, and the computational grid has the minimum size of a cell ~0.4 RE in the 

278


regions of magnetotail current sheet and magnetopause. The tilt of the magnetic dipole to the ecliptic plane 

was 0 degrees during the whole run (5 hours), the coordinate system GSE was used. Three simulations 

(Victor_Sergeev_040607_1, Victor_Sergeev_010907_1, VictorSergeev_031307_1; further refered to as run1, 

run2, run3 accordingly) with various initial conditions in a solar wind have been considered. 

In the interplanetary environment for run1 we have set initial conditions as follows. The parameters Vx 

=-450 km/s, Vy = 0, density of solar wind n = 2 cm -3 , temperature 6000 K, Bx = 0 and By = 0 nT have been 

kept constant during the run. The Bz-component during the first hour of simulation was put -5 nT, then it 

sharply changed to +2 nT and was kept the same till the end of simulation. We have also set the changes of 

Vz-components of solar wind speed from -30 to 30 km/s starting from ST = 01:40 of the simulation time 

(ST). For simulation runs 2 and 3 the initial conditions were similar except for Vx = -600 km/s and n = 5 cm -3 

for run2 and Vx = -300 km/s with n = 20 cm -3 for run3. 

a) 

b) 

c) 

Figure 1: Results of 3D MHD modeling for Run1 at 01:56ST. The figuresa,b,d show the distribution of 

parameters in the neutral sheetsurface. a) colors indicates Ey = -[VxB]y, contours indicate the ratio Jz/Jy> 

0.7 (from fig.1b); b) color shows the ratio Jz /Jy ; d) colour shows Zns. In figure 1c red, black and blue lines 

indicate Zns(Y) profiles at distances 12, 18 and 26 RE. Crosses in figures c) and d) indicate points of a 

neutral sheet where the surface is not reliably determined (correlation coefficient Bx & Z is less than 0.85). 

In figures b, d the arrows show the vectors of horizontal plasma flow . 

Computed parameters from the tail current sheet area interesting to us were taken by using the 

interpolation procedure with step 0.5 RE in X gse (from -30 to -10 RE), with the step 0.2 RE in Y gse (from - 

15 to 15 RE), and with the step 0.2 RE in Z gse (from -6 to 6 RE). For any [X,Y] we obtained the coordinate 

of a neutral sheet (ZNS) by analyzing the regression Bx(Z) as the point, where the corresponding regression 

line crosses the axis Bx=0. The reliability of so defined neutral sheet position ZNS can be controlled by the 

value of the correlation coefficient between Bx and Z: points XY characterized by low correlation coefficient 

(CC


Zns(Y) at fixed X-distances (Fig.1c) as well as the tilts of neutral sheet current vector (Fig.1b). To identify 

the bursty bulk flows we used the values characterizing the magnetic flux transfer, as given by y-component 

of local electric field Ey = -[VxB]y in the neutral sheet (see Fig.1a). 

In Figure 1 we show one example from the simulation Run1 (at simulation time ST=01:56) which 

displays one of few intense flapping events identified. For visual identification of distortions in the shape of 

the neutral sheet we show Figure 1d where, according to a color palette on the right, the color represents the 

coordinate Z of the neutral sheet in XY coordinates. Here we also overlap the plasma bulk flow vectors 

shown by the black arrows. The neutral sheet shape across the tail is shown in Fig.1с by the profiles at the 

distances X = -12 RE (red line), X = -18 RE (black line) and X = -26 RE (dark blue line). Further, to identify 

the neutral sheet tilts we presented on fig.1b the ratio between z-components to y-component (Jz/Jy) of 

electric current in the neutral sheet, here we also put on the same coordinate grid the projections of plasma 

flows (white vectors). 

The presence of two folds, one on the dawn side and another one on the dusk side of magnetotail can be 

easily seen in Fig 1d. The first fold (passing over [-25; -7] RE in X,Y, is marked by dark color in the 

described area), it is well seen in fig.1c at the profiles at X= -18 and -26 RE. Approximate coordinates of the 

second fold are [-25; 7] RE , its Z-coordinate is not as accurately defined due to the very turbulent B-field 

structure in this area (the big error in the finding the neutral sheet, fig.1c). The tilt of the neutral sheet 

corresponding to the first fold are visible in the same area in fig.1b (they are defined by the light color in the 

specified area), for the second fold the tilt is difficult to obtain due to the error in finding the neutral sheet. As 

concerns the BBFs, in figure 1a in areas [-25;9] RE and [-25;-9] RE one can see the green color region with 

Ey increased above ~1 mV/m, i.e. regions with fast flux transfer. Here the plasma flow is increased as 

revealed by the larger length of white vector, the average speed of fast flow was 400 km/s. Obviously, in this 

example the areas corresponding to the flapping appeared near the narrow BBF streams on them flanks. 

Initial development of these structures is difficult to obtain with 2 min resolution available. Later in time, we 

observe a gradual synchronous displacement of BBF stream and flapping fold toward the tail flanks with a 

speed ~100 km/s, in this example it continued during 18 minutes until their total disappearance. One may 

note the initial y-components of fast stream flow velocity leaving of reconnection region (fig.1 (a), areas [- 

15:-3] RE and [-15:4] RE). 

For this example the spatial scale of a riffle on the dawn side was about 4 RE in Ygse (in the widest part) 

and about 1 RE in Z, it extends in X by more 17 RE, the cross-tail velocity was of the order of ~100 km/s. It is 

more difficult to tell something about the sizes of the riffle on the dusk side due to turbulent structure of the 

plasma sheet in this area. These two folds were the most strong and easily identified in the whole Run 1. 

We also observed some fold structures of the neutral sheet (flapping) in runs 2 and 3, but they were not 

as isolated as in our example and it was difficult to identify reliably the same structure on the subsequent 

times (at 2 min time step), most typically because of strong turbulence in the current sheet. The most difficult 

(turbulent and with large-amplitude up-down large scale motions induced by the variations of solar wind Vz 

which mask the kink-like structure development ) was the run3 in which the solar wind velocity was slowest 

(300 km/s). Here we have found many fast streams, but could not clearly identify and follow the flapping 

events. The life time flapping of the identified structures was about 2 to 20 minutes. Only three long duration 

flapping events, identified on the subsequent shots (with duration above 10 min), have been found in 3 

simulations. 

The fast streams have accompanied the flapping in all identified kink-like perturbations of the neutral 

sheet, from which we may infer that flapping is not possible without fast flows (in 3d simulations with 

OpenGGCM code). However, the presence BBF is not a sufficient condition to generate the flapping: we 

observed many cases in which the strong and clear narrow flows (like those shown on fig.1a) were not 

accompanied by the Y kink-like folds of the neutral sheet surface. Particularly, such situation dominate 

during first 100 min of simulations in all runs, during which there was a southward Bz but solar wind blowed 

strictly antisunward, with Vz,Vy=0. Only after the start of Vz perturbations in the solar wind flow, which 

destroyed the symmetric shape of the magnetotail, the flapping folds (like those in fig.1) were noticed. 

Therefore, either symmetry distortions or (other effects) of solar wind perturbations were second factor, 

favorable for the appearance of flapping folds. Further simulations are necessary to confirm and extend our 

conclusions on the role of BBFs and of the external factors in the generation of MHD flapping events. 

280


THEMIS results 

Satellite segment of THEMIS system consist of 5 spacecraft on the equatorial orbits synchronized so that 

every 4 days they form a radial configuration in their apogees. Their apogees are: for most distant spacecraft 

B it is ~28 RE, for spacecraft C ~18 RE, the apogees of three nearby spacecrafts A, D and E are about 10 RE. 

One of THEMIS purposes is a studying of the large-to-medium scale dynamical structures in the 

magnetosphere, their radial configurations are especially interesting to specify the geometry of kink-like 

flapping folds in the tail current sheet. Here we use magnetic measurements from the FGM instrument with 

the 3 sec time resolution. 

a) B 

D 

E 

C 

A 

b) 

c) 

d) 

e) 

f) 

Figure 2. Flapping event on March 5, 2008 registered by the THEMIS spacecrafts. Lines #1, #2, #3, #4, #6, 

#7 indicate the variations for which the calculated MVA normals are shown in Table 1. a) the approximate 

shape of the structure and relative locations of spacecrafts consistent with observations, Lx and Ly — 

approximate sizes of scale-sizes of flapping structrure, dark blue arrows show the expected MVA normals; b) 

true spacecraft locations in XY plane; c) Bz-component of magnetic field of spacecrafts B, C, E colored 

according to the legend; d) Bx-component of magnetic field at spacecraft B, C, E e) Bx-component of 

magnetic field at spacecraft D (the dark blue line) and A (the violet line); f) Bx-component of a magnetic field 

of spacecraft D (the dark blue line) with a time shift-8 minutes and A (the violet line) with a time shift of +8 

minutes. 

We present here a remarkable event on March, 5th, 2008, between 9-11 hours (fig.2), when the 

spacecraft were in a radial configuration (have been placed approximately in one line along X axis, fig.2b). 

The distance between spacecrafts E and B is here about 6 RE (fig.2b). The event is remarkable because the 

spacecrafts B, C, E simultaneously observed similar large-amplitude variations of magnetic field Bxcomponent 

(fig.2с) with almost no time shift. Although only the most distant spacecraft B actually crossed 

the neutral sheet (all others probed the variations in the negative Bx range), the structure looks similar to the 

previously described Y-kink flapping structures (Runov et al., 2005, Sergeev et al., 2006). (In the following 

we confirm this conclusion by analyzing the geometry of the perturbations using the MVA analyses.) In a 

striking difference, even if the Bx variations are synchronous (fig.2c) over the distance > 6 RE in Xdirection(B, 

C, E), the similarity is lost between the nearby spacecrafts E, D and A, over much shorter 

distances about ~1Re but across the tail. This immediately suggests (fig 2a) that the measured structure is a 

281


riffle which is elongated along X (spacecraft B, C, E) but has a small size along Y (because the 

synchronization of variations at E with those at the spacecraft A and D is lost). 

Let's check up this statement using the Minimum Variance Analyses method (MVA, [Sonnerup et.al 

1998]). If the structure can be approximated locally as 1d structure, the MVA allows to estimate the 

orientation of the normal to this structure by defining a direction of smallest variability of a magnetic field 

(vector n3). The reliability of its determination is shown by the value of the ratio of two lowest eigenvalues 

λ2/λ3 of the covariation matrix. In recent studies it was often used as reliable estimate if λ2/λ3 > 2.5 [e.g. 

Sergeev et.al 2006]. If the geometry in Fig.2a is valid: (1) the B,C,E spacecrafts measure the same slope of 

radially-elongated structure and therefore for all spacecrafts the normals direction should agree; (2) the sign 

of y-component of the normal (z-direction is always taken positive) should change after the passage of next 

slope and (3) it should correlate with the sign of Bx variations (which goes up and down on the neighboring 

slopes). 

THEM 

IS 

B 

C 

E 

№ 

norm 

als 

T1 

(h:m:s) 

T2 

(h:m:s) 

Sing 

ΔBx 

N λ2/λ3 

Normals MVA [ 

n3x ; n3y ; n3z ] 

[ X ; Y ; Z ], gsm, RE 

#1 9:36:51 9:38:19 + 29 9.67 [ 0.12 ; 0.92 ; 0.38 ] [ -16.5 ; 2.78 ; -1.62 ] 

#2 9:38:48 9:39:45 - 19 5.01 [ -0.24 ; -0.27 ; 0.93 ] [ -16.48 ; 2.77 ; -1.61 ] 

#3 10:10:37 10:14:33 + 78 14.86 [ 0.03 ; 0.91 ; 0.42] [ -15.94 ; 2.43 ; -1.52 ] 

#4 10:18:19 10:20:57 - 56 5.39 [ -0.37 ; -0.38 ; 0.85] [ -15.87 ; 2.39 ; -1.51 ] 

#6 10:45:40 10:46:40 + 19 8.5 [ 0.14 ; 0.9 ; 0.42] [ -15.42 ; 2.12 ; -1.43 ] 

#7 10:47:15 10:49:37 - 47 2.67 [ -0.19 ; -0.89 ; 0.41 ] [ -15.39 ; 2.10 ; -1.42 ] 

#1 9:36:29 9:38:38 + 43 6.75 [ -0.22 ; 0.54 ; 0.81 ] [ -13.78 ; 2.46 ; -2.35 ] 

#2 9:46:46 9:47:28 - 14 13.22 [ -0.06 ; -0.72 ; 0.69] [ -13.69 ; 2.37 ; -2.33 ] 

#3 10:13:00 10:14:35 + 32 9.4 [ 0 ; 0.86 ; 0.51 ] [ -13.35 ; 2.07 ; -2.26 ] 

#4 10:18:58 10:21:41 - 54 2.75 [ -0.23 ; -0.83 ; 0.5 ] [ -13.29 ; 2.02 ; -2.24 ] 

#6 10:45:25 10:46:31 + 22 14.6 [ 0.29 ; 0.89 ; 0.34 ] [ -12.93 ; 1.73 ; -2.16 ] 

#7 10:49:11 10:50:12 - 20 15.05 [ 0.04 ; -0.93 ; 0.36 ] [ -12.89 ; 1.7 ; -2.15 ] 

#1 9:35:25 9:38:27 + 60 5.56 [ 0.01 ; 0.26 ; 0.96 ] [ -10.96 ; 2.45 ; -2.28 ] 

#2 9:48:34 9:49:19 - 15 2.52 [ -0.2 ; -0.73 ; 0.65 ] [ -10.93 ; 2.33 ; -2.27 ] 

#3 10:10:42 10:12:47 + 42 4.86 [ 0.17 ; 0.96 ; 0.23 ] [ -10.86 ; 2.05 ; -2.24 ] 

#4 10:20:00 10:23:34 - 71 5.81 [ -0.26 ; -0.27 ; 0.93 ] [ -10.83 ; 1.96 ; -2.23 ] 

#6 10:45:55 10:47:31 + 32 9.09 [ 0.1 ; -0.94 ; 0.34 ] [ -10.71 ; 1.65 ; -2.18 ] 

#7 10:47:42 10:49:41 - 39 6.75 [ 0.11 ; 0.99 ; 0.05 ] [ -10.71 ; 1.64 ; -2.18 ] 

Table 1. Results of the Minimum Variance Analyses analyses of THEMIS magnetic measurements during 

flapping events on 05.03.2008. 

Let check these predictions with normals obtained from MVA for the events #1 to #7, they are presented 

in Table 1. The normals x-component is always small, so the normal lies close to the YZ plane. The first 

prediction is well confirmed: the tilt of the normal in YZ plane has nearly same direction on spacecraft B, C, 

E, in most cases the n3y (y-coordinate of normal to one-dimensional structure) is the largest component. The 

second and 3 rd predictions are also mostly confirmed, as emphasized by the shading in Table 1 which 

corresponds to the sign of Bx-variation. In 8 of 9 unshaded rows (dBx>0) the y-component of the normal is 

positive, whereas in 8 of 9 shaded rows (dBx


components is unreliable because it is chosen based on the sign of z-component (which is not reliably 

known). The reason of anomaly for #6E crossing is not obvious, we however note that it was the weakest of 

all other Bx variations. 

Using figure 2а for visualization and our results, we can infer that the structure moves towards positive 

Y (from dusk to dawn). Let now concentrate on the variations seen at azimuthally separated spacecraft A,E 

and D. Indeed in some cases like variations #1 and #2 we may identify similar variations at A and D, and 

then introduce the relative time shift between them to coincide. This was done in fig2f for #1,2 by 

introducing the time shifts about +/-8min. The sign and value of the time shift correspond to the dawnward 

propagation at the velocity of ~80km/s, whereas the total observation time for this structure may exceed 15- 

20min. This may be one of the first estimates indicating a quite long lifetime of the y-kink-like flapping 

structure. We however have to note that in cases #6 and 7 here is no sign of comparable (but time-shifted) 

variation at the spacecraft A, which indicate that either its lifetime was short, or it stopped its motion. 

Conclusion 

By analyzing the 3D MHD simulations we identified flapping-like structures and have obtained the 

following preliminary results: the kink-like flapping structures have appeared in MHD in association with 

the fast streams (BBFs), although the BBF is not a sufficient condition to form the flapping folds. We 

observed that flapping structures (extended along X) were displaced across the tail and had the duration 

between 2 and 20 minutes. We noticed that flapping appeared in our cases in connection with the BBF during 

period of fluctuating Vz-components of a solar wind. 

We showed a remarkable event in which the five THEMIS spacecraft observed a seria of very narrow 

(~1Re) kink-like riffles elongated along the tail by >6Re. For these events we found, that the time of life of 

flapping structure may reach 15-20 min, and that some long-lived structures moved across a tail (at ~80 

km/s). We noticed that many flapping events have been registered during the quiet period of magnetic 

activity, frequently in the absence of fast flow observed locally. 

Acknowledgments. We thank the group of OpenGGCM global MHD simulation runs , which were 

performed computation via public Runs on Request system (http://ccmc.gsfc.nasa.gov). We thank S.V. 

Apatenkov for his support in programming. The work by D.A. Sormakov and V.A. Sergeev was supported by 

the RFFE grants 07-05-91109 and 07-02-91703 and Intergeophysics program. 

References 

Angelopoulos, V., Baumjohann, W., Kennel, C. F., Coroniti, F. V., Kivelson, M. G., Pellat, R., Walker, R. J., 

Lühr, H. and Paschmann, G.: Bursty bulk flows in the inner central plasma sheet, J. Geophys. Res., 97, 

4027 – 4039, doi:10.1029/ 91JA02701. 

Raeder, J.: Global Magnetohydrodynamics — A Tutorial, in: Space Plasma Simulation, edited by: Buechner, 

J., Dum, C. T., and Scholer, M., Lecture Notes in Physics, vol. 615, Springer Verlag, Heidelberg, 2003. 

Runov, A., Sergeev, V.A., Baumjohann, W., Nakamura, R., Apatenkov, S., Asano, Y., Volwerk, M., Vörös, Z., 

Zhang, T.L., Petrukovich, A., Balogh, A., Sauvaud, J.A., Klecker, B., and Rème, H.: Electric current and 

magnetic field geometry in flapping magnetotail current sheets, Ann. Geophys, 23, 1391-1403, 2005. 

Sergeev, V.A., D.A.Sormakov, S.V.Apatenkov, W. Baumjohann, R. Nakamura, A.V. Runov, T. Mukai and T. 

Nagai, Survey of large-amplitude flapping motions in the midtail current sheet, Ann.Geophysicae, 24, 

2015-2024, 2006 

Sonnerup, B. U. and Schneible, M.: Minimum and maximum variance analysis, Analysis Methods for Multi- 

Spacecraft Data, edited by: Paschmann, G. and Daly, P., ISSI Scientific Report SR-001, ISSI/ESA, 185– 

220, 1998. 

283


SPACE CLIMATE AND HISTORICAL DATA OF THE RUSSIAN 

MAGNETIC NETWORK: RETROSPECTIVE ANALYSIS OF THE 

SEPTEMBER 1859 SUPERSTORM 

M.I. Tyasto 1 , N.G. Ptitsyna 1 , I. S. Veselovskii 2 , O.S. Yakovchuk 3 

1 St. Petersburg Filial of Institute of Terrestrial Magnetism, Ionosphere, and Radiowave 

Propagation, Russian Academy of Sciences, St. Petersburg, Russia, email: nataliaptitsna@ya.ru; 

2 Skobeltsyn Institute of Nuclear Physics, Moscow State University, Russia; 3 Space Research 

INTRODUCTION 

Institute, Moscow, Russia 

Abstract. The study of space climate involves both long-term average characteristics as well as 

extreme deviations from the average behavior. Here we present analysis of extreme solarterrestrial 

event on 1-5 September, 1859 associated with the well-known Carrington flare. The 

analysis is based on hourly geomagnetic data (H-component) for 1-5 September 1859 measured by 

Russian stations St. Petersburg, Ekaterinburg, Barnaul and Nerchinsk. For St. Petersburg and 

Ekaterinburg also 5-min data were available. The data demonstrate complex structure of the 

geomagnetic activity, which comprises several disturbed periods. On 2 September between 4 and 

6 UT all stations registered very strong short magnetic disturbance (duration t1=1-2 hours). 

Magnetometers at all stations except Nerchinsk went out of scale. The size and direction of the 

registered geomagnetic disturbances testify that all Russian stations were inside the polar cap or 

the auroral oval, which size was expanded to the South relatively to its usual location. 

Longitudinal dependence, absence of “out-of-scale” measurements in Nerchinsk for the storm on 

2 September, is interpreted as a possible manifestation of an asymmetry of the effective electric 

current circuit in the disturbed magnetosphere and ionosphere for very short period of just 1-2 

hours. 

The study of space climate involves long-term mean characteristics as well as extreme events. Super-intense 

magnetic storms (Dst


DATA 

We used hourly geomagnetic data (H-component) for 1-5 September 1859 that were observed by magnetic 

stations in St. Petersburg, Ekaterinburg, Barnaul and Nerchinsk. For St. Petersburg and Ekaterinburg also 5min 

data for the most disturbed periods were available. In Table 1 coordinates of the magnetic stations are 

shown. 

Table 1. Coordinates of the Russian stations 

Station Geograph. coordinates, deg. Geomag. coordinates, deg. 

latitude longitude, Е latitude longitude, Е 

St. Petersburg 59.9 27.9 56.8 115.7 

Ekaterinburg 56.8 58.25 49.5 139.8 

Barnaul 53.3 81.6 43.9 158.2 

Nerchinsk 51.3 117.25 41.15 187.6 

All magnetic stations used the same instruments and methods. The data were published in yearly books [1]. 

RESULTS 

In Figures 1 and 2 we show variations of H-component of the geomagnetic field measured by Russian 

stations. In Figure 1 it is shown a detailed view of the magnetic disturbances on 2 September 1859 associated 

with the famous Carrington flare [2]. It is seen very good agreement between the data measured in St. 

Petersburg and Ekaterinburg, which prove reliability of these historical data. Figure 2 shows magnetic field 

variations during the period 1 - 5 September 1859. 

In Figure 2 it is clearly seen a solar flare event Sfe, or crochet. Sfe is a type of sudden ionospheric 

disturbance caused by a soft X-ray/EUV-driven enhancement of the ionospheric current vortices responsible 

for the regular daily variation observed on magnetograms. It has been detected by three Russian stations 

simultaneously with the Carrington flare. The magnitude of the observed crochet depends on longitude being 

the highest (60 nT according to 1-hour data) in the most western station St. Petersburg (the smallest zenith 

angle z). 

Fig. 1. Variations of 5-min H–component on 2 Sep 1859 (from arbitrary level, as given in original tables). 

285


The presented data demonstrate complex structure of the geomagnetic storm, which comprises several 

disturbed periods. On 2 September between 4 and 6 UT all stations registered very strong short magnetic 

disturbance (duration t1=1-2 hours). Magnetometers at all stations, except Nerchinsk, went out of scale. The 

available 2.5-min data in Ekaterinburg allows to establish exact moment of the storm beginning: at 9:52 LT 

(5:42 UT). 

Figure 2. Hourly data for H-component on 1-5 September, 1859 (variations from mean value of the period). 

For St. Petersburg and Ekaterinburg the three short thick lines are the minimal and maximal H during the 

Carrington event taken from 5-min data. 

286


In Nerchinsk and Ekaterinburg according to hourly data the direction of the first sharp change is negative, 

being in agreement with magnetic data in Kew and Bombei [3-5]. Ranges of H-component variations during 

this disturbance were >1000 nT in Ekaterinburg and Barnaul, > 700 nT in St.Petersburg and ≈400 nT in 

Nerchinsk. The durations of next two disturbances were t2∼14 h and t3∼22 h. The most clearly these last two 

disturbances are seen in the most high-latitude station St. Petersburg: maximal range of H reached up to 1000 

nT for the second and ∼ 500 nT for the third disturbance. This multiple geomagnetic event on 2-3 September 

1859 could be caused by a series of three eruptive solar flares that occurred within ∼40 hours. The first of the 

flares was registered near the center of the solar disk on 1 September in white light by two independent 

observers in England. A solar flare is normally only visible when observing the Sun at a single wavelength. 

Occasionally, a very large flare releases sufficient energy to be visible in the unfiltered light from the Sun. It 

was such a white light event on September 1, 1859 that was the first solar flare ever to be recorded by 

humankind. The flare was registered near the center of the solar disk and it was known as the Carrington 

flare named after one of its observers [2]. 

CONCLUSIONS 

� It is demonstrated good agreement of data registered by Russian stations; they do not contradict data 

of few other stations (Kew, Colaba), where the magnetic storm was observed. 

� Thus, the Russian geomagnetic network data must be considered reliable for space weather and 

space climate research. The Russian data are of particular value because of identical instruments and 

methods used by all stations. 

� Complex structure of the September 1859 storm comprises three the most disturbed periods. The 

extreme multiple event on 2-3 September could be caused by a series of three eruptive solar flares 

that occurred within ∼40 hours. The first one was the Carrington flare. 

� For the most time, observed disturbances in H-component were positive. It indicates that at mid 

latitudes large electrojet intensification and magnetospheric currents were present during the extreme 

September 1859 storm. 

� Longitudinal dependence, absence of “out-of-scale” measurements in Nerchinsk, could be 

interpreted as a possible manifestation of an asymmetry of the effective electric current circuit in the 

disturbed magnetosphere and ionosphere for very short period of just 1-2 hours. 

REFERENCES 

1. Kupfer А.T. (Ed). (1862), Annuaire Magnetique et Meteorologique, Annee 1859, Corps des Ingenierus 

des Mines de Russie, St. Petersbourg. 

2. Carrington, R.C. (1860), Description of a Singular Appearance seen in the Sun on September 1, 1859. 

Monthly Notices of the Royal Astronomical Society. 20, 13-15. 

3. Cliver E.W. (2006), The 1859 space weather event: Then and now. Adv. Space Res, 38, № 2, 119-129. 

4. Tsurutani,B.T., Gonzales,W.D., Lakhina,G.S., Alex, S. (2003). The extreme magnetic storm of 1–2 

September 1859. J.Geophys.Res.108, doi:10.1029/2002JA009504. 

5. Boteler, D.H. (2006), The super storms of August/September 1859 and their effects on the telegraph 

system. Adv. Space Res. 38, 159 –172. 

287


SOLAR ACTIVITY EFFECTS ON THE CHARACTERISTICS OF 

FRONTAL ZONES IN THE NORTH ATLANTIC 

S.V. Veretenenko, V.A. Dergachev, P.B. Dmitriyev 

Ioffe Physico-Technical Institute RAS, St.Petersburg, 194021, Russia, e-mail: svetaveretenenko@mail.ru 


Abstract. Long-term changes of the characteristics of frontal zones, which are the regions of high 

temperature contrasts influencing extratropical cyclone formation and development, were studied 

in the North Atlantic, the ‘reanalysis’ data NCEP/NCAR being used. It was found that in the cold 

half of the year (the period of most intensive cyclogenesis at middle latitudes) the oscillations of 

the temperature gradients in the layer 1000-500 hPa near the south-eastern coasts of Greenland 

(the Arctic frontal zone) reveal strong ∼10-yr and ∼22-yr periodicities. The detected effects 

provide evidence of the influence of solar activity and related phenomena on the structure of the 

thermo-baric field of the troposphere at middle and high latitudes resulting in the enhancement of 

temperature contrasts in the frontal zones. In turn, the revealed changes of the frontal zone 

characteristics may be a reason for long-period changes of cyclonic activity at middle latitudes. 

It is known that the temperature field of the troposphere is highly inhomogeneous due to the difference of 

thermal characteristics of air masses forming over different kinds of surface (e.g., over the warm ocean or the 

cold land in winter). This difference results in the formation of the regions of high temperature contrasts near 

the eastern coasts of continents, so called ‘frontal zones’. Cyclonic activity at middle latitude is closely 

related to the frontal zones, since they determine the potential energy supply which may be transformed to 

the kinetic energy of cyclones [Vorobjev, 1991]. The high temperature contrasts in the frontal zones and 

related atmospheric fronts create favorable conditions for cold advection contributing to the intensification of 

cyclonic vortices. Indeed, the effects of energetic Solar Proton Events on the cyclone development were 

found in the region of the Arctic frontal zone near the south-eastern coasts of Greenland [Veretenenko and 

Thejll, 2004, 2008]. In this work we study long-term variations of the temperature contrasts in the Arctic 

frontal zone (AFZ) and compare them with solar activity and galactic cosmic ray (GCR) variations. 

2. Analysis of experimental data and discussion 

As experimental base of our investigation we used the NCEP/NCAR ‘reanalysis’ data [Kalnay et al., 1996] 

on the geopotential heights of different pressure levels for the period 1958-2006 (http://www.cru.uea.ac.uk). 

We calculated the mean monthly charts of the temperature in the layer 1000-500 hPa (Fig.1), using the 

dependence of the temperature T in the layer between the pressure levels p1 and p2 on the difference of 

geopotential heights of these levels Φ1 and Φ2 : Φ − Φ = . 4 ⋅T 

⋅ lg( p p ) . The mean monthly charts 

Latitude, deg.N 

90 

80 

70 

60 

50 

40 

30 

20 

Arctic frontal zone 

Polar frontal 

zone 

10 

Layer 1000-500 hPa. 

February 2003. 

0 

-80 -60 -40 -20 0 20 40 60 80 

285 

280 

275 

270 

265 

260 

255 

250 

245 

2 

1 

67 1 2 

°K 

°C/100 km 



Fig.1. The Arctic and Polar frontal zones on the mean monthly charts of the temperature in the layer 1000-500 hPa (left 

panel) and of the magnitude of the temperature gradient in this layer (right panel). 

288 

Latitude, deg.N 

90 

80 

70 

60 

50 

40 

30 

20 

10 

0 

Arctic frontal zone 

Polar frontal 

zone 

Layer 1000-500 hPa. 

February 2003. 

-80 -60 -40 -20 0 20 40 60 80 

1.6 

1.4 

1.2 

1 

0.8 

0.6 

0.4 

0.2

Temperature gradient, °С/100 km 


1.5 

1.4 

1.3 

1.2 

1.1 

1 

0.9 

1.5 

1.4 

1.3 

1.2 

1.1 

1 

0.9 

AFZ 

λ = 40°W 

temperature gradient 

3-yr running averages 

1950 1960 1970 1980 1990 2000 2010 

AFZ 

λ = 40°W 



1950 1960 1970 1980 1990 2000 2010 

Years 

1.8 

1.7 

1.6 

1.5 

1.4 

1.3 

1.2 

1.8 

1.7 

1.6 

1.5 

1.4 

1.3 

1.2 

AFZ 

λ = 30°W 



1950 1960 1970 1980 1990 2000 2010 

AFZ 

λ = 30°W 



1950 1960 1970 1980 1990 2000 2010 

Years 

Fig.2. Time series of the maximum temperature gradient in the layer 1000-500 hPa near the south-eastern coasts of 

Greenland (longitudes λ= 30° and 40°W) in the cold half of the year (October-March). 

Normalized spectral density 

8 

6 

4 

2 

AFZ 

λ = 40°W 

22 yrs 

10 yrs 

4 yrs 

0 

30 20 10 0 

HFC, T cut-off = 3,7,11,17,19,23 yrs Period, years 

12 

8 

4 

0 

AFZ 

λ = 30°W 

22 yrs 

10 yrs 

4 yrs 

30 20 10 0 

Period, years 

Fig.3. Spectral density curves of the AFZ temperature gradients for the source time series (black lines) and their highfrequency 

components with the different cut-off parameters (color lines). 

of the temperature were used to calculate the charts of the temperature gradients in the layer 1000-500 hPa, 

in order to find the maximum values of the magnitude of the gradients at different longitudes in the region of 

the AFZ near Greenland for every month. The obtained values were averaged for the cold months (October- 

March) which is the period of most intensive cyclogenesis at middle latitudes. 

The time series of the temperature gradients in the Arctic frontal zone near the south-eastern coasts of 

Greenland are presented in Fig.2, the long-term oscillations of the AFZ temperature contrasts are distinctly 

seen. Having smoothed the data with 3-yr and 11-yr running averages, we can see the periodicities ∼10-11 

and ~22 years which are close to the main cycles of solar activity. This allows the suggestion that the 

temperature characteristics of the Arctic frontal zone are affected by solar activity and related phenomena. In 

order to confirm a reliability of the observed periodicities, an analysis of the normalized spectral density 

periodograms [Jenkins and Watts, 1969] was carried out both for the source time series and for their highfrequency 

components according to the method by Dmitriyev et al. (1996). The results of the spectral 

analysis confirmed (see Fig.3) that the harmonics with the periods ~10 and ~22 years are really the main 

harmonics in the spectra of the AFZ temperature gradients with a rather stable position on the periodogram. 

289


Δ(gradt),°C/100 km 

N, *100 hour -1 

Nyr - N yr-1 , *100 hour -1 

4400 

4200 

4000 

3800 

3600 

3400 

3200 

400 

200 

0 

-200 

-400 

0.3 

0.2 

0.1 

0 

-0.1 

-0.2 

-0.3 

AFZ 

λ = 40°W 

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 

Year relative to the sunspot maximum 

a 

Climax Neutron Monitor 

19 cycle 

20 cycle 

21 cycle 

22 cycle 

23 cycle 

Mean 

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 

b 

19 cycle 

20 cycle 

21 cycle 

22 cycle 

23 cycle 

Mean 

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 


20 cycle 

21 cycle 

22 cycle 

23 cycle 

Mean 

0.3 

0.2 

0.1 

0 

-0.1 

-0.2 

-0.3 

AFZ 

λ = 30°W 

20 cycle 

21 cycle 

22 cycle 

23 cycle 

Mean 

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 


Fig.4. Superposed epoch analysis of the variations of the AFZ temperature gradients in the 11-yr solar cycles. The 0 

year corresponds to the year of the maximum of sunspot numbers. 

The results obtained provide evidence of the influence of solar activity and related phenomena on the 

thermo-baric field structure of the high-latitude troposphere that manifests in the periodic increases of the 

temperature contrasts in the Arctic frontal zone. Let us consider what may be the factors influencing the 

temperature gradients. 

In Fig.4 we can see a superposed epoch analysis of the variations (the deviations from the 11-yr 

running averages) of the AFZ temperature gradients in the 11-yr solar cycles, the zero year corresponding to 

the year of the maximum sunspot numbers. The data in Fig.4 show that in all the cycles under study the 

minima of the temperature gradients are observed in the years of solar activity maxima. The greatest values 

of the temperature gradients are observed in the +3/+4 yr after the sunspot maxima, i.e. at the declining phase 

of solar cycle. The variations of the AFZ temperature gradients averaged over 4 cycles under study are 

shown by the red thick lines. We can see that in the 11-yr solar cycle the temperature gradients in the AFZ 

near Greenland vary on the average by ±0.15°С/100 km, i.e. by ±10−15% relative to the mean values. 

Fig.5. Mean yearly values N of the NM counting rate in 

Climax (а) and the difference of the yearly values of the 

NM counting rate between the current and the previous 

years (b) in the 11-yr solar cycles. The 0 year 

corresponds to the year of the maximum of sunspot 

numbers. 

290 

Let us compare the variations of the AFZ 

temperature gradients with solar-geophysical 

indices. It is known that GCR fluxes reduce as the 

solar activity increases, the minimum of GCR 

intensity is usually observed in the +1 yr after the 

sunspot maximum (see Fig.5a). However, the rate of 

the changes of GCR fluxes varies in the solar cycle. 

The difference of yearly values of the neutron 

monitor (NM) data in Climax (geomagnetic cutoff 

rigidity R=2.99 GV) in the 11-yr solar cycle is 

presented in Fig.5b. It is seen that GCR fluxes start 

to decrease rather sharply 1 or 2 years before the 

sunspot maximum, the sharpest drop in GCR 

intensity compared with the previous year is usually 

observed in the 0 year of solar cycle. The recovery 

of GCR intensity starts in the +2 yr, and the sharpest 

increase is observed in the +3/+4 yr after the 

maximum of solar activity. Comparing the data on 

the temperature gradient variations and the rate of 

GCR intensity changes (Fig.4 and 5), we can note 

their rather similar features. Indeed, the minima of 

the AFZ temperature gradients are observed at the 

maxima of the solar cycles and coincide with the 

highest rate of GCR flux reduction. The maxima of 

the AFZ temperature gradients are observed in the 

+3/+4 yr after the sunspot maxima and coincide with 

the highest rate of GCR intensity increase. Thus, we 

can suggest that a physical mechanism of solar

Δ(gradt), °C/100 km 

0.2 

0.1 

0 

-0.1 

-0.2 

Δ(gradt), λ=40°W 

Δ(gradt), λ=30°W 

Δ(ΣKp) 

1960 1970 1980 1990 2000 

Years 

4 

2 

0 

-2 

-4 

Δ(ΣKp) 

activity influence on the temperature 

contrasts in the frontal regions involves 

the rate of the changes of GCR intensity 

in the 11-yr solar cycle. 

The study of the geomagnetic ΣKpindices 

showed that there is also an 

enhancement of geomagnetic activity at 

the sunspot maxima and at the declining 

phase of the solar cycle, the maximum of 

the variations of ΣKp–indices (the 

deviations from the 11-yr running 

averages) being found in the +3 yr of the 

cycle. The variations of the AFZ 

temperature gradients as well as the 

variations of ΣKp–indices smoothed with 

3-yr running averages are shown in Fig.6. 

It is seen that there is also a rather good 

correlation between the temperature 

gradients and geomagnetic indices: the 

maxima of the temperature gradients in 

the Arctic frontal zone coincide with the periods of highest (or increasing) geomagnetic activity. 

Thus, the results obtained provide evidence of the influence of solar activity on the thermo-baric field 

structure of the high-latitude atmosphere at the decadal and bi-decadal time scales which is manifested in the 

variations of the temperature gradients in the Arctic frontal zone with the main solar periods ~10 and ~22 

years. We can suggest that two main factors influencing the inhomogeneity of the thermo-baric field and the 

temperature contrasts in the frontal zone are the variations of GCR intensity and geomagnetic activity. 

It should also be noted that the 22-yr periodicity observed in the AFZ temperature gradients seems to 

speak in favor of the suggestion above. Indeed, this periodicity is rather weak in the sunspot number 

variations [Vitinsky et al., 1986], however it is observed in the magnetic polarity of sunspot pairs (the Hale 

cycle) as well as in geomagnetic aa-indices and the concentration of cosmogenic isotope 10Be in the 

Greenland ice cores (see Fig.7) whose production in the atmosphere is due to cosmic rays. So, the 22-yr 

periodicity in the AFZ temperature gradients seems to be related to the corresponding variations in 

geomagnetic activity and cosmic ray fluxes. 

Spectral density 


Fig.6. Time series of the variations of the AFZ temperature gradients 

and of geomagnetic ΣKp –index for the cold half of the year. 

30 

20 

10 

aa-index 

0 

50 40 30 20 10 0 

HFC, Тcut-off =7,11,17,23,37,43 yrs Periods,yrs 

22 

11 

20 

16 

12 

8 

4 

0 

10Be 

50 40 30 20 10 0 

Period, yrs 

Fig.7. Spectral density curves of geomagnetic aa-indices and of the 10Be concentration in the Greenland ice-cores for 

the source time series and their high-frequency components. The 10Be data were taken from [Beer et al., 1990]. 

A possible reason for the changes of the temperature field structure may be changes of the radiation 

budget of the troposphere due to the cloudiness changes associated with the factors above. Clouds are known 

to produce different effects on the temperature field depending on latitude, season and the surface character 

and, thus, they may contribute to the increase of its inhomogeneity. The enhanced cloudiness formation may 

result from the changes of the global atmospheric electric circuit associated with the ionization changes due to 

GCR variations as well as with the increases of the difference of ionospheric potential across the polar caps 

during geomagnetic storms due to the negative B z component of the interplanetary magnetic field [Tinsley, 

291 

22 

11


2008]. Electrical effects on the intensity of microphysical processes in clouds (“electroscavenging”, “ionmediated 

nucleation”) seem to result in the enhanced ice nucleation, changes in the size distribution and 

optical characteristics of cloud particles. The radiative forcing of the changed cloud cover and the latent heat 

release accompanying the cloudiness formation may contribute to the enhancement of the temperature 

contrasts in the frontal zone near the Greenland coasts. Indeed, in the cold half of the year, when the income 

of solar short-wave radiation at high latitudes is rather small, clouds influence mainly the outgoing long-wave 

radiation of the Earth’s surface and the atmosphere. The fluxes of outgoing radiation differ significantly 

depending on the surface character, and in the cold period they amount on the average to ∼140-150 W/m 2 

over Greenland and ∼180-200 W/m 2 over the warmer ocean near the south-eastern coasts of Greenland 

(http://www.cdc.noaa.gov). Thus, the radiative forcing of the cloudiness changes may differ depending on the 

surface character and result in an increase of the temperature contrasts near the coastline. 

We should note that the detected changes of the temperature contrasts in the Arctic frontal zone are of 

great importance for the variations of cyclonic activity at middle latitudes. Cyclonic activity is a natural 

mechanism to reduce the potential energy contrasts in the atmosphere which are concentrated in the frontal 

zones, so the temperature contrasts in these regions determine the potential energy amount which may be 

transformed to the kinetic energy of cyclones [Vorobjev, 1991]. Thus, the variations revealed in the AFZ 

temperature gradients seem to imply the changes in the potential energy in the high-latitude atmosphere 

which may be considered as a possible energetic source for solar activity effects on extratropical 

cyclogenesis at the time scale ∼10-20 yrs [Veretenenko et al., 2005]. The results obtained confirm a 

suggestion that a mechanism of the influence of solar activity phenomena on the development of baric 

systems at middle latitudes involves changes of the frontal zone characteristics [Veretenenko et al., 2007; 

Veretenenko and Thejll, 2004, 2008]. 


This study revealed the oscillations of the temperature gradients in the Arctic frontal zone near the southeastern 

coasts of Greenland, which is the region of the predominating cyclongenesis, with the main solar 

periods ∼10 and ∼22 years. The results obtained provide evidence of the changes of the thermo-baric field 

structure in the troposphere of middle and high latitudes associated with solar activity phenomena. The main 

factors affecting the temperature contrasts of the Arctic frontal zone seem to be geomagnetic activity and the 

rate of the changes of galactic cosmic ray fluxes in the 11-yr solar cycle. A possible reason for the frontal 

zone enhancement may be the radiative forcing of the cloudiness changes associated with these factors. The 

discovered changes of the temperature gradients in turn may influence the intensity of cyclonic processes at 

extratropical latitudes. 


This work was supported by the Program №16 of the Presidium of the Russian Academy of Sciences 

“Changes in Environment and Climate: Natural Disasters”. 

References 

Beer, J., A. Blinov, G. Bonani, et al., (1990), Use of 10Be in polar ice to trace the 11-year cycle of solar 

activity, Nature, 347, 164-166. 

Dmitriyev, P.B, I.V. Kudryavtsev, V.P. Lazutkov, et al. (1996), Specific features of X-ray emission from 

solar flares registered with “IRIS” spectrometer during CORONAS-F flight, Astronom. Vestnik, 40, 160- 

170 (in Russian). 

Jenkins,G.M., and D.G.Watts, (1969), Spectral Analysis and its Applications. Holden-Day, London. 

Kalnay, E., M. Kanamitsu, R. Kistler et al. (1996), The NCEP/NCAR 40-year reanalysis project, Bull. Amer. 

Meteorol. Soc., 77, 437-472. 

Tinsley, B.A. (2008), The global atmospheric electric circuit and its effects on cloud microphysics, Reports 

on Progress in Physics, 71 (6), 66801-66900. 






Russian). 

292


Veretenenko, S.V., and P. Thejll (2004), Effects of energetic solar proton events on the cyclone development 

in the North Atlantic, Journal of Atmospheric and Solar-Terrestrial Physics, 66 (5), 393-405. 

Veretenenko, S.V., and P. Thejll (2008), Solar proton events and evolution of cyclones in the North Atlantic. 

Geomagnetism and aeronomy, 48(4), 542-552 ( in Russian). 






Russian). 

Vitinsky, Yu. I., M. Kopecky, and G.V. Kuklin (1986), Statistics of Sunspot Activity of the Sun, Moscow, 

Nauka, (in Russian). 

Vorobjev, V.I. (1991), Synoptic meteorology, 616 pp., Leningrad: Hydrometeoizdat (in Russian). 

293


THE FORMATION OF THE FIELD-ALIGNED CURRENTS DURING 

DIPOLARIZATION OF THE EARTH MAGNETIC FIELD 

M.A. Volkov 1 , N. Yu Romanova 2 

1 Murmansk State Technical University, 13 Sportivnaya Str., Murmansk, 183010, 

e-mail: Volkovma@mstu.edu.ru ; 2 Polar Geophysical Institute, 15 Halturina Str., Murmansk, 

183010, e-mail: Romanova@pgi.ru 

Abstract. The appearance of the currents in the ionosphere and magnetosphere of the Earth during 

the expansive phase of the substorm have been studied in this work. It has been shown that the 

formation of the field-aligned currents and westward Cowling currents in the ionosphere can be 

generated by dipolarization of the magnetic field lines. The model distribution of the plasma 

pressure, balanced with the magnetic field, has been taken during the growth phase of the 

substorm. The conditions of the formation of the currents wedge have been received. In the work 

the density of the field-aligned currents in the midnight sector of the auroral ionosphere has been 

estimated within the adiabatic approach. 

Introduction. One of the most important features of the expansive phase of the substorm is the sudden 

intensification of the western electrojet and the dipolarization of the Earth magnetic field lines. The Earth 

magnetic field lines, stretched in the magnetosphere tail, are shortened during the expansive phase of the 

substorm and take form close to the dipolar on distances equal to 6 radiuses of the Earth (RE) and more. 

Because of the shortening of the Earth magnetic field lines the plasma pressure varies and it causes 

appearance of the currents along the magnetic field lines. In this paper we have investigated the problem, 

whether these currents can cause the intensification of the western electrojet during the substorm expansive 

phase. 

The model of the magnetic field. The magnetic field on distances 6-10 RE is considered potential and equal 

to the sum of a dipole magnetic field and a disturbed field, connected with the currents along the 

magnetopause and currents in the magnetosphere tail. The contribution of the disturbed magnetic field is 

limited by two first harmonics of the magnetic potential, the second one is azimuthally–asymmetrical 

harmonic. In the geocentric coordinates system, where the axis x is directed to the Sun and the axis z 

corresponds to the direction of the axis of the Earth magnetic dipole, the formula for the magnetic potential 

with two harmonics of the disturbed field is: 

3 

B0RE ψ = − z − γ 1z 

− γ 2xz 

, (1) 

3 

r 

where γ1=115 nT, γ2- the coefficient of the azimuthally-asymmetrical harmonic. At the end of the substorm 

growth phase γ2=10.85/RE nT, for the expansive phase substorm γ2=5.425/RE nT. These values have been 

selected so that in the best way to correspond to the observations [1]. 

The formula for calculation of the field-aligned currents. Processes in the magnetosphere on distances 6- 

10 RE we shall consider in the magnetohydrodynamic approach. The pressure of plasma p we consider 

constant along the Earth magnetic field lines. The equation for the adiabatic process is: 

d γ 

( pV ) = 0 , (2) 

dt 

ds 

where V = BI 

∫ - the volume of the magnetic flux tube with unit magnetic flux in the ionosphere, BI - 

B 

the induction of the magnetic field in the ionosphere, γ=5/3 – the ratio of the adiabatic process. 

The field-aligned currents can be calculated by the formula [2-3]: 

294


1 r 

( e [ ∇p 

× ∇V 

]) , (3) 

B 

j// = z 

I 

where еz − 

r 

the unit vector directed along the magnetic field. The current flowing from the ionosphere of the 

northern hemisphere defined to be positive, the gradients are calculated at the ionospheric level. 

Formula (3) can be rewritten in the other form: 

1 

B V 

j// = γ z 

I 

r 

( e [ ∇pV 

γ 

× ∇V 

]) 

We calculate the field-aligned currents neglecting the magnetic flux tubes drift. It is justified if the magnetic 

γ 

γ 

flux tubes drift along the longitudinal direction. In this case solution of the equation (2) is p 1V1 

= p2V2 

, 

where the volume of the magnetic flux tube and the plasma pressure at the end of the growth phase and the 

expansive phase of the substorm are marked by indexes 1,2. We shall assume for convenience that the fieldaligned 

currents at the end of the growth phase are zero, then the vectors ∇ p1 

and ∇ V1 

are collinear. In this 

case the model pressure profile in the plasma is: 

p V 

p 1 = (5) 

V 

α 

0 0 

α 

1 

γ 

The outer boundary of the plasma layer is stable with respect to the interchange instability if ∇ pV > 0, in 

our case this condition is fulfilled at α < γ. 

According to observations in the plasma layer of the magnetosphere tail there are plasma flows before the 

expansive phase substorm as towards the Earth and in the opposite direction as well, which are accompanied 

by magnetic impuls. It can mean development of the interchange instability of the plasma layer in this area. 

γ 

We shall consider that in this area ∇ pV < 0, and α> γ. The formula for the field-aligned current at the end 

of expansive phase substorm is: 

−α 

−1 

p V ( γ − α) 

r 

( e [ ∇V1 

× ∇V2 

]) 

γ 

B V 

j// = 0 

γ 

1 

z 

I 2 

Spatial distribution and values of field-aligned currents. Volume of the magnetic flux tubes V1 and V2 for 

the magnetic potential (1) are calculated numerically in each mesh point with step 1 0 on latitude and 5 0 on 

longitude, since 16 0 colatitude. Figures 1 and 2 show the values of the volumes V1 and V2 accordingly for the 

substorm growth phase and expansive phase substorm. The values of volumes are given in terms m 2 RE. It is 

clearly seen that the isolines of the equal volume during the growth phase and expansive phases substorm do 

not coincide, there are the currents along magnetic field lines. Figure 3 shows the distribution and values of 

the currents. The plasma pressure p0 in the plasma layer on distances 8RE at the end of the growth phase was 

10 nPa. The power of the plasma pressure decrease assumes equal α=1 down 22 0 and α=2.5 in the interval 

16 0 -22 0 . According to calculations the value of currents reaches 0.7 A/km 2 , the maximum of the current 

flowing from the ionosphere locates close to 20 MLT, the maximum of the current flowing in the ionosphere 

locates close to 04 MLT. The obtained system of field-aligned currents should be closed in the ionosphere by 

the western direction current. This current should have the Hall nature, as the current flowing in the plasma 

layer. Observations of the electric fields in the midnight sector of ionosphere during the expansive phase 

substorm also show the Hall nature of the western electrojet. According to observations the electric field in 

this region has the predominately southern direction [4]. Fig.4 shows radial distribution of the plasma 

pressure in the equatorial cross section of the magnetosphere along the noon-midnight line on the night side 

of the magnetosphere at the end of growth and expansive phase substorm. The pressure on distances more 

then 6 RE during the expansive phase substorm decreases to some extent, the decreasing pressure in the 

magnetosphere tail during the expansive phase substorm is obtained by results of the observations [5]. 

295 

(4) 

(6)


Fig.1 The distributions magnetic flux tubes for the substorm growth phase. 

Fig.2 The distributions magnetic flux tubes for the substorm expansive phase. 

Summary. According to the obtained results the intensification of the western electrojet and dipolarisation 

of the Earth magnetic field lines during an expansive phase substorm are interdependent phenomena. At 

depolarization of the Earth magnetic field lines the system of field-aligned currents are formed, the currents 

flowing from the ionosphere in premidnight hours and flowing in the ionosphere after midnight. The 

intensity of field-aligned currents of this system is sufficient to increase the transverse ionospheric current of 

the western direction. This current will have the Hall nature, as well as currents flowing in the plasma layer. 

The appearance of the current wedge of the substorm can be caused by the decrease pressure near midnight 

γ 

in the plasma sheet as a result of the dipolarization magnetic field lines with the assumption ∇ pV


Fig.3 The distributions field-aligned currents (A/km 2 ) for the substorm expansive phase. 

r/RE 

Fig.4 The radial profile of the plasma pressure (nPa) in the equatorial cross section of the magnetosphere 

along the noon-midnight line on the night side of the magnetosphere at the end of growth (green line) and 

expansive phase (red line) of the substorm. 

References. 

1.Hamilton D.C.,Gloeckler G.,Ipavich F.M., Studemann W.,Wilken B., Kremser G., Ring current 

development during great geomagnetic storm of February 1986. J.Geophys.Res., 1988, 93, №A12, 14343- 

14355. 

2. Vasyliunas, V. M.: Mathematical models of magnetospheric convection and its coupling to the ionosphere, 

in Particles and Fields in the Magnetosphere, edited by B. M. McCormac, 60–71, D.Reidel, Norwell, Mass., 

1970. 

3. Tverskoy B.A. Field-aligned currents in magnetosphere. Geomagnetism and aeronomy (in Russian), 1982, 

22, №6, 991-995. 

4. Gjerloev, J. W., and R. A. Hoffman, The convection electric field in auroral substorms, 

J.Geophys.Res.,106, 12, 919, 2001. 

5. L. R. Lyons, C.-P. Wang, T. Nagai,2 T. Mukai, Y. Saito, and J. C. Samson , Substorm inner plasma sheet 

particle reduction, J.Geophys.Res., 108, A12, 1426, 2003. 

297


THE MODEL OF MULTISCALE THIN CURRENT SHEET WITH TWO- 

TEMPERATURE PLASMA COMPONENTS: THE COMPARISON WITH 

EXPERIMENTAL DATA 

L.M. Zelenyi 1 , H.V. Malova 1,2 , V.Y. Popov 1,3 , A. V. Artemyev 1 , A.A. Petrukovich 1 

1 Space Research Institute, RAS, Moscow, Russia 

2 Institute of Nuclear Physics, Moscow State University , Russia , email: hmalova@yandex.ru 

3 Physics Department, Moscow State University, Russia 

Abstract. The self-consistent theory of current sheets (CSs) in double-temperature (2T) 

collisionless plasma is developed taking into account two kinds of magnetotail plasma: more cold 

ions and more hotter ones. Quasi-adiabatic approximation is used for description of ion 

populations, whereas the fluid approximation is found to be more appropriate for electrons. The 

Grad-Shafranov equations are obtained for 1D current sheet. It is shown that its self-consistent 

equilibrium solutions exist in a wide range of parameters of the system. The corresponding 

profiles of current densities and magnetic fields might be quite variable dependently from the 

relative plasma density and temperatures of plasma sources. These solutions might describe single 

and several-peaked current sheets. The thicknesses of received solutions are several times more 

larger in comparison with the model with a single plasma component. This work demonstrates that 

characteristic profiles of double-temperature current sheet are in good agreement with 

experimental observation, therefore this model allows to explain the observations of thin current 

sheets with thicknesses about several gyroradius in the Earth’s magnetotail. 

Introduction. Recent in-situ measurements by CLUSTER spacecrafts (Sergeev et al., 2003, Asano et al., 

2005) during substorm perturbations demonstrated that current sheet (CS) in the Earth's magnetotail might 

be transformed in very thin CS at the near-Earth region (15-20 RE from the Earth). The thickness of CS 

might decrease from several RE to 250-2500 km, which is comparable with ion Larmor radii (Runov et al., 

2006). Now it is clear from in situ measurements that during the growth phase of substorm the magnetotail 

become to be very elongated due to enhancement of the magnetic flux in the tail. After formation CS in 

very stretched magnetic field might play an important role as a cite of the magnetic energy storage and 

release. These thin CSs (with thicknesses about one or several ion gyroradius) possess the complicated non- 

Harris (Harris, 1962) profiles of current density with hierarchic spatial scales (Sergeev et al., 1993) and 

non-monotonous splitted current density profiles. The essential properties of these CS are different from 

ones of isotropic Harris-like current sheets that almost always observed in a quiet magnetotail. The satellite 

investigations showed two essential properties of the observed thin CSs: the anisotropy of plasma sources 

outside CS and the non-Maxwellian character of the distribution functions. 

Various observations in lobes and plasma sheet revealed that plasma in the magnetotail has the 

content with characteristic two-temperature plasma distributions or the distribution function have a power 

tail form on energies. A part of plasma sheet population, i.e. lower energy protons and oxygen ions, might 

arrive plasma sheet directly from the ionosphere (Vaisberg et al., 1998), from LLBL (presumably at the 

Northern direction of interplanetary magnetic field) and it might be somewhat accelerated in plasma sheet 

during substorms. Solar wind plasma might also come from mantle along the reconnected magnetic field 

lines in distant magnetotail region, then these particles drift earthward with the general convection flow. 

During this drift motion the particles can be strongly energized by electric field during multiple bounceoscillations 

and repeated crossings of the neutral sheet (Ashour-Abdalla et al., 1996). As a result the 

distribution function of plasma particles in the near-Earth region of the CS have characteristic ''kappa''-like 

shape with power-law tail of distribution function. 

Many models were proposed last decades to describe equilibrium CSs in the magnetotail. The 

isotropic models where the magnetic tension of curved field lines is balanced by the plasma pressure 

gradient historically were developed the first ones (Schindler, 1974; Kan, 1973). In contrast to isotropic 

models another class of equilibrium CSs were proposed where the anisotropy of plasma pressure, supported 

by the electric field, present the necessary condition to reach the total equilibrium of the system (Speiser, 

1965). 

The numerical kinetic modelling by Eastwood (1972) and another investigators demonstrated that 

the essential current carriers in thin current sheets are so-called Speiser's ions with open-ended orbits at the 

infinity. Non-selfconsistent studies of anisotropic ion CSs by Alexeev and Malova (1995) and by Kaufmann 

298


(1997) demonstrated the important role of totally trapped ions in a redistribution of current density. The 

trapped plasma do not carry any current, but can locally redistribute the essential current thus effectively 

increasing substantially CS thickness. 

The analytical self-consistent solutions for the class of anisotropic CSs were investigated in detail 

by Zelenyi et al. (2000, 2004). This model of anisotropic CS based on a quasiadiabatic approximation 

demonstrated quite good agreement (Artemyev et al., 2008) with the part of experimental observations of 

thin current sheets in the near-Earth magnetotail, but another part of data is different from the results of this 

model: the real thickness of CSs is often several times larger than aforementioned theoretical solutions. It 

become clear that, to reach the good coincidence with measurement data, it is necessary to take into account 

plasma populations with two different temperatures, that reflect the non-Maxwellian power law character of 

the real distribution function of the charged particles in the Earth's magnetotail. The ratio between the 

transient and quasi-trapped ion populations is not very good investigated, therefore there exists the 

definitive arbitrariness in the definition plasma distribution function in our model. 

The aim of our work is the investigation of the equilibrium structure of current sheets in the 

magnetotail with a plasma distribution having high energy tail. As the most simple example we investigated 

CS model with two – temperature ion populations. We use two modifications of 1D model of anisotropic 

CS: 1) both ion populations, as warmer as colder ones, are transient and current carrying; 2) the cold ion 

populations is almost transient, another ion population has a dense quasi-trapped component. Both results 

have been used to compare theory with experimental data and the conclusion is made about the adequacy of 

our approach. 

2T TCS Self-Consistent Model. The essential assumptions of the model are following: 

1) Impinging plasma flows go from plasma sources towards current sheet along the magnetic field which is 

homogeneous in X and Y direction in GSM system of reference (Fig.1); 

(Zelenyi et al., 2000, 2002). 

Fig.1. The scheme of the model. Current carrying transient ions move 

from the Northern (or Southern) hemisphere toward the CS center. 

Near the neutral plane they cross the separatrix of motion and are 

demagnetized then going with serpentine-like orbit. After the next 

crossing of separatrix of motion they leave CS. Quasi -trapped plasma 

move along so called “cucumber” orbit and do not carry any current 

due to close orbit; their local currents are opposite to ones of transient 

particles, i.e. it is a negative in the center and positive at CS edges 

2) Three essential plasma populations are taken into account: electrons (with temperature T e ), both warm 

( T i1 

) and cold ( T i2 

) ions; 3) The cross-sheet electric field E y = 0 because deHoffmann-Teller frame of 

reference is considered. Due to different dynamics of electrons and ions inside CS the ambipolar magnetic 

field z E is not equal to zero; 4) The ion dynamics is quasi-adiabatic, i.e. the jumps z I ∆ of adiabatic integral 

of motion I z = ( m 2 π ) ∫� vzdz when particles cross separatrix of motion are larger than the values of adiabatic 

invariant itself; contrary, the electron dynamics might be described in fluid (Boltsmann) approximation in 

perpendicular to magnetic field lines direction and in guiding center approach in parallel direction. 5) In 

some modifications of the model the trapped and quasi-trapped (warm and/or cold) ions are taken into 

account. They are separated from transient ions in a space of velocities and adiabatic invariants I z . 

Very important question in considering Vlasov-Maxwell system of equations is the form of the distribution 

function of transient particles. Far from the sheet we suppose this form as the bi-Maxwellian distribution 

(Zelenyi et al., 2000) 

( ) 2 

vII − vDj 

2 

� n ⎧ 

0 j 

v 

⎫ 

⎪ ⊥ ⎪ 

ftransient , j ( v) = exp , v 0 

3 ⎨− − 2 2 ⎬ � > 

v v 

( π vTj 

) ⎪ Tj Tj 

⎩ ⎪⎭ 

299 

(1)

Vy 

Here index j =1,2 characterizes, correspondingly, the hot and the cold ion populations, coefficient n is the 

0 j 

plasma density outside TCS, v Dj and vTj are, correspondingly, averaged flow and the thermal ion velocities. 

The distribution of trapped ions is sewed together with the distribution (1) at the velocity v � = 0 : 

n ⎧ v + v ⎫ 

2 2 

� 

0 j ⎪ Dj ⊥ ⎪ 

ftrapped , j ( v) 

= exp 3 ⎨− 2 ⎬ 

⎪ v 

Tj ⎪ 

( π vTj 

) 

⎩ ⎭ 

It is significant that the trapped population does not carry any current, but its local current density might 

redistribute the essential shape of the current density in the sheet (Zelenyi et al., 2002). Near the center of the 

sheet the distribution functions (1)-(2) are not valid, however one can relate the distribution in central region 

with its simple form outside the sheet (1) using the relation I z = 2 mcµ / e (Zelenyi et al., 2000) between the 

approximate invariant of fast motion z I and the magnetic moment 2 

µ = mv⊥ 2B 

at the edges of CS. Therefore, 

one can transform the distribution function in a form, depending from two integrals of motion: the square of 

the total velocity 2 2 2 

v0 = v� + v⊥ = const and adiabatic invariant I z : 

f j ( v , v⊥ ) f ( v0, I z ) ⇒ ̃ 

� 

(3) 

The Liouville theorem allows extending this ion distribution in the whole space (Zelenyi et al., 2000). This 

distribution function has characteristic-bi-Maxwellian form at the edges of CS and non-Maxwellian form in 

the center, as it is shown in Fig2. 

3 

2 

1 

0 

-1 

-2 

-3 


-3 -2 -1 0 1 2 3 

Fig.2. The contour plots of ion distribution function in the neutral plane 

of thin anisotropic current sheet. The characteristic “hat-like” 

distribution is supported by transient Speiser ions supporting a shear of 

velocities in Y direction near the central plane. The “stem-like” region at 

small v x velocities is occupied by trapped protons moving generally in a 

negative direction (Zelenyi et al., 2003). One can see the clear separation 

of both phase regions in a phase pane. 

For the 1D geometry under consideration the self-consistent Vlasov-Maxwell equations acquire the 

following simple form: 

dB 4π 

⎧⎪ � � ⎫ 

3 3 ⎪ 

f j = const, = ⎨ v y f1( v) d v vy f2 ( v) d v je 

dz c ∫ + ∫ + ⎬ 

⎪ 3 3 

⎩V V 

⎪⎭ 

B( z = L) = B , ϕ( 

z = L) 

= 0 

0 

Vx 

Despite a small thickness on the ion scale, thin current sheet really is “thick” for electrons. Therefore in the 

model the electron current je is obtained on the base of a semi-fluid description of electron motion, which is 

given in details in paper by Zelenyi et al. (2004). 

Results of the self-consistent 2T CS modeling. The system of equation (4), with distribution functions of 

two-temperature ion components (1)-(2) have been solved numerically. Self-consistent profiles of plasma 

density, current density and magnetic field were obtained. In this paper we show current density profiles, 

which will be compared in the next paragraph with experimental data. Fig.3 demonstrates CS equilibrium 

where we have taken into account ions of a single temperature. Here the ratio of ion-to-electron temperature 

is equal to 5. Here the following values of parameters are used: vTi/ vDi = 1, Bz / B0 = 0.1, ni / ne 

= 1 , where vTi 

and v Di are correspondingly ion thermal and flow velocities, z B and B0 are the normal and total magnetic 

field components, ni / ne is the ratio of ion-to electron densities at the edges of CS. 

300 

(2) 

(4)


Jy 

2 

1.6 

1.2 

0.8 

0.4 

0 

-8 -4 0 4 8 

ζ 

Fig. 3. Current density profiles in self-consistent one-temperature 

CS. Black line is the total current density, red and blue lines 

describe, correspondingly, partial currents of protons and 

electrons. 

Fig.4 demonstrates total and partial current densities in 2T CS where both ion populations consist from 

transient particles. The essential parameters of the system were following: 

vT 2 / v Te = 5, vTj / v Dj = 1, Bn / B 0 = 0.1 , n1 / n 2 = 3, vT 1 / v T 2 = 2 (left Fig4), vT 1 / v T 2 = 3 (right Fig.4), 

vD1 / v D2 

= 1. 

The comparison of Fig. 3 and Fig. 4 allow to understand the important role of warm plasma in 

a formation of CS structure. Thus the CS in 2T plasma is several times thicker than in one-temperature 

plasma. The electron current is less expressed in thicker CS with the warmer ion component (Fig.4, at the 

right). As in the previous case (Fig.3), the center of CS is dominated by electrons, whereas the CS 

peripheries are dominated by hot ions. 

Jy 

0.8 

0.7 

0.6 

0.5 

0.4 

0.3 

0.2 

0.1 

0.0 

Cold ions 

Hot ions 

Electrons 

Total 

-8 -6 -4 -2 0 2 4 6 8 

ζ 

Jy 

-8 -6 -4 -2 0 2 4 6 8 

ζ 

Fig. 4. Self-consistent current density profiles in 2T CS with warm and cold populations of transient ions. 

The particle currents are marked by color lines (the corresponding legend is presented in figure. At the left 

figure the ratio of temperatures T1 / T 2 = 2 , at the right T1 / T 2 = 3 . 

Below we show the results of self-consistent modeling when we have taken into account the trapped warm 

plasma. We see that its role might be substantial in equilibrium current sheet. Fig.5 demonstrates that trapped 

particles carry the current opposite to one of transient ions (Zelenyi et al., 2000, 2002), although their total 

current is equal to zero. Therefore in the presence of trapped plasma the total current should be redistributed 

from the center to peripheries. At the left figure the trapped plasma decrease the current density in the very 

center and form characteristic three-maximum CS. At the right figure the density of trapped hot plasma is so 

abundant that three narrow peaks appear in current distribution. We see that taking into account 2T plasma 

populations and some variation (in realistic limits) of parameters of the system provides a variety of shapes 

of current density profiles that might be used for comparison with very different and variable experimental 

data in the Earth’s magnetotail. 

Comparison with experimental data. Current density profiles of thin current sheets, crossed by four 

Cluster spacecraft in the magnetotail are compared with the self-consistent model of anisotropic 1D 

equilibrium, including several species of quasi-adiabatic (transient) ions and drifting electrons (Artemiev et 

al., 2008). In order to examine ion-scale features of the current density profile Cluster data from the 2001 and 

0.8 

0.7 

0.6 

0.5 

0.4 

0.3 

0.2 

0.1 

0.0 

301 

Cold ions 

Hot ions 

Electrons 

Total

Jy 


0.6 

0.5 

0.4 

0.3 

0.2 

0.1 

0.0 

q^2=0.5 TauPar=5 Eps=1 

Bn=0.1 kTrap1=1 kTrap2=4 

n2/n1=3 vT2/vT1=2 vD2/vD1=1 

1 - cold ions, 2 - hot ions 

Cold ions 

Hot ions 

Electrons 

Total 

-0.1 

-10 -8 -6 -4 -2 0 

ζ 

2 4 6 8 10 

Jy 

ζ 

0.0 

-12 -8 -4 0 4 8 12 

Fig. 5. Current density profiles of equilibrium CS with two-temperature plasma with transient and trapped 

ions. Essential parameter values are the same as in the previous cases; the distribution of a cold trapped 

plasma is sewed with distribution function of transient ions. At the left figure the distribution function of a 

hot trapped plasma is added in the system with weight factor 4 to make the role of hot trapped ions more 

clear; at the right figure the weight factor is 8, i.e. there are many trapped warm ions in the system. 

2004 tail seasons were used when the spacecraft separation was about 2000 and 1000 km, respectively, while 

electron-scale features are studied using Cluster data from the 2003 season , when the spacecraft separation 

was about 200km. Two characteristic examples of our comparison are presented in Fig. 6 where current 

density profiles are plotted with respect to the spatial coordinate and local magnetic field. The optimal model 

to compare has parameters (current density, ion temperature, B ext , 0 B , Bz / B 0 ) which are different from 

experimental one no more than 30% . 

Fig. 6. Comparison of experimental (black) and model (blue) current density profiles versus coordinate along 

the normal and magnetic field component B l . The dates of cases are indicated at the top of figures. 

As one can see from Fig. 6 with comparison of the model and experimental CS profiles the model is capable 

to reproduce the shape and maximum value of current density, including both ion and electron contributions 

as well as embedding property. While the initial model (results shown in Fig. 3) with only one sort of 

transient ions produces relatively thin sheet (intense current), one can make a sheet thicker by adding trapped 

ions or ions with larger Larmor radius. Our investigation demonstrate that only one from 22 available thin 

CS crossings can be described using the 1T model. A variety of observed current sheets is quite thick 

therefore 2T CS model is better to describe them. 

Conclusions. Self-consistent equilibrium 2T model of a thin magnetotail current sheet is developed and 

investigated in detail. The comparison of the model results with experimental data demonstrates that the 

model of anisotropic CS can adequately describe the properties and structure of current sheets observed by 

302 

2.5 

2.0 

1.5 

1.0 

0.5 

-0.5 

Cold transient ions 

Hot trapped ions 

Electrons 

Total


Clusters in 2001-2004 years in the magnetotail. The model generally well describes non-Harris profiles and 

embedded maxima of current. The complicated profiles of current density and comparatively thick ones 

might be well approximated by anisotropic CS models with multicomponent plasma. 

Acknowledgments. This work was supported in part by the RF Presidential Program for State Support of 

Leading Scientific Schools (project no. NSh-472.2008.2), the RFBR grant number 08-02-00407, 06-05- 

90631, 06-02-72561 and Program P-13 of the Russian Academy Council on Nonlinear Dynamics. 

References. 

Alexeev I. I., Malova H. V. (1995), On the model of current sheet in the magnetosphere tail, taking into 

account the interaction of transit and traped particles., Advances in Space Research, 16, 205-208. 

A. V. Artemyev, A. A. Petrukovich, L. M. Zelenyi, H. V. Malova, V. Y. Popov, R. Nakamura, A. Runov, 

and S. Apatenkov (2008), Comparison of multi-point measurements of current sheet structure and analytical 

models, Ann. Geophys., 26, 2749–2758. 

Asano Y., Nakamura R., Baumjohann W., Runov A., Vörös Z., Volwerk M., Zhang T. L., Balogh A., 

Klecker B., Rème H. (2005), How typical are atypical current sheets?, Geophys. Res. Lett., 32 (3), CiteID 

L03108, doi:10.1029/2004GL021834. 

Ashour-Abdalla M., Frank L. A., Paterson W. R., Peroomian V. , Zelenyi L. M. (1996), Proton velocity 

distributions in the magnetotail: theory and observations, J. Geophys. Res., 101 , 2587. 

Delcourt D.C., J.-A.Sauvaud, R.F. Martin Jr., and T.E.Moore (1996), On the nonadiabatic precipitation of 

ions from the near-Earth plasma sheet, J.Geophys. Res., 101, 17409-17418. 

Eastwood, J. W. (1972), Consistency of fields and particle motion in the 'Speiser' model of the current sheet, 

Planet. Space Sci., 20, 1555-1568. 

Harris E. G. (1962), On a Plasma sheath separating regions of oppositely directed magnetic fields, Nuovo 

Chimento, 23, 115-119. 

Kan, J.R. (1973), On the Structure of the Magnetotail Current Sheet, J. Geophys. Res., 78, 3773. 

Kaufmann R.L., I.D. Kontodinas, B.M. Ball, and D.J. Larson (1997), Nonguiding center motion and 

substorm effects in the magnetotail, J. Geophys. Res., 102, 22155-22168. 

Runov, A.; Sergeev, V. A.; Nakamura, R.; Baumjohann, W.; Apatenkov, S.; Asano, Y.; Takada, T.; 

Volwerk, M.; Vörös, Z.; Zhang, T. L.; Sauvaud, J.-A.; Rème, H.; Balogh, A. (2006), Local structure of the 

magnetotail current sheet: 2001 Cluster observations, Annales Geophysicae, 24 (1), 247-262. 

Sergeev V. A., Mitchell D. G., Russell C. T., Williams D. J. (1993), Structure of the tail plasma/current 

sheet at 11 Re and its changes in the course of a substorm, J. Geophys. Res., 98, 17345-17365. 

Sergeev V., Runov A., Baumjohann W., Nakamura R., Zhang T. L., Volwerk M., Balogh A., Rème H., 

Sauvaud J. A., André M., Klecker B. (2003), Current sheet flapping motion and structure observed by 

Cluster, Geophys.Res.Lett., 30 (6), 1327, doi:10.1029/2002GL016500. 

Schindler K. (1974), A theory of the substorm mechanism, J. Geophys. Res., 79, 2803-2810. 

Speiser T. W. (1965), Particle trajectories in model current sheets; 1. Analytical solutions, J. Geophys. Res., 

70, 4219-4226. 

Vaisberg O. L., Burch J. L., Russell C. T., Skalsky A. A., Dempsey D. L. (1998), Observation of isolated 

structures of the low latitude boundary layer with the INTERBALL/Tail Probe, Geophysical Research 

Letters, 25 (23), 4305-4308. 

Zelenyi L.M., M.I. Sitnov, H.V. Malova, and A.S. Sharma (2000), Thin and Superthin Ion Current Sheets, 

Quasiadiabatic and Nonadiabatic Models, Nonlinear processes in Geophysics, 7, 127-139. 

Zelenyi L.M., D.C. Delcourt, H.V. Malova, A.S. Sharma (2002), “Aging” of the magnetotail thin current 

sheets, Geophys. Res. Lett., 29, 10.1029/2001GL013789, 49-1 – 49-4. 

Zelenyi L. M., H. V. Malova, V. Yu. Popov, D. C. Delcourt, A. S. Sharma (2003), Evolution of ion 

distribution function during the “aging” process of thin current sheets, Advances in Space Research, 31 (5), 

1207-1214. 

Zelenyi L. M., Malova H. V., Popov V. Yu., Delcourt D., Sharma A.S. (2004), Nonlinear equilibrium 

structure of thin currents sheets: influence of electron pressure anisotropy, Nonlin. Proc. Geophys., 11(5/6), 

579-587. 

Zelenyi L. M., Malova H. V., Popov V. Y., Delcourt D. C., Ganushkina N. Y., Sharma A. S. (2006), 

‘‘Matreshka’’ model of multilayered current sheet, Geophys. Res. Lett., 33, L05105, 

doi:10.1029/2005GL025117. 

303


MODEL INTERPRETATION OF THE UNUSUAL F-REGION NIGHT-TIME 

ELECTRON DENSITY BEHAVIOUR OBSERVED BY THE MILLSTONE 

HILL INCOHERENT SCATTER RADAR ON APRIL 16-17, 2002 

Yu.V.Zubova 1 , A.A.Namgaladze 1 , L.P.Goncharenko 2 

1Murmansk State Technical University, Murmansk,183010, Russia, e-mail: y-zubova@yandex.ru; 

2 Massachusetts Institute of Technology, Haystack Observatory, Westford, MA, USA 

Abstract. The numerical experiments with the global numerical Upper Atmosphere Model (UAM) 

have showed that the mechanism of the unusual night-time F-layer electron density enhancement 

over Millstone Hill was related to the zonal plasma drift caused by the convection electric field. The 

electric field values observed during the night hours of April 16 and 17, 2002 in Millstone Hill 

corresponded to the “anomalous” convection pattern with the converging zonal plasma flow, which 

succeeded to increase the night-time F2 electron density. Such convection pattern could occur when 

the FAC2 had intensified and extended to the middle latitudes. The UAM has produced the 

“classical” convection pattern with diverging zonal plasma flow, which decreased the electron 

density over Millstone Hill during that period. This explains the fact that the model F2-layer electron 

density strongly underestimated the measurements performed by the Millstone Hill radar during the 

night hours of April 16-17. 

Introduction 

We have investigated the F2-layer behaviour during the April 2002 magnetic storms using the global 

numerical Upper Atmosphere Model [Namgaladze et al., 1998]. The behaviour of electron density (Ne), ion 

temperature (Ti), electron temperature (Te) during April 15-20, 2002 has been modeled by two versions of 

the UAM. The version UAM(TM) solved the continuity and heat balance equations in order to obtain 

neutral composition and temperature, the version UAM(MSISE) calculated the thermospheric composition 

and temperature using the empirical model NRLMSISE-00 [Picone et al., 2002]. The calculated ionospheric 

parameters have been compared with the data of seven incoherent scatter radars (ISR) [Goncharenko et al., 

2005] and the IRI-2001 [Bilitza et al., 2004] results. The worst agreement between the UAM results and the 

observation data took place for the night hours on April 16 and 17, 2002 over Millstone Hill when the 

numerical model strongly underestimated the ISR electron density (see Figure 1). The empirical model IRI 

also underestimated the night-time F2-layer electron density, so the F2-layer behaviour observed over 

Millstone Hill during that period can be described as “unusual”. 

Figure 1. Time variations of the electron density over Millstone Hill calculated by the UAM(TM) and 

UAM(MSISE) for April 15-17, 2002 in comparison with the observation data. 

304


The Millstone Hill observatory (43°N) is situated in the middle geographic latitudes. The mid-latitude 

ionosphere behaviour depends mainly on the neutral composition (n(O)/n(N2)) and the thermospheric winds. 

However the magnetic latitude of the station is subauroral (54.4° mag.lat.). So the electric field variations 

and hence the ion drift velocities play also a great role in the ionospheric behaviour over the observatory. 

Recent results 

The reason of the poor agreement of the model results with the measurements during the night and morning 

hours of April 16 and 17, 2002 in Millstone Hill was not related to the neutral composition calculation in the 

UAM [Namgaladze et al., 2005]. 

Zubova et al., 2007 described the results of the model experiments, in which the neutral wind velocities were 

calculated using the empirical model HWM-93 [Hedin et al., 1996]. The comparisons with the observation 

data obtained by seven incoherent scatter radars showed that using of the HWM-93 winds did not improve 

the agreement between the model results and measurements, only several details of the F2-layer behaviour 

may be attributed to the influence of the winds calculated in the UAM. The Figure 2 shows that using the 

HWM thermospheric winds improved the agreement of the UAM results with the Ne values observed in 

Millstone Hill, but only partially. 

Figure 2. Time variations of the electron density over Millstone Hill calculated by the UAM(TM) and 

UAM(TM-HWM) for April 15-17, 2002 in comparison with the observation data. 

Model calculations 

The UAM calculates the electric field as the electric potential gradient. The electric potential is calculated in 

the UAM by solving the Poisson equation. The potential drop across the polar cap describing voltage 

supplied from the solar wind is used as a boundary condition of the equation. In the version UAM(TM) the 

potential drop is set according to the DMSP satellite data approximations. 

We have performed the numerical experiments in order to estimate the electric field influence on the F2layer 

behaviour in Millstone Hill. 

We calculated the ionospheric parameters (Ne, Ti and Te) and the electric field values for April 15-17, 2002 

using two versions of the UAM with the theoretical neutral composition and temperature: 

− with the potential drop across the polar cap taken from the DMSP satellite data (used in the previous 

calculations) – marked as UAM(DMSP); 

− with the constant potential drop equal to 10 kV - marked as UAM(10 kV). 

We have compared the model results with the measurement data (see Figure 3 and Figure 4). 

305


Figure 3. Time variations of the northward electric field over Millstone Hill calculated by the UAM(DMSP) 

and UAM(10 kV) for April 15-17, 2002 in comparison with the observation data. 

Figure 4. Time variations of the electron density over Millstone Hill calculated by the UAM(DMSP) and 

UAM(10 kV) for April 15-17, 2002 in comparison with the observation data. 

Another numerical experiment was related to changing the field-aligned currents (FAC) position. The 

ionospheric parameters and the electric field were calculated using two versions of the UAM with the 

theoretical neutral composition and temperature: 

− with the FAC1 at 75° mag.lat., the FAC2 at 70° mag.lat.; 

− with the FAC1 at 80° mag.lat., the FAC2 at 75° mag.lat. 

In the base version UAM(TM) the FAC1 were set at the polar boundary and the FAC2 - at the equatorial 

boundary of the auroral oval. The boundaries of the auroral oval were taken from the DMSP satellite data 

approximations and amounted on average 73° (the polar boundary) and 66° (the equatorial boundary) for the 

modeled period. 

The results of the calculations are presented in Figure 5 and Figure 6. 

Figure 5. Time variations of the northward electric field over Millstone Hill calculated by the UAM with 

various FACs positions for April 16-17, 2002 in comparison with the observation data. 

306

Figure 6. Time variations of the electron density over Millstone Hill calculated by the UAM with various 

FAC positions for April 16-17, 2002 in comparison with the observation data. 

Discussion 

In Figure 3 we can see that the UAM(TM) northward electric field was opposite to the observed values 

during the most part of the modeled period. The Millstone Hill measurements demonstrate the northward 

electric field component increasing from April 15 to 16 and during the night hours of April 17 while this 

component is decreasing to negative values in the UAM results. It means that during the first hours of April 

16 and 17, 2002 the real electric field over Millstone Hill caused the ion drift to change its direction from 

eastward to westward. But the northward electric field calculated by the UAM(TM) changed the ion drift 

direction from westward to eastward (see Figure 7). The UAM version with Δϕ = 10 kV gives lower ion drift 

velocities and hence produces a slower plasma flow. Figure 3 shows that the UAM version with Δϕ = 10 kV 

has a better agreement with the ISR data because of a less Ne decrease during the night hours of April 16 and 

17, 2002. 

Magnetic latitude, grad. 


Plasma drift velocity, m/s 

05 UT of April 16, 2002 06 UT of April 16, 2002 

Magnetic longitude, grad. 

Magnetic longitude, grad. 

Figure 7. Time variation of the plasma drift velocity at the magnetic latitudes 50°-60° at 05 UT (left) and 06 

UT (right) of April 16, 2002 calculated by the UAM(TM) 

So, at night on April 16 and 17 over Millstone Hill the real electric field corresponded to the “anomalous” 

convection pattern with the converging zonal plasma flow, which succeeded to support the night-time F2 

electron density. The UAM produced the “classical” convection pattern with diverging zonal plasma flow, 

which decreased the electron density over Millstone Hill during this period. The “anomalous” convection 

pattern could be caused by the FAC2 moving to higher latitudes. 

As we can see in Figure 5, the northward electric field values calculated with setting the FAC1 at 80° 

mag.lat., the FAC2 at 75° mag.lat. had the time variations very similar to the observed variations. The Figure 

6 shows that setting the FACs at higher magnetic latitudes than in the base version UAM(TM) improved the 

agreement between the model results and the electron density observed during the night hours of April 16 

and 17, 2002. The best agreement with the ISR electron density belongs to the version with the FACs at 

magnetic latitudes 80°-75°. 

307 

Magnetic latitude, grad.


Conclusion 

The numerical experiments have showed that the reason of the poor model-measurement agreement was the 

difference in the electric field variations over Millstone Hill calculated by the UAM and observed by ISR 

and thus the difference of the plasma drift velocities. At the night hours of April 16 and 17, 2002 the fieldaligned 

currents of the second zone moved to higher latitudes and acted so that the real electric field over 

Millstone Hill caused the converging zonal plasma flow. The electric field calculated by the UAM for the 

same time period agreed with the classic convection pattern with diverging zonal plasma flow decreasing 

electron density. 

Acknowledgments. This work was supported by the Grant No. 05-05-97511 and by the Grant No. 08-05- 

98830 of Russian Foundation for Basic Research. Millstone Hill radar observations and analysis are 

supported by a NSF cooperative agreement with the Massachusetts Institute of Technology and NASA grant 

NAG5-13602. The Kharkov incoherent scatter radar is supported by the Ministry of Education of Ukraine. 

The Irkutsk incoherent scatter radar is supported by the state grant (NSh-272.2003.5) for Leading Scientific 

Schools of the Russian Federation and Russian Foundation for Basic Research (grant 03-05-64627). 

References 

Bilitza, D., K. Rawer, and B. Reinisch (2004), Path Toward Improved Ionosphere Specification and Forecast 

Models. Advances in Space Research, V. 33, N. 6. 

Goncharenko L., J. E. Salah, A. Van Eyken, V. Howells, J. P. Thayer, V. I. Taran, B. Shpynev, Q. Zhou, and 

J. Chau (2005). Observations of the April 2002 geomagnetic storm by the global network of incoherent 

scatter radars. Ann. Geophys., 23, 163-181. 

Hedin A.E., E.L. Fleming, A.H. Manson, F.J. Scmidlin, S.K. Avery, R.R. Clark, S.J. Franke, G.J. Fraser, T. 

Tsunda, F. Vial, and R.A. Vincent (1996), Emperical Wind Model for the Upper, Middle, and Lower 

Atmosphere. J. Atmos. Terr. Phys., 58, 1421-1447. 

Namgaladze A.A., O.V.Martynenko, M.A.Volkov, A.N.Namgaladze, and R.Yu.Yurik (1998), High-latitude 

version of the global numerical model of the Earth’s upper atmosphere. Proceedings of the MSTU, V.1, 

N.2, 23-84. 

Namgaladze A.A., Yu.V. Zubova, A.N. Namgaladze, O.V. Martynenko, E.N. Doronina, L.P.Goncharenko et 

al. (2005), Modelling of the ionosphere/thermosphere behaviour during the April 2002 magnetic storms: A 

comparison of the UAM results with the ISR and NRLMSISE-00 data. Advances in Space Research: 

doi:10.1016/j.asr. 2005.04.013. 

Picone, J. M., A. E. Hedin, D. P. Drob, and A. C. Aikin (2002), NRLMSISE-00 empirical model of the 

atmosphere: Statistical comparisons and scientific issues, J. Geophys. Res., 107, 1468, 

doi:10.1029/2002JA009430. 

Zubova Yu.V., A.A. Namgaladze, and L.P. Goncharenko (2008), A model study of the wind influence on 

the ionospheric F2-layer behaviour during the April 2002 magnetic storms. Proceedings of the XXX 

Annual Apatity Seminar “Physics of Auroral Phenomena”, p.202-204. 

308


DEEP STUCTURE OF THE KARELIAN PART OF THE FENNOSKANDIAN 

SHIELD (SEISMOLOGICAL AND GEOELECTRICAL RESEARCH) 

M. V. Cherevatova 

Institute of Physics, St. Petersburg University, St. Petersburg, 198504, Russia, 

e-mail: Maria.Cherevatova@gmail.com 

Abstact. In the paper we give a review and analysis of the geologic, deep seismologic and 

geoelectric research at the eastern (Russian) part of the Fennoskandian Shield for the past 10 years. 

Due to the absence of a sedimentary cover, the Fennoskandian Shield represents a natural proving 

ground for geophysical research. We have analyzed results of the deep lithosphere studies to 

define which areas demand more careful data consideration, using newly developed approaches. 

Geoelectrical methods revealed the presence of two conducting layers: the first one is the crust 

layer, at the depth of 10-15 km, and the other is the under-crust one, at the depth of 40-160km, 

which is observed almost throughout at the eastern part of the Fennoskandian Shield. Nowadays, 

the nature of the crust conducting layer usually connects with astenosphere. Furthermore, the 

seismic research has been examined too, aimed at investigating the deep structure of the 

Fennoskandian (Baltic) Shield construction. Joint interpretation of the seismic and geoelectric data 

reveals that their results do not contradict to each other, and supplement more likely. 

Bases on the observed results in geologic and geophysics we are planning to reanalyze 

magnetotelluric data using 2D approach, to invert some invariants of impedance tensor data using 

REBOCC by Siripunvaraporn&Egbert and also 3D inversion based on SVD method (St.Petersburg 

State University). 

The eastern part of the Fennoskandian Shield, which incorporates the Murmansk Oblast and Karelia, 

has been studied both geologically and geophysically. Due to the fact that there is no sedimentary cover, it 

can be used as natural proving grounds to update old concepts, to develop new models in order to fill the 

gaps in our deep structure knowledge of the continental crust and old-crust forming processes. The structure 

of the earth crust and upper mantle was found to be highly heterogeneous both vertically and laterally. 

The greatest contribution to the understanding of the lithosphere is made by geophysical studies. 

Seismic methods, such as deep seismic sounding (DSS), increase our knowledge of the composition of deep 

lithospheric horizons, and heterogeneities like faults, intrusions, and low velocity layers. In the past few 

years the Fennoskandian Shield has been studied using the common deep point (CDP) method to obtain 

images of seismic heterogeneities that seem to be in better agreement with geological observations. The 

Magnetotelluric and Magnetovariational methods in geoelectric allow penetrating to the deepest horizons of 

the crust and the upper mantle. We managed to get the electro conductivity distribution in the large intervals 

−3 4 

of the periods ( 10 −10 sec.). Joint interpretation of the seismic and geoelectric data reveals that their 

results do not contradict to each other, and supplement more likely. 

The Fennoskandian Shield is an outcrop of Pre-Cambrian basement in a northwest part of East- 

European platform. It is consisted of Archaean and low Proterozoic rocks (gneisses, crystal slates, etc.) and it 

covers almost all territory of Scandinavia, Karelia, Kola Peninsula. This region is precisely divided into 

three geological structural areas. The northern part is Kola Peninsula. The central part of considered territory 

is the large site of the earth crust which is named Karelian Craton unchanged rather steadily during all Pre- 

Cambrian histories. From the northeast it is adjoined with Belomorian Folded belt, and from the southwest 

there is an extensive Svekofennian folded area. 

Karelian Craton has a two-storeyed structure (fig.1) [13]. The low structural floor is granitegreenstone 

basement. It consists of gneisses tonalities, granite diorites and diorites. The greenstone belts are 

pressed in them in the form of narrow and lengthy lines (width less then 10 km and extensions more then 200 

km). The greenstone belts are formed by the sedimentary-volcanic rocks of the late Achaean. The top 

structural floor consists of sedimentary-volcanic rocks of the early Proterozoic, which lies at the rocks with 

the structural variance. Along the western coast of the White Sea stretches a narrow 50-150 km zone of the 

amphibolites, different gneisses and migmatites – Belomorian Folded belt. It differs sharply from the rest of 

the Fennoskandian Shield and represents the most ancient collision structure in Europe. Belomorian Folded 

309


Belt is formed by Achaean sedimentary-volcanic rocks, undergoing the repeated folding, metamorphism and 

migmatism at the large depths. The extensive Fennoskandian folded area occupies a small part of the Russian 

territory. But the greatest advantage of this fact is that this is a region of a joining with Karelian Craton. The 

Ladoga zone of the Svekofennian Folded area is formed of the early Proterozoic rocks, the Achaean Granit 

gneisses were saved in the contact zone with Karelian Craton. 

fig. 1 Geological sketch map of the Karelian region 

Made by Y. Systra using the bedrock maps of Finland [Korsman et al., 1997] and the Fennoscandian Shield [Koistinen et al., 2001]. 

Post-Svecofennian bedrocks: 1 — Vendian-Paleozoic sedimentary of the Svecofennian Orogeny: 6 — alkaline diorites and platform 

cover; 2 — Ladoga aulacogene; 3 — rapakivi granites; 4 — Vepsian dolerite sills; 5 — Vepsian sedimentary rocks. Rocks of the 

Svekofennian Orogeny:6 – alkaline diorites and gabbro;7- granites; 8 — gabbro; 9 — diorites; 10 — Kalevian volcanic-sedimentary 

rocks; 11 — 1.98—1.95 Ga ultramafic rocks; 12 –Ludicovian and Jatulian sedimentary and volcanic rocks. Sumian and Sariolian 

(2.5—2.3 Ga) bedrocks: 13 — komatiitic basalts in the Windy (Vetreny) Belt; 14 — layered peridotite-gabbronorite massives of the 

Karelian Craton and complex Iherzolites-gabbronorites in the Belomorian Folded Belt; 15 — palingenetic and other granites near 

layered massifs; 16 — sedimentary-volcanic rocks. Late Archean (Lopian) 2.65—3.0 Ga rocks: 17 — granites; 18 — diorites; 19 — 

gabbro; 20 — sedimentary-volcanic rocks in greenstone belts; 21 — Belomorian Folded Belt, undivided. The oldest rocks in the 

Karelian region: 22 — basement granitic gneisses in the Karelian Craton; 23 — relics of the oldest sedimentary and volcanic 

sequences; 24 — thrust zones 

310


The deep structure of the Russian part of the Fennoskandian Shield has been studied by the seismic 

and seismologic methods using the special and industrial explosions, registration of the distance and near 

earthquakes, vibraseismic sources and pneumosignals. This territory has been studied by 32 regional profiles 

with total extension 10500km and still the most studied by the seismologic methods. Since 1995 the most 

important project aimed to the deep structure studying of the crust and upper mantle using the common deep 

point modification method (CDPM) has been realized in the East – European platform [11]. We have 

decided to consider only to seismic profiles, 1-EU transect and 4B profile. The 4B profile crossed the 

considerable part of the Karelian Craton and its boundary with Belomorian area. The 1-EU transect traversed 

all over territory of the Karelia from the north-west to the south-east [1]. We did not consider the technique 

and peculiar properties of the experiments. Here are the main research results at these profiles: 

• Geological interpretation of the data received as a result of seismological researches along 1-EU 

transect and profile 4B, crossing Karelian granite-greenstone complex, Belomorian belt, a number of 

Paleoproterozoic sedimentary-volcanic belts and Svecofennian accretion orogeny structure, testify 

that the early Pre-Cambrian crust is characterized by inclined structural stratification. 

• Formation of inclined-lying structural ensembles occurred both in Paleozoic, and in Neoarchaean. 

• Paleoproterozoic East-Karelian sedimentary-volcanic belt is formed by a system of monoclinal 

dipping tectonic plates. 

• Detailed figure of structural lines in the low crust testifies to the tectonic nature of Moho border 

which, apparently, represents a powerful zone of tectonic current and moving of large plates of the 

crust, accompanied immersion of separate fragments of the low crust to the mantle. 

• Accommodation slightly-inclined borders on a day surface are defined by a level of an erosive 

section and cannot be accepted as the borders any “tectonic blocks” in traditional understanding. 

Nowadays, the most of the geological objects of this region are covered by the deep geoelectrical 

research. The deep sounding has been carried out by the magnetotelluric and magnetovariational methods, in 

general [6]. Throughout 20 years the staff of SPbGU continues the magnetotelluric research in the limited 

interval of periods in the eastern part of the Fennoskandian Shield, for the purpose of studying the 

construction of crust and upper mantle of this region. The research points are situated along the profiles 

Teriberka-Kovdor-Suoyarvy, Suoyarvi-Vyborg (LADOGA), SVEKA. The eastern part of the Shield 

consists of the fifty blocks (third order), separated by the faults, which has the different geological structure. 

One picks out the four mega blocks – Kola, Belomorian (southern and northern), Karelian (western, central 

and eastern) and Svekofennian [7]. 

The profile Teriberka – Kovdor – Suoyarvy – Vyborg was studied using the MT and AMT methods. 

Even point of this profile was characterized by the four components of the impedance tensor. It gives the 

complete information about the geoelectrical structure but extraction of this information is very difficult 

problem, especially if to take into account the blocked structure of the region [10]. The LADOGA and 

SVEKA profiles has a compact net of the observations, in practice it allows getting the electro conductivity 

distribution up to the 300 – 400 km [8]. Furthermore, the soundings in the external interval of periods have 

been realized in the profile SVEKA. It is crosses the western and central Karelian and southern Belomorian 

megablocks just as junction zone between the Karelian and Belomorian megablocks. The great interest to the 

LADOGA profile is connected with the fact that this profile crosses Ladoga – Bothnic zone (LBZ) of the 

faults, which is situated in the Karelian and Svekofennian megablocks zone of a joint. The area of the LBZ 

there is the largest anomaly of the electro conductivity in the north-west of the East – European platform. 

This anomaly was revealed by the MVS and tested by the MTS. The MTS allows studying the structure of 

the upper mantle. But there are some problems, caused the large depth. Than more depth there is worse data 

over the 3D environment influence. Thanks to the international experiment BEAR the opportunity to reach 

the great depth is realized. Now we able to use both module and phase of the impedance. In contrast to the 

amplitude curves the phases curves do not shift over the 3D and 2D effects and can be used for getting of the 

conductivity distribution at the great depths [9]. 

• Geoelectrical interpretation of the data received as a result of research along profile Teriberka - 

Kovdor – Suoyarvi crossing Kola, Belomorian and Karelian megablocks, revealed the presence of 

two conducting zones, at the depth 10-15 km where specific resistance reaches a minimum from 70 

up to 2000 Ohm⋅ m , and 40-160 km, with specific resistance from 40 up to 400 Ohm⋅ m . 

• The data received during international project SVEKALAPKO, along structure SVEKA-2 crossing a 

zone of a joint Karelian and Belomorian megablocks, have specified the presence of extensive area 

of the faults separating the West-Karelian block from Central-Karelian. Tectonic activity has led to 

311


the extensive area occurrence of the lowered resistance up to depth more 50 km in the field of a joint 

Central-Karelian and Belomorian megablocks. 

• Magnetotelluric sounding along structure Suoyarvi - Vyborg (LADOGA), crossing East-Karelian 

and Svekofennian megablocks, allow revealing distinctions of this geoblocks: on the Karelian block 

increase electro conductivity at the depth 40-160 km, connected with astenosphere. On Svekofennian 

geoblock resistance goes down smoothly and conducting layers distinctly are not allocated, that 

allows speaking, that on this block astenosphere distinctly does not come to light. 

• Geoelectrical research by method MTS in the top mantle have allowed construction of two types 

sections of the top mantle. The first type resistance distribution of the crust is widely spread on the 

Kola geoblock and north Belomorian geoblock. Distribution of resistance to the Central-Karelian 

block in the further has formed a basis for introduction of concept "normal" resistance distribution in 

the mantle. The basic geoelectrical characteristics of the received "normal" section is the following: 

resistance within the limits of 10 km grows, reaching maximal size in hundred thousands of Ohm ⋅ m 

on 4-8 km, then it decreases up to a minimum on depth 15 km, equal 1500-2000 Ohm ⋅ m (the width 

of a minimum does not exceed 15 km), further resistance slightly increases, and the second reduction 

of resistance begins with depths 70-100 km (on these depths resistance reaches 400-500 Ohm ⋅ m ), 

from depth 100 km there is qualitatively new, fast growth of total conductivity of the section. 

• Owing to international experiment BEAR one more opportunity of research resistance distribution 

on the low depths has been realized, using not only "longitudinal" values of impedance, but also a 

phase of impedance. Interpretation of phase curves has shown presence of a small minimum on a 

curve in an interval of depths 200-350 km on a background of the general decrease of resistance 

from depth 100 km. Longitudinal conductivity of a layer on depths 200-350 km which can be 

connected with existence of area of the lowered resistance, makes nearby 3000-4000 Sm, and 

average resistance on these depths does not exceed 10-30 Ohm ⋅ m . 

As it has been said above, joint interpretation of the seismic and geoelectric data reveals that their results 

do not contradict to each other, and supplement more likely. We have tried to compare results both of 

them and have received the following: 

• The seismic data along the transect 1-EU points out a presence of a tectonic plate in northern and 

central parts in the low crust of profile. It is possible to compare confidently to the crust plate which 

is formed by the rocks of the West-Karelian granite-greenstone complex. The given statement will 

be coordinated with results of geoelectric research along Teriberka-Kovdor-Suoyarvi-Vyborg 

profile, where it is found out a conductive layer at the depth 40 – 60 km in the north and 90 – 160 in 

the center of the profile. Longitudinal conductivity reaches several hundreds Sm. Such correlation 

between depth deposition and longitudinal conductivity is typically for S – effect. 

• The great interest is represented with zones of a joint such megablocks as Karelian and Belomorian. 

Seismic data along the profile 4B allows allocating an inclined plate which separates Belomorian 

province from Karelian Craton. It includes a series structurally - homogeneous domains. Data of 

SVEKA profile also find out more than 50 km zone of a joint of the plates, showing the different 

periods of tectonic activity which has led to occurrence of extensive area of the lowered resistance 

up to depth more than 50 km. Most likely anomaly carries 3D character besides it is not shown in 

any way in cross-section polarization of a field that speaks about more complex, scaly structure 

when the conductive body is broken by non - conductive objects into small objects. 

• Seismic profile the Zelenaya Roshcha – Kurkieki – Lahdenpohja – Sortavala crosses key structure of 

southern slope of the Baltic Shield - the Ladoga anomaly. The seismology data specifies a presence 

of Priozersk and Ruskealsk junction which is falling towards to each other under corners 60 – 40 

degree. It is having the obvious tendency to a joint in the top mantle at the depths 100 - 120 km. 

According to the geoelectric research the North-Ladoga block is shown in the form of the inclined 

prism shifted to the north with the increased conductivity. Except for that the geoelectric and seismic 

data along Northern part of Ladoga Lake unequivocally enough allocate geoblocks of the third 

orders and interblocks junctions. 

312


Despite of the many research at the Fennockandian Shield as geological as geophysical, there is 

lots of questions which is not answered yet. This brief review allows understand which regions and 

questions require more careful attention. The question of astenosphere under the Fennoskandian Shield is 

still opened. There are too many unexplored opportunities for an explanation of the received distribution 

of resistance in mantle at the depth of 200-350 km. An area of a joint of two plates, Svekofennian and 

Karelian where is the complex zone of increased electro conductivity, provokes interest. As well as zone 

of a joint Karelian and Belomorian megablocks represents the big interest from the point of view of 

studying tectonic development of the Baltic Shield. The structure of this area causes many discussions to 

this day. Results of seismological research allow defining more precisely geometrical position of layers 

and inclusions, and the geoelectric data give distribution of conductivity. For the preliminary analysis 

the area of joint Belomorian and Karelian megablocks has been chosen. With using of BEAR and the 

St.Petersburg State University data have been constructed pseudo sections of a phase and the module of 

effective impedance, and also skew. 

References 

1. Berzin R.G., Andruschenko Yu.N., Zamojnyaya N.G., Mintz M.V., etc. The combined seismic 

research in the Karelian region, //Deep structure and seismicity of the Karelian region// 

Petrozavodsk, 2004, p. 35-37, (in Russian) 

2. Miller Yu.V. The tectonic of the Belomorian Belt and Karelian Craton joint area. Geotectonica, 2002, 

№ 4, p.14-24, (in Russian) 

3. Mintz Yu.V. Deep structure of the Karelian Craton, transect 1-EU. Geotectonica,2004, № 2, p.10-29, 

(in Russian) 

4. Klabukov B. N. Background and anomaly electro conductivity of the Karelian crust. Fizica Zemli, 

1996, № 4, (in Russian) 

5. Kosminskaia I.P., Sharov N.V., Zverev S.M. The crust and upper mantle studying of the Baltic 

Shield. DAN, 1987, №5, p.64-71, (in Russian) 

6. Kovtun A. A. Application of the natural electromagnetic field in the electroconductivity studing of 

the Earth. L.:, 195 p., 1980, (in Russian) 

7. Kovtun A. A., Vagin S. A., Vardaniants B. L. Magnetotelluric research of the crust and upper mantle 

in the eastern part of the Fennoskandian Shield. Fizika Zemli, St. Petersburg, 1994, № 3, p. 111-116, 

(in Russian) 

8. Kovtun A. A., Vagin S. A., Vardaniants B. L. Structure of the crust and upper mantle by the profile 

Suoyarvi – Vyborg using MT data. Vestnic SPBGU. Vol. 4, 1998, № 4, p. 25-33, (in Russian) 

9. Kovtun A.A., Vagin S.A., Vardaniants I.L., Legen’kova N. P., Smirnov M.Yu., Uspenskiy N.I. and the 

BEAR working group. Analysis of magnetotelluric and magnetovariational results in daily variations 

range from BEAR data and the construction of the normal section of the Baltic Shield, Fizika Zemli, 

St.Petersburg, 2002, №11, p.34-53, (in Russian) 

10. Kovtun A. A., Vagin S. A., Vardaniants B. L., Legen’kova N. P., Smirnov M. Yu., Uspenskiy N. I. The 

pecularities of the Karelian region by the geoelectrical data. .//Deep structure and seismicity of the 

Karelian region// Petrozavodsk, 2004, p. 102 – 123, (in Russian) 

11. Sharov N.V., A brief review of the history and results of the regional research.// Deep structure and 

seismicity of the Karelian region// Petrozavodsk, 2004, p.30-35, (in Russian) 

12. Sharov N.V., Berzin R. G., Andruschenko Yu. N., etc. Lithosphere structure by the seismic research. 

Petrozavodsk, 2004, p. 30 – 60, (in Russian) 

13. Systra Yu. Yi. The main features of the geological structure of the Karelian region.//Deep structure 

and seismicity of the Karelian region// Petrozavodsk, 2004, p. 14 – 28, (in Russian) 

14. Systra Yu. Yi. Tectonic of the Karelian region. Nauka, St.Petersburg, 1996, 176 p. (in Russian) 

313


MANTLE ELECTROCONDUCTIVITY OF THE FENNOSCANDIAN 

SHIELD BY THE RESULTS OF COMBINED INTERPRETATION 

OF DEEP MTS AND GLOBAL MVS DATA 

A.A. Kovtun, I.L.Vardaniants 

Institute of Physics, St.Petersburg University, St.Petersburg, 198504, Russia, e-mail: 

akovtun@geo.phys.spbu.ru 

Abstract. The deep distribution of the mantle electroconductivity of the Fennoscandian Shield 

has been studied on the base of analysis of the international experiment BEAR data. For the 

analysis there where taken “longitudinal” curves and maximal impedance phase curves which give 

good agreement with the global MVS curve. 

It was shown that till the depth 100 km “longitudinal” and phase curves give different 

distributions but at the depths lower then 100 km these distributions practically coincide which 

makes it possible to build the common mean curve of the deep mantle conductivity distribution for 

all Fennoscandian Shield with exception of the regions with the anomalous mantle conductivity 

located in the northern part of the Bothnia Gulf and on the Belomorskiy block. 

The gradient of the electroconductivity has noticeable peculiarities only within the first 100-200 

km of the mantle. Within the 200-600 km interval it does not noticeably change and increases 

again after 700 km depth. At the depth 1000 km the maximum of the conductivity can be seen. 

In order to rise the reliability of these results there is necessary to raise the quality of the 

MVS and MTS data within the interval of daily variations. 

For the analysis there were taken experiment BEAR data obtained in 45 sites of the Fennoscandian 

Shield within the period range from 10 s till 24 hours. Location of the sites is shown on the fig.1. On the 

figure there are shown also the main tectonic boundaries: between the Svecofennian geoblock at the South- 

West and the Karelian geoblock at the North-East, between the White Sea geoblock at the East and the 

Karelian geoblock and between the Caledonides at the West and the Svecofennian geoblock at the East. 

10 o 

60 o 

65 o 

10 o 

05 

02 

10 

09 

11 

08 

15 

16 

12 

20 o 

20 o 

22 

17 

19 

18 

31 

30 

29 

28 

27 

25 

24 

34 

32 

100 km 

38 

37 

Fig1. Location of BEAR sites; blue squares – sites where there were taken phase curves, red diamonds 

– longitudinal" curves; dashed lines – boundaries of geoblocks. 

314 

41 

30 o 

39 

36 

42 

40 

30 o 

50 

46 

40 o 

65 o 

60 o 

40 o


The main purpose of the analysis was studying the structure of mantle and transitional region within the 

depth interval 100-700 km. 

We used approach based on the interpretation of the “longitudinal” curves adjoining at large periods 

the global magnetovariational sounding (GMVS) curve. These curves bring the information less distorted by 

the influence of the upper part of the section on the deep structure. As a rule in quasi 2D case it is the 

maximal or the minimal curve. In general case the analogues of these curves are curves corresponding to 

Eggers’ invariants (Eggers, 1982). Analysis of the behaviour of these curves shows that even in typical 3D 

cases one of the Eggers’ invariants curves gives good accordance with the GMVS curve. As GMVS data 

there was taken the set close to the set which we used earlier (Rotanova et al., 1993). We declined other 

GMVS data variants as, for example, curves supplemented by satellite data (Oraevskiy, 1986) and data by 

V.Yu. Semenov obtained by records in observatories located at the East-European platform but roughly 

thousand kilometers southward of the Fennoscandian Shield (Semenov, 1998). Besides, using these data 

does not considerably change the results of the interpretation within the depths of interest. The chosen 

GMVS curve covers periods range from daily variations till the half-year variation (10 4 -10 7 s). The 

overlapping of the BEAR and GMVS data within the daily variations interval makes it possible to expect the 

reliable results for the depths 200-700 km. 

In addition to these curves we used the phase curves of the maximal impedance which at large periods 

comes to the normal level in case of any dimensionality of the medium. If we take as the “normal” level the 

GMVS curve then beginning with some depth depending on the horizontal non-homogeneity of the upper 

part of section we shall receive the same resistivity distribution as distribution received by the ”longitudinal 

curves”. The first results of this approach were presented in our works (Kovtun, 1989, Kovtun et al., 2002). 

As a rule within the range of daily variations the phase curves of the maximal impedance are in good 

accordance with the GMVS phase curves. Only in some regions this accordance is absent. The most 

pronounced this difference is in sites located along the Gulf of Bothnia which can be connected with the 

noticeable crust and perhaps mantle non-homogeneity. 

The 1D interpretation was performed using the program by L.Porokhova and M.Kharlamov based on 

the method of effective linearization (MEL) (Porokhova and Kharlamov, 1990). The quality of the 

interpretation is estimated by the value of the discrepancy between the solution and the experimental data 

and also by the characteristics of the solution built in frame of the gradient model: smoothing interval and 

discrepancy. The smoothing interval defines the resolvability of the electromagnetic method for the 

estimation of resistivity depth distribution, and discrepancy – the stability of the solution to data random 

errors. The combined interpretation allowed to raise the resolvability of data at the depths 200-700 km nearly 

twice. The error of the solution is defined by the errors of experimental data. At the periods till 2000 s, which 

allows to define the conductivity distribution till 200-300 km, the data error for apparent resistivity does not 

exceed 5%. It must be noted that we can’t define the true errors of GMVS data because besides the 

processing errors they include errors of the spherical analysis which as a rule is performed using a simplified 

model in form of DR-current system. So the estimation of the errors of the resistivity which we receive 

performing interpretation by MEL technique can be used only for depths not exceeding 300 km. 

At the new stage of studying the results of “longitudinal” and maximal impedance phase curves 

interpretation we paid the main attention to the selection of the experimental data and the quality of the 

interpretation. There were taken for the analysis only sites where the discrepancy of the interpretation for the 

chosen curve did not exceed the errors of the experimental data which ensure the absence of the noticeable 

influence of the upper crust horizontal non-homogeneity at the site and the fulfillment of the phase-amplitude 

relation corresponding to the horizontally homogeneous medium. 

Sites chosen for the interpretation of the “longitudinal” and phase curves are shown on the fig.1. There 

were taken for the interpretation “longitudinal” curves in 16 sites and phase curves in 19 sites. In four sites 

there were interpreted both curves. So there were used for the analysis 35 curves in 31 sites which is 2/3 of 

all BEAR sites. The sites are practically evenly distributed on the territory of the experiment. For the 

“longitudinal” curves there were taken curves corresponding to the one of Eggers’ invariants, in few cases – 

effective curves. On fig.2 there are presented resistivity distributions by interpretation of the phase (a) and 

“longitudinal” (b) curves in different sites. There are shown also the mean curves and mean square deviation. 

315


� , S/m 

� ,S/m 

a 

10 

1 

0.1 

0.01 

0.001 

0.0001 

b 

10 

1 

0.1 

0.01 

0.001 

0.0001 

B02, B05, B09, B10, B11, B12, B15, B17, B18, B19, 

B22, B24, B25, B27, B28, B31, B34, B39, B40 

0 200 400 600 800 1000 1200 

H, km 

B08, B12, B15, B16, B25, B29, B30, B32, B34, 

B36, B37, B38, B41, B42, B46, B50 

0 200 400 600 800 1000 1200 

H, km 

Fig2. Depth conductivity distribution on the Fennoscandian Shield by the results of 1D interpretation 

of maximal impedance phase curve (a) and "longitudinal" curve (b); bold lines – the mean 

curves; thin dashed lines – mean square deviation. 

There can be noted the following peculiarities in behaviour of the resistivity distribution. 

1. Till the depth 100 km values of the conductivity received by the interpretation of phase curves exceed 

values received by the interpretation of “longitudinal” curves. 

2. Till the depth 300 km spread of conductivity distribution curves received by “longitudinal” curves is 

noticeably larger then in case of phase curves. 

At the same time the mean curves of conductivity distributions for both cases practically coincide. 

On the fig.3 there are shown mean curves of conductivity distribution for both cases and the mean curve for 

all 31 sites. It is seen that within the depth interval 100-900 km conductivity distribution curves obtained by 

“longitudinal” and phase curves practically coincide and lie within the limits of mean square deviation for 

the general curve. 

316


� , S/m 

10 

1 

0.1 

0.01 

0.001 

0.0001 

0 200 400 600 800 1000 1200 

H, km 

Fig.3. Mean conductivity depth distribution on the Fennoscandian Shield: blue line – by phase curves, 

red line – by 'longitudinal" curves, bold line – both kind of curves, thin dash lines – mean 

square deviation for general curve. 

It is interesting to compare this distribution with the conductivity distribution taken earlier as the 

“normal” distribution for the Eastern part of the Fennoscandian Shield which was obtained by the results of 

combined interpretation of MTS data received at the Central-Karelian block (CKB) within the range 10 -3 -10 4 

s together with the GMVS curve. This curve was named "the normal curve corresponding to the dry and hot 

mantle" (Vanyan, et al., 1980). Both curves are presented on the fig.4. It is seen that the conductivity of the 

upper part of the Fennoscandian Shield noticeably exceeds the conductivity of CKB. After 200 km the 

curves draw nearer. 

� , S/m 

10 

1 

0.1 

0.01 

0.001 

0.0001 

0 200 400 600 800 1000 1200 

H, km 

Fig.4. Comparison of mean conductivity depth distributions on the Fennoscandian Shield (black line) 

and on the Central-Karelian block (green line); thin dash lines – mean square deviation for the 

Fennoscandian Shield curve. 

317


On the Fennoscandian Shield mean curve there is difficult to distinguish any peculiarity in the upper 

mantle structure, for example, location of the astenosphere or of the phase transition zone. On the fig.5 there 

is presented the behaviour of the parameter γ = dlnσ dz which describes the relative gradient of the 

conductivity with respect to depth. This parameter may reflect changes of chemical composition and physical 

state of the upper mantle substance. However, taking into account the weak resolvability of the 

electromagnetic techniques at large depths we can’t expect noticeable changes of this parameter. 

d (ln� � / dz, km -1 

0.004 

0.003 

0.002 

0.001 

0 

100 200 300 400 500 600 700 800 900 

H, km 

Fig.5. Relative gradient of the conductivity with respect to depth. 

At the first 150 km there can be seen fast rise of γ. At the depth 150 km this parameter reaches its 

maximal value. Further it decreases which reflects the change of conductivity mechanism. Probably, 

decreasing of γ is caused by transition to the ionic type of conductivity which increasing become slower 

under the influence of rising pressure. Decreasing of γ continues till the value 0.012 km -1 at the depth 300 

km. The depth interval from 180 till 300 km is characterized by the minimal rise of γ which may be 

connected with the transition to the substance with the higher plasticity and lower dependence on the 

pressure. It may indicate presence of the astenosphere on the Fennoscandian Shield. After 300 km we can see 

rise of γ till the value 2.02 km -1 at the depth 800 km. The noticeable rise of γ after 500 km may be caused 

by the change of the chemical composition of the mantle, which takes place at about 670 km depth. At this 

depth olivine which presents about 60% of the pyrolyte mantle turns into the modified pyroxene (perovskit) 

and ferric and magnesium oxides (magneowηstite). 

However these conclusions need the additional investigations. 

First of all there is necessary to perform dividing the Fennoscandian Shield territory into the regions 

according the behaviour of γ at different sites and to make sure of the stability of this parameter in each 

region. It should be expected that for the depth intervals 50-150, 150-300 and 400-800 km this parameter is 

stable within the limits of each region characterized by the same age and tectonic development. 

The next moment which requires the serious attention is the careful selection of the GMVS set and 

improving of the magnetovariational data. The quality of the MV data may noticeably influence the received 

values of mantle conductivity at depths 300-800 km. 

In order to estimate the influence of difference in GMVS data on the results of the combined 

interpretation let us compare our conductivity distribution with distribution built using GMVS curve by 

Semenov who used data of eleven European observatories within the period range from one day till 11 years 

(Semenov, 1998). On the fig.6 there are presented the results of combined interpretation in two BEAR sites 

located in Eastern part of the Fennoscandian Shield with both sets of GMVS data. It can be noted that till 400 

km distributions are practically the same but after this depth the resistivity corresponding to Semenov’ data 

decreases more rapidly and the resistivity minimum moves to 800-900 km. 

318


� , S/m 

10 

1 

0.1 

0.01 

0.001 

0.0001 

B13 

B41 

0 200 400 600 800 1000 1200 

H, km 

Fig.6. Comparison of conductivity depth distribution by the results of combined interpretation using 

GMVS sets by Rotanova (solid line) and by Semenov (dashed line) for sites B13 and B41. 

The authors are thankful to all members of BEAR working group for the unique material which made it 

possible to carry out this analysis. 

References 

Eggers D.E. (1982), An Eigenstate formulation of the magnetotelluric impedance tensor, Geophysics, Vol 

47, No 8, 1204—1214. 

Kovtun, A.A. (1989), The crust and upper mantle structure of the North-Western part of the East-European 

Platform by the magnetotelluric data, Leningrad State University, 284p. 

Kovtun A.A., S.A. Vagin, I.L. Vardaniants, N.P. Legen'kova, M.Yu. Sminov, and N.I. Uspenskiy (2002), 

Analysis of the magnetotelluric and magnetovariational results within the daily variations period range 

by the BEAR data and defining the "normal" section of the Baltic Shield, Izvestia RAN , Fizika Zemli, 

No 11, 34-53. 

Oraevskiy V.N., N.N. Rotanova, V.I. Dmitriev, T.N. Bondar' and D.Yu. Abramova (1986), Results of the 

deep magnetovariational sounding of the Earth by the surface data and satellite measurements 

(«MAGSAT»), Geomagnetism and Aeronomy, Vol 26, No 1,60-69. 

Porokhova L.N. and M.N. Kharlamov (1990), The solution of the one-dimensional inverse problem for 

induction sounding by an efficient linearization technique, Earth and Planet. Inter., 60, 68-79. 

Rotanova N.N., M.V. Fiskina and O.K. Zakharova (1993), Experimental data on the global 

magnetovariational sounding, Geomagnetism and Aeronomy, Vol 33, No 2, 120-127. 

Semenov V.Yu. (1998), Regional conductivity structures of the Earth’s mantle, Publications of the institute 

of geophysics Polish Academy of sciences, Warszava, 120p. 

Vanyan L.L., M.N. Berdichevskiy and N.D. Vasin (1980), On the normal geoelectrical section, Izvestia AN 

USSR, Fizika Zemli, 73-76. 

319


PRELIMINARY RESULTS OF THE BEAR DATA PROCESSING WITH 

APPLICATION OF NONLOCAL RESPONSE FUNCTIONS 

V.V. Plotkin 1 , A.Yu. Belinskaya 1 , P.A. Gavrysh 1 and BEAR Working Group 

1 Trofimuk Institute of Petroleum Geology and Geophysics SB RAS, Novosibirsk, 630090, Russia, 

e-mail: plotkinVV@ipgg.nsc.ru 

Abstract. The data processing with the Tikhonov-Cagniard model becomes essentially complicated in a 

real situation, when a primary field of a natural source and medium properties change appreciably on lateral 

coordinates. Results of synchronous array data processing are given which take into account nonlocal 

electromagnetic response functions. The fact is used that the electromagnetic field inside any volume is 

completely determined by the surface distribution of tangential components either electrical or magnetic 

fields. The solution of the inversion problem can be carried out by the correlation with each other of surface 

distributions of mentioned tangential components during search of the spatial conductivity distribution in 

the volume. 

The data processing with the Tikhonov-Cagniard model becomes essentially complicated in a real 

situation, when a primary field of a natural source and medium properties change appreciably on lateral 

coordinates. The unique synchronous data from the magnetotelluric and magnetovariation station array are 

received during the project BEAR by study of the conductivity spatial distribution on the Baltic Shield. 

Alongside with traditional methods, it enables to use nonlocal electromagnetic response functions at data 

processing. In this study we show these possibilities by the regional magnetotelluric sounding. 

The fact is important that the electromagnetic field inside any volume is completely determined by the 

surface distribution of tangential components either electrical or magnetic fields (the uniqueness theorem). 

The solution of an inversion problem can be carried out by correlation with each other of surface 

distributions of mentioned tangential components during search of the spatial conductivity distribution in the 

volume. 

The appropriate algorithm of data processing was developed. The spatial approximation of the data of 

discrete observation points on all area of region is at first necessary for practical realization of this algorithm. 

With this purpose for each of registered field component, we applied 2-D Fourier harmonics. 

At the analysis of the synchronous array data, we entered for convenience the electromagnetic 

potentials which are taking into account two mode structure of the field. There are potentials of magnetic and 

electric fields of both modes. The equations for these potentials are received. In 3-D case, these equations are 

interconnected. 

During inversion, the approach of the medium smooth heterogeneity is used for the calculation 

reduction. The field of the TM mode is found by the approximation method in this case. The observable 

component distributions of the electromagnetic field are recalculated in values of the entered potentials on 

the surface of the investigated volume. These values are coordinated during search of the conductivity spatial 

distribution in the volume by optimization methods. 

Testing the developed algorithm is carried out on synthetic models of the medium heterogeneity taking 

into account the component variations of the electromagnetic field really observed in the project BEAR. At 

testing algorithm, the lateral non-uniform medium models are applied. Using the exact program developed, 

the synthetic input data of some prospective experiment are simulated. Processing of these data was made by 

the described algorithm further with the purpose of restoration of the test heterogeneity. The advantage of the 

offered data processing is that it does not assume use of any model of a source of a field when there are 

synchronous array data. Nevertheless for realization of testing it is necessary to set somehow data on 

components of the field in observation points. Whenever possible to come nearer to conditions of real 

experiment, we used the data on the vertical component of the magnetic field received in one of sessions of 

the project BEAR. Values of the apparent conductivity are chosen to correspond to the Baltic Shield 

conditions. The model takes as ring area with increased conductivity in the central part of polygon (Fig. 1a). 

The influence of density and point arrangement on results of restoration of test heterogeneity was studied. 

With increase of the network density, the quality of restoration of test heterogeneity grows (Fig. 1b, 1c). It is 

established that at a successful random arrangement of stations the functional minimum can be least. This or 

that purposeful choice of an arrangement of stations (in particular uniform arrangement on circles around of 

320


the centre of polygon etc.) to any successes has not resulted. It is noticed that the increase of stations quantity 

at some part of polygon promotes the restoration of the test distribution in this part. 

a b 

c d 

e f 

Fig. 1. The model of the conductivity lateral heterogeneity (a) and results of its restorations in cases: 

60 points located randomly on polygon (b), 32 points located as in project BEAR (c); with data 

accumulations: the average map received on 31 neighbouring time periods (d), by averaging results of 

repeated sessions with a new point arrangement - 32 points in 500 sessions (e) and 45 points in 66 sessions 

(f). 

321


As deficiency of stations and observation errors do not allow to receive the complete information on 

spatial changes inside investigated volume, the various variants of accumulation of the information in 

repeated sessions are considered. It is established using synthetic data that restoring of contours of test 

heterogeneity is quite possible by averaging results of repeated sessions with small quantity of stations at 

their changed arrangement (Fig. 1e, 1f). It is established also that the influence of observation errors is 

eliminated by averaging received results on several neighbouring time periods (Fig. 1d). 

There can be a doubt, whether are the received maps of heterogeneity only a reflection of the available 

arrangement of observation points at their small quantity. Whether it is possible to estimate the contribution 

of the arrangement of observation points to the conductivity result map? In this connection, we studied an 

opportunity of accumulation of the information by averaging received results on set of several sessions at the 

same point arrangement (that is, actually on set of varied sources of a field). We used synthetic input data for 

test model of lateral heterogeneity of the conductivity, both at a random choice of station arrangement, and 

for the real situation of the project BEAR. The spectra (which are also both random and from experiment 

BEAR) of vertical component of the magnetic field variations are used as the initial data. The synthetic data 

on other components of the electromagnetic field are calculated then for test model of heterogeneity and 

given arrangement of stations. Processing synthetic input data was carried out by described algorithm. The 

restoration of test heterogeneity in conditions of the real arrangement of points and with use of the real data 

on the vertical component of the magnetic field of the project BEAR has confirmed an opportunity of 

accumulation of the useful information about heterogeneity by averaging results of various sessions at the 

fixed points of the network. 

It is studied also the influence of the chosen sizes of polygon on results of regional data processing by 

the offered algorithm. The synthetic data received using numerical simulation for given test model of the 

conductivity lateral heterogeneity are applied. Values of components of this field in network points are 

calculated using these received potentials of the electromagnetic field. Further these values are used as an 

experimental input. The restoration of lateral dependence of test heterogeneity is made by offered algorithm 

at the distinguished sizes of polygon and with different sets of approximation trigonometrical functions. To 

not take into account influence of small quantity of points by the observation, the network got out enough 

dense. It is established that there are optimum sizes of polygon for the spatial approximation quality of 

experimental data on field components at the given network. In the investigated situations, the increase or 

reduction of the polygon sizes by the first parts of percent did not result in appreciable differences of the 

restored lateral distribution from initial one. The sizes of spatial "window" actually varied only, through 

which the heterogeneity "was observed". However the distortion became essential with the further increase 

of deviations of the polygon size from initial one up to units of percents. At five-percentage deviations of the 

polygon sizes, the restored lateral distribution reminded only in general an initial contour of conductivity test 

heterogeneity. With increased polygon sizes, sets with the same quantity of trigonometrical functions cease 

to represent input experimental values of field components in network points. Increased errors in initial 

electromagnetic potentials complicated the solution of the inversion problem by offered algorithm. At the 

large deviations these errors masked a useful signal about test heterogeneity in components and in input 

potentials for the inversion. There is also necessity to increase quantity of the polygon points and the 

network density to improve the approximation quality using large numbers of spatial harmonics and their 

quantity. The optimum set of discussed parameters for polygon can be determined at the real data processing 

on fall of error values at the inversion by optimization methods. The BEAR real data processing with the 

polygon various sizes also has confirmed said. 

At study of a normal deep section, the low-frequency approximation of dependence of apparent 

resistance on the time period is used for definition of depth of the perfectly conducting basis. The depth of 

this basis is presumably established in a range of 200-300 km, with average value of 250 km. The subsequent 

definition of a normal deep section with several layers specifies existence of set of the equivalent solutions. 

The exact knowledge of dependence of apparent resistance on the time period is necessary for reduction of 

the equivalent solutions. 

Some preliminary results of real BEAR data processing are received by the described method. The 

interval from June 19 till July 3, 1998 was selected with the greatest quantity of synchronously working 

stations. The maps of the lateral distribution of the apparent conductivity are constructed depending on the 

time period. As an example, in Fig. 2 one of such maps is given for the period 50 seconds. Crosses mark 

observation points. The pseudo cross-section is shown also in Fig. 3 for profile displayed in Fig. 2 by straight 

line. 

322


Fig. 2. Contours of the apparent conductivity for time period of 50 s in Baltic Shield (in mS/m). The straight 

line displays a profile, for which the pseudo cross-section is shown in Fig. 3. 

Fig. 3. Pseudo cross - section for profile displayed in Fig. 3 by straight line. The axis OX is directed to north. 

323


The map of Earth’s crust thickness [Sandoval et al., 2003] is shown in Fig. 4 for comparison. The 

comparison was spent also with the known conductance map of the top layers on depths up to 10 km [Lahti 

et al., 2005] and with the map of P-velocity variations on depth of 100 km [Sandoval et al., 2004] received 

by the teleseismic tomography data in the specified region of the Baltic Shield. Some similarity of the 

specified maps, in particular, increased conductivity values are traced along tectonic sutures between the 

Svecofennian and Karelian terrains and between the Karelian and Lapland-Kola terrains. The correlation 

between distributions of conductivity minima and maxima of Earth’s crust thickness is observed also. 

Fig. 4. Contour map of the derived crustal thickness (in km) for the study area and main tectonic 

regions (solid thick lines) [Sandoval et al., 2003]. 

Acknowledgements. We would like to thank A.A. Zhamaletdinov for the delivered opportunity to 

work with BEAR database and A.A. Kovtun and S.A. Vagin for useful comments. The study was supported 

by RFBR (project № 07-05-00007). 

References 

Lahti, I., T., Korja, P. Kaikkonen, K. Vaittinen and BEAR Working Group (2005), Decomposition 

analysis of the BEAR magnetotelluric data: implications for the upper mantle conductivity in the 

Fennoscandian Shield, Geophys. J. Int., 163, 900–914. 

Sandoval, S., E. Kissling, J. Ansorge and the SVEKALAPKO Seismic Tomography Working Group 

(2003), High-resolution body wave tomography beneath the SVEKALAPKO array: I. A priori threedimensional 

crustal model and associated traveltime effects on teleseismic wave fronts, Geophys. J. Int., 153, 

75–87. 

Sandoval, S., E. Kissling, J. Ansorge and the SVEKALAPKO Seismic Tomography Working Group 

(2004), High-resolution body wave tomography beneath the SVEKALAPKO array - II. Anomalous upper 

mantle structure beneath the central Baltic Shield, Geophys. J. Int., 157, 200–214. 

324


ONE- AND TWO-DIMENSIONAL INVERSION OF 

MAGNETOTELLURIC DATA BY THE REGULARIZATION 

SVD METHOD 

S. A. Vagin 

Institute of Physics, St. Petersburg University, St. Petersburg, 198504, Russia, 

e-mail: stvagin@gmail.com 

Abstact. In work algorithms and programs for one-dimensional and two-dimensional inversion of 

magnetotelluric data by the regularization SVD method are presented. Questions of convergence 

and stability of algorithms, and also such important geophysical questions, as resolvability of data, 

information pithiness of data and optimal parameterization are considered. There is investigated 

the work of algorithms depending on model parameters and data. Comparison of offered algorithm 

with other algorithms is carried out. 

At present many geophysicists show interest for using the method SVD in solving inverse problem 

(Christensen-Dalsgaard et. al.,1993), (Pedersen, 2004). Let us consider the solution of the inverse problem 

using this method for 1D and 2D models. 

1. Inverse problems and linearization of a forward problem operator 

The nonlinear discrete inverse problem is described by the operator equation 

Φ ( m) = d , 

Ф — the nonlinear operator of a forward problem, m — vector of modeling parameters, d — data vector: 

T 

d = [ d1, d2,..., dN] 

, 

(1) 

T 

m = [ m1, m2,..., mK] 

. 

Let m (0) be the initial approach, 

( s) ( s−1) ( s−1) 

AΔ m =Δ d = d−Φ( m ) , 

(2) 

where A is the n× k Freshe matrix (the sensitivity matrix) of the linear operator with elements 

⎛∂Φ ⎞ 

i Aij 

= ⎜ ⎟ . 

(3) 

⎜ m ⎟ 

⎝∂j⎠ ( s−1) 

m= m 

Further we will write down a linearization problem as 

Am = d , 

(4) 

where m is the model correction vector, d is the data correction vector. 

2. Singular Value Decomposition (SVD) and regularization 

The theory of SVD is described in many works, see e.g. (Menke, 1989). 

The SVD possesses a property which connects the problem of searching for singular decomposition 

with the problem of searching for eigenvectors. An eigenvector x of a matrix A is such a vector which 

satisfies the condition: 

Ax = λx 

, 

where λ is eigenvalue of the matrix A . 

Let us apply the SVD method to the matrix A: 

( ) ( ) ( ) ( ) , 

T 

A n× k = U n× rΛ r× rV r× k 

(5) 

Avi = λiu 

i, 

T 

Au= λ v , 

i i i 

325


where k and n are defined according to (1); r = min( n, k) 

; Λ is the diagonal matrix with elements λ i ; u i 

and v i are columns of orthogonal matrixes U and V . 

The pseudo inverse matrix H and the pseudo-solution of the system (4) are: 

-1 

T 

H=VΛ U , 

m= Hd. 

For a regularization solution of an inverse problem (4) let us introduce a parametric functional 

(Tikhonov and Arsenin, 1977), 

( , ) ( ) ( ) 

T T 

P α 

m d = Am−d Am− d + α m m. 

The minimization of the functional P ( , ) 

α m d gives the solution (Yanovskaya and Porokhova, 2004) 

m= H d, (7) 

where λi are elements of diagonal matrix A. 

reg 

⎛ λ ⎞ 

i T 

Hreg = Vdiag⎜ 2 ⎟U 

, 

λi+ α 

⎝ ⎠ 

3. Algorithms of one- and two-dimensional inversion 

In the Fig. 1 it is shown the unified scheme of 1D and 2D inversion algorithms which distinguish 

only by the components. 

data 

d 

rms 

m (0) 

Φ(m (0) ) 

Fig.1. The scheme of 1D and 2D inversion algorithms. 

In case of 1D inversion as initial data there are taken either apparent resistivities ρ a , or impedance 

phases arg Z with one or several values of apparent resistivities. In the second case if all values of ρ a and 

arg Z are used we obtain the joint interpretation: 

1-D Algorithm 

( T ) it = nt 

Z ( T ) ρ ( T ) 

d : 1) ρ , 1,2, ..., 

a it 

In case of 2D inversion as initial data there are taken 

2) arg and one or more values . 

it a it 

E 

ρ a , or 

2-D Algorithm 

( T ) it = nt 

( ) = 

( ) ( ) 

E 

d : 1) ρ , 1,2, ..., 

a it 

A AΔm=Δd m (s) =m (s-1) +Δm (s) 

Φ(m (s) rms>δ 

) 

H 

2) ρ T , it 1,2, ..., nt 

a it 

H 

ρ a , or 

E 

ρ a and 

E H 

3) ρa Tit and ρa 

Tit , it = 1,2, ..., nt. 

The building of the working net for the solution of the forward problem is the same as in the work 

(Vagin, 2004). 

3. Testing of algorithms 

326 

rms 

model 

H 

ρ a : 

(6)

In the Fig. 2, a the results of 1D interpretation of ρ a using program SVD and MEL are shown. The 

model represents a 7-layer section (a black line). The number of data ρ a was 20 values per a decade of 

square root of Т (in logarithmic scale). The regularization parameter was α = 0,005 , the number of iteration 

iter = 15 , discrepancy rms = 0,01 . It is necessary to notice, that the algorithm of program MEL is 

constructed on Backus and Gilbert method (Backus and Gilbert, 1967) which is a special case of method 

SVD. Program MEL is one of the successful programs 1D inversion (Porokhova and Kharlamov, 1990). In 

the Fig. 2, b the results of modeling in the presence of 20% of noise and corresponding confidence intervals 

are given. 

a b 

Resistivity, Ohm m 

10000 

1000 

100 

10 

1 

model 

mel 

svd 

svd (minimum of layers) 

0.1 1 10 100 1000 

Depth, km 

Resistivity, Ohm.m 

10000 

1000 

100 

10 

1 

0.1 1 10 100 1000 

Depth, km 

Fig.2. Results of 1D interpretation of ρ a : a) the comparison of program SVD and MEL; b) the result of interpretation 

(red line) - in the presence of noise (20 %) in data, black lines - boundaries of confidence intervals. 

In the Fig. 3 it is shown the dependence of 1D interpretation on the number of model layers and periods. It 

can be seen that the optimal variant is 10 layers per a decade of depths and 5 values per a decade of square 

root of T (in logarithmic scale). In the figure these values are noted by the asterisk. 

Resistivity, Ohm.m 


10000 

1000 

100 

10 

1 

a b 

1 Depth (km) 

20 

*10 

5 

10 

0.1 1 10 100 1000 

Depth, km 

327 

Resistivity (Ohm.m) 

10000 

1000 

100 

10 

1 

1 sqrt [Period(s)] 

20 

10 

*5* 

2,5 

10 

minimum of Periods 

1 2 5 10 s 

0.1 1 10 100 1000 

Depth (km)

Fig. 3. Dependence of 1D interpretation on the number of layers of model per a decade of depths (a) and the number of 

periods per a decade of square root of T (b). 

In the Fig. 4 the results of 1D interpretation of global magnetovariational sounding (GMVS) data 

( ρ a ) by both programs (MEL and SVD) are presented. For SVD the confidence intervals of interpretation 

are given. 

Apparent resistivity (Ohm . m) 


100 

10 

1 

a b 

MEL 

SVD 

100 1000 10000 

sqrt [Period (s)] 

Resistivity (Ohm.m) 

1000 

100 

10 

1 

0.1 

MEL 

SVD 

skin depth(1) skin depth(nT) 

10 100 1000 10000 

Depth (km) 

Fig. 4. Results of 1D interpretation of GMVS data by MEL and SVD programs. Black points show confidence 

intervals for SVD method. 

For testing 2D algorithm there was taken the simple model in form of a conductive rectangular twodimensional 

body with the resistivity 40 Ohm.m in homogeneous semi-space with the resistivity 1000 

Om.m, as is shown by red colour in Fig.5, b. In Fig. 5, a the change of discrepancy with the iteration number 

is shown in case of 20 layers and 14 points on the profile. For decreasing discrepancy it is required to 

increase the number of layers and of points on the profile. 

Discrepancy 

a b 

1 

0.8 

0.6 

0.4 

0.2 

0 

0 4 8 12 16 20 

Number of iteration 

Depth (km) 

-20 

-40 

-60 

-80 

-100 

-120 

Distance along profile (km) 

-200 -150 -100 -50 0 50 100 150 200 

Fig. 5. Results of 2D interpretation in case of model of a conductive rectangular body in homogeneous semi-space (b) 

and behaviour of discrepancy with encreasing of iteration number (a). 

328 

lg ρ[Ohmm] ⋅ 

3.2 

3 

2.8 

2.6 

2.4 

2.2 

2 

1.8 

1.6 

1.4 

1.2

In work the question on the resolvability of two conductive bodies located close to each other has 

been investigated. Results of interpretation are presented in Fig. 6. Red color notes the true models. The 

considered models are reliably distinguished. 

Depth (km) 

Depth (km) 


-50 

-100 

-50 

-100 


-200 -100 0 100 200 


-200 -100 0 100 200 

Fig. 6. The 2D Interpretation of two close located conductive bodies. Red colour notes the true models. 

References 

lg [Ohm ⋅m] 

Backus, G., and F. Gilbert (1967), Numerical applications of a formalism for geophysical inverse problems. 

Geophys. J.R. Astr. Soc., 13, 247-276. 

Christensen-Dalsgaard, J., P. Hansen, and M. Thompson (1993), Generalized singular-value decomposition 

analysis of helioseismic iversions, Monthly Notices of the Royal Astronomical Society, 264,541-564. 

Yanovskaya, T.B. and L.N. Porokhova (2004), The inverse problem of geophysics, SPbU, 214. 

Menke, W. (1989), Geophysical Data Analysis: Discrete Inverse Theory, Academic Press, Inc. 

Pedersen, L. (2004), Determination of the regularization level of truncated singular-value decomposition: the 

case of 1D inversion of MT data, Geophys. Prospect., 52(4), 261-270. 

Porokhova, L.N., and M.N. Kharlamov (1990), The solution of the one-dimensional inverse problem for 

induction sounding by an efficient linearization technique, Earth and Planet. Inter., 60, 68-79. 

Tikhonov, A.N., and V.Y. Arsenin (1977), Solution of ill-posed problems. Winston and Sons, 258 pp. 

Vagin, S.A. (2004), Algorithms of two-stage building of 1D и 2D geoelectrical sections by control 

transformation method, Voprosi geofiziki, 36, SPbU, 156-163 (in Russian). 

329 

3.2 

3 

2.8 

2.6 

2.4 

2.2 

2 

1.8 

1.6 

1.4 

1.2


THE DEEP TENSOR CSMT SOUNDING WITH INDUSTRIAL POWER 

LINES AT THE EASTERN PART OF THE FENNOSCANDIAN (BALTIC) 

SHIELD (FENICS EXPERIMENT) 

Zhamaletdinov A.A. 1,2,3 , Shevtsov A.N. 1 , Korotkova T.G. 1 , Efimov B.V. 2 , Barannik 

M.B. 2 , Kolobov V.V. 2 , Prokopchuk P.I. 2 , Kopytenko Yu.A. 3 , Kopytenko Ye.A. 3 , 

Ismagilov V.S. 3 , Smirnov M.Yu. 4 , Vagin S.A. 4 , Tereschenko Ye.D. 5 , Vasiljev A.N. 5 , 

Gokhberg M.B. 6 , T. Korja 7 

1 Geological Institute of the Kola Sci. Center of RAS, Apatity, 184209, Russia, e-mail: 

abd.zham@mail.ru; 2 Centre for Phys. & Tech. Probl. of Energy in North, Kola Sci. Center of RAS, 

Apatity, 184209, Russia; 3 St. Petersburg Branch of IZMIRAN, Saint Petersburg, 191023, Russia; 

4 St. Petersburg State University, St. Petersburg, 199034, Russia; 5 Polar Geophysical Institute of the 

Kola Sci. Center of RAS, Apatity, 184209, Russia; 6 Institute of Physics of the Solid Earth of RAS, 

Moscow, 123995, Russia; 7 University of Oulu, FI-90014, Finland 

Abstract. An international experiment FENICS (Fennoscandian electrical conductivity from 

results of soundings with Natural and Controlled Sources) on the deep tensor electromagnetic 

sounding of the Fennoscandian (Baltic) shield has been carried out at the summer 2007. According 

to data analysis the maximal distance of signals registration reached to 1300 km (observatory 

Barentsburg). The uniform primary database of the FENICS experiment is in progress. For the 

data treatment the program of synchronous spectral analysis of current and measured signals is 

developed. The programs of the forward and inversion problems solution for the deep soundings 

with taking into account the influence from ionosphere and displacement currents are developed. 

The inversion problem is solved on the basis of bimodal scheme with taking into account both (NS 

and EW) polarizations of the primary source. 

By results of tensor sounding the parameters of a "normal" geoelectrical section of the lithosphere 

are specified. On the basis of the experiment "FENICS" data it is made the preliminary modeling 

of the tectonic and physical conditions in lithosphere of the Fennoscandian (Baltic) shield at the 

transition zone “crust-mantle” and constructed the scheme of location of the low boundary of the 

"cold" lithosphere. Connected to the data, the boundary between pseudo-brittle and ductile 

conditions of substance is studied. 

INTRODUCTION 

The Kola science centre of Russian Academy of Sciences (Apatity) on behalf with Saint Petersburg Branch 

of IZMIRAN, State University of Saint Petersburg, and University of Oulu Finland at the support from 

Russian Fund of Basic Research (RFBR) provided in 2007 year experimental research on the deep control 

source electromagnetic sounding named FENICS (Fennoscandian Electrical conductivity from results of 

soundings with Natural and Controlled Sources). The experiment has been aimed both on the deep 

electromagnetic sounding of the earth crust and upper mantle and on the study of electromagnetic waves 

propagation in the wave guide “Earth-ionosphere” at distances up to 1300 km. 

TECHNIQUE 

The experiment FENICS-2007 has been done with the use of two mutually orthogonal industrial power lines 

(PL) of East-West orientation (L-1 of 109 km extent) and North-South orientation (line L-2 of 120 km 

extent). Location of the power lines and the field measuring points (receivers) is presented on the Fig 1. 

The technique is named as controlled source magnetotellurics (CS MT-AMT) [Zhamaletdinov et al., 2005; 

Zhamaletdinov et al., 2007]. Compare to the well known controlled source audio magnetotellurics (CSAMT) 

[Boerner, 1991; Zonge & Hughes, 1991], the CS MT-AMT technique operates in an extremely lowfrequency 

band (0.1 – 200 Hz) and is forwarded to study the deep electrical conductivity of the Earth crust 

and upper mantle. The principal scheme of the controlled source MT-AMT sounding is presented on the 

Fig.2. The natural variations and controlled source signals are registered simultaneously by the same MT- 

330


AMT stations. Harmonic signals from the controlled source is separated from MT variations by means of the 

Fast Fourier Transformation (FFT) or by another digital filtering technique. Application of two mutually 

orthogonal antennas gives possibility to estimate the dimensionality of the lower half space and to take into 

account the possible influence from lateral heterogeneity of the earth crust on results of the data 

interpretation. 

Generator “Energy-1” of 100 kW power has been used as the source of alternating current The current 

intensity in antennas (for the half-period, for the first harmonic) changed from 150-200 A at low frequencies 

(0.1 – 1 Hz ) to 20-60 A at high frequencies (100-200 Hz ) The current in radiating antennas has been 

measured by digital data logger with the rate of sampling from 100 Hz up to 2 kHz in dependence from 

frequency of a current. The synchronization of a current of the generator and measuring signals is supplied 

on the basis of GPS satellite system and Blue Tooth interface. 

The current has the shape of the sine with stability on frequency up to 10 -7 Hz. 

DATA ANALYSUS AND PRELIMINARY RESULTS 

Electromagnetic signals measurements were executed on the territory of the Kola-Karelian region, in 

Northern Finland and on the Spits Bergen. According to data analysis the maximal distance of signals 

registration reached to 1300 km (observatory Barentsburg) (Fig. 1) measuring stations from Russian 

Academy of Sciences, from Saint Petersburg University and from Oulu University (Finland) took part in the 

control source signals registration. The uniform primary database of the FENICS-2007 experiment is in 

progress. The program of synchronous spectral analysis of current and ents measured signals is developed. 

The example of Power Spectral Density (PSD) curves for electric and magnetic components is presented on 

the Fig. 3 for three points – Oulu, Finland (r=450 km), Peninga, Southern Karelia (r=601 km) and 

Barentsburg, Spits Bergen (r=1300 km). For Barentsburg the PSD curve is presented only for N-S magnetic 

component and in conventional (N) unit. All measurements, presented on the Fig 3 are made from the 

transmitting power line L1 of E-W orientation. The appropriate PSD curve of current in the transmitting 

power line L1 is shown on the Fig. 3. Location of receiving points and transmitting industrial power lines L1 

and L2 is shown on the Fig. 1. 

Resulting apparent resistivity curves from FENICS experiment along sub-meridian profile are shown 

on the Fig. 4-a. Measuring points are located at distance range from 186.2 km (Upol) till 701.3 km (Poros). 

Apparent resistivity curves from FENICS experiment measurements in frequency range 0.1-200 Hz were 

calculated at impedance approach. High frequency parts of apparent resistivity curves on the Fig. 4 (higher 

then 200 Hz) were obtained from DC soundings with spicing up to 2 km. DC apparent resistivity curves were 

inverted into frequency domain and interpolated with the CSMT-AMT data. 

For three points (Tung, Kost and Poros) the soundings are made with two polarizations, from E-W power 

line L1 (black lines) and N-S power line L2 (blue lines). For other points the soundings are made with the 

use only one polarization from E-W power line L1 (see location of power lines and measuring points on the 

Fig.1). 

The programs are developed for the forward and inversion problems solution for the deep soundings with 

taking into account the influence from ionosphere and displacement currents. On the Fog 4-b the electrical 

sections from results of inversion problem solution are presented. The inversion problem for the tensor 

soundings has been solved on the basis of bimodal scheme with taking into account both (NS and EW) 

polarizations of the primary source. The detailed processing and interpretation is providing in complex with 

MT soundings. 

By results of tensor sounding the parameters of a "normal" geoelectrical section of the lithosphere are 

specified. The direct correlation of apparent resistivity curves is established at axial and equatorial 

installations at distances of up to 600-700 km. That points out on the high horizontal uniformity of substance 

at the low crust and upper mantle depth. The received data have allowed to specify parameters of a 

lithosphere electrical conductivity in a transition zone "crust-mantle". On the basis of the experiment 

"FENICS" data the preliminary modeling is performing for the tectonic and physical conditions in 

lithosphere of the Fennoscandian (Baltic) shield at the transition zone “crust-mantle” and constructed the 

scheme of location of the low boundary of the "cold" lithosphere. Connected to the data, the boundary 

between pseudo-brittle and ductile conditions of substance is studied. 

On the Fig. 5 the summary diagrams of apparent resistivity curves (a) and electrical sections from results 

of inversion problem solution (b) are presented for results of FENICS experiment measurements along the 

North-South profile. From the Fig. 5 the preliminary conclusion is extracted about regional decrease of 

transversal resistance of lithosphere over the Middle Karelian and Finland part of the measured profile. 

331


The experiment FENICS is now in progress and planned to be continued at 2009 year for to provide more 

extensive measurements and for to make following complex interpretation with earlier made BEAR 

experiment and seismic researches [Hjelt et al., 2006]. 

Acknowledgments. The research is done under support from Department of Earth Sciences, Russian 

Academy of Sciences (project N 6 “Geodynamics and deformation mechanisms of the lithosphere”) and 

from Russian Fund of Basic Research (grants N 06-05-64429-a and N 07-08-00181-a). 

Fig. 1. The sketch with location of power lines L-1 and L-2 and with location of measuring points. 

1 – points, measured by stations of Geological institute of the Kola Science. Centre of RAS; 2 and 3 – same by Saint 

Petersburg Branch of IZMIRAN, 4 – same by Saint Petersburg University, 5 – same by Polar geophysical institute of 

the Kola Science Centre of RAS, 6 – same by Oulu University (Finland) 

332


Fig. 2. Principal scheme of the controlled source MT-AMT sounding. 

Fig. 3. Power spectral density (PSD) diagrams from results of electrical (Ey, East-West) and magnetic (Hx, North- 

South) signals registrations at distances of 450 km (Northern Finland), 601 km (South Karelia) and 1300 km (Spits 

Bergen) from the experiment FENICS-2007. All signals are registered from the power line L1 (see PSD I). Location of 

transmitting line LI and receiving points is shown on the Fig. 1. 

333


Fig.4. The diagrams of apparent resistivity curves (a) and electrical sections from results of inversion problem solution 

(b) for results of FENICS experiment measurements along the North-South profile. For three points (Tung, Kost and 

Poros) the soundings are made with two polarizations, from E-W power line L1 (black line) and N-S power line L2 

(blue line). For other points the soundings are made with only one polarization from E-W power line L1. (see location 

power lines and measuring points on the Fig.1). 

334


Fig.5. The summary diagrams of apparent resistivity curves (a) and electrical sections from results of inversion 

problem solution (b) for results of FENICS experiment measurements along the North-South profile. 

REFERENCES 

Boerner D.E. 1991, Controlled source electromagnetic deep sounding: theory, results and correlation with 

natural source results: Invited Rewiew Paper for the 10th Workshop on EM Induction Ensenada Mexico, 

3-50. 

Hjelt, S.-E., Korja, T., Kozlovskaya, E., Lahti, I., Yliniemi, J. & BEAR and SVEKALAPKO Seismic 

Tomography Working Groups, 2006. Electrical conductivity and seismic velocity structures of the 

lithosphere beneath the Fennoscandian Shield. Pp 541-559 in: Gee, D. G. & Stephenson, R. A. (eds) 

2006. European Lithosphere Dynamics. Geological Society, London, Memoirs, 32. The Geological 

Society of London, 2006. 

Zhamaletdinov A. A., Korotkova T. G., Tokarev A. D., Shevtsov A. N., Nevretdinov Yu. M., Zarkhi I. M., 

Kopytenko Yu. A., Kopytenko E. A., Gokhberg M. B., Pesin L. B., Shershnev Yu.A. 2005. Superdeep 

Sounding of the Lithosphere in the Baltic Shield Using Industrial Electric Power Lines, Doklady Earth 

Sciences, Vol. 405A, No. 9, 2005, pp. 1373–1376. Translated from Doklady Akademii Nauk, Vol. 405, 

No. 5, 2005, pp. 666–669. 

Zhamaletdinov A. A., Shevtsov A. N., Korotkova T. G., Efimov B.V., Barannik M.B., Kolobov V.V., 

Prokopchuk P.I., Kopytenko Yu. A., Ismagilov V.S., Pesin L.B., 2007. The deep soundings with 

industrial power lines in complex with MTS. Proceedings of Russian Academy of Sciences. Physics of 

the Solid Earth, № 3, p. 74-80. 

Zonge K.L., Hughes L.J. Electromagnetic sounding. Nabighian M.N. Eds., Electromagnetic methods – 

Theory and Practice, Vol. 2; Soc. Expl. Geophys., 1991. P. 713–809. 

335


INFLUENCE OF TIDAL FORCES (THE EARTH – MOON- SUN SYSTEM) 

ON SOME GEOLOGICAL PROCESSES IN THE EARTH’S CRUST 

Yu.N. Avsjuk, Yu.S. Genshaft, A.Ja. Saltykovsky, Yu.F. Sokolova, 

and S.P. Svetlosanova 

Institute of the Physics of the Earth, Russian Academy of Sciences, Moscow, 123995, 

e-mail: saltyk@ifz.ru 

Abstract. It was shown that oscillating regime of tidal evolution in the Earth – Moon – Sun 

system results in periodical changes of velocity rotation and incline angle of the axis rotation. 

According to geological data it has been distinguished epoch intervals of maximum Phanerozoic 

sedimentation, magmatism and folding stages. These are compared with calculated changes of 

velocities and orientation of the Earth rotation axis (the model of cyclic motion of tidal evolution 

in the Earth – Moon – Sun system.) It has shown a steady trend of high Earth’s activation during 

Phanerozoic epoch within the range of latitudes (20º-40º Northern latitudes) that confirms the 

opinion on inherent of tectonic processes. It has been established the minimal transgression for 

subequatorial areas and noticeable increase to the Polar latitudes, in particular for the South 

hemisphere. This fact is accord to the conclusion on variations of the World Ocean level in 

equatorial and high latitude areas at the Earth’s axial rotation of velocity change. It was 

demonstrated that the tidal forces in the Earth – Moon – Sun system may influence greatly on the 

intensity and latitudinal zoning of geological processes in the Earth’s crust. 

It was shown [Avsjuk, 1996; Avsjuk et.al., 1996, 2005, 2007] that oscillating regime in the tidal evolution of 

the Earth – Moon – Sun system should produce periodical changes of velocity rotation and incline angle of 

the axis rotation. The increase of the Earth angle rotation velocity (+ω) should be accompanied with increase 

of the World ocean level within the range of low latitudes (equatorial) and decrease ones in high latitudes 

(Polar areas). Another situation has to observed with decrease of the velocity rotation of the Earth (-ω). 

(Fig.1). According to the principles the latitudinal zoning has to take place in distribution (in geological scale 

of time) of some geodynamical processes within the lithosphere (we mean Phanerozoic epoch only). 

It was calculated the sedimentation areas (the areas of transgression and regression) in geological 

intervals including of Mesozoic and Cenozoic epochs based on the Atlas of Lithological-Paleogeographical 

formations (Ed. V. Khain, 1982). The latitudinal zoning of sedimentary basins in latitudinal intervals 0-20, 

20-40, 40-60 to the South and to the North correlates with the periodical movement of axis rotation into the 

Earth’s body and change of the rotation velocity. The intensity of sedimentary areas expansion is minimal in 

Jurassic and Cretaceous and much more in Triassic and Cenozoic especially. The transgression maximum 

was in latitude interval 20-40 O for the North hemisphere for the all studied geological epochs. It has been 

established the minimal transgression for subequatorial areas and notable increase to the more higher 

latitudes, in particular for the South hemisphere. 

336


This fact is accorded to the conclusion on variations of theWorld Ocean level in equatorial and high 

latitude areas at the Earth’s axial rotation of velocity change. It has been distinguished intervals of magmatic 

activation in Phanerozoic stage according geological data. These are compared with precalculated of changes 

of velocity and the axis of rotation of the Earth. 

The oscillating evolution of the tidal forces in the Sun-Earth-Moon system should be produce 

temporal cycles in the Earth’s geodynamic processes and latitudinal shifts in the geological scale of time. 

The Phanerozoic history of the Earth includes phenomena of acceleration of tectonic movements that are 

marked in rock sequences of the Earth’s crust by folding, angular unconformities, fault tectonics, 

emplacement of large and small intrusions, rock deformations, transgression –regression phases and so on. 

Irregularity in the Earth’s tectonic history is characterized by a cycle pattern. In addition, periods of 

tectonic activation and intervals between tectonic cycles have different durations. An overview of cyclic 

manifestations in the Earth’s tectonic history given in V.Khain [2000]. It is devoted to analysis of quasiperiodic 

tectonic activity (known as Wilson, Bertrand, and Stille cycles) with a significantly different 

duration. H.Stille considered the relatively short-term (about 30 Ma) planetary orogenic phases and devided 

them into epochs of relative tectonic repose. M.Bertrand devided the Earth’s geological history into five 

cycles with a longer duration (Baikalian, Caledonian, Hercynian, Cimmerian, and finally, Alpine). Wilson’s 

cycles are long-term ones. The cyclicity is attributed to diverse processes ranging from predominant vertical 

movements, with produce geosynclinal-orogenic structures, to tectonics of lithospheric plates (convection in 

337


the mantle and horizontal displacements of continents) and galactic processes (intersections of asteroids and 

comets by the solar system and the Earth). 

Our previous works devoted to the latitudinal shift of domains of continental sedimentation amd 

magmatism in the Phanerozoic history of the Earth revealed significant correlations with the trend of tidal 

evolution of the Earth – Moon – Sun system [Avsjuk et al., 2005, 2007]. Continuing these investigations, we 

analyzed the areas (within the present day continents) of the Caledonian (terminal Early – initial Middle 

Paleozoic), Hercynian (terminal Devonian – initial Triassic), Cimmerian (Mesozoic), and Alpine (terminal 

Mesozoic–Cenozoic) terranes in separate latitudinal zones (with latitudinal intervals of 60° – 40°, 40° – 20°, 

and 20° – 0° N and S) in order to assess the possible contribution of the tidal forces to the Earth’s tectonic 

activity at the Phanerozoic stage of its evolution. Counting of areas based on the Tectonic Map of the World. 

Scale1 : 25 000 000 [Khain,1982] was carried out using an overlay grid ( 0,5 x 0,5 cm in size) with the 

subsequent adjustment to the map scale (Table 1, Fig.2). 

Tectonic 

cycle 

Alpides 

Cimmerides 

Hercynides 

Caledonides 

Phanerozoic folding areas in latitudinal zones; relative areas 

Northern latitudes Southern latitudes 

Table 1. 

60° - 40° 40°- 20° 20°- 0° 0° - 20° 20°- 40° 40°- 60° 

0.107 

0.041 

0.023 

0.051 

0.232 

0.098 

0.048 

0.031 

0.149 

0.019 

0.021 

0 

0.178 

0.001 

0.012 

0.002 

0.053 

0.015 

0.012 

0.020 

0.054 

0.046 

0 

0.020 

The graph shows that the Northern Hemisphere is characterized by a continuous expansion of areas 

occupied by the Hercynian, Cimmerian, and Alpian stages. Domains of the Caledonian orogeny do not fit 

this pattern, probably because their areas are very small and the Caledonides are overlapped by younger 

geological processes. The folding is maximal in the 20° – 40° N belt for the Hercynian, Cimmerian, and 

Alpine stages. 

In the Southern Hemisphere, the maximal tectonic activity is recorded in the equatorial belt (0°– 

20° S) for the Hercynian and Alpine stages. In general, the latitudinal dependence of tectonic activity is less 

prominent for the Southern Hemisphere, probably due to the small area of continents in this part of our 

planet. 

Thus, the analysis of domains subjected to different stages of folding during the Phanerezoic history 

of the evolution of the Earth indicates that the Earth’s tectonic activity was maximal in the 20° – 40° N belt. 

This fact confirms that processes of tectonic activity were inherited in time. 

Comparison of plots of variation in the relative intensity of folding (Stille cycles) for different 

latitudinal intervals (Fig. 1) with the plot of tidal evolution of the Earth – Moon – Sun system [Avsyuk et al., 

2008] (Fig.2) revealed the following fact: taking into consideration uncertainties of age intervals of tectonic 

338


activities of the four cycles indicated in Fig.2, their timings fit the periods of rapid variations in the 

equatorial position, shape, and rotation velocity of the Earth. We believe that precisely these time intervals 

were characterized by intense variations in the stressed state of the lithosphere (vertical and horizontal 

components), resulting in irregular deformations (folding, overthrust folding, and so on). According to model 

[Avsyuk, 1996], tectonic activity is manifested in various latitudinal intervals during different geological 

periods. This feature is particularly prominent in the Northern Hemisphere. 

Fig. 2.Scheme of the relative intensity of manifestation of different 

epochs of folding in latitudinal zones in the Northern and Southern 

hemispheres: (1) Alpides; (2) Cimmerides; (3) Hercynides; 

(4) Caledonides. 

ACKNOWLEDGMENTS 

This work was supported by the Russian Foundation for Basic Research, Project no. 07-0-500-387. 

REFERENCES 

Avsyuk, Yu.N. (1996), Tidal strengths and natural processes, Moscow, UIPE, 188 pp. 

Avsyuk, Yu.N., Yu.S. Genshaft, A.Ya. Saltykovsky (2005), Latitude dependence of sedimentation 

basins as a result of tidal evolution and change of rotation’s velocity of the Earth, Europian 

Geophys. Union. General Assembley Abstracts, vol.7, Vienna, Austria. 

Avsyuk, Yu.N., Yu.S.Genshaft, A.Ja. Saltykovsky et al. .(2007). Lateral activation of magmatism 

as reflection of cycle movement of tidal evolution in the Earth-Moon-Sun system. Doklady 

Academii Nauk , vol. 413, N1, 66-67. 

Khain, V.E. (2000), Geotectonics, no. 6(3), 43.1 

Khain V.E. (1982), Tectonic map of the World 1:25 000 000, Depart .of Geodez. and chartography. 

Glavn. Upravl. Geodez. Kartograph. Sov. Min. SSSR, Moscow. 

Avsyuk Yu.N., Yu.S. Genshaft, A.Ya. Saltykovsky, Yu.F. Sokolov, Z.P. Svetlosanova (2008), 

Specific Features of the Latitudinal Manifestation of different-age Folding Phases in the Earth’s 

Tectonic History. Doklady Earth Sciences, vol. 419a, no.3, 400-402. 

339


Introduction 

MULTIFRACTAL AND TOPOLOGICAL ANALYSIS OF SOLAR 

MAGNETIC FIELD COMPLEXITY 

Knyazeva I.S., Milkov D.A. 

The Central Astronomic Observatory RAS, St. Petersburg, Russia, 

e-mail: milkov@yandex.ru 

Abstract. The main purpose of this work is searching of the probable precursors of X-flare 

events using MDI data of full solar disk. To analyze this data we use the multifractal 

microcanonical formalism applying Choquet capacity as measure. We build the map of 

exponent so-called Holder exponents for every MDI fragment containing an active region. 

These values specify the sudden change in a picture contrast. In addition, we provide the same 

analyze for inverted image. After that we estimate the two first Betti numbers for both couple 

of MDI fragments and corresponding couple of Holder maps. The first one specify the number 

of image connectedness components and second one define the number of “holes” of one 

polarity relatively another. We suppose that the Betti numbers variation may be used as a 

precursor of X-flare event. 

We analyze the four active regions and obtained the following result. For MDI data the Betti 

numbers variations of X-flare active region are very different from flare-quiet active region. 

Furthermore, the Betti numbers for Holder maps display the sudden change for 24 hours before 

the X-flare event. 

In the beginning of the work for searching the X-flare event precursors, we proceed from the following 

assumptions. We suppose that the X-flare event precursor (i.e. event with power more then 10 -4 Wt/m 2 ) must 

be connected with magnetic flux buoyancy in active region. This flux changes the topology of digital image. 

Consequently, the changes of this topology should be contained in variations of picture contrast gradient. 

We use the Michelson-Doppler Imager (MDI) magnetograms of full solar disk 1 . The main difficulties we 

faced to challenge during working with nagnetograms were connected with the features of high-resolution 

digital images. First of all, MDI magnetograms are characterized by high variability of contrast, what means 

that values of grey-level changes significantly form pixel to pixel. Second, statistics of brightness distribution 

of magnetograms have power law dependence as in the most nature images [1,2], so the dispersion increases 

without the limit with sample extension (Figure 1). That’s why, we couldn’t apply the standard methods based 

on second order Pearson’s statistics to magnetograms analysis. 

Multifractal microcanonical formalism [3] is used as a main approach for such image processing. In addition, 

we use the methods of computational topology for X-flare event precursor diagnostics. 

Methods 

Let’s suppose that our magnetogram given as intensity field: I( xy , ); xy , ∈ Z× Z . Let’s define the image 

intensity measure by following formula [3]: 

2 2 

μ = lim∫ ε →0 

A 

⎛I( x+ ε, y) − I( x, y) ⎞ 

⎜ ⎟ 

⎝ ε ⎠ 

⎛I( x, y+ ε) 

−I( 

x, y) 

⎞ 

+ ⎜ ⎟ dS , 

⎝ ε ⎠ 

where A is a compact, dS = dx ∧ dy . 

If we want to use a multifractal formalism for image analysis the measure of the image should satisfy the 

scale invariance properties[4]: 

h( x) 

μ ( A)~ r . 

1 http://soi.stanford.edu/magnetic/index5.html (1024x1024 resolution, 90min discrete) 

340


σ 

× 500 

Figure 1 

Dispersion increases without limit during extension sample 

In fact, the image measure yields such condition if the original image has typical spectrum (Figure 2). 

Apparently, such spectrum exists also for MDI magnetograms [5-7] and we could use multifractal formalism 

in MDI magnetogram analysis. 

As a matter of fact, multifractal analysis is transition at each point of the image from measure to Holder 

exponent[3]. The main idea is as follows. In neighborhood of pixel Br ( x) we find the amount of grey μ 1 1 . 

Further, with increasing the neighborhood to Br ( x ) on a whole number of pixels and deriving the series of 

2 

neighborhood sizes r1 < r2 < r3 < r4 

< ... we’ll receive the set of measures μ1, μ2, μ3, μ 4... 

. Then in a double 

double logarithmic scale we find Holder exponent for every pixel as the slope log μ = hx ( ) log r. 

However, in general the sequence of log μ1/ log r1; log μ2 / log r2; log μ 3/ log r3;... 

is not stable for MDI 

data. Therefore, we cannot to draw a straight line for exponent computing. To overcome this difficulty we use 

as a measure the Choquet capacity [8]. The main feature of such measures is monotonicity property. In other 

words, if A⊆ B then μ( A) ≤ μ( 

B) 

. We may obtain the Choquet capacity by various methods. In figure 3, 

we could see the example of estimation Choquet capacities for one of neighborhood. The μ max capacity is 

defined by maximum value in consider neighborhood. The μ min capacity is defined correspondingly by 

f(α) 

2 

1.8 

1.6 

1.4 

1.2 

1 

0.8 

0.6 

0.4 

0.2 

0 

-1 0 1 2 3 4 5 6 7 8 

α 

Figure 2 

Obtaining multifractal spectrum for MDI magnetogram 

341


minimum value in consider neighborhood. The μ iso capacity is defined as the number of pixels that differs 

from central pixel by definite level: 

| p( i) − p( j)| ≤δ⇒ p( i) p( j) 

. 

μ = #{ j| p( j) p( i )} 

In our work, we use the μ iso capacity. 

Figure 3 

Corresponding Choquet capacity: 

= 255, = 25, = 2( = 2) 

μ μ μ δ 

max min 

iso center 

Thus for every pixel we receive correspondent Holder exponent and as a result we obtain the Holder exponent 

map (Figure 4). Then we invert original magnetogram and her exponent map. 

Later we use the methods of computing topology [9]. We use the variation of topology invariants (calling 

Betti numbers) as a precursor of X-flare event. With these characteristic we distinguish one magnetogram 

from another. Roughly speaking, the β 0 number display the component number of image connectedness and 

the β 1 number display the “holes” number. For example in figure 5, it is shown the digital image piece and its 

Betti numbers. As we can see at this Figure there is a one connectedness area as well as the “hole” is one. 

In formal approach for the Betti numbers calculation the homology theory is used [9]. Within the bounds of 

this theory cycles which could not be retract to point and boundaries which could be retract to point could be 

distinguished. Therefore, as we can see at Figure 5, the three cycles could be built. At this Figure I, J and K 

are cycles, but K is a boundary. I and J are homologous, but K is not. Betti numbers are defined with the set 

of all such cycles. 1 

β the number of connectedness. 

β gives us the number of holes and 0 

Active 

region 

iso 

Figure 4 

The Holder exponent map for active 

342 

⎛ 25 0 27⎞ 

⎜ 

0 255 0 

⎟ 

⎜ ⎟ 

⎜ 254 25 0 ⎟ 

⎝ ⎠ 

backgro 

und


We compute topological invariants both for original and inverted magnetograms and for original and inverted 

image of Holder maps. As a result we get four couple of such numbers. So, for active region which was 

observed during five days we obtain time series of Betti numbers with near 80 values. 

Results 

For exploration of the original magnetogram it was decided to investigate difference of corresponding Betti 

numbers for positive and negative images. We found out the distinction in variation of such difference for Xflare 

active region and flare-quiet active region. For flare quiet regions the differences oscillates near zero, but 

for flare active regions Betti differences were strongly above or under the zero level (Figure 6). From 

physical point of view such behavior signals that during the activity in region there is a prevalence of one 

polarity before another. 

p n 

-β0 

β 0 

p n 

-βi ; i=0,1 

β i 

700 

600 

500 

400 

300 

200 

100 

1500 

1000 

500 

0 

-500 

0 10 20 30 40 50 60 70 80 

# fits 

flare-quiet active region 

-1000 

0 10 20 30 40 

Figure 5 

For given image digital piece β 0 =1, β 1=1. 

Cycle I and J are 

homologous. Cycle K retracts to point 

# fits 

X-flare active region 

p n 

-β1 

β 1 

500 

0 

-500 

-1000 

-1500 

-2000 

-2500 

0 10 20 30 40 50 60 70 80 90 

# fits 

p n 

β -β0 

0 

p n 

β Figure 6 

-β1 

1 

We find out the distinction in variation of 

such differences for X-flare active region and 

flare-quiet active region. The difference 

oscillates near zero or in the various half 

planes 

343


The second result is connected with the investigation of Holder exponent maps. It was observed that 24 hours 

before the X-flare event there was a sudden change in Betti numbers for Holder maps images (Figure 7). 

Probably this confirms our assumption about magnetic flux buoyancy before the X-flare event and changes in 

the image topology. 

Conclusions 

The results obtained during the research are very interesting. The sudden change of gradient 24 hours before 

the X-flare events gives us evidence that we choose the right way of investigation. Further, of course we must 

increase the amount of exploration regions to provide more statistical significance results. The same is correct 

for effects of flare active or flare quiet regions. Naturally it is very useful to distinguish only by image 

whether region is flare active or flare-quiet. 

Reference 

β i ; i =0,1 

12000 

10000 

8000 

6000 

4000 

2000 

0 

0 10 20 30 40 50 60 70 80 

1. Turiel, A., N. Parga, The multi-fractal structure of contrast changes in natural images: from sharp edges 

to textures, Neural Computation, (2000). 12, P.763-793 

2. Huang J., D. Mumford, Statistics of Natural Images and Models, Proc. of the ICCV, (1999). № 1. P. 541– 

547 

3. Turiel, A., H. Yahia, C.J Pérez-Vicente, Microcanonical multifractal formalism — a geometrical 

approach to multifractal systems: Part I. Singularity analysis, J. Phys. A: Math. Theor., (2007). 41. 

015501 

4. Falconer K. Fractal geometry. Mathematical foundations and applications. John Wiley & Sons. (1990). 

5. Lawrence J.K., Ruzmaikin A.A., Cadavid A.C., Multifractal measure of the solar magnetic field, The 

Astrophysical Journal, (1993). 417, P.805-811 

6. Abramenko, V.I.: Multifractal analysis of solar magnetograms, Solar Phys., (2005), 228, P.29–42. 

7. Conlon, P.A., P.T. Gallagher, R.T.J. McAteer et al., Multifractal Properties of Evolving Active Regions, 

Solar Physics, (2007). 10.1007/s11207-007-9074-7 

8. Kruglun, O.A., L.M.Karimova et al. Multifractal analysis and simulation of magnetograms of the full 

Solar disk, Solnecno-Zemnaya Physika, (2007). 10. P.31-42 (in Russian) 

9. Zomorodian, A. Topology for Computing. (2007) Cambridge Monographs on Applied and 

Computational Mathematics 

flare 

# fits 

p 

β (h) 0 

n 

β (h) 1 

flare 

Figure 7 

We can see the sudden change 24 hours before the X-flare event 

344


NONLINEAR ANALYSIS OF CAUSAL RELATIONSHIPS BETWEEN 

SOLAR AND GEOMAGNETIC TIME-SERIES BY MEANS OF SYMBOLIC 

DYNAMICS 

O. L. Oposhnyan 1 , D. I. Ponyavin 1 , N. G. Makarenko 2 

(1) Institute of Physics, St. Petersburg State University St. Petersburg, Russia, 

e-mail: karina2383@yandex.com, dponyavin@mail.ru; 

(2) Central (Pulkovo) Astronomical Observatory of RAN, St. Petersburg Russia, 

e-mail: ng-makar@mail.ru 

Abstract. Causal relationships between geomagnetic indices aа and sunspot numbers were 

analyzed over a period 1868-2006. We studied nonlinear dynamics of time series by transforming 

them into symbolic words, according ordering relationships between records. The technique was 

tested first using logistic maps. It was shown that the method can be applied to detect regularities 

in a raw data and reveal intercorrelations of time series. Correlations between solar and 

geomagnetic dynamics are low and relatively best with delay of 3-4 years. 

Introduction 

Detection and estimation of interrelations between two dynamical systems using observable time series is a 

complex and ambiguous problem [1]. The linear analysis is focused on revealing linear correlations, and can 

lead to the false results, due to the noise of unknown origin. Besides that, linear relationships can simply be 

absent. In the present paper one of nonlinear tools, based on symbolical dynamics is tested [2, 4]. The main 

idea of this technique consists in transformation of time series into symbolic form by using order 

relationships between values. Each word of this text represents the definite code, taking into account the 

order ship between successive records [2, 3]. The primary advantage of this method is in admission of errors 

but only those which do not disturb the orderships in records. Moreover this technique allows use short time 

series. Further, it will be shown, that the method is quite sensitive to the level of connectivity between 

systems. 

Let n { i} i 1 

Symbolic technique 

n 

≡ - scalar time series, consist of n scores and { m} 

X X X Р 1 2... 

X x = 

m extracted from X n . For instance, assume that first four indications are: 

P 

1 

{ X X X } = ( 90 , 60 , 120 , 30 ) 

= X 

1 

2 

3 

4 

= , be a sequence of length 

We will code this sequence by 4-h numerals of natural series being based on the attitude of the strict order 

between readouts (>,


Test model 

To test model two raw data generated by the logistical equations [1] are used: 

⎧⎪ xn ( + 1) = λ1xn 

( )(1 −xn 

( )) 

⎨ 

⎪⎩ 

yn ( + 1) = λ2yn ( )(1 − yn ( )) + ε y n −x( 

n) 

with parameters λ λ x( ) y( 

) 

2 2 ( ( ) ) 

1 = 2,5; 2 = 3.2; 0 = 0 = 0.1. 

Coupling parameterε is introduced, number 

N = , word length m = 4 . 

of iterations 1000 

Occurrence rate of the words for each of time series was compared, by means of difference of 

corresponding histograms. It was supposed that the histograms differ slightly from each other in case of 

interaction of the systems. And, by contrary, difference is essential if systems are independent. 

The degree of difference of the histograms can serve as estimation of degree of coupling between systems. 

We notice that some of the words are frequently occurred or absolutely absent. 

0132 

0132 

0231 

0312 1230 

0213 1302 1320 

0231 1230 

0312 

0312 

1320 2013 3102 

2013 

2031 

3021 

0132 

0213 

0231 

0132 0213 

0312 

1302 

1230 

1320 2013 

1302 1320 

0312 2031 

(1) 

A B 

С D 

Figure 1. Histograms of occurrence rate of all possible words of time series produced by system (1): A. At 

parameter ε = 0 (no coupling); B. ε = 0.6; C. ε=0.8; D. ε=1.1 (strong interaction). 

The sum of bars of difference histograms for various values of ε is presented in Table 1. 

Table 1 

Parameter of coupling, ε Sum, ∆ 

ε = 0 ∆ =100 

ε =0.6 ∆ = 43 

ε =0.8 ∆ = 16 

ε =1.1 ∆ = 6 

From the Table 1 it follows that the value of sum ∆ depends strongly on the interaction between systems. 

346


Application to the real-world data 

We have used annual means of geomagnetic indices аа 1 and sunspot numbers 22 for the period 1868- 

2006. It is known, that the geomagnetic cycle is not completely synchronized with 11-year cycle of solar 

activity. The geomagnetic cycle in average lasts a sunspot cycle. 

At the same time the recurrent geomagnetic activity during a declining phase of solar cycle correlates 

with subsequent solar cycle [5] that can is used in forecasting of solar activity [6]. 

Thus, the dynamics of geomagnetic activity are controlled by a current cycle and, apparently, correlates with 

the following cycle. Herewith we compare the time series of solar and geomagnetic activity by shifting 

sunspot series back relative to geomagnetic records. 

In case of shifts for 3 and 4 years the sum of bars of difference histograms became a minimal. A similar 

result has appeared for shifts of 2 and 5 years. 

Аa-Volfs_without lag 

0123 

0213 1023 

А a-Volfs_with lag 3 years 

0123 

0213 1023 

2130 3012 

2130 

3012 

3210 

3201 

3210 

3201 

А a-Volfs_with lag 6years 

0123 

0213 

1023 2130 3012 

3201 

А a-Volfs_with lag 12 years 

0123 

0213 

3210 

3210 

1023 2130 

3201 

2103 

2310 

3102 

Figure 2. A difference of frequency histograms of sunspot and geomagnetic time series for various shifts. 

In the Table 2 the sum of column differences of histograms for various shifts are presented. 

Table 2 

Shift, years Sum, ∆ 

without shift ∆ =98 

1 year ∆ =99 

2 years ∆ =96 

3 years ∆ =92 

4 years ∆ =92 

5 years ∆ =96 

6 years ∆ =94 

12 years ∆= 99 

1 http://www.wdcb.rssi.ru/stp/data/geomagni.ind/aa/aa/ 

2 http://www.ngdc.noaa.gov/stp/SOLAR/ftpsunspotnumber.html 

347


Conclusions 

• Symbolic analysis can be applied for revealing of nonlinear coupling between dynamical systems. 

• Correlations between sunspot and geomagnetic dynamics are low. The best correspondence is 

observed at delay 3-4 years of geomagnetic activity relative to sunspot time series. 

Bibliography 

1. Bezruchko B.P., D.A. Smirnov. Mathematics modeling and chaotic time series. Saratov State Univ. 

Press, 2005, 320 p. 

2. Daw C.S., C.E.A. Finney, E.R.Tracy. A review of symbolic analysis of experimental data, Rev. 

Scientific Instruments, 2003, vol. 74, 915-930. 

3. Bandt C., B. Pompe. Permutation entropy: a natural complexity measure for time series, Phys. Rev. 

Lett., 2002, vol. 88, 174102. 

4. Monetti R., W. Bunk, F. Jamitzky. Characterizing synchronization in time series using information 

measures extracted from symbolic representations./ arXiv: 0804.4634. 

5. Ohl A.I., G.I. Ohl. A new method of very long-term prediction of solar activity, In: Solar-Terrestrial 

Predictions Proc., Boulder Colo., 1979, vol. 2, 258-263. 

6. Hathaway D.H., R.M. Wilson. Geomagnetic activity indicates large amplitude for sunspot cycle 24, 

Geophys. Res. Lett., 2006, vol. 33, L18101, doi:10.1029/2006GL027053. 

348


MULTISCALE INTERMITTENCY IN PHYSICS AND PHYSIOLOGY 

Introduction 

V.M. Uritsky 1 and N.I. Muzalevskaya 2 

1 University of Calgary, AB, Canada, e-mail: vuritsky@phas.ucalgary.ca; 

2 St. Petersburg State University, St Petersburg, Russia 

We review our recent results in multiscale intermittency analysis of correlated stochastic behavior 

in complex natural systems. The approaches discussed include spatial higher-order structure 

functions, fractal time-series analysis methods, as well as spatiotemporal decomposition of timedependent 

turbulent fields into sets of discrete dissipation events. These approaches are illustrated 

by several examples, including flaring activity in the solar corona, electron precipitation dynamics 

in the auroral zone, and multiscale fluctuations in human cardiovascular system. In each 

application, the proposed intermittency measures provide significant new information about the 

scaling regimes, correlation patterns, and the underlying thermodynamic states of studied systems. 

This paper summarizes recent advances in the applications of methods of dynamical complexity to 

complex physical and physiological systems. Due to the size limitation, it primarily focuses on original 

contributions by the authors. To compensate for this bias, references to more comprehensive review articles 

will be given throughout the text. The main outcome of our analyses is an innovative methodology relating 

statistical properties of intermittent processes in natural systems with their large-scale, low-dimensional 

behavior. This conceptual link provides an opportunity to better understand the relationship between 

stochastic and deterministic dynamics of complex systems, to classify their internal instabilities as well as the 

response to an external driver, and to predict future changes. 

The paper starts with a brief systematic overview of computational approaches for dealing with complex 

intermittent signals. Next, we present two examples of intermittent complexity and critical avalanching in 

turbulent space plasmas. Our third example (stochastic aspects of heart rate variability) features intermittency 

beyond physics, and shows diagnostic capabilities of multiscale complexity analysis in medical applications. 

Mathematical details will be kept at a minimum, with the emphasis placed on the interpretation of the 

processes under study. 

Spatial and temporal measures of intermittency 

Multiscale intermittency is a manifestation of dynamical complexity in driven spatially distributed 

nonequilibrium systems. Self-organized criticality (SOC) and intermittent turbulence (IT) represent two 

major paths to this dynamical state [3, 29]. In the classical fluid turbulence, scaling is often associated with a 

hierarchical structure of eddies extending over the inertial range, while in SOC, avalanches of localized 

instabilities organize the system toward a steady state exhibiting long-range correlations up to the system 

size. In both scenarios, intermittency implies strongly non-Gaussian behavior of studied variables which 

undergo frequent and sudden changes often resulting in “fat-tailed” distributions functions such as those 

descried by the Levy statistics. The statistical structure of intermittent signals also involves long-range (nonexponential) 

autocorrelations observed over many decades of temporal and spatial scales. The hierarchy of 

memory effects behind this structure is usually described by fractal and multifractal models, and it tends to 

exhibit nonstationary properties when studied over restricted time intervals. 

The nontrivial statistical signatures of intermittent signals makes it difficult to obtain their quantitative 

parameters. Slow convergence of sample estimates, undefined statistical moments, unresolved low-frequency 

spectral components, poor reproducibility of results, broad confidence intervals, and other complications are 

very common when such signals are analyzed by standard statistical tools. These problems reflect principle 

limitations of classical probability theory which, according to its underlying axiomatics, is not intended to 

deal with cooperative stochastic processes with many interacting degrees of freedom, and can only tackle 

their simplified counterparts obtained as expansions about solutions that disregard the interactions. 

A more adequate framework for dealing with multiscale intermittent processes is offered by the modern 

theory of dynamical complexity which aims at a quantitative analysis and physical interpretation of 

correlated stochastic behaviors in nonlinear interactive systems. The data analysis tools designed in this 

actively growing research field have been successfully applied to a variety of problems unsolvable by 

classical methods. 

349


Spatial intermittency. A large group of complexity methods is based on a generalization of the classical 

turbulence theory to the case when the dissipation field is represented by an inhomogeneous spatially 

correlated multifractal set [1, 29]. Following the ideas originated by A.N.Kolmogorov (1941), such irregular 

turbulent fields can be characterized by a collection of (unsigned) structure functions Sq (l) = 〈| A(x) – 

A(x + l) | q 〉x,|l|=l, where A is the variable under study (velocity, magnetic field, Elsässer variables, or a 

relevant passive scalar), x – spatial coordinate, l – displacement vector, q – the order of the structure 

function. It is expected that each structure function varies with the spatial scale as Sq ~ l ζ (q) . The ζ (q) 

dependence plays an important role in identifying the nature of the turbulent fluid. It takes the linear ζ =q/3 

form for the non-intermittent (homogeneous) 3D turbulence, and exhibits a more complicated scaling in 

intermittent systems [19]. In certain cases, the so-called extended self-similarity (ESS) analysis is also 

applied in which Sq is plotted versus a reference structure function (e.g. Sq (S3)). Such normalization yields 

relative values of ζ exponents, which is sufficient for validating many turbulent models. 

Temporal intermittency. The second group of tools that are commonly used to study intermittent systems 

is fractal and multifracal time series analysis methods. A time-series generalization of the structure function 

analysis is straightforward, and it provides a spectrum of temporal ς exponents. Some other methods are the 

detrended fluctuation analysis, wavelet transforms, methods relying on singular value decomposition of 

temporal signals in the vector space, a variety of fractal and multifractal tools, and adaptations of Fourier 

power spectral analysis for processing nonstationary signals [8, 11, 22]. The intermittency measures provided 

by these methods are scaling exponents and scaling functions describing the relationship between statistical 

memory effects across different time scales. Some of these methods are applicable to spatially distributed 

data fields and can be used as auxiliary tools for examining inhomogeneous scaling of turbulent processes. 

Intermittency in space-time. The third group of methods addresses the coupling between spatial and 

temporal aspects of the behavior of the complex system. This coupling is important because in many 

situations, complex processes simultaneously evolve in space and in time, and the interaction between the 

two is farily nontrivial. Paradigmatic examples of spatiotemporal intermittency in nonlinear systems with 

spatially extended degrees of freedom are critical avalanches of instabilities in sandpile SOC models and 

bursty localized energy dissipation in high-Reynolds number fluids. In our earlier works [23, 26], we have 

developed an approach for quantifying such manifestations of complex intermittent behavior which are 

abundant in nature and simulations. The approach is based on spatiotemporal decomposition of a continuous 

time-dependent turbulent field into a collection of discrete dissipation events composed of contiguous spatial 

regions of propagating activity. This nonlinear decomposition provides a detailed representation of the 

intermittent component in the studied dynamics in terms of its most essential statistical and topological 

features, while significantly reducing the amount of stored information. It also allows to selectively address 

different classes of intermittent disturbances based on multidimensional filtering criteria. 

Example 1: Solar corona 

Dissipation mechanisms in the solar corona are activated by changes in the configuration of its magnetic 

field which has distinct IT signatures [1]. Convection of magnetic fields leads to radiative transients, plasma 

jets, and explosive events known as flares. The latter are associated with spatially concentrated release of 

magnetic energy accompanied by localized plasma heating up to temperatures of 10 7 K, and can be observed 

by short-wavelength light emission. Flares tend to appear at irregular times and locations and exhibit 

broadband energy, size, and lifetime statistics with no obvious characteristics scales. This behavior is often 

interpreted as a signature of SOC [5]. 

We have studied time series of full-disk digital images of the corona taken by the extreme ultraviolet 

imaging telescope (EIT) on board the SOHO spacecraft in the 195A° wavelength band corresponding to the 

Fe XII emission. The data included two observation periods: 3240 images from a solar minimum period and 

4407 images from a solar minimum period, with a typical time resolution of 13.3 min. The EIT luminosity 

was analyzed as a function of time and position on the image plane. To characterized spatial intermittency of 

SOHO EIT images, we computed higher-order structure functions in which the luminosity was used as the 

relevant field variable A. To identify SOC avalanches, we used the spatiotemporal decomposition method 

[23] resolving concurrent events. Avalanching regions were identified by applying an activity threshold 

representing a background EUV flux. Contiguous spatial regions above the threshold were treated as pieces 

of evolving dissipation events, and their statistics have been evaluated. 

Our results suggest that the intermittency in the corona has a fundamental impact on the dissipation 

mechanism in this system (Fig. 1). The main energy resource for the flaring activity is the photospheric 

magnetic field. Its complex, highly fragmented spatial geometry contributes to the intermittent scaling of the 

350


radiated UV flux described by a nonlinear ζ (q) dependence. The model by Müller & Biskamp [19] which 

provides a reasonable fit to our data describes IT in an ideal MHD plasma resulting from direct energy 

cascades. On the hand, the power-law statistics of energy release events suggests that a significant fraction of 

plasma energy is liberated in the form of inverse cascades characteristic of SOC systems. The apparent 

contradiction cannot be resolved in frames of existing coronal heating theories, and can be a starting point of 

building a more general framework which would incorporate a bi-directional energy cascade associated with 

collaborative IT and SOC scenarios. 

(a) 

(b) 

Fig. 1. Coexisting signatures of IT and SOC in the activity of solar corona [26]. (a) Higher-order spatial structure 

functions of the EIT luminosity. The inset shows ESS plots exhibiting broad-band power-law scaling. (b) Relative 

(ESS-based) structure function exponents compared to turbulence models due to Kolmogorov (K41), She & Leveque 

(SL) and Müller & Biskamp (MB) [19]. (c) Energy distributions of coronal avalanches during periods of solar minimum 

and maximum showing robust power-law scaling indicative of SOC. The solar min distributions are shifted for easier 

comparison. Different colors represent several activity thresholds used to identify the avalanches. 

From a more practical point of view, it is evident that the process of coronal dissipation can not be 

predicted without taking into account its stochastic intermittent component which seems to control the 

primary energy conversion in the turbulent solar plasma [1]. One way to model future dynamical transitions 

in the corona is to reconstruct its magnetic network and to run a SOC algorithm that would reconnect 

magnetic loops thus producing flaring events. Such simulation would help reveal unstable magnetic 

topologies responsible for major flares, coronal mass ejections, and other space weather phenomena. 

Example 2: Earth’s magnetosphere 

The necessity of using complexity tools in magnetospheric research has fundamental reasons. Unlike 

solar wind turbulence which at the distance 1 AU from the coronal source can be considered as "fully 

developed", many, if not all, magnetospheric processes are usually in a highly intermittent transient state [4, 

28]. Sporadic bursts of energy dissipation, localized acceleration processes, non-steady driving, strongly 

inhomogeneous fluctuations involving both kinetic and MHD domains, and other forms of transient 

stochastic activity are fairly common in magnetospheric plasma. This messy, non-steady turbulent dynamics 

can not be adequately described by any of the established turbulence theories. However, it naturally fits in a 

more general framework of multiscale dynamical complexity providing a rich variety of methods for dealing 

with non-classical stochastic processes such as those observed in Earth's magnetosphere [7, 27]. 

Magnetospheric substorms are accompanied by a variety of intermitted processes in the auroral zone. 

Soon after the development of the basic substorm phenomenology, it has been realized that the nighttime 

auroral oval is not a simple latitudinally bound distribution of emission brightness and electric currents. The 

activity of this part of the ionosphere is extremely complex, and it incorporates a multitude of effects 

reflecting different conditions on the solar wind - magnetosphere - ionosphere coupling system. Examples of 

these are substorm expansion onsets, pseudobreakups, steady magnetospheric convection events with or 

without substorm activity, bursty bulk flows, sawtooth events, and other processes [2, 6, 21]. Despite a 

remarkable diversity of physical phenomena involved in the magnetospheric response to the solar wind 

driver, the output energy dissipation flux as estimated from particle precipitations in the nighttime aurora 

tends to cluster in intermittent spatiotemporal bursts obeying simple and nearly universal scale-free statistics 

[10, 12, 23]. 

351 

(c)


The term ”scale-free” has been coined in statistical mechanics of turbulent and/or critical phenomena to 

describe correlated perturbations with no characteristic scales other than the scales dictated by the finite size 

of the system, as opposed to scale-dependent perturbations reflecting physical conditions that vary across 

different scales [29]. Considered in the context of other geophysical processes, the nighttime auroral activity 

provides one of the most impressive examples of scale-free behavior in Nature. Thus, the energy probability 

distribution of electron emission regions as seen by the POLAR satellite exhibits power-law shape over 

about 6 orders of magnitude [23]. By combining POLAR data with ground-based TV observations [10], the 

power-law scaling range has been extended up to 11 orders of magnitude (Fig. 2). The consistency of the 

power-law slopes obtained from high-resolution ground-based auroral observations and those characterizing 

POLAR ultra-violet imager (UVI) data reveals an extremely wide range of power-law scaling of energy 

dissipation in the nighttime magnetosphere. 

(a) 

(b) 

Fig. 2. (a) A diagram explaining the 

idea of spatiotemporal tracking of 

auroral emission regions in time 

series of POLAR UVI frames 

(LBH-long filter). (b) Power-law 

probability distributions of electron 

emission areas obtained from 

ground-based all-sky camera data 

(triangles) and the POLAR UVI 

observations (squares) [10, 23]. 

It is worth noting that these scale-free statistics represent long-term ensembles-averaged properties of 

nighttime magnetospheric disturbances, and they can mask a more complex dynamics on the level of specific 

plasma sheet structures responsible for the generation of various forms of auroral precipitations. Our recent 

results [24, 25] confirm the causal relationship between the auroral precipitation statistics and the nonuniform 

morphology of the central plasma sheet. They show that the inner and the outer plasma sheet regions 

are responsible for distinct scaling modes of the auroral precipitation dynamics which can a manifestation of 

two competing substrm scenarios represented by the current disruption and the midtail magnetic 

reconnection models [13, 20]. Exploring such second-order scaling effects could help build a more solid 

theoretical link between the statistical and dynamical plasma descriptions, evaluate predictability of different 

classes of magnetospheric disturbances, and obtain statistical guidelines for designing future space missions 

targeted at multiscale plasma phenomena. 

Example 3: Human heart rate variability 

This section illustrates an intermittent stochastic behavior in a quite different system – the system of 

human homeostasis, monitored by the low-frequency component of heart rate variability (HRV) [9,17]. HRV 

is the temporal variability of the beat-to-beat RR-interval in human electrocardiogram which exhibits distinct 

intermittent properties in the frequency range 10 –5 − 10 –2 Hz [14]. In many cases, this variability is described 

by the power-law 1/f β dependence of Fourier power spectral density on the frequency f [9]. Typically, 1/f β 

HRV spectra with constant β are observed in healthy people, whereas pathologies and malfunctions are 

associated with more complex forms of spectral behavior. The connection between the broken fractality and 

the disease [15-18, 22] indicates a possibility of using 1/f β fluctuations for the purposes of clinical 

diagnostics, and stimulates further investigation of this phenomenon. In our previous studies, we have 

explored fractal and multifractal properties of HRV using a variety of time series analysis tools [15,17,18]. 

The results have confirmed that the low-frequency HRV is a sensitive marker of homeostatic processes. Here 

we present new results showing that intermittency measures of HRV can be used for early identification of 

pathological conditions. 

In addition to power-law spectral exponent β, we consider two intermittency parameters (a and T) 

describing nonstationary behavior of standard deviation in HRV signals as explained in Fig. 3. In medical 

applications, extreme abnormal values of σ and β are informative state parameters. The interpretation of σ 

is largely empirical and is carried out on the individual basis for different sets of symptoms. Earlier, we have 

proposed an interpretative system for σ understanding measurements in the SOC region of HRV regulation 

352


where the standard deviation plays a role of stochastic magnitude of dissipation losses under the conditions 

of fractal symmetry of homeostatic dynamics (σ i = σ F =σ ). Since the constant magnitude is a signature of 

the stationary balance between the supplied and dissipated regulatory energies, we suggest that in general, 

the parameter σ F can be used as a sensitive statistical marker of the current amount of available regulatory 

energy characterizing fractal self-organization of HRV for a broad range of physiological conditions. 

Distortion of fractal symmetry of HRV occurring outside the SOC region [17] reduces the scaling range of 

fractal R-R fluctuations, decreases available energy resource, and increases nonstationarity and intermittency 

in HRV, which requires a substantially different approach to interpreting σ and β measurements. 

σ = 

i 

−β 

( ) σ F = min{ 

σ i | S( 

f ) ∝ f } 

ti 

+ N 

1 2 

∑ RR t − RR t [ ti 

ti 

N 

N 

] , 

∈ , + 

+ 1 t= 

t 

Intermittency 

measures : 

i 

σ −σ 

F a = ; 

σ 

F 

T = 

a 

RR 

norm 

σ −σ 

F ≡ 

σ 

F 

1 

RR 

norm 

Fig. 3. Analysis of intermittency of HRV 

signals. The HRV sample is divided into 

subintervals of length N characterized by 

different degree of intermittency as 

measured by local estimates σ i of the 

standard deviation σ. The subinterval 

with the smallest σ =σF describes the 

“laminar” fractal component of HRV and 

is used to evaluate the intermittency 

indices a and T. 〈RR〉norm is the 

normalized age-adjusted average value of 

the R-R interval. 

Table 1. Intermittency measures of HRV for several cardiovascular disorders ( n – number of cases ) 

n a norm T Physiological characteristics 

Pathoadaptation dynamics prior to onsets of cardiac arrhythmias 

1.1 11 1.40 1.20 ± 0.06 1.27 ± 0.30 One week before an atrial fibrillation (AF) event 

11 4.20 1.19 ± 0.08 3.60 ± 0.20 3 days before AF 

11 7.30 1.37 ± 0.04 5.30 ± 0.10 1 day before AF 

1.2 7 1.40 0.89 ± 0.03 1.60 ± 0.40 Prior to atrial palpitation (AP), sinus tachycardia 

1.3 9 1.50 1.18 ± 0.04 1.30 ± 0.30 Prior to AP, sinus bradycardia 

9 7.40 1.35 ± 0.02 5.50 ± 0.20 Same, 1 day before AP event 

Myocardial infarction, case 1 

2.1 1 4.26 0.82 5.19 Acute condition, first week 

1.10 0.93 1.18 3 weeks later 

0.54 0.98 0.56 4 months later 

0.24 1.07 0.22 Rehabilitation 

Myocardial infarction, case 2 

2.2 1 >10 0.78 >10 Acute condition 

4.60 0.86 5.35 Intensive care (reanimation) 

>10 0.79 >10 Critical condition 

Ischemic brain stroke, case 1 

3.1 54 2.81 1.08 ± 0.05 2.60 ± 0.60 Acute condition 

54 0.86 1.08 ± 0.02 0.79 ± 0.29 Before discharge from hospital 

Ischemic brain stroke, case 2 

3.2 14 3.45 0.96 ± 0.03 3.59 ± 0.73 Acute condition 

12 7.12 0.80 ± 0.06 8.80 ± 0.90 Coma 

To evaluate the intermittency of HRV signals, we use two constituents of the standard deviation – its 

stationary fractal component σ F as well as the nonstationary component σ –σ F. Each component has its own 

diagnostic value, while their balance which is reflected by the definitions of a and T (see Fig.3) is a sensitive 

measure of turbulent intermittency in the HRV signal. Both a and T are small (of the order of 0.1) for healthy 

unperturbed homeostatic regulation, and they gradually increase with an increase of mental concentration 

and emotional load. Pathological conditions (Table 1) are characterized by much higher levels of a and T 

353


indicating a significant increase of HRV intermittency in disease. For T >10, self-organization homeostatic 

processes necessary to maintain normal HRV are effectively replaced by random intermittency, a signature 

of a severe medical condition. 

Our new findings strongly suggest that the intermittency measures a and T can be used as empirical 

proxies for the available energy resource of the adaptation system. In pathological conditions, this resource 

significantly decreases as reflected by abnormal a and T values. Considering inherent nonstationarity of 

HRV signals observed for such conditions, it is also evident that the physiological interpretation of the 

standard deviation of R-R intervals – the quantity most widely used in clinical applications [14] – must be 

adjusted for different diseases and adaptation scenarios, depending on the relative contribution of the fractal 

(1/f β ) and the intermittent (a, T) variability to the studied stochastic signal. 

Concluding remarks 

We have provided several illustrative examples in which intermittency measures of seemingly random 

signals carry new information about system-level properties of studied processes. The common element of 

the complexity techniques that have been invoked in this context is their ability to characterize multiscale 

hierarchy of studied physical or physiological processes. This methodological advantage proves quite 

valuable when the macroscopic behavior is critically dependent on cross-scale interactions. The latter can be 

implemented in a real-space of spatially distributed geophysical systems, or in an abstract state-space of of 

complex dynamical system such as the system of human homeostasis. In both cases, adequately chosen 

intermittency measures can be used to obtain significant new information about the scaling regimes, 

predictability, correlation pattern, and functional stability of the studied system. 

References 

1. Abramenko,V. I. and V. B. Yurchyshyn, Astrophys. J., 597: 1135, 2003. 

2. Angelopoulos, V. et al. Phys. Plasmas, 6(11):4161–4168, 1999. 

3. Bak, P. et al., Phys. Rev. Lett., 59: 381, 1987. 

4. Borovsky, J. E. et al. J. Plasma Phys., 57:1–34, 1997. 

5. Charbonneau, P. et al. Sol. Phys., 203(2):321–353, 2001. 

6. Donovan, E. et al. J. Atmos. Sol. – Terr. Phys., 68(13):1472–1487, 2006. 

7. Freeman, M. P. and N. W. Watkins. Science, 298(5595):979–980, 2002. 

8. Glenny, R.W. et la. J. Applied Physiology, 70(6): 2351-2367, 1991. 

9. Kobayashi, M. and T. Musha. IEEE Trans. Biomed. Eng.,29:456–457,1982. 

10. Kozelov, B.V. et al. Geophysical Research Lett., 31(20 ), 2004. 

11. Kumar, P, and FoufoulaGeorgiou, E. Reviews of Geophysics, 35(4): 385-412, 1997. 

12. Lui, A. T. Y. J. Atmos. Sol.-Terr. Phys., 64(2):125–143, 2002. 

13. Lui, A. T. Y. Space Science Rev., 95(1-2):325–345, 2001. 

14. Malik, M. et al. Circulation, 93:1043–1065, 1996. 

15. Muzalevskaya, N.I and V.G. Kamenskaya, Human Physiology, 33(2): 179-187, 2007. 

16. Muzalevskaya, N.I et al., Zhurnal Nnevropatologii i Psikhiatrii Imeni Korsakova, 7: 54-58, 2002. 

17. Muzalevskaya, N. I. and V. Uritsky, In: Telemedicine: the 21st Century Informational Technologies, St. 

Petersburg: Anatolia Press, 209–243, 1998. 

18. Muzalevskaya, N.I. and V.M. Uritsky, In: Longevity, Aging and Degradation Models in Reliability, Public Health, 

Medicine and Biology, 1: 283–297, St.Petersburg: SPbGTU Press, 2004. 

19. Müller, W.-C. and D. Biskamp, Phys. Rev. Lett., 84: 475, 2000. 

20. Ohtani, S. I. Space Science Rev., 113(1-2):77–96, 2004. 

21. Sergeev, V. A. et al. J. Geophys. Res. – Space Phys., 98(A10):17345–17365, 1993. 

22. Stanley, H. E. et al. Physica A, 270:309–324, 1995. 

23. Uritsky, V. M. et al. J. Geophys. Res. – Space Phys., 107(A12):1426, 2002. 

24. Uritsky, V. M. et al. Ann. Geophys. (submitted), 2008. 

25. Uritsky, V. M. et al. Geophysical Research Lett., 35:L21101, 2008. 

26. Uritsky, V.M.. et al., Phys. Rev. Lett., 99: 025001-1 – 025001-4, 2007. 

27. Valdivia, J. A. et al. Advances in Space Research, 35(5):961–971, 2005. 

28. Voros, Z. et al. Space Science Rev., 122(1-4):301–311, 2006. 

29. Warhaft, Z. Proc. National Acad. Sciences United States Am., 99:2481–2486, 2002. 

30. Waldrop, M. M. Complexity: The Emerging Science at the Edge of Order and Chaos. New York: Simon & 

Schuster, 1992. 

354


FRACTAL CHARACTERISTICS OF THE SOLAR AND 

MAGNETOSPHERIC ACTIVITIES AND FEATURE OF THE AIR 

TEMPERATURE DYNAMICS 

O.D. Zotov 1 , B.I. Klain 1 


Abstract. Series of daily values of solar activity (Wolf's numbers), magnetospheric activity (Apindex), 

air temperature and global seismic activity for 1930-2000 were analyzed. Dynamics of the 

Hurst exponent and dynamics of the average for all series of the data were defined. The 

comparative analysis of geophysical environments characteristics has been made. Correlation in 

dynamics of the fractal dimensions of investigated series was found. Feature near 1960 year in 

dynamics of the Sun activity and the magnetospheric activity was found. It was revealed that till 

1960 dynamics of the air temperature does not correlate with dynamics of the magnetosphere 

activity, and after 1960 high correlation is observed. The hypothesis probably explaining features 

of investigated processes dynamics is considered. The change of a chaotic mode of the Sun 

activity there was near 1960. It has led to change of the geospheres dynamics character. This 

phenomenon can be interpreted as the noise induced phase transition in the Earth’s system. 

The view on a problem of Solar-Terrestrial interaction is that the Earth as the complex system of 

cooperating geospheres is a nonlinear system with own noise and the external stochastic influence caused by 

non-stationary processes on the Sun. We shall consider long period variations (duration of several tens years) 

of solar activity parameters of chaotic component, variations of amplitudes and fractal dimensions of 

geomagnetic activity and air temperature. 

Data. Series of daily values of solar activity (SSN - Sun Spot Numbers) [www.wdcb.ru] and solar 

activity chaotic component (SSN_Ch), geomagnetic (magnetospheric) activity (Aр-index) [ww.wdcb.ru], air 

temperature (Т) for six meteorological stations in Russia along Volga-river (Fig.1) from Astrahan to Vologda 

[www.meteo.ru] and geophysical parameters for other geospheres for 1930-2000 were analyzed. 

Fig. 1. Six meteorological stations in Russia along Volga-river. 

355


Method. For all series we calculated and analyzed: 

dynamics of sliding average ( for example Ap with letter M – Ap M ), sliding windows 365 points (1 year) 

and step 50 points (50 days); 

dynamics of sliding parameter of Hurst or Hurst exponent ( for example SSN H ), windows 365 points (1 

year), step 50 points (50 days). Hurst's parameter is interpreted as a fractal dimension; 

dynamics of sliding correlation coefficient (Ccor), windows 3650 points (10 years), step 365 points (1 year); 

dynamics of cumulative deviation from the average or difference integral curve (for example iTM); 

Algorithm of calculation of cumulative deviation from the average: 

n 1 

where xm 

= ∑ n i= 

1 

x 

i 

y 

k 

= 

k 

∑ 

i= 

1 

( x − x ) , 

and n – a number of the points in series. 

i 

Note. Dynamics of magnetospheric activity (Ap M) has features which are not present in dynamics 

of solar activity (SSN M). Dynamics Ар M contains 11-years component of dynamics of solar activity, but 

has essential differences. They are visible in details with characteristic time scale of several years order. 

Namely: local minimum Ар when SSN having maximum or maximum Ар on a SSN declining phase is 

observed. Dynamics of SSN amplitude does not define dynamics of amplitude of magnetospheric activity, at 

least, with time scales of solar cycle duration (Fig. 2a). 

At Fig. 2b we see feature of Ccor dynamics: its sharp declining begins in area of 1960. 

Fig. 2. a - dynamics of sliding average of solar SSN M and magnetospheric Ap M activities, b - dynamics of 

sliding correlation coefficient Ccor between SSN M and Ар M. The yellow vertical columns indicate the 

feature in area of 1960 here and further. 

Analysis: SSN – Ap. 

Dynamics of the sliding Hurst exponent for solar (SSN H) and magnetospheric (AP H) activity show 

on Fig. 3a. We see no correlation between these processes. At Fig. 3b we see good correlation between 

dynamics of cumulative deviation from the average Hurst exponent for solar and magnetospheric activity. 

Note the dynamics of i SSN H and i AP H curves means that amplitude of low-frequency components in 

spectra of solar and magnetospheric activity chaotic components was more till 1960 then after 1960. Fig. 3c 

shows a burst of amplitude of solar activity chaotic component near 1960 also. 

356 

m


Fig. 3. a - dynamics of the sliding Hurst exponent (H) for solar (SSN H) and magnetospheric (AP H) activity, 

b - dynamics of cumulative deviation from the average Hurst exponent for solar (i SSN H) and 

magnetospheric (i AP H) activity, c - dynamics of cumulative deviation from the average of solar activity 

chaotic component (i SSN_Ch M). 

We observe the feature of dynamics of chaotic component of solar and magnetospheric activity 

around 1960 year. 

Analysis: Ap – Temperature. We see some high correlation between dynamics of cumulative 

deviation from the average of chaotic components for all meteorological stations. Fig. 4a shows data for 

three stations only. Data of the other three stations have similar dynamics. 

Fig. 4. a - dynamics of cumulative deviation from the average (Hurst exponent) for air temperature i Т H, b - 

dynamics of sliding average amplitudes Ap and T, c - dynamics of cumulative deviation from the average 

amplitudes Ap and T. 

357


Also we see feature in dynamics of chaotic component of temperature: its sharp declining begins in 

area of 1960 (Fig. 4a). Simultaneously we see an appearance of correlation between an average amplitude of 

Ap-index and T near 1960 year (Fig.4b and Fig.4c).). We see low correlation till 1960 and after 1960 high 

correlation (see also Fig. 5b) 

What happens? What has occurred in dynamics of geospheres (correlation between magnetosphere 

activity and air temperature after 1960)? How this phenomenon can be explained? 

Correlation in dynamics of the fractal dimensions of the investigated series was found. Feature near 

1960 year in dynamics of the Sun activity chaotic component and the magnetospheric activity also was 

found. The dynamics of the air temperature does not correlate with dynamics of the magnetosphere activity 

till 1960 and high correlation is observed after 1960. 

First hypothesis: The change of a spectral structure (Hurst exponent) and burst of amplitude of 

chaotic mode of the Sun activity was near 1960. It has led to change of the geospheres dynamics character. 

The phenomenon can be interpreted as the noise induced phase transition in the Earth’s system. 

Second hypothesis: The technogenic influence on geospheres connected with a significant 

intensification of nuclear tests and the beginning of a space age has sharply increased in area of 1960. There 

is other possible reason of effect of correlation changes between temperature and magnetic field in this 

situation, namely, influence of the anthropogenous factor. 

Analysis: other geospheres. We find the features in dynamics of parameters of other geospheres in 

area of 1960 (Fig. 5 and Fig. 6). We used our results (Fig. 5b and Fig. 5c) and the published information 

(data, plots) for an illustration of the phenomenon 1960. We have changed appearance of some plots in 

comparison with originals, but have not changed their information. 

We see features in other geospheres dynamics in area 1960 year (Fig. 5 and Fig. 6). 

Fig. 5. a - global nuclear testing [npc.sarov.ru/issues/testing.html], b - correlation coefficient Ccor between 

average amplitude of Ap-index and T, c - global seismic activity M > 6, d - parameter of chaos in E-layer of 

ionosphere [Givishvili and Leschenko, 1998] 

358


Fig. 6. a - space launches and dynamics of ozone layer (www.evolunity.ru/books/dmitriev/TechOnNature), b 

-temperature in Sikhote-Alinsky reserve (www.tigers.ru/res/klm/klimat.html), c -equivalent height of the Flayer 

of ionosphere (www.kosmofizika.ru/irkutsk/kok/TMP183.htm). 

Conclusion. Simultaneous changes in geospheres (magnetosphere, ionosphere, stratosphere, 

atmosphere and lithosphere) in area of 1960 are the real geophysical phenomena. 

We are still far from clear understanding the concrete physical mechanisms of the Solar or human 

impacts on the Earth’s geospheres. 

First hypothesis: feature in geospheres dynamics near 1960 year is phenomenon of the solar noise 

induced phase transition in the Earth’s system of geospheres. 

Second hypothesis: feature in geospheres dynamics near 1960 year is phenomenon of the human 

impacts. 

The question of a source of changes in geospheres in area of 1960 for the time present remains still 

opened. It is not excluded also that both sources act on geospheres simultaneously. It is clearly we must 

consider all anthropogenic influence when analyzed the long period dynamics of various parameters of 

geospheres, and especially by search of correlations with solar activity. 

We would like to thank Prof. A.V. Guglielmi for his interest to this work and for some valuable 

remarks. This work was supported by Basic Research Program no. 16 “Changes in the Environment and 

Climate: Natural Catastrophes” of the Russian Academy of Sciences and Russian Foundation for Basic 

Research, project nos. 06-05-64143. 

REFERENCIS. 

Givishvili, G.V., L.N. Leshchenko (1998), Rhythms in ionosphere and in upper atmosphere of the Earth, 

Atlas of temporal variation of natural, anthropogenic and social processes. Volume 2. Cyclical 

dynamic in the nature and the society. M. Scientific World. 432 с. 

359


STOCHASTIC RESONANCE IN THE EARTH’S MAGNETOSPHERE 

O.D. Zotov 1 , B.I. Klain 1 , N. A. Kurazhkovskaya 1 


Abstract. The relationship between dynamics of average daily values of solar activity chaotic 

component (Sunspots number) and dynamics of average daily values of the Earth magnetospheric 

activity (Ap-index) has been investigated. The magnetosphere can be viewed as the system which 

is in a metastable state. The influence of external noise on such systems will lead to occurrence of 

casual switching between attractors of the system. As a result the geomagnetic activity will be 

defined by properties of the external noise. It is shown that exactly chaotic component of the solar 

activity defines features of magnetospheric activity dynamics. It is shown that using the method of 

nonlinear dynamic scanning it is possible to explain the dynamics of magnetosphere by the effect 

of a stochastic resonance. The simple model which explains statistics of the Ap-index has been 

suggested. In this model the Gaussian noise (the solar activity chaotic component) has an 

influence on an input of the system (magnetosphere). At the output of the system (Ар-index) the 

distribution of the noise has properties of the so-called “heavy tail”. 

Keywords: solar activity, magnetosphere, stochastic resonance. 

This paper deals with the problem of solar activity influence on the Earth magnetospheric activity. 

Series of daily values amplitude of solar activity (SSN - Sun Spot Numbers - Wolf's numbers) 

[www.wdcb.ru] and geomagnetic (magnetospheric) activity (Aр-index - Ap) [www.wdcb.ru] (Fig. 1a) for 

1930-2000 were analyzed. 

Fig.1. a - daily values dynamics of solar activity SSN and Earth magnetospheric activity Ap, b - dynamics of 

average amplitudes of solar SSN_M and magnetospheric activity Ap_M, c - dynamics of chaotic component 

amplitude SSN_Сh, d - dynamics of average amplitudes of chaotic component SSN_Ch_M and SSN_M. 

360


Dynamics of magnetospheric activity (Ap_M) has features which are not present in dynamics of 

solar activity (SSN M) (see Fig. 1b). Dynamics Ар_M contains an 11-year component of dynamics of solar 

activity, but has essential differences. They are visible in details with characteristic time scale in some years. 

Namely: a local minimum of Ар when SSN has maximum or a maximum of Ар on a SSN declining phase 

are observed. So dynamics of SSN amplitude does not define dynamics of amplitude of magnetospheric 

activity, at least, with time scales in solar cycle duration. 

In this paper we wish to answer the question – whether the solar activity contains the information on 

dynamics of magnetospheric activity? If “yes”, what parameter of dynamics SSN defines dynamics of Ар, 

what parameter SSN is geoeffective? The magnetosphere is a dynamic system in which the external force is 

generated by the sun. This force consists of quasi-periodic and chaotic components. Can exactly the solar 

activity chaotic component define the features of the Earth magnetospheric activity? 

Chaotic component SSN_Ch (see Fig. 1c) will be analysed. Note that dynamics of average amplitude 

of chaotic component SSN_Ch_M is also not define Ap_M, as SSN_Ch_M correlates with SSN_M (see Fig. 

1c). 

We have developed the approach considering the Earth’s magnetosphere as a nonlinear system with 

own noise, being under action of external force which is the Solar activity chaotic component. Even a weak 

external noise influencing nonlinear system can change effectively its condition. If there exists an optimum 

amplitude of chaotic influences on the nonlinear system, when a required signal-to-noise ratio has a 

maximum, it can be attributed to a stochastic resonance effect - SR. In the experiment, when there is no 

opportunity to operate the amplitude of chaotic influences, for search of the effect SR it is possible to use the 

concept which has the name of not dynamic threshold effect. [Anishchenko at all, 1999]. When analyzing 

chaotic components of solar activity for search of the parameter correlating with dynamics of the Ap-index, 

we have applied the SR method modified by us. 

Daily values of a chaotic component of the solar activity SSN_Сh have been analyzed. At each level 

of the comparison we get a signal which contains the basic features of a chaotic signal, namely a level of 

amplitude and an “average frequency” of dynamics SSN_Ch corresponding to this level. The concept of 

nondynamic threshold scanning was used in the authors modification. The signal SSN_Ch was transformed 

for the given level of comparison S so that signal SR SSN_Ch = 1 if SSN_Ch is transition through S and SR 

SSN_Ch = 0 if SSN_Ch is not transition through S. Further, we scanned the level S and for each level of a 

comparison S we calculated the correlation coefficient between average series SR SSN_Ch_M and the 

Ap_M. 

The result of analysis of chaotic component SSN_Ch by the method SR – curve SR SSN_Ch_M and 

its comparison with Ap_M at Ccor = maximum = 0.75 is presented at Fig. 2. SR SSN_Ch_M has a features 

of magnetospheric activity AP_M which are not present in dynamics of solar activity SSN_M. 

Fig. 2. Dynamics of geoeffective parameter SSN (SR SSN_Ch_M) and magnetospheric activity Ap_M at 

maximum Ccor. 

The magnetosphere can be viewed as the system which is in a metastable state. The influence of an 

external noise on such systems will lead to occurrence of casual switching between attractors of the system. 

As a result the geomagnetic activity will be defined by properties of the external noise. 

At the Fig. 3 we can see that there is an optimum of chaotic amplitude influences on nonlinear 

system (magnetosphere) when the required signal-to-noise ratio has a maximum. It is an essential attribute of 

361


SR. The magnetosphere is not so much sensitive to the amplitude, as to an nonstationarity external chaotic 

signal. 

Fig. 3. Correlation coefficient Ccorr for different levels of comparison. 

It is known [Horsthemke and Lefever, 1984], that if on an input the simple nonlinear system 

m 

x� = ( λx− x ) + σ ⋅ f( t) 

operates the δ - correlated noise, on an output of system the signal which distribution of amplitudes has a 

so-called “heavy tail” turns out. In such systems there are noise induced phase transitions. If magnetosphere 

belongs to a class of such systems and if solar activity chaotic component is a Gauss process, Ар with 

necessity will have Levy statistics (“heavy tail”). Whether this simple model explains the statistics of the Apindex? 

Fig. 4a shows that the distribution of daily values chaotic component of solar activity is a good δ - 

correlated noise (Gaussian noise - dark blue line). The correlation coefficient is 0.93. At the Fig. 4b and 

Fig.4c we can see distribution of daily values amplitude of Ap. 

Fig. 4. a - distribution of daily values chaotic component of solar activity, b and c - distribution of daily 

values of magnetospheric activity. 

Fig.5 shows that experimental distribution function of Ap-index amplitude (black points) is 

approximated by multiplication of power function and exponent function (dark blue line). This distribution 

with a “heavy tail”. Hence, the statistics of magnetosphere dynamics can be described by the model resulted 

above. 

362


Fig. 5. Distribution function of Ap-index amplitude. 

The main result of this study is that exactly chaotic component of the solar activity defines features 

of magnetospheric activity dynamics. 

Using the method of nonlinear threshold scanning it is possible to explain the dynamics of 

magnetosphere by the effect of a stochastic resonance. 

The simple model which explains statistics of the Ap-index has been suggested. In this model the 

Gaussian noise (the solar activity chaotic component) has an influence on an input of the system 

(magnetosphere). On an output of the system the noise (Ар-index) has properties of the distribution with a 

“heavy tail”. 

One of the primary goals of the research of a stochastic resonance (SR) in the Sun - Earth system is the 

search of geoeffective parameters in Sun Spot numbers. In systems with SR the basic processes leading to 

changes in structures do not belong to internal dynamics of system. Earlier in some works it has been shown 

that in large-scale dynamics of the magnetosphere (АЕ –index) an internal attractor is absent. Our researches 

of SR have shown that the ordered motion in magnetospheric dynamics is defined by the chaotic component 

of Wolf's numbers. 

We would like to thank Prof. A.V. Guglielmi for his interest to this work and for valuable remarks. 

This work was supported by Basic Research Program no. 16 “Changes in the Environment and Climate: 

Natural Catastrophes” of the Russian Academy of Sciences and Russian Foundation for Basic Research, 

project nos. 06-05-64143. 

REFERENCIS. 

Anishchenko, V.S., Neiman, A.B., Moss, F., Schimansky-Geier L. (1999), Stochastic resonance: noise 

enhanced order, UFN, 169(1), 7-38 (in Russia). 

Horsthemke, W., Lefever, R. (1984), Noise-Induced Transitions, Berlin, Heidelberg, N. Y., Tokio, Springer- 

Verlag. 

363


RESEARCH OF SHORT-PERIODICAL VARIATIONS OF INTENSITY 

OF THE GEOMAGNETIC FIELD IN SECOND HALF OF FIRST 

MILLENNIUM BC 

K.S. Burakov, I.E. Nachasova 

Institute of Physics of the Earth RAS, Moscow, e-mail: archaeomag@yahoo.co.uk 

Abstract. As a result of research of residual magnetisation of narrowly dating ceramics 

(amphoras with the seals) by the modified Thellier’s method were obtained the data about 

intensity of a geomagnetic field in East Mediterranean during V-III centuries BC. It was 

constructed averaged 11-annual curve for V-IV centuries BC that has allowed to find out 

"centenary" variation of intensity of a field on this time interval. 

For research “short-periodical” (with the periods in some tens – first hundreds years) variations of intensity 

of a geomagnetic field it is necessary to have detailed numbers data in hundreds years. Such data authors 

managed to receive only for of some areas of East hemisphere (from Spain up to Central Asia) for separate 

time intervals of last eight millennia [Burakov, et al. 2005; Nachasova, 1972; Nachasova, Burakov, 1994; 

1995; 1998; Nachasova, et al., 2007]. In all cases in change of intensity of an ancient geomagnetic field have 

been found out “short-periodical” variations. They have been allocated in change of intensity of a field in 

VI–V, II millennia BC. and last two millennia. 

Research of variation of intensity of a geomagnetic field in I thousand BC, lead on magnetization of a 

ceramic material from archeological monuments of Black Sea Coast (Crimea and Taman peninsulas) 

[Nachasova, Burakov, 2002; Nachasova, et al., 2007], has shown, that “short-periodical” variations are 

allocated not on all temporary pieces. So "centenary" fluctuation is allocated in variation of intensity of a 

geomagnetic field on a time interval II century BC. – II century AD., and practically it is not appreciable on 

more ancient temporary piece (V – III centuries BC.) on which, there is a fast sharp falling intensity of a 

geomagnetic field in I a millennium BC. On I thousand BC. the maximal values of intensity of a 

geomagnetic field for all period of last eight millennia have and during same time occurs there is one of the 

most essential changes of an average level of intensity of a field that does especially interesting research of 

structure of variations of a field during this period. 

For finding-out of a question on existence of a "centenary" variation on temporary piece V – III 

centuries BC., it was necessary receptions of some data about intensity of a field on magnetization of a 

ceramic material with narrow (within the limits of 20 – 30 years) dating. Such material is the imported 

ceramics from islands of east part of Mediterranean sea and from Asia Minor which is dated much more 

precisely, than the Caucasian and Crimean ceramics. The ceramics from islands of east part of Mediterranean 

sea (Kos, Lesbos, Fasos, Chios, Rhodes, etc.) and from Asia Minor (the cities of Gerakleja and Sinop) has 

been selected. The collection will consist of fragments of the amphoras selected from cultural adjournment 

of archeological monuments of peninsula Taman (basically from Phanagoria). 

Laboratory researches have been lead by means of the variant of Thelliers technique modified by 

authors (with amendments on anisotropy and chemical changes) [Burakov et al., 2005]. The researches lead 

earlier, have shown, that the regular divergence of the data received on materials from different areas of 

region east Mediterranean – Black Sea Coast is not present. 

For construction of a picture of variation of intensity of a geomagnetic field in second half of I 

thousand BC 61 determinations have been used. The determinations received on samples from one object 

(with one dating) were averaged. On a data set by means of sliding averaging the curve of variation of 

intensity of a field in V – IV centuries B.C., presented on Fig. 1 (the filled in points) is constructed. Interval 

of averaging – 11 years, shift – 10 years. Determinations of intensity of the geomagnetic field, received on a 

material, dated as III century BC. - only six. Obtained data are shown on fig. by hollow points. 

364


В, mkT 

90 

85 

80 

75 

70 

65 

60 

-550 -500 -450 -400 -350 -300 -250 -200 -150 

Years B.C. 

Fig. 1. Geomagnetic field variations in the eastern Mediterranean: suffused points - the curve of geomagnetic 

field variations obtained using all determinations; crosses -such a curve constructed using the most accurate 

data; the data obtained using the material dated as the 3-th century BC are marked by hollow points. 

The data received during the present research, have enabled to construct a curve of change of intensity 

of a geomagnetic field with a much greater detail and accuracy, than earlier. On this curve it is possible to 

allocate confidently time pieces on which the average level of intensity of a field varies a little. It is first half 

V of century B.C. and the second - the third quarters of IV century B.C. Distance between the middle of 

these time pieces approximately 120 – 130 years. Such kind of change of intensity of a field is reflection of a 

"centenary" variation. Fluctuation can be tracked on a time interval second half V – IV century B.C. It passes 

on a background of almost constant average level of intensity of field, its characteristic time can be defined 

approximately in 110 years. Thus, specification of a picture of change of intensity of a geomagnetic field on 

time interval V – IV centuries B.C. has allowed to find out a "centenary" variation of intensity of a field on 

this time interval. 

In the previous research mentioned above, the "centenary" variation on this time site has not been 

allocated, that, apparently, has been connected, on the one hand, with prevailing falling intensity of a field 

during second half of I millennium B.C., with another, - with influence of wide dating the investigated 

material led some distortion of a picture of change of intensity of a field on this time interval. 

That with the greatest probability to exclude influence of mistakes of definitions of intensity of a 

geomagnetic field at an assessment of limits of variation of intensity of a geomagnetic field on a considered 

time interval, from the received definitions the definitions received with high accuracy and certainty have 

been selected only. 

The definitions received on a material have been taken, which magnetic characteristics do not change 

after heatings (by results of research of variation of a magnetic susceptibility during heatings), and for which 

type of parity In/Irt (natural residual magnetization and thermomagnetization), as well as the constancy of a 

direction of vectors partial thermomagnetizations attests to absence of secondary heatings. It has allowed to 

receive determinations of intensity of an ancient geomagnetic field with the least deviation from true values 

(39 determinations). 

The picture of change of intensity of a field is well traced and on this data set (crosses on figure). On a 

curve constructed on the most exact data, "centenary" variation are shown more precisely. The maximum of 

a "centenary" variation is more brightly allocated, it is necessary on the middle of IV century B.C. The first 

minimum of this fluctuation is necessary on IV quarter of V century B.C. Position on a time scale of the 

365


second minimum of centenary fluctuation is defined less precisely, it is necessary approximately on a 

boundary IV – III centuries B.C. (probably – on IV quarter of IV century B.C.). 

Thus, received for V and IV centuries B.C. data about intensity of a geomagnetic field speak about 

presence of a "centenary" variation in this time interval, that in aggregate with results of some the previous 

researches testifies to a continuity of existence of this variation on an extent at least last two millennia. 

This work was supported by the Russian Foundation for Basic Research, project no. 06-05-65219. 

References 

Burakov, K.S., I.E. Nachasova, T. Najera, F. Molina and H.A. Camara, (2005), Geomagnetic Intensity in 

Spain in the Second Millennium BC. Izvestiya, Physics of the Solid Earth, V. 41, No. 8, pp. 622-633. 

Nachasova I.E., K.S. Burakov, (1994), Geomagnetic field intensity from the 3rd Century B.C. to the 6th 

Century A.D. in Termez (Uzbekistan). Geomagnetism and aeronomy, V. 34, No. 3, pp. 409-412. 

Nachasova, I.E., K.S. Burakov, (1995), Archaeointensity of the Ancient Geomagnetic Field in the 5th 

Millennium BC in Northern Mesopotamia. Geomagn. Aeron., No. 3, pp. 131–137. 

Nachasova, I.E., K.S. Burakov, (1998), Geomagnetic Field Intensity Variations in the 6th and 5th Millennia 

BC. Geomagn. Aeron., No. 4, pp.125–129. 

Nachasova, I.E., K.S. Burakov, (2002), Geomagnetic field intensity in century VI BC – century II AD. 

Geomagn. Aeron., V. 42, No. 2, pp. 284-287. 

Nachasova, I.E., K.S. Burakov, T.A. Ilina, (2007), Geomagnetic field intensity in the eastern Mediterranean 

region in the second half of the 1-st millennium BC and the beginning of our era. Izvestiya, Physics of 

the Solid Earth, V. 43, No. 12, pp.1024-1030. 

366


DATING OF THE CERAMIC MATERIAL FROM MONUMENT 

“MAISKAJA GORA”, USING DATA ABOUT INTENSITY OF THE 

GEOMAGNETIC FIELD 

K.S. Burakov, I.E. Nachasova 

Institute of Physics of the Earth RAS, Moscow, e-mail: archaeomag@yahoo.co.uk 

Abstract. Comparison of data about intensity of the geomagnetic field, received as a result of 

research of magnetization protomy from the Mayskaya Gora site with the data received on 

narrowly dated ceramics, has enabled to conclude, that the time-interval of their manufacturing 

consists 70 – 80 years and the most probable time of manufacturing protomy - second half IV – the 

first quarter of III century B.C. 

Quite often at dating a ceramic material of archeological monuments by archeological methods there are 

difficulties. Correlation of a picture of variation of intensity of the geomagnetic field received as a result of 

research of magnetization of a ceramic material of an archeological monument, allow to specify a temporary 

binding of this material and, consequently, and all monument. 

Reception of detailed data about change of intensity of a geomagnetic field in area East Mediterranean 

– Black Sea Coast in second half of I thousand BC. has enabled a time binding of a ceramic material of 

Maiskaya Gora - one of archeological monuments of the peninsula Taman located in 1 km to the south from 

site of ancient settlement Phanagoria. All material is dated the long period - from the end VI till III century 

B.C. 

Magnetization protomy (ceramic top on a breast images of goddesses) from a sanctuary of a 

monument on Maiskaya Gora was investigated. During manufacture forms (matrix) are removed from one 

original (maiella) for manufacturing several series of terracottas. At long manufacturing protomy their sizes 

decrease from generation to generation. It is possible to track these changes in series from generation to 

generation, to establish relative chronology. However the question of absolute dating remains opened. 

For realization of a time binding it is necessary to have longer number of pottery which sequence of 

manufacturing is known. The opportunity of an establishment of sequence of manufacturing of some pottery 

in case of research protomy, allows to lead a time binding of this material. Magnetization of a material of 

series of protomy of 9 types differing on appearance has been investigated. It is carried out research of 

magnetization of 76 samples, 3 detrminations are rejected. The longest number (from seven generations) 

would be available for protomy of B-type. 

The time binding of data about intensity of the field, received on magnetization protomy, is spent on 

the basis of affinity of averages for generations of values of intensity of a geomagnetic field to the basic 

curve constructed by means of sliding averaging with an interval of averaging of 11 years according to, 

received as a result of research of magnetization is narrow (within the limits of 30 years) dated the ceramic 

material selected from area of East Mediterranean – Black Sea Coast (the filled in points on figure). 

It has been constructed two versions of basic curves – on all data set, and on set of the determinations 

received with high accuracy and certainty (crosses on fig.). The second set has consisted of the 

determinations received on a material which magnetic characteristics do not change after heatings and there 

are no secondary heatings that allows to receive detrminations of intensity of an ancient geomagnetic field 

with the least deviation from true values. Character of variation of intensity of a field on both data sets 

practically is identical. Divergences are insignificant. The picture received by the most precise 

determinations is less smoothed. 

According to the obtained results, the geomagnetic field decreases in the time of production of 

protomy of the first four generations, then it increases The average values of intensity of a field change 

within the limits from 75.9 up to 69.1 mkT. 

On basic curves intensity of a geomagnetic field changes in a similar way in close intervals of values 

of intensity on two time intervals: second half V – the first quarter of IV century B.C. and second half IV – 

the first quarter of III century BC. And in that and in another case the best concurrence of the data received 

on a material protomy, to basic curves of variation of intensity of a field turns out if to have time intervals of 

367


manufacturing protomy of different generations through 10 – 13 years. Thus, the time interval of 

manufacturing protomy could be estimated in 70 – 80 years. 

В, mkT 

90 

85 

80 

75 

70 

65 

60 

-550 -500 -450 -400 -350 -300 -250 -200 -150 

Years BC 

On figure are presented two possible versions of dating a protomy (hollow squares and hollow 

triangles). Data obtained on protomy will better be coordinated with a curve constructed on the welldetermined 

data. 

To prefer one of two variants of a time binding on the basis of only data about intensity of a 

geomagnetic field it is not obviously possible. If to consider opinion of some researchers protomy , that 

protomy type (Praksitelevsky type of the person) have appeared only in IV century B.C. it is necessary to 

carry time of manufacturing protomy of type to second half IV–of first quarter of III century B.C. 

Concerning dating of protomy of other kinds it is possible to make only some observations which are 

reduced to that all investigated protomy have been made in close time pieces a little shifted on a time scale 

rather each other. 

In all cases the time interval of manufacturing of protomy can be carried and to an interval of second 

half V – the first quarter of IV century B.C. and to the time interval shifted to the present (approximately for 

century). 

Reception of the new data on magnetisation of narrowly dated material for construction of the in 

regular more intervals distributed row on a time interval V – IV centuries B.C. and constructions of a 

representative row for III century B.C. can contribute some share of definiteness at the decision of a problem 

of dating. 

It is obvious, that at the decision of challenges of dating of a ceramic material carrying out of the 

complex researches including all possible independent ways of a time binding (archeological, physical and 

geophysical) is necessary. 

Thus, comparison of the data about intensity of the geomagnetic field, received as a result of research 

of magnetization of a ceramic material of an archaeological monument Maiskaya Gora of peninsula Taman, 

with the data received on precisely dated ceramics, has given the chance to conclude that the time piece of 

their manufacturing makes 70 – 80 years and the most probable time of manufacturing of this material are a 

time interval second half IV – the first quarter of III century B.C. 

This work was supported by the Russian Foundation for Basic Research, project no. 06-05-65219. 

368 

1 

2 

3 

4 

5


SIMULATION OF DIFFERENT SCRIPTS OF THE MAIN GEOMAGNETIC 

FIELD VARIATIONS ON THE BASE OF THE FORECAST OF THEIR 

SOURCES DYNAMICS 

Demina I., Farafonova Yu., Koroleva T. 

Pushkov Institute of Terrestrial Magnetism, Ionosphere, and Radiowave Propagation, St. Petersburg 

Branch, Russian Academy of Sciences, Muchnoi proezd 2, St.- Petersburg, 191023 Russia p.b. 88 

e-mail: irina_demina@mail.ru 

The dynamic model of the main geomagnetic field sources has been developing by 

authors for several last years. Up to now dipoles of 3 magnitude levels are obtained as such 

sources. The most part of them exists and continuously develops over last 100 years. The time 

series of dipole parameters obtained are smooth enough to be extrapolated. But for a long-range 

forecast some more assumptions are required about a global tendency of the sources variations. 

Depending on assumptions made the possible scripts of the main geomagnetic field 

variations are worked out for the 1000 next year. The main development tendency which was 

obtained for 20 century is that decreasing magnitude of the main dipole is followed by forming 

and increasing the geomagnetic field non-dipole part. 

It is shown if such tendency holds the large local anomalies of a geomagnetic field spatial 

structure can start to dominate due to increase of power of the non-dipole part sources. In this case 

additional poles and local reversals can originate. 

Introduction 

The purpose of this paper is to attract attention of researchers to the fact that our interpretation of 

experimental data depends substantially on the present-day state of affairs. Whether or not we wish we use 

present-day general concepts and present-day terminology in our investigations. Since we managed to 

construct the dynamic model of the main geomagnetic field sources and obtain the 100 year series of their 

parameters we used this model as a investigation instrument. Thus we divided the dynamics of the main 

dipole from the same of sources determining the so-called nondipole part of the geomagnetic field. The 

technique and principal results are presented in papers [Demina et al. 2003, Demina,I.,Farafonova Yu. 2004, 

Demina et al. 2006]. This fact allows us to compile the forecast of the development of the main dipole and 

other sources separately. 

Background suggestions 

About non-dipole part sources we have nothing more the 100 year series of parameters obtained by 

us. Therefore we can only suppose for a long-term prediction that the variation of these sources parameters 

will keep tendencies which were obtained for them over the last 100 year. As for the main dipole we used the 

literary data about its magnetic moment variations over the last 3000 years (Fig.1). So on the base of these 

data and data which were obtained by us we compiled 3 scripts of development of the geomagnetic field 

sources for the next 1000 year. These scripts differ in the main dipole magnitude change only. The change of 

other sources parameters is the same for all scripts. For the forecast we took into account such dipoles only 

which time parameters series are obtained longer than 95 year. As for the main dipole to predict its 

parameters change we used the MathCAD function which realizes new auto regression Burge method with 

different parameters. The result is shown in Fig.1 lines 2, 3 and 4. Line 1 is symmetrical to the left branch of 

the main 8000 year period. 

We consider that the line 1 is not realistic in spite of the correspondence with the 8000 year period 

suggested. It is obviously that the decrease velocity of the right branch is higher than the increase of the left 

one. As we think the most realistic script is the line 2 although the line 3 shows the best correlation with the 

global tendency in MM variation over last 1500 year. The line 4 presents the catastrophic script of the main 

dipole development but only concerning the high velocity of MM decreasing because the value of MM equal 

the 0.1 from its recent one was not so rare in the past according the paleomagnetic data. 

In conformity with these three assumptions about the main dipole development we calculated the 

hypothetic spatial structure of the geomagnetic field for next 1000 year. The results for 2nd and 4th scripts 

are presented in Fig.2 and Fig.3 accordingly. In these figures the spatial structure of the vertical component Z 

and horizontal component H is shown for three epochs. It can be seen that the spatial components structure 

which was obtained for the script 2 is characterized by the motion on the North magnetic Pole and the 

369


formation and development of a large anomaly between the South Africa and the Brazilian east coast. This 

anomaly is similar to the additional South Pole. This effect intensifies if the 3rd script was taken. 

relative ММ 

2.5 

2 

1.5 

1 

0.5 

0 

4 

-40 -30 -20 -10 

centure 

0 10 20 30 

Fig.1 The forecast of the main dipole MM variation in comparison with literary data. 

1 –nonrealistic, 2 – realistic 3 – compromise 4 – catastrophic variants. 

Literary data are taken from Burlatskay S.P. Physics of the Earth 1985, N2, P. 96-101. 

If the 4th script is accepted it can be seen in Fig.3 that the total level of the anomalies magnitude 

would decrease. In this case regions with the opposite Z sign toward 3000 would form and areas with a low 

H would be larger and increase in number. So the special structure of field components takes a mosaic shape. 

And so the usual magnetic pole concept starts to lose significance. We should take into account that the 

magnetic moment vector of the main dipole keeps its direction at the whole time in all scripts. So we can’t 

say about a transition period or moreover about an inversion. But if we consider the declination and 

inclination variations at different points so we can discover local anomalies right up to local inversions. 

All scripts considered above don’t take into account that decreasing the main dipole magnetic 

moment can be accompanied by a new nondipole part source formation. Such situation we can observe in the 

middle of the 2 nd millennium. Unfortunately it isn’t possible to consider all changes of nondipole part 

sources which follow such kind of the main dipole variation because the earliest mathematical presentation 

of a spatial geomagnetic field structure is referred to 1690. But if we return back to the Fig.1 we can see that 

anomaly decreasing the magnetic moment was obtained just nearly this year. Such decreasing can be 

interpreted as the part of a 1200 year oscillation which was noted by many authors. In this case we can 

suppose that during next 1200 year similar decreasing will occur again. In 1690 this decreasing was 

accompanied by a new nondipole part sources formation. Of course we can’t predict time and place of the 

appearance of new source since we can only assume the cause and mechanism of this process. 

Therefore to estimate the new sources formation effect on the spatial field structure we compiled 

such two sources combinations. We added the source which we managed to obtain for 1690 to sets 

corresponding to 2 nd and 4 th scripts for two epochs: for 2600 and for 2850. Some additional decreasing the 

main dipole was not provided for. The spatial structure of Z and H components calculated are presented in 

Fig. 4. The comparison of Fig.4 with Fig.2 and Fig. 3 shows that a formation of new source produces the 

intensification of all features which were obtained for scripts 2 and 4. And what is more the transformation 

of the spatial field structure from a dipole to mosaic one would occur much quickly in this case. We have to 

take into account that such sharp situation can be temporary because the additional sources, as we obtained 

for the 18 th century, can be unstable and transform to another sources with time. 

370 

1 

2 

3


Fig. 2 Spatial structure of Z and H field components corresponding to the 2 nd script. 

371


Fig. 3 Spatial structure of the Z and H field components corresponding to the 4th script. 

372


Fig. 4 Spatial structure of Z and H field components for the model with new source formation 

373


Conclusions 

- If the most realistic script of the main magnetic field sources development took a place the opportunity of 

some catastrophes caused by the geomagnetic field variation is not well founded at least during next 1000 

years. 

- At the same time if the suggestion that the long-period variation of the main dipole started to decrease is 

right then the events development would depend on the dynamics of the nondipole field part sources. 

- If the magnetic moment of the main dipole decreases two times only likelihood appears that conception of 

the magnetic pole (in its present sense) starts to lose meaning because such points where the horizontal 

component value approaches zero can increase in number. 

- The change of ratio between dipole and nondipole part of the geomagnetic field can cause first of all the 

appearance of local variations of declination in some regions. But in any case it can be a variation of 

inclination right up to a sign change. 

- The determination of the paleopoles locations and the value of virtual magnetic moment is based on the 

suggestion about a dipole character of the geomagnetic field in the past. But this suggestion in one’s turn is 

founded at our resent experience which is in fact determined by the high level of the magnetic moment value 

in the recent past. If this value decreases up to the nondipole part sources level the concept of the field 

polarity starts to lose a meaning. 


This work is supported by grant MK-2618.2007.5 

References: 

Demina, I., Yu. Farafonova, A. Sas-Uhrynowski, and E.Welker (2003), Modeling of the Main 

Geomagnetic Field by Set of Optimal Dipoles, in: Proc. of the 4 th Oersted Intern. Science Team 

Conf. (OIST-4) (Copenhagen, 23-27 September 2002), ed. by P. Stauning et al, Danish 

Meteorological Institute, narayana press, Copenhagen, 43–44. 

Demina, I., and Yu.Farafonova (2004), Dipole Model of the Main Geomagnetic Field in the 20th 

Century, Geomagn. Aeron., 44, 4, 521–525. 

Demina I., Yu. Farafonova, and L. Nikitina (2006). Non-dipole Part of the Main Magnetic Field of 

the Earth and the Movement of the North Magnetic Pole, in: Proc. of the 6 th International 

Conference “Problems of Geocosmos” (St.-Petersburg, Petrodvorets, May 23-27, 2006), ed. by 

V.N. Troyan, V.S. Semenov, and M.V. Kubyshkina, Saint-Petersburg, 305-308. 

374


THE LAST GEOMAGNETIC REVERSAL MATUYAMA-BRUNHES IN 

LOESS-PALEOSOL SEQUENCES OF 

PRIOBSKOE PLATEAU 

Z.N. Gnibidenko 

Petroleum Institute Geology and Geophysics of Siberian Branch of Russian Academy of Sciences, 

Novosibirsk, 630090, Russia, e-mail: magnit@uiggm.nsc.ru 

Abstract. Paleomagnetic record of the Matuyama-Brunhes polarity reversal has been studied. For 

our study, two closely spaced sections of loess-paleosol sequences (one section is 14 m thick and 

another is 1.8 m thick) on the left bank of Ob’ River near village Volodarka (52°41'N, 83°38'E) 

were sampled continuously. Stepwise thermal demagnetization up to 685ºC yielded two natural 

remanent magnetization (NRM, Jn) components: secondary and primary. The secondary NRM 

component is broken in the 250-500°С intervals. The primary NRM component, which is isolated 

at the 250-500°C, is characteristic component (ChRM). Magnetite, maghemite, and haematite are 

as the main magnetic mineral - carriers of natural remanent magnetization. The characteristic 

component forms the complex succession of normal, reversal, and intermediate directions. This 

succession reflects the Matuyama-Brunhes polarity reversal. 

Introduction 

One of the actual problems of paleomagnetology and geophysics, as a whole, is study reversals of 

the Earth’s magnetic field, caused by processes in the core and on the core-mantle boundary. The reversals 

are significant for development of the theory of geomagnetic dynamo. Therefore, interest in study of reversal 

transitions increased in the last time. The reversal transitions are studied in the age interval of the whole 

geological time, but at present, investigators focus their efforts mostly on young reversals. Thus, 

characteristics of a magnetic field are studied during reversal transition, as well as, during stationary periods 

of this field before and after reversals. 

This work presents the results of study of geomagnetic field during the Matuyama-Brunhes reversal 

that took place 780 ka ago and recorded while magnetostratigraphic investigations were carried out on the 

Priobskoe Plateau. 

Geology and rocks sampling 

Studied section is located on the high left bank of Ob’ River 70 km upstream of Barnaul city. 

Geographical coordinates of the section are as follows: 52°41' N, 83°38' E. Here in the steep of the bank 

about 50 m in height, deposits represented by loess-paleosol sequences are exposed. The subsurface geology 

of the loess-paleosol sequence on the Priobskoe Plateau as a whole, and, particular, that of this section being 

studied is represented by three thicknesses. The lower thickness, which is revealed above the water level, is 

consists of gray and blue colored clays and loams. This thickness is the upper part of Kochkovka suite 

[Martynov, 1966]. Loams are heavy, limous, and unstratified. Paleontological remains (small rodents, 

ostracoda, and seed flora) revealed in Kochkovka suite deposits allow these rocks to be dated by Upper 

Pliocene [Martynov and Nikitin, 1968]. These deposits are of subaqual and subaerial genesis. The middle 

thickness represented by loams and white farinaceous sands with horizons of paleosols is the lower part of 

the Krasnodubrovka suite. The deposits are of alluvial genesis. The upper part of the Krasnodubrovka suite 

represented by loess-like loams, sandy loams, and sands with paleosols is the upper thickness of the loesspaleosol 

sequences. Based on paleontological remains (mammal fauna, ostracoda, spores, pollen, and seed 

assemblages) the age range of Kochkovka suite is defined as Late Pliocene-Early Pleistocene, and that of 

Krasnodubrovka suite is dated as Early Pleistocene-Late Pleistocene. 

Studied section Volodarka is represented by Pliocene-Pleistocene deposits composed of alternating 

horizons of loess-like loams, paleosols, and compact loams lying horizontally. From two closely-spaced (at 

the distance of 1 km) sections of the Volodarka, 490 oriented specimens representing 200 temporal 

stratigraphic levels were taken. The most of these specimens were taken continuously; other specimens were 

taken 10, 20, and 40 cm apart. At first, the samples were taken in the shape of a lump 5-20 cm thick, the 

upper part of such is horizontal. At a later time, the specimens were cut into slices (stratigraphic levels) 2 cm 

thick, from which cubic specimens of 2×2×2 cm were made. 

375


Methods 

Both magnetic and paleomagnetic characteristics of deposits such as – susceptibility (χ), intensity 

and direction of NRM were studied. These experiments were done in the IPGG paleomagnetic group 

(Novosibirsk) and in the VNIGRI paleomagnetic laboratory (St. Petersburg). The NRM intensity and 

direction 

376


1 – compact loam, 2 – loess loam, 3 – paleosol, 4 – reversal polarity, 

5 – normal polarity, 6 – transition zone 

were measured on JR-4 and JR-6 spinner magnetometers (AGIGO, Brno, Czech Republic). 

The initial magnetic susceptibility was measured using KLY-2 susceptometer. Magnetic mineralogy 

investigations included thermomagnetic analysis of remanent magnetization of saturation Jrs(T), analysis of 

normal magnetization curves Jn(H) (remanent magnetization of saturation Jrs and of saturation field Hs). Part 

of specimens was stepwise thermally demagnetized up to 685ºC, another part it was demagnetized by 

alternating fields up to 70-80 mT. To determine the natural remanent magnetization components, principal 

component analysis was performed [Kirschvink, 1980]. Zijderveld diagrams [Zijderveld, 1967] showed that 

in each magnetic polarity zone two sometimes three components with different directions are isolated in 

different temperature intervals. In this case, the computer program package by R. Enkin [Enkin, 1994] was 

used. Temperature cleaning was implemented by equipment at institutes IPGG and VNIGRI (TD48, 

Carlsbad, USA). AF demagnetization was performed using LD-3A equipment (AGIGO, Brno, Czech 

Republic). 

Results 

Previous investigations [Pospelova, Gnibidenko, 1971, 1982] showed that two large magnetic 

polarity zones were revealed in the paleomagnetic section of the loess-paleosol sequences of Priobskoe 

Plateau: Matuyama (reversal polarity) and Brunhes (normal polarity). It has been established [Pospelova, 

Gnibidenko, 1971] that normal and reversal magnetic polarity zones have equal consist of magnetic 

377


minerals. It has also been established that loesses, loams, and paleosols are not different from each other in 

consist of carriers of 

Results 

Results 

magnetization [Pospelova, Gnibidenko, 1971, 1982; Bolshakov, 2001, 2007]. The main carriers of 

magnetization in paleosols, loams and loesses are magnetite, maghemite and haematite. The magnetic 

378


susceptibility of studied deposits in the sections changes in the range from 45×10 -5 to 170×10 -5 SI-units. The 

intensity of NRM changes in the range from 0,62 to 24,3 mA/m. Difference in rock types (loesses, loams, 

and paleosols) by magnetic susceptibility it is not observed. By results of stepwise thermal demagnetization, 

two components of natural remanent magnetization, primary and secondary are present in loesses and 

paleosols. Secondary component of NRM is broken within the 250-300°С ranges, sometimes at 500°C. 

Primary component NRM is allocated at 250-500°C (Fig. 1). By the results of stepwise alternating field 

demagnetization, two components of natural remanent magnetization, stable and unstable are present in 

loesses and paleosols. Unstable component of NRM viscous origin destroys at 10-20 mT. 

Field investigations, analysis of magnetic and paleomagnetic parameters of deposits from two 

closely spaced sections Volodarka allowed to construct the section of the transition zone as well as 

paleomagnetic section of normal and reversal zones before and after reversal transition. Reliability of 

obtained paleomagnetic data is proven by determination of magnetic minerals - carriers of magnetization, by 

the nature of NRM, and by the component analysis of natural remanent magnetization. 

The Matuyama-Brunhes reversal transition has been fixed in compact brownish-yellow loams at the 

depth of 43 m from the day surface and its thickness is about 1,8 m. As a result of studying distribution of 

vectors of NRM has been constructed paleomagnetic section of Pleistocene deposits of lower part 50-m 

section and of the transition zone (Figures 2, 3). The transition interval from reversal to a normal polarity 

represents numerous alternation of polarity with short-term full and partial reversals paleomagnetic field. 

The record transition reversal can be divided into several stages. The initial stages of transition represent 

R→N→R cycle and the final N→R→N transition. In some stages the field does not reach full normal or 

reversal polarity. 

The mean direction of the reversal stationary geomagnetic field in a time interval approximately 0,9- 

0,78 Myr is characterized: D = 169º, I = - 64º, α = 4,8º, K = 13. The mean direction of the normal stationary 

geomagnetic field in a time interval approximately 0,02-0,78 Myr is characterized: D = 4º, I = 70,5º, α = 1,5º, 

K = 55. Studying of behavior of the Earth’s magnetic field of and its intensity during transition reversal 

Matuyama-Brunhes continues. 

These investigations are carried out at support of the Russian Foundation of Basic Research (Grant 

No 07-05-00582). 

References 

Martynov V.A. (1966), Upper Pliocene and Quaternary deposits of South of the West Siberian Plain. 

Quaternary period of Siberia. Moscow, Nauka, 9-22. 

Martynov V.A., V.P. Nikitin (1968), To stratigraphy of Neogene deposits of the West Siberian Plain. 

Geologiya i Geofizica, 12, 3-15. 

Zijderveld J.D.A. (1967), A.C. demagnetization of rocks analysis of results. Methods in paleomagnetism. 

Amsterdam, 254-718. 

Enkin R.J. (1994), A computer program package for analysis and presentation of paleomagnetic data. Pacific 

Geoscience Centre, Geol. Survey Canada. Sidney, 16 pp. 

Kirschvink J.L. (1980), The least square line and plane and the analysis of paleomagnetic data. Geophys. J. 

Roy. Astron. Soc., 62, 699-718. 

Pospelova G.A., Z.N. Gnibidenko (1971), Nature of remanent magnetization in the Pliocene-Quaternary 

deposits of the Ob’ River Area. Geologiya i Geofizica, 5, 78-88. 

Pospelova G.A., Z.N. Gnibidenko (1982), Magnetostratigraphic sections of Quaternary and Neogene 

formations of southeastern Europe, and problems of correlation. Geophysical Methods in Regional Geology, 

Novosibirsk, 76-94. 

Bol’shakov V.A. (2001), Data of magnetic investigation of loess deposits, its interpretation and applied use. 

Fizica Zemli, 8, 86-96. 

Bol’shakov V.A. (2007), New data of magnetic and paleomagnetic investigation of section Volodarka on 

River Ob’. Fizica Zemli, 2, 66-74. 

379


MAGNETISM AND PALEOMAGNETISM OF THE RUSSIAN ARCTIC 

MARINE SEDIMENTS 

E.G. Guskova 1 , O.M. Raspopov 1,4 , A.L. Piskarev 2 , V.A. Dergachev 3 

1 SPbF IZMIRAN, St.-Petersburg, Russua; 2 VNIIOkeangeologia, 190121, Anglijsky pr. 1, 

St.Petersburg, Russia, apiskarev@googlemail.com, 3 Ioffe Physico-Technical Institute of RAS, St. 

Petersburg, Russia, 4 Polar Geophysical Institute, Kola SC of RAS, Murmansk, Russia. 

Abstract. Last years two main types of the Arctic Ocean sediment cores were studied: from 

sequences of very slow sedimentation area in the deep parts of East Siberian Sea, and from shelf 

sequences in the Barents Sea. 

Sea depths in the 7 sites of the core sampling in the northern East Siberian Sea are between 1.5 and 

3.3 km, core length is between 2.1 and 3.35 m. Boundary Bruhnes-Matuyama (0.73 my BP) and 

subchron Jaramillo (1.07-0.99 my ВР) are clearly fixed in all seven cores; subchron Olduvai (1.95- 

1.77 my ВР) is marked in two cores, subchron Reunjon (2.13 my ВР) – in one core, boundary of 

subchron Matuyama-Gauss (2.6 my ВР) is marked in three cores. 

Barents Sea sediments were studied in central and northern parts the Sea. Sea depths in 30 sites of 

the core sampling in Barents Sea are between several tens and 400 m. 

The fine temporal structure of the geomagnetic field for the past 30 kyr manifests itself in the 

development of geomagnetic field excursions (sharp geomagnetic pole displacements in latitude 

and longitude) and in slow variations in the geomagnetic field elements. An analysis of the 

paleomagnetic characteristics shows the Etrussia-Sterno (2300-3000 years ego) and Solovki 

(4500-7500 years ego) geomagnetic field excursions, the Gothenburg excursion at the Holocene- 

Pleistocene boundary (12-13 kyr ago) marking the end of the last glaciation. The cyclic component 

of the variation in the geomagnetic field inclination with period about 15 kyr has been revealed. 

Paleomagnetic study of the northern East Siberian Sea sediments was implemented using the cores 

that were sampled in 2000 during cruise of the research vessel “Akademik Fedorov”. The cores from the 

crest of Mendeleev Ridge (AF07, AF08), from the eastern flank of Mendeleev Ridge (AF01, AF03, and 

AF04), and from Podvodnikov Basin to west from Mendeleev Ridge (AF23, AF28) were studied. 

Fig. 1. Map of the sampling sites in the northern East Siberian Sea. 

380


Coordinates of the sampling are listed in the Table 1. 

Core Latitude Longitude Sea depth, m Core length, 

m 

AF01 82°00,51'N 171°58,60'W 3110 2.75 

AF03 81°48,71'N 171°38,50'W 3321 2.95 

AF04 82°03,45'N 175°09,20'W 2704 2.3 

AF07 82°03,24'N 179°56,17'W 1555 2.1 

AF08 82°05,22'N 179°52,00'W 1490 2.5 

AF23 82°00,95'N 171°53,99'E 2750 3.25 

AF28 81°54,90'N 167°52,32'E 2814 3.35 

Table 1. 

Primary measurements of the natural remanent magnetization were executed in the cores with 

interval 2-2.5 cm. 

Two physical parameters were measured: magnetic susceptibility κ and remanent magnetization of 

the samples Jn. Kappameter KLY-2 with sensibility 4х10 -8 SI and accuracy of calibration ±3% was used. For 

Jn measurements rock-generator JR-4 with accuracy 1% ±3 pT was used. 

As we can see at the figures 2-4 the measured magnetic susceptibility κ is alternating in limits (2- 

6)x10 -4 SI, the core intervals with outlying κ values (up to 12x10 -4 SI) are revealed. Natural remanent 

magnetization Jn alternates in cores in limits (1.7-3.2) nT. Average Jn value of the normal magnetized layers 

is about 3 nT while the reverse magnetized layers are characterizing by Jn values about 1.5 nT. 

Ridge. 

Fig. 2. Magnetic parameters of the AF03 sediment core sampled from eastern flank of the Mendeleev 

381


Fig. 3. Magnetic parameters of the AF08 sediment core sampled from crest of the Mendeleev Ridge. 

Magnetic susceptibility can be considered as independent characteristic for definition of the layer 

boundaries as soon as alteration of κ is directly related to composition of layers and ferromagnetic 

particles content. Note that high values of κ are registered in cores AF08 and AF23 near the 

boundary Bruhnes-Matuyama and this is additional evidence for correlation of this boundary. 

Values of Jn can also be used for age identification and correlation of sediment cores. Average Jn 

value of the normal magnetized layers is remarkable higher then of the reverse magnetized layers. Difference 

is consequence of the viscous magnetization. Magnetic cleaning in alternating magnetic field to 123 E let us 

to get partly rid of viscous magnetization. After this procedure average Jn value of the normal magnetized 

layers decreased and of the reverse magnetized layers – increased. 

The boundary Bruhnes-Matuyama is surely defined in all studied sediment cores. For the better 

recognition of episodes we calculated average rate of sedimentation. Average sedimentation rate during 

Bruhnes epoch is, according to our measurement data, 1-1.4 mm/kyr in five cores from Mendeleev Ridge, 

and 2.6-3.0 mm/kyr – in two cores from Podvodnikov Basin. These calculations are in the good agreement 

with other data from Mendeleev Ridge (Clark, 1970; Steuerwald et al., 1968) where values 0.8-1.6 mm/kyr 

were defined. 

Taking in consideration of Bruhnes, Matuyama and Gauss subchron durations and according to data 

of our measurements it is reasonable to assume of approximately constant sedimentation rate during last 4 

my. So, it is possible to relate peculiarities of the sediment magnetic parameters to the definite age intervals. 

Boundary Bruhnes-Matuyama (0.73 my BP) and subchron Jaramillo (1.07-0.99 my ВР) are clearly fixed in 

all seven cores; subchron Olduvai (1.95-1.77 my ВР) is marked in two cores, subchron Reunjon (2.13 my 

ВР) – in one core, boundary of subchron Matuyama-Gauss (2.6 my ВР) is marked in three cores. 

382


Fig. 4. Magnetic parameters of the AF23 sediment core sampled from western flank of the 

Mendeleev Ridge – Podvodnikov Basin. 

The final recognition of paleomagnetic epochs in studied cores that is presented in figures 2, 3, and 4 

is based on the scale, table 2. 

Names of Chrones, Subchrones and Excursions and their ages (Ma) (Pospelova, 2004) 

Chron NN Age Name Simbol 

Bruhnes 1 0.3-0.2 Biva B 

2 0.7-0.4 Elunino Elun 

Matujama 3 0.73 - Br-M 

4 0.87 Kamikasutra Km 

5 0.94 Santa Rosa S-R 

6 1.07-0.9 Jaramillo Jar 

7 1.6 Gilsa Gil 

8 1.95-1.77 Olduvai Old 

9 2.13 Reunion R 

Gauss 

10 2.6 - M-G 

11 3.1-3.0 Kaena K 

12 3.35-3.2 Mamot M 

383 

Table 2.


Studying of the Barents Sea sediments we continued investigations of V.V. Kotchegura (1992) 

expanding his study to central and northern parts of Barents Sea. Sea depths in the sites of core sampling in 

Barents Sea are between several tens and 400 m. 

The fine temporal structure of the geomagnetic field for the past 30 kyr manifests itself in the 

development of geomagnetic field excursions (sharp geomagnetic pole displacements in latitude and 

longitude) and in slow variations in the geomagnetic field elements. An analysis of the paleomagnetic 

characteristics shows the Etrussia-Sterno (2300-3000 years ego) and Solovki (4500-7500 years ego) 

geomagnetic field excursions, the Gothenburg excursion at the Holocene-Pleistocene boundary (12-13 kyr 

ago) marking the end of the last glaciation. A significant increase in the magnetic susceptibility at the 

Holocene-Pleistocene boundary, observed in many Barents cores, reflects climate changes during this period. 

The cyclic component of the variation in the geomagnetic field inclination with period about 15 kyr has been 

revealed. 

Column 1157 (70°33.0' N and 52°48.0' E, depth 169 m), taken during the 13th voyage of the R/V 

Akademik Sergei Vavilov, was analyzed most thoroughly. The column bottom is dated as 10 ka old by the 

radiocarbon method (Murdmaa and Ivanova, 1999). Thus, the column has revealed only young (Holocene) 

sediments formed after the last glaciation (Fig 5). 

Fig. 5a-b. Geomagnetic field excursions in the Holocene sediments from the Barents Sea shelf 

(column 1157): a change in (a) magnetic susceptibility, (b) natural remanent magnetization (In*10 -2 A/m). 

Figure 5 a indicates that the magnetic sensitivity (к) values are (0.2-0.8) x 1 0 3 SI at an average value 

of 0.5 x 10~ 3 SI. This shows that magnetic minerals are regularly distributed in the Holocene sediments on the 

Barents Sea shelf. Natural remanent magnetization (Jn) is highly variable (Fig. 5b): a sharp minimum is 

observed at a depth of 75 cm where Jn decreases from 2.0 x 10 -2 to 0.1 x 10 -2 A/m; below 90 cm, In 

increases to 2.5 x 10 -2 A/m and varies about an average value of 1.5 x 10 -2 A/m to a depth of 230 cm. 

Below this depth, sharp changes in Jn are not observed, and its average value is about 1.0 x 10 -2 A/m. Figure 

5c demonstrates the variations in the Jn vector inclination (I) averaged for three samples. In this case, I 

sharply changes from 85° to 5° at a depth of 75 cm, and a gradual sawshaped decrease in I is observed below 

a depth of 350 cm. Note that a rather weak bioturbation (Levitan et al., 1999) was observed at a depth of 49- 

78 cm in column 1157, whereas a decrease in the inclination (I) at a depth of 75 cm can hardly be related to 

this phenomenon. 

384


In the course of the study, the sample thermal cleaning is performed by means of stepped heating to 

100 and 200°C and the following cooling in a nonmagnetic space in order to more distinctly reveal specific 

features in the inclination (I) behavior. 

Fig. 5c-d. Geomagnetic field excursions in column 1157: (c) inclination (I), and (d) inclination(j) 

before thermal cleaning (1) and after thermal cleaning to 100˚(2) and 200˚(3). 

Figure 5с shows the I4 C absolute age measured with the help of acceleration mass-spectrometry 

(Levitan et al., 1999). The average sedimentation rate is 45 cm per 1000 years according to column 1157. 

Consequently, the anomalous I values at depths of 75 and 200 cm should be dated as approximately 2200 

and more than 4000 years old, respectively. Since the amplitude of variations at these depths exceeds 60° (it 

is equal to 130° and 75° according to the nonaveraged values) such inclination variations can indicate that 

the geomagnetic field excursion was possible in the considered time interval. 

We have indicated (data of column 1157) that the Etrussia-Sterno excursion lasted 100-300 years. 

For this time, the geomagnetic pole shifted from the region of the geographic pole to the equator and 

backwards, which causes one to pay serious attention to a sharp present-day acceleration of the magnetic pole 

displacement and to possible consequences of this displacement. 

ACKNOWLEDGMENTS 

This work was supported by the Russian Foundation for Basic Research, project no. 06-05-64200a. 

References 

Clark D.L. (1970). Magnetic reversals and sedimentation rates in the Arctic Ocean. Geological 

Society of America Bulletin. V.81. October. N10. P. 3129-3124. 

Kochegura V.V. (1992). Application of Paleomagnetic Methods during the Geological Survey 

of the Shelf. VSEGEI, SPb, 143 p. 

Levitan M. A., Duplessy J.-C., Khusid. T. A. et al. (1999). Holocene Sediments of the 

Southern Novaja Zemlya Trough (the Pechora Sea) and Brines History in IMAGES (Shirshov Inst. 

Oceanol. Russ. Acad. Sci..Moscow,), pp. 11-12. 

Murdmaa I. O. and Ivanova E. V. (1999). Postglacial Sedimentation History in Shelf Troughs of the 

Barents Sea, Litol. Polezn. Iskop., No. 6, 576-595. 

Pospelova G.A. (2004). Geomagnetic excursions. In: Short history and modern status of 

geomagnetic research activity in the Institute of Physics of the Earth of Russian Academy of Sciences. M., p. 

44-55. 

Steuerwald B.A., Clark D.L., Andrew J.A. (1968) Magnetic stratigraphy and faunal patterns in 

Arctic Ocean sediments. Earth and Planet Science Letters. V.5.. P. 79-85. 

385


PALEOMAGNETIC RECORD OF KARADJA LATE PLEISTOCENE 

SECTION REFLECTS GLOBAL VARIATIONS OF THE 

GEOMAGNETIC FIELD AND PALEOENVIRONMENTAL CHANGES 

O.V. Pilipenko 1 , N. Abrahamsen 2 , Z. V. Sharonova 1 , V.M. Trubikhin 3 

1 Institute of Physics of the Earth RAS, Bolshaya Gruzinskaya, 10, Moscow, 123995, Russia, 

e-mail: pilipenko@ifz.ru; 

2 Dept. of Earth Sciences, University of Aarhus, Aarhus, Denmark; 

3 Geological Institute RAS, Moscow, Russia 

Abstract. New detailed rock magnetic and paleomagnetic investigations of the 

lagoon/marine loess-like loams samples from the Karadja range section equals Khvalynian 

horizon (ca. 45-20 ka B.P.) are presented. Karadja range is located in Azerbaijan not far from 

the town Mingechaur (Mingechaur Reservoir, 47 0 E, 40 0 N). By means of the standard 

methods of paleomagnetism and a high-resolution environmental magnetic study the object 

was to test whether a clear magnetic signature is associated with the geomagnetic field 

variations or climatic changes. The variability of the scalar magnetic parameters were 

examined and reflect the rhythmic character of transgression and regression of the Caspian 

paleobasin. The composition of the magnetic minerals was determined by thermomagnetic 

analysis and isothermal remanent magnetization experiments. Rock magnetic properties 

showed that there is no uniformity in terms of magnetic mineralogy, concentration and grain 

size of the main carriers of the NRM. Determination of the angle elements of the 

geomagnetic field (declination and inclination) gave information about intervals of abnormal 

behavior of magnetization. Some of these diagnostic intervals can be associated with the 

existence of anisotropy of magnetic susceptibility (AMS). The AMS indicates movements of 

deposited layers down the core which was the cause of the ChRM vector turn. The 

paleomagnetic study showed that there are intervals of abnormal behavior of the NRM 

during about ~25, ~29 and ~39 ka B.P. which are not connected with the AMS. These 

diagnostic intervals probably reflect global geomagnetic field changes during the deposition 

and may be associated with the Mono Lake and Laschamp geomagnetic excursions. 

Introduction 

Differences in formation of sedimentary rocks may be reflected in the content of main magnetic 

minerals. The present work is devoted to a paleomagnetic and rock magnetic study of the Karadja range 

marine terrace deposits. Karadja range is located in Azerbaijan not far from the town Mingechaur 

(Mingechaur Reservoir, 47 0 E, 40 0 N). This section is classical and has many times been subjected to 

various geological, stratigraphical and paleomagnetic investigations. The upper part of the Pleistocene 

deposits of the Karadja range section are horizontal and form a marine terrace. This terrace corresponds 

to the socalled Khvalynian transgression of the Caspian paleobasin the age of which is associated with 

the middle and late Valdai interstadials (~50-10 ka BP). 

The Pleistocene transgression of the Caspian paleobasin had a glacial-eustatic nature and a 

rhythmic character. In the cold climatic periods the water in the world oceans were stored in the acecaps 

and glaciers, and the sea water level was reduced (regression). During the warmer periods there was a 

reduction of the glaciers and this led to an increase in the water level. It was a gradual and slow process. 

The surpluses of water from the Caspian paleobasin ran out through the Manych strait. A tectonic 

activity in the Kaukasian region shut off the Manych strait and the sea level increased locally up to the 

~70 m. When this barrior was eroded the sea level again falled down to the ~30 m level. 

These periods of transgression and regression of the Caspian paleobasin were reflected in the 

structure of the marine terrace. Two sections were formed corresponding to the transgression of the 

Caspian paleobasin (worm periods) separated by a section corresponding to the period of regression 

(cold period). The low part of the terraсe was made of the marine deposits in the form of carbonate 

loess-like loam sediments. During the second later stage of the transgression subaeral deposits were 

deposited in the form of sandy loess-like loam sediments. These two parts are separated by a sand layer 

which corresponded to the decreasing sea level. The thickness of the sequence is about 13 m. 

386


The age of two levels in the section can be obtained by correlation. The transgressions of the 

Caspian and Black sea paleobasins had a glacial-eustatic nature and should be synchronic. The 

Khazarian deposits of the Caspian paleobasin is synchroneous with the Karangatian deposits of the 

Black sea paleobasin, which were established reliably from unstable uranium [Dodonov et al., 2000]. 

These deposits correspond to the oxygen-isotope stage 5, revealing an age of the base of the Khvalynian 

deposits of the marine terrace as ~45 ka. The upper part of the marine terrace coincides with the 

regression of the Paleocaspiy in the middle Valdai and to the oxygen-isotope stage 3, corresponding to 

an age of ~ 20 ka. 

Selection of the collection 

Loess-like loam hand blocks of the Karadja section were collected by the method of continuous 

sampling from the two parts of marine terrace corresponding to two parts of the transgression of the 

Caspian paleobasin. Hand blocks oriented after the magnetic meridian were sawed into horizontal plates. 

The latter were used to prepare oriented 2-cm cubic samples with three duplicates for each level. The 

number of levels of the marine terrace amounted to 406. 

Methods 

A complex of methods well established in rock magnetism was applied to examine the 

ferromagnetic composition of the loess-like loam deposits from the Karadja section by construction of 

saturation isothermal remanent magnetization (SIRM) curves, determination of the values of coercivity 

of remanence (Bcr), the temperature dependence of the saturation magnetization and the blocking 

temperatures. The experiments were conducted at the Paleomagnetic laboratory at the University of 

Aarhus (Denmark) and at the “Laboratory of main geomagnetic field and petromagnetizm” of Institute 

of physics of the Earth RAS, Moscow (Russia). The composition of the magnetic minerals (magnetite, 

maghemite and hematite) was determined by thermomagnetic analysis and isothermal remanent 

magnetization experiments. 

The main magnetic parameters such as low-field magnetic susceptibility (Klf), natural remanent 

magnetization (NRM), SIRM, anhysteretic remanent magnetization (ARM), Bcr were measured in 2-cm 

intervals throughout the profile. The variation in the concentration of magnetic minerals typically can be 

monitored by measurering the susceptibility Klf and the SIRM. For the marine terrace sediments both 

ratios of maximum to minimum values of Klf and SIRM are around ~ 15. The high values of Klf and 

SIRM belong to the sandy horizons which correspond to the phases of Caspian paleobasin regressions. 

The water of the basin was redrawed and the deposition of a coarse ferromagnetic fraction was 

increased. 

The magnetic mineralogy of selected samples from each stratigraphic level was inferred from 

isothermal remanent magnetization (IRM) experiments. Stepwise acquisition of IRM in fields up to 1.5 

T shows that 90% SIRM is acquired by samples in a field up to 0.3 T. This suggests that the main NRM 

carrier is a low coercivity mineral such as magnetite or maghemite. In some samples there is a 

permanent increase up to 1.5 T which indicates the existence of grains of high coercivity minerals, such 

as hematite. 

By the measurements of the S-ratios (S=IRM-0.3T/SIRM) (King and Channell, 1991) this provide 

a fair estimate of the relative importance of antiferromagnetics versus ferrimagnetics. In various parts of 

the section the value of the S-ratio changes in the range -0.54 to -0.95. The majority of the samples had 

values around S~-0.9. This indicates a dominant role of low coercivity minerals such as magnetite or 

maghemite. But in the sand horizons which coincide with the regression phases of the Caspian 

paleobasin the S= -0.5 to -0.6 which reflects a majority of a high coercivity mineral such as hematite. 

This conclusion is supported by measurements of the coercivity of remanence BBcr. In the same samples 

Bcr 

B varies between ~60 and ~90 mT. For the main part of the collection Bcr typically falls between ~30 

and ~40 mT. 

IRM experiments using the method of Lowrie (1990) were also made on 34 samples of a pilot 

collection. An IRM in 1.5 T was induced along the sample X orthogonal axis, 0.5 T field along Y-axis 

and finally 0.2 T field along the Z axis and thereafter stepwise thermally demagnetized, with 

measurements of the resultant remanence performed after each step. The thermal unblocking 

characteristics of the IRM show the presence of a dominant low coercivity magnetic phase (0.2 T) with 

387


unblocking temperatures of 580-620 0 C on all representative samples. These results indicate that 

magnetite and slightly oxidized magnetite is the dominant magnetic mineral. In all curves there is also an 

inflection between 300 0 and 400 0 C. This can be attributed to the presence of maghemite, which 

transforms to hematite on heating. The presence of a hematite phase is also indicated by a higher 

coercivity unblocking temperature (675 0 -700 0 C). 

ARM*10 -6 , A*m 2 /kg 

SIRM 1.5 *10 -3 , A*m 2 /kg 

K*10 -7 , m 3 /kg 

NRM *10 -6 , A*m 2 /kg 

300 

200 

100 

0 

0 

15 

1 2 3 4 5 6 7 8 9 10 11 12 13 

10 

5 

0 

15 

10 

5 

120 

80 

40 

0 

0 1 2 3 4 5 6 7 8 9 10 11 12 13 

0 

0 1 2 3 4 5 6 7 8 9 10 11 12 13 

H, m 

0 1 2 3 4 5 6 7 8 9 10 11 12 13 

23 21 19 17 15 1 11 9 7 5 3 

Hence the various experiments show that magnetite, magemite and hematite are the dominant 

magnetic carriers of the remanence. 

The ARM/SIRM, SIRM/klf and ARM/klf ratios were applied as grain size indicators for 

magnetite. In the Karadja range section the ratios vary ~3 to 4 times indicating that the grain size 

variations in general are not very strong in the section. For the sandy horizons the values ARM/SIRM 

and ARM/klf show larger values which can be associated with the growth of the super-paramagnetic 

388


particle concentration. At the same intervals the values of the frequency-dependent susceptibility 

Kfd=(Klf-Khf)*100%/Klf are higher than 8 %. That means that the percentage of the supper-paramagnetic 

particles is more than 50 % (Dearing, 1999). 

The anisotropy of magnetic susceptibility (AMS) was used for checking of reliability of the 

NRM directions. When the AMS results show any tilting or deformation of the sedimentary layers, the 

orientation of the remanence carriers can also be effected. Prior to AF-demagnitisation of the samples, 

AMS was measured on 3 samples from the level. An increasing trend of F=Ky/Kz with depth is observed 

beginning from ~10 m. This may relate to compaction of the loams. More over a sharp fall of F is seen 

at the interval 8.4-8.8 m. 

Stepwise alternating field demagnetization (AF) was carried out on representative samples in 

order to extract the component parallel and proportional to the geomagnetic field coeval with 

accumulation and fixation of magnetic grains in the sediments. To determine the range of AF 

demagnetization values required to extract the primary magnetization component, representative 34 

samples were subjected to a full stepwise AF demagnetization (5-90 mT) in steps of 5 mT. 

The majority of samples exhibit a secondary VRM overprint which was easily removed by 

moderate AF-demagnetization, and the stable ChRM isolated at 25 mT. Seldom after removing of the 

secondary VRM there were two very close directional low coercivity and high coercivity components. 

On the base of full AF-demagnetization of the pilot collection, the collection of two duplicate samples 

from each of the 375 levels was AF-demagnetized in the interval 15-35 mT when the main carrier was a 

low coercivity mineral and 15-60 mT in case of a high coercivity carrier. 

Results 

Using the principle component analysis (PCA), variations in the inclination I and declination D 

were plotted as a function of the section depth . The mean direction calculated after AF demagnetization 

may be compared to the present day value for the geomagnetic field at the sampling site (I0= 59 0 , D0= 

5.5 0 ). For the depth intervals 3.65-3.74, 5.15- 5.24, 8.58-8.69 and 11.14-11.38 m in the section the values 

of D and I deviate significantly from the average. 

The first diagnostic interval 3.65 to 3.74 m covers 5 levels of the layer 19 in the upper part of the 

terrace and show inclination values I =-7 0 to -54 0 and the declination D=101 0 to 119 0 . The main carrier of 

magnetization is hematite. Low cercitivity and high coercitivity components have similar direction of 

magnetization. The AMS measurements showed that this interval of the section has a normal 

sedimentary fabric. 

The next diagnostic interval (5.15 to 5.24 m) demonstrates abnormal directions of magnetization 

on 3 levels of the layer 17 when inclination fall down to I=27 0 and the declination D=190 0 . The main 

carrier of magnetization is hematite. The AMS results show that there is no tilting or deformation of the 

sedimentary layers. 

The third interval (8.58 to 8.69 m) comprise 6 levels in layer 13. Values of I varies between 39 0 

and 57 0 and D between 166 0 and 187 0 . The scalar magnetic parameters show values characteristic for the 

low coercitivity minerals such as magnetite or magemite. The deviations of angle elements coincide with 

sharp variations of the parameters F=Ky/Kz and L= Kx/Ky. Stereographic projections of the main axes of 

AMS ellipsoid show linear anisotropy which was caused by sedimentary layers movements down slope. 

This could cause a rotation of the ChRM vector. 

The forth diagnostic interval (11.14 to 11.38 m) is found in layer 7 and covering 11 levels, where 

D deviates up to 167 0 . Thermomagnetic analysis indicates that hematite is the main carrier of the 

magnetization. There is an increasing trend of F with depth up to the 10 % . This may be related with 

compaction of the loams and it is natural for a normal sedimentary fabric. 

Discussion 

The samples which show an abnormal behavior of the NRM except the interval of 8.58 to 8.69 m 

have the hematite like a main carrier of NRM. These intervals can be associated with chemical 

oxidation processes in the deposits and reflect the environmental and climate changes during the 

deposition process. However, these samples had the abnormal direction from elementary measurements 

of NRM only. After AF-demagnetization the RM did not show the direction of the dipole field 

characteristic for the given geographic site. The Zijderveld diagrams demonstrated two very close 

directional components: low and high coercivity components. That is why one can conclude that these 

389


grains of magnetite and hematite were magnetized before a transport and compaction of the sediments. 

During deposition and eventual lithification, the detrital magnetic particles became aligned parallel to the 

Earth’s magnetic field and acquired a detrital remanent magnetization. If we take into account the data 

described above, we obtain the following age estimates for the diagnostic intervals: 3.65 to 3.74 m: ~25 

ka B.P., 5.15 to 5.24 m: ~29 ka B.P., 11.14 to 11.38 m: ~39 ka B.P. These directional anomalies may be 

interpreted as evidence of reduced Mono Lake and Laschamp excursions recorded in the Karadja 

section. Hence the magnetic characteristics of the Karadja deposits appear to carry information not only 

about environmental conditions which took place during accumulation and litification of the sediments 

but probably also about global changes in the geomagnetic field recorded elsewhere. 

Inclination 

Declination 

90 

45 

0 

-45 

-90 

180 

90 

0 

270 -90 

0 1 2 3 4 5 6 7 8 9 10 11 12 13 

Н, m 

0 1 2 3 4 5 6 7 8 9 10 11 12 13 

23 21 19 17 15 13 11 9 7 5 3 


This research was supported by RFBR grant no. 08-05-00627-a. 

References 

Dearing, J. (1999), Environmental magnetic Susceptibility. Using the Bartington M32 System, 

104 pp. England, Chi Publishing. 

Dodonov, A. E., A.L. Tchepalyga, and C.D. Mihailescu (2000), Last interglacial records from 

Central Asia to the Northern Black Sea Shoreline: stratigraphy and correlation. J.Geosci., 79, 303-311. 

King, J.W., and J.E.T. Channell (1987-1990), Sedimentary magnetism, invironmental 

magnetism, and magnetostratigraphy. 1991. U.S. Natl. Rep. Int. Union Geod. Geophys. Rev. Geophys., 

29, 358-370. 

Lowrie, W. (1999), Identification of ferromagnetic minerals in a rock by coercivity and 

unblocking temperature properties. Geophys. Res. Lett., 17(2), 159-162. 

390


PLANETARY CONVECTION AND MAGNETIC STABILITIES 

S.V. Starchenko 

Pushkov Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation, Russian 

Academy of Sci. (IZMIRAN), Russia, 142190, Troitsk, Moscow region, e-mail: 

sstarchenko@mail.ru 


Abstract. I argue convection-driven magnetic dynamos are in magnetostrophic balance with 

rather strong and symmetric (to the rotation axis) magnetic field in the deep interiors of the Earth, 

Jupiter and Saturn. The dynamos of Uranus and Neptune with their asymmetric internal magnetic 

fields should be close to the non-magnetic inertia-buoyancy-Coriolis balance. Buoyancy 

(Archimedean) force could not be smaller than inertia or/and magnetic (Lorentz) forces because 

buoyancy is considered here as the only drive to the planetary convection and magnetism. The 

non-magnetic balance could result in relatively higher velocities, but its magnetic dynamo action 

could be not so efficient due to its gyroscopic effects. The last could be the reason for the current 

magnetic dynamo absence in Venus. The magnetostrophic or MAC balance between Magnetic, 

Archimedean and Coriolis forces is arising when the magnetic field becomes strong enough. This 

MAC balance suppresses the velocity to rather lower value comparing with IAC balance 

[introduced in this paper] between Inertia, Archimedean and Coriolis forces. However, MAC 

balance removes almost 2D (two dimensional) symmetry in the flow making rather efficient 

dynamo action with 3D MAC flow. So, I found that the principal balance between Magnetic, 

Archimedean and Coriolis force is in the Earth, Jupiter and Saturn with strong magnetic field in 

their cores. In Uranus, Neptune and perhaps Ganymede, magneto-convection is supported by the 

balance between Inertia, Archimedean and Coriolis forces those exceed or are about the magnetic 

force. 

The main objective of this paper is to find and to investigate possible dynamical regimes and force balances 

determining the velocity and magnetic field strength in planetary interiors, based on the assumption that the 

magnetic fields are produced by convection-driven dynamo action. I consider the planets with electrically 

conducting region of liquid were the dynamo is active enough to form the magnetic field that is eventually 

observable by spacecrafts. This dynamo region consists of rather thick shell of metallic hydrogen in the case 

of Jupiter and Saturn with conductivity about 3×10 7 S m −1 [6, 28], while it is principally iron in the case of 

the Earth’s outer core with conductivity about 4×10 5 S m −1 [2]. Those dynamo regions are not so well 

determined in Uranus and Neptune where smaller, but sufficient for dynamo action, ionic conductivity about 

10 3 S m −1 [13] or few times larger is possible in relatively wider [15, 8] or thin [19] deep internal shells. 

In the preceding paper [23] we argued the dynamical regime and force balance in the outer cores of Jupiter 

and Saturn is similar to the regime and balance in the Earth’s outer core. In this paper I will further develop 

and specify our [23] arguments comparing Earth, Jupiter and Saturn with Uranus and Neptune where another 

regimes and balances are also possible. My arguments are based on the governing anelastic equations [2, 22, 

23] with entropy and concentration variables which are convenient for our rough estimations here and for 

further detail numeric/analytic modeling. I assume the dynamos in all five planets are driven by convection 

arising from the cooling and gravitational rearrangements of the deep planetary interiors. All the direct 

observation of magnetic field rotation is just slightly different from the rotation of the planetary surface [6, 8, 

9, 14, 15, 18] providing us with magnetic proves of an almost rigid rotation of the deep planetary interiors 

where those magnetic fields are generated. From very general point of view, when there is no magnetic field 

yet, the corresponding planetary hydrodynamics is in the balance between the only driving buoyancy 

Archimedean force and inertia force. The last is converted to ‘turbulent’ viscosity a diffusivity actually 

becoming the main friction force. This buoyancy-inertia balance should be supplemented with balance to the 

Coriolis force due to the almost rigid rotation of planetary interiors. When magnetic field starts due to the 

dynamo action to grow from zero the initially small magnetic Lorents force is at first not able to participate 

in the initial IAC balance between Inertia Archimedean and Coriolis forces. I argue theoretically that such 

IAC balance is dominated in the magnetic dynamo regions of Uranus and Neptune. Additional observation 

evidence to it is surprisingly strong asymmetry in magnetic field relative to the rotation axis of both planets 

[8, 14, 15]. Indeed, such asymmetric field could be first created by the nearly z-independent and axially 

391


symmetric IAC balance almost 2D flow. Inversely, if the dynamo is strong enough as in the Earth, Saturn 

and Jupiter the magnetic field reaching the magnetostrophic or MAC balance will tends to create rather 

symmetric magnetic field that is supported by sufficiently asymmetric 3D velocity field. I assume the same 

basic equations as those had been presented in [23]. So, I do not repeat their details here referring on the 

necessary formulas of [23]. 

2 MAC Balance in Jupiter, Saturn and Earth 

In this section I briefly repeat the results that have been obtained for the Jupiter, Saturn and Earth in [23] 

where MAC [1] balance was developed. In MAC balance, the buoyancy forces work against the magnetic 

Lorentz force, and this energy is transferred to magnetic fields where it is dissipated as Ohm heating. Since 

in MAC balance Coriolis and buoyancy forces are comparable, from (3) of [23] we see that Ω V* ≈ T '* S* 

in 

Jupiter and T '* 

≈ 3×10 −4 K m −1 is the typical reference state (RS) temperature gradient in its outer core 

(OC). Using (12) of [23] we can now estimate the typical entropy fluctuation and velocity in Jupiter’s OC: 

QoΩro 

S* 

= ≈ 10 

M oT* 

T '* 

−3 J kg −1 K −1 Qoro 

T '* 

, V* 

= ≈ 10 

M oT* 

Ω 

−3 ms−1. (1) 

We now get our estimate of the magnetic field by balancing the Lorentz force with either the Coriolis force 

or the buoyancy force since these are of the same order in MAC balance. This gives 

B* ~ r* 

μ 0 ρ * T '* 

S* 

, (2) 

where the current density j is estimated as B * /( r* 

μ0 

) so that r * is a typical length scale for the magnetic 

field. Numerical simulations suggest that r * is somewhat smaller than the length scale of the whole dynamo 

region, ro. In the kinematic regime of a dynamo process, this typical length scale is about roRm −1/2 where Rm is 

the magnetic Reynolds number (e.g., see [20]). However, when saturation is reached in a dynamo, that is 

when Lorentz force becomes significant, there is a tendency for the length scale of the magnetic field to 

increase [11]. This is reasonable, because if the flux is concentrated into thin ropes, the Lorentz force gets 

locally large, opposing the concentration process. So whereas r * ~ roRm −1/2 is reasonable for metallic core 

dynamos such as the Earth, where Rm is only a few hundred, this formula gives a value of r * which is too 

small at the much larger value of Rm in Jupiter. Therefore it more likely that r * / ro is independent of the 

molecular diffusivity at large Rm. Numerical simulations at Rm = V * ro/η~200 give fields with Elsasser 

number B 2 /(2Ωρμη) ~ 4 [11], which implies that for these simulations r * / ro ~0.02, and we take this ratio for 

our estimates. 

On the basis of these arguments, for Jupiter we take r * / ro ~0.02~10 6 m and the typical magnetic field 

B* = r* 

μ0 

ρ * T '* S* 

. (3) 

Which with (1) gives a field strength of 2×10 −2 T. This is about 10 times higher than the observed Jovian 

magnetic field [4], but this is reasonable, as in geodynamo simulations (e.g., see [5, 10]) the strength of the 

field trapped in the core can easily be 10 or even more times the strength of the field that escapes the core to 

form the observed field. The corresponding value of the “turbulent” magnetic diffusivity is V * r * ~ 10 3 m 2 s −1 . 

There are two factors which make the dynamo process in Saturn’s interior even more difficult to predict than 

in the Jovian case. First, its metallic outer core lies much further below the surface than does the Jovian core. 

The assumption that the bulk of the observed heat flux comes from the core is therefore probably incorrect 

for Saturn. Second, Saturn may have a stable layer above its convective core, due to the “helium raindrop” 

phenomenon [25]. In the outer part of the ionized metallic zone, helium condenses into drops, which fall into 

the interior where they recombine with the ambient fluid releasing gravitational energy. This results in a 

lower density, primarily hydrogen, stable layer in the upper part of the metallic hydrogen zone, while the 

lower part is stirred by compositional convection. 

To quantify this compositional buoyancy effect we suppose that it is K-times more efficient than thermal 

buoyancy, in the sense that K-times more energy goes into magnetic field production than would be the case 

without a compositional effect. This K could be between 2 and 5 if we compare with the Earth [2, 5]. In our 

estimations K and ξ appear in the balance K T '* S* 

= ΩV* 

= μ'* 

ξ* 

. The total heat flux coming out of 

Saturn’s interior is estimated at 9 × 10 16 W, [4], and we suppose that the total heat flux coming out of 

Saturn’s core is a fraction L of this. If we assume the bulk of the interior is adiabatically stratified, and 

392


remains so during cooling, then a reasonable estimate for L would 0.5. Using the Saturnine values, e.g. from 

[23], we get 

S 10 L / K 

3 − 

* ≈ J kg −1 K −1 −3 

, V* 

≈ 2× 

10 LK ms −1 −2 

4 

and B* 

≈ 2× 10 LK T. (4) 

We finish this section with the Earth because although far more is known about the Earth’s magnetic field 

than that of other planets, the heat flux coming out of the core is rather uncertain. Thus, it is not entirely clear 

how to estimate S * in the Earth’s OC. Therefore start by estimating the non-uniform concentration ξ * from 

(10)-(11) of [23]. The available estimates of its energy source give d ξ / dt = (8 ± 4)×10 −20 s −1 , based on the 

density jump at the inner core (IC) at the present epoch [17, 2]. The simulations of [5] suggest a value of ˙_ 

about 8×10 −20 s −1 , based on the age of the IC being around 1.3 billion years. This age of the IC agrees with 

the self-consistent thermal history models [27]. We adopt this value as our typical value; it gives a 

compositional energy rate ~1TW and corresponding latent heat flux ~3TW. Unless too large value of the 

CMB heat flux is chosen, compositional convection contributes a few times more energy to the dynamo than 

does thermal convection in the Earth’s OC. 

So, we obtain an approximate equation and an estimate: 

π 2π 

2 

r ∫∫ ξVr 

sinθdθdϕ ≈ −M 

odξ 

/ dt and V* ξ* = ro 

dξ 

/ dt ≈ 3×10 

0 0 

−13 m s −1 . (5) 

Using this estimate and balancing the Coriolis force to the compositional buoyancy force as ΩV * = μ'* 

ξ* 

we get the typical velocity and concentration. 

−1 

V* = Ω ro 

μ' dξ 

/ dt ≈ 2×10 −4 m s −1 −1 

and ξ* = Ωro 

( μ') 

dξ 

/ dt ≈ 2×10 −9 . (6) 

Here μ ' = 5 m s −2 is a typical (average) magnitude of the radial derivative of the chemical potential in the 

Earth’s OC in accordance with PREM [3]. Balancing Lorentz and Coriolis force and using (20)-(21) of [23] 

we get the typical magnetic field in the Earth’s core 

B r μ ρ Ωr 

V ≈ 4×10 −3 T for r * = 10 5 m. (7) 

* = * 0 * * * 

3 Is MAC Balance in Uranus and Neptune? 

The first row of Table 1 for Jupiter is taken from Table 1 of [23]. Two following rows summarize the typical 

MHD values those could be possible if MAC balance is in Uranus and Neptune. The radial velocity and 

entropy fluctuation estimates came from (1) above. Magnetic field estimates are derived from (3). All the 

estimations are based on spacecraft [14, 15, 18], fully self-consistent theoretical [4, 8, 9, 25] and 

experimental [13] data. For simplicity in Neptune and Uranus the same estimation methods have been using 

as in [23] for Jupiter. Thus, in Table 1 the heat flux from each planetary liquid core is about 70% from the 

upper limit for the observed surface heat flux. Besides, we use the upper limit for this metallic core radius in 

Uranus and Neptune. All that should eventually lead to the upper possible MAC velocity values. 

However, even those upper possible MAC values are not enough to support the magnetic dynamo action. 

Indeed, the upper limit for conductivity is σ ≈ 2×10 3 S m −1 [4, 8, 13, 15] there. So, there is a lower limit for 

the magnetic diffusivity η ≈ 1/μ0σ ≈ 400 m 2 s −1 . Thus, the magnetic Reynolds number Rm = V * ro/η based on 

the typical radial velocity is about 12 in Uranus and about 25 in Neptune. Flow with such lower magnetic 

Reynolds number could hardly support any magnetic dynamo action [10, 19, 20]. Hence MAC balance is 

impossible in Uranus and Neptune. 

Impossibility of MAC balance in those planets is also seen from too larger values of their MAC magnetic 

fields in Table 1. Those internal values should 

be reduced by factor ~10 (~R f m with 0 < f < 1 [5, 10, 23]) in order to estimate the surface values. The reduced 

values are still ~10 times larger than the magnetic field observed at Uranus and Neptune [4]. Moreover, if we 

allow low magnetic Reynolds dynamo action in those planets then scale ~roRm −1/2 should be sufficiently 

larger (see previous section and [23] for details) than in Table 1. Thus, MAC magnetic field becomes even 

larger than in Table 1 and hence it will not match observations at all. In the following section we consider 

another balance that could match to those relatively low observed magnetic field. 

393


Table 1: Typical values for MAC balance in planetary cores 

4 Inertia-Archimedean-Coriolis (IAC) Balance 

Following (12) of [23] we first repeat the heat transport estimate that should be valid for considered 

convection in the planetary cores: 

V* / ro 

S* 

= dS* 

/ dt . (8) 

Now neglecting by magnetic contribution in the force equation (3) of [23] we are only left with inertia to 

Archimedean active working force balance: 

V * V* 

/ r* 

= S* 

T '* 

/ r* 

. (9) 

Typical scale r_ should be determined by inactive (because it can not do work) but leading Coriolis force in 

Neptune and Uranus. 

Thus, we complete the determination of IAC balance by the third estimate 

Ω V* / ro 

= S* 

T '* 

/ r* 

. (10) 

Here we considered the well-known curl of the momentum equation (3) of [23] equating in order the Coriolis 

term of this curl to the Archimedean term. Remind that the flow is just slightly dependent on height or zcoordinate 

under strong influence of Coriolis force. Thus, the outer radius of a planet ro is used on the left 

hand side of (10) where only z-derivative is estimated. While, smaller Rhines scale r *


Table 2: Typical and maximal magnetic values for IAC balance 

Acknowledgments: This work was supported by RFBR grants: 06-05-65162 and 07-05-90006. 

References 

[1] Braginsky, S. I. (1967) Magnetic waves in the Earth’s core, Geomagn. Aeron., Vol. 7, pp. 1050-1060. 

[2] Braginsky, S. I. and Roberts, P. H. (1995) Equations governing convection in the Earth’s core and the 

geodynamo, Geophys. Astrophys. Fluid Dynamics, Vol. 79, pp. 1-97. 

[3] Dziewonski, A. M. and Anderson, D. L. (1981) Preliminary reference Earth model, Phys. Earth Planet. 

Inter., Vol. 25, pp.297-356. 

[4] Connerney, J. E. P. (1993) Magnetic field of the outer planets, J. Geophys. Res., Vol. 98 (E10), pp. 

18659-18679. 

[5] Glatzmaier, G. A. and Roberts, P. H. (1997) Simulating the geodynamo, Contemporary Physics, Vol. 38 

(4), pp. 269-288. 

[6] Guillot, T. (1999) A comparison of the interiors of Jupiter and Saturn Planet, Space. Sci., Vol. 47, pp. 

1183-1200. 

[7] Hide, R. (1974) Jupiter and Saturn, Proc. Roy. Soc. Lond. A., Vol. 336, pp. 63-84. 

[8] Holme, R. and Bloxham, J. (1996) The magnetic fields of Uranus and Neptune: Methods and models, J. 

Geophys. Res., Vol. 101, (E1), pp. 2177-2200. 

[9] Hubbard, W. B. and Marley, M. S. (1989) Optimazed Jupiter, Saturn, and Uranus interior models, Icarus, 

Vol. 78, pp. 102-118. 

[10] Jones, C. A. (2000) Convection-driven geodynamo models, Phil. Trans. R. Soc. Lond. A, Vol. 358, pp. 

873-897. 

[11] Jones, C. A. and Roberts, P. H. (2000) Convection-driven dynamos in a rotating plane layer, J. Fluid 

Mech., Vol. 404, pp. 311-343. 

[12] Kirk, R. L. and Stevenson, D. J. (1987) Hydromagnetic constraints on deep zonal flow in the giant 

planets, Astrophys. J., Vol. 316, pp.836-846. 

[13] Nellis, W. J. et al. (1988) The nature of the interior of Uranus based on studies of planetary ices at high 

dynamic pressure, Science, Vol. 240, pp.779-781. 

[14] Pearl, J. C. and Conrath, B. J. (1991) The albedo, effective temperature, and energy balance of Neptune, 

as determined from Voyager data, J. Geophys. Res., Vol. 96, pp. 18,921-18,930. 

[15] Podolak, M., Hubbard, W. B. and Stevenson, D. J. (1991) Models of Uranus’ interior and magnetic 

field, in Uranus, edited by J. T. Bergstralh, E. D. Miner, and M. S. Matthews, University of Arisona 

Press, Tucson, pp. 29-61. 

[16] Rhines, P. B. (1975) Waves and turbulence on a beta plane, J. Fluid Mech., Vol. 69, pp. 417-433. 

[17] Roberts, P.H., Jones, C.A. and Calderwood, A.R. (2001) Energy fluxes and ohmic dissipation in the 

Earth’s core, to appear in Earth’s core and lower mantle eds. C.A. Jones, A.M. Soward and K. Zhang, 

Gordon and Breach. 

[18] Russell, C.T., Yu, Z.J., Khurana, K.K. and Kivelson, M.G. (2001) Magnetic Field Changes in the Inner 

Magnetosphere of Jupiter, Adv. Space Res., Vol. 28, No. 6, pp. 897-902. 

[19] Ruzmaikin, A. A. and Starchenko, S. V. (1991) On the origin of Uranus and Neptune magnetic fields, 

Icarus, Vol. 93, pp. 82-87. 

[20] Starchenko, S. V. (1994) Dynamo models with strong generation 1. Kinematic solution and 

axisymmetric α 2 ω-dynamo, Geophys. Astrophys. Fluid Dynamics, Vol. 77, pp. 55-77 

395


[21] Starchenko, S. V. (2000) Supercritical magneto-convection in rapidly rotating planetary cores, Phys. 

Earth Planet. Inter., Vol. 117 (1-4), pp. 225-235. 

[22] Starchenko, S. V. (2001) Anelastic planetary magnetohydrodynamics, NATO Science Series II: 

Mathematics, Physics and Chemistry, Vol. 26, pp. 217-224. 

[23] Starchenko, S. V., and Jones, C. A. (2002) Typical velocities and magnetic field strengths in planetary 

interiors, Icarus, Vol. 157, pp. 426–435. 

[24] Stevenson, D. J. (1979) Turbulent thermal convection in the presence of rotation and magnetic field: a 

heuristic theory, Geophys. Astrophys. Fluid Dynamics, Vol. 12, pp. 139-169. 

[25] Stevenson, D. J. (1982) Interiors of the giant planets, Ann Rev. Earth Planet. Sci., Vol. 10, pp. 257-295. 

[26] Taylor, J. B. (1963) The magneto-hydrodynamics of a rotating fluid and the Earth’s dynamo problem, 

Proc. R. Soc. London Ser., Vol. A 274, pp. 274-283. 

[27] Yukutake, T. (2000) The inner core and the surface heat flow as clues to estimating the initial 

temperature of the Earth’s core, Phys. Earth Planet. Inter., Vol. 121, pp.103-137. 

[28] Zhang, K., Jones, C.A., and Chen, D. (1996) Estimates for the effective electrical conductivity of the 

core in the interior of Jupiter and Saturn, Earth, Moon and Planets, Vol. 73 pp. 221-236. 

396


CO�VECTIO� STABILITY A�D THE EARTH’S TYPE PLA�ETARY 

MAG�ETISM 

S.V. Starchenko 1 , M.S. Kotelnikova 2,3 

1 IZMIRAN, Troitsk, Moscow region, Russia, e-mail: sstarchenko@mail.ru; 2 Lavrentyev Institute of 

Hydrodynamics SB RAS, 3 Novosibirsk State University, Novosibirsk, 630090, Russia 

Abstract. Almost adiabatic states are typical for the deep convective interiors of all known planets 

and their moons, e.g., the deviations from the adiabatic state in the Earths' outer core and in the 

MHD dynamo region of Jupiter are about or less than 10 -5 %. We considered the marginal stability 

of well mixed almost adiabatic states in rapidly rotating thick spherical shells, whose inner to 

outer radius ratio does not exceed that of the modern Earth. The critical Rayleigh-type numbers, 

frequencies and solution structures of the marginal states were determined by both analytical and 

numerical methods. Our new estimates differ from those obtained previously using the Boussinesq 

equations, suggesting that the earlier Boussinesq results for convection in the deep planetary 

interiors should be re-assessed. The small molecular Prandtl number limit was adopted to model 

the marginal stability of thermal planetary convection. It was found that the critical Rayleigh 

number for convection sharply diminished as the radius of the inner rigid core is increased. We 

modeled the instability of the combined compositional-thermal turbulent geo-convection for 

Prandtl number unity. When thermal convection is in opposition to compositional convection, 

extremely large critical Rayleigh numbers are possible. This might happen for a terrestrial planet 

during its later stage of evolution. Pure compositional convection has been investigated in the 

large compositional Prandtl number limit, for which the critical Rayleigh number is rather large 

and the variations of all critical parameters are small. The large size of the critical Rayleigh 

number ensures that the actual values used in numerical dynamo experiments are only moderately 

supercritical. 

Introduction. 

During the last hundred years, the classical Boussinesq approximation was widely used for 

modelling convection in various astrophysical objects. It is based on the assumptions that buoyancy and 

thermal energy variations are relatively small and they exist mainly due to the temperature variations. 

However, although the Boussinesq approximation is valid for many convecting systems, it is not applicable 

to studies of convection in most part of the deep stellar and planetary interiors (e.g. see Spiegel and Veronis 

1960), because the energy assumption of the Boussinesq approximation cannot be applied to the thick 

convective shells in the planetary interiors. Thought the correct set of non-Boussinesq equations are well 

known, they have rarely been used for modelling planetary convection (one successful recent application is 

Glatzmaier and Roberts 1996) mostly because it seems too complicated for numerical modelling. But it 

appears possible to consider the well-known (e.g. see Braginsky and Roberts 1995, Glatzmaier and Roberts 

1996) anelastic planetary convection system and simplify them by introducing almost adiabatic 

approximation. Generally, this approximation can give better than 10 -5 % accuracy in the deep convective 

interiors of the Earth, Jupiter and other planets or moons. In contrast, the values of some important 

geometrical, gravitational, thermodynamic and hydrodynamic parameters are only known to a low accuracy 

with errors of more than 10%. Thus, although we tried to retain all possible non-Boussinesq effects, it is 

convenient to neglect some terms in order to make our almost adiabatic convective system as simple as 

possible while keeping 10% accuracy. Eventually we derive an almost adiabatic system of equations, that 

consists of equation of momentum, continuity equation and entropy equation, somewhat similar to the 

classical Boussinesq system but more appropriate for studying convection in deep planetary interiors. In its 

dimensionless form it can be presented as follows 

DV 

2 

∇ ⋅ V = 0 , E + 1z 

× V + ∇p 

= ERθ 

r + E∇ 

V , (1, 2) 

Dt 

ν Dθ 

2 

= −∇θ 

S ⋅ V + ∇ θ . (3) 

κ Dt 

397


2 2 

We use 4π 

) ν g ραT 

( ro o as the unit of heat power, ro as the unit of length, ro 2 /ν as the unit of time, 

4π oα oν 

/ g r as the unit of entropy to obtain the dimensionless 

2Ων as the unit of effective pressure and κ 

system: Here go is the gravitational acceleration at the outer liquid core boundary r=ro, κ is the thermal 

diffusivity, ν is the molecular diffusivity, Ω is constant rapid planetary angular velocity, α is the thermal 

expansion coefficient. Henceforth, values corresponding to the inner (inner core boundary) and outer (outer 

core boundary) boundaries are denoted by ‘i’ and ‘o’ respectively. 

We split the complete non-adiabatic entropy θc into its convective part θ and non-convective (but rather 

crucial for convective instability) part θS: θc=θ +θS. The usual Ekman number and our newly modified 

adiabatic Rayleigh number in (27) are E =ν/2Ωro 2 2 2 −1 

, R = 4π 

( αgoro 

) TCP 

/ κν . 

The buoyancy source in the homogeneous system (1-3) is the non-convective entropy gradient ∇θS. 

That is purely radial and can be written as 

3 −3 

dθ S Qo 

− Qi 

+ ( Qi 

− b Qo 

) r 

= −r 

, (4) 

3 

dr 

1− 

b 

where b=ri/ro is the aspect ratio. The input super-adiabatic heat power flux Qi>0 is able to drive the 

convection as well as the output super-adiabatic heat power flux Qo>0, when Qo > Qi and b is small enough. 

Negative sub-adiabatic fluxes suppress the convective instability. Therefore, contrary to the Boussinesq 

approximation, the convection is driven not by bulk temperature gradient or/and internal heat but by those 

super-adiabatic or positive heat sources Qo and Qi directly at the boundaries in (32). 

For our final homogeneous system (1-3) the non-dimensional integral d 0 

3 ρ θ r = and 

∫ 

ri 

≤r ≤ro 

boundary conditions on the convective part of non-adiabatic entropy θ (simply entropy hereafter) also 

become homogeneous: 

3 ⎛ ∂θ 

⎞ 

⎛ ∂θ 

⎞ 

∫θ d r = 0, 

⎜ ⎟ = 0, 

⎜ ⎟ = 0. 

(5,6,7) 

b≤r 

≤1 

⎝ ∂r 

⎠ r = 1 

⎝ ∂r 

⎠r 

=b 

In addition, we consider homogeneous no-slip and/or stress-free boundary conditions on the planetary 

velocity V for our investigation of marginal stability. 

Convective instability appears only when (32) is negative making possible convection instability to 

arise. Otherwise, the liquid is stably stratified with entropy gradient S / r > 0 d dθ opposing convection. 

Thus, roughly speaking (our more accurate estimates for particular cases will be presented in the next 

section) the necessary condition for the global convective instability is that the volume integral IS of (32) is 

negative: 

3 2 

dθ S 3 

b + b + b − 3 

I S d r < 0 ⇔ Qo > −F 

( b) 

Qi 

, F = 

. (8, 9) 

3 2 

dr 

3b 

− b − b −1 

≡ ∫ 

b≤r 

≤1 

Marginal stability at small Ekman numbers. 

To investigate linear stability of almost adiabatic convection, we just replace D/Dt in (1-3) by ∂ / ∂t 

. 

In this section, we first consider the general relations for asymptotic and numerical analysis and then obtain 

the specific solutions of the problem. To begin the small Ekman number asymptotic analysis, we set 

V = ∇ × Ψ1z 

+ ∇ × ( ∇ × ξ1 

z ) . 

In this standard Toroidal-Poloidal representation, the velocity field satisfies the solenoidal condition (1). The 

corresponding vertical velocity and horizontal Laplacian operator are defined as 

2 

z W ∇ Hξ 

= = ⋅1 V , 2 

2 1 ∂ ⎛ ∂ ⎞ 1 ∂ 

∇ H ≡ ⎜ s ⎟ + . 2 2 

s ∂s 

⎝ ∂s 

⎠ s ∂ϕ 

Following Jones et al. (2000) we choose the asymptotic solution at small Ekman number in the WKBJ 

form 

⎡ mϕ 

+ ∫ k( 

s) 

ds iω 

⎤ 

n / 3⎛ 

Wn 

Ψn 

⎢ 

⎥ 

⎞ 

−4 

/ 3 

n / 3 

( W , Ψ, 

θ ) = exp i 

− t 

1 / 3 

2 / 3 ∑ E ⎜ , , θ 

2 / 3 1/ 

3 n ⎟ , R = E ( ℜ + ∑ E ℜn 

) .(10,11) 

⎢ E E ⎥ n≥0 

⎣ 

⎦ 

⎝ E E ⎠ 

n≥1 

Here the growth rate -iω/E 2/3 is the complex egenvalue, the Rayleigh number ℜ is a real positive number, 

while the wave-number k is an unknown function of the distance s from the axis of rotation. The 

398 

c


representation (10) directly satisfies the condition of zero-entropy integral (5) because m/E 1/3 is a non-zero 

integer. 

After substitution (10-11) into the system that consists of radial component of the curl and double curl of 

the momentum equation (1) and entropy equation (3), we obtain an asymptotic system without E for every n. 

The leading order n=0 system is 

2 

2 

⎛ 2 m ⎞⎛ 

2 m ⎞ ∂W0 

⎜ 

⎜i 

ω − k − 

Ψ0 

+ − ℜ 0 = 0 

2 ⎟ 

⎜ 

⎜k 

+ 2 ⎟ im θ , (12) 

⎝ s ⎠⎝ 

s ⎠ ∂z 

∂Ψ 

0 

∂z 

2 

⎛ 2 m ⎞ 

+ ⎜iω 

− k − ⎟W0 

+ ℜzθ 

0 = 0 , (13) 

2 

⎝ s ⎠ 

2 

⎛ ν 2 m ⎞ 

( imΨ0 + zW0 

) θ ′ S − ⎜i 

ω − k − ⎟θ 

0 = 0 . (14) 

2 

⎝ κ s ⎠ 

−1 

Here θ ′ S ≡ r d θ S / dr 

is the buoyancy source of the convective instability which we define using 

the gradient of non-convective entropy (4). 

From (14) we deduce that non-penetrative boundary condition for the radial component of the velocity 

and condition 

θ0=0 at z = (1-s 2 ) 1/2 and at z = - (1-s 2 ) 1/2 (15) 

are equivalent. This contradicts the original boundary condition (6) for entropy, but it can be resolved by the 

existence of thin entropy boundary layer (see e.g. Glatzmaier and Roberts 1996) on the inner boundary at the 

outer edge of which the condition (15) is satisfied. We shall consider only the modes with W0 antisymmetric 

about the equator z=0, because it is the physically realized solution with smallest critical Rayleigh number 

(Busse 1970). Thus, we need only consider one-half of the spherical domain using the boundary condition 

W 0 at z = 0. (16) 

0 = 

The turbulent Prandtl number equals unity 

Thermal and compositional turbulent Prandtl numbers must be both of order of unity in the Earth’s 

outer core and in the fluid cores of similar planets and moons with vigorous basic uniform convection (see 

e.g. Braginsky and Roberts 1995,, Starchenko and Jones 2002). Thus, to investigate marginal stability of 

non-uniform turbulent convection, it is preferable to set the Prandtl number to unity. 

Furthermore, at our approximation level, the source of compositional buoyancy can be well 

approximated (see e.g., Lister and Buffet 1995, Braginsky and Roberts, 1995; Starchenko and Jones, 2002) 

by a fixed unit input of compositional power Qi=1 in (4). This does not restrict us from using any positive 

2 2 

dimensionless input power flux Qi (measured in ( 4π 

) ν g ραT 

), after redefining the entropy unit as 

ro o 

2 2 −1 

4π Q iro 

αg 

oν 

/ κ together with the Rayleigh as R = 4π 

Qi 

( αg 

oro 

) TCP 

/ κν . 

We estimate the lowest limit of the thermal heat flux Qo by equating the integral IS in (8) to zero. 

These marginal heat fluxes Qo are plotted in figure 3 as functions of b. We expect that when we approach the 

negative values of Qo, the critical Rayleigh numbers will start to tend to infinity. 

Our main interest concerns the current Earth, where b=0.35. The corresponding buoyancy source θ′ S 

being negative (in average) supports the convection in the Earth’s outer core when Qo > -2, as it roughly 

follows from (4) when we set output heat flux Qo with Qi=1 and b=.35. 

To investigate the marginal stability of an almost adiabatic convection we introduce the additional 

notation for Pr=1 (used for Pr≠1 below as well) 

2 

2 2 2 2 

γ = iω − a , a ≡ k + m / s , θ ′′ z ≡ ∂θ 

′ S / ∂z, 

and rewrite system (48-50) for Pr=1 as a single second-order ordinary differential equation 

2 

2 

2 

d W0 

m ℜθ 

′′ ⎡ 0 2 2 ⎛ 2 2 2 

′ 

/ ′ ⎞⎤ 

z dW 

im ima γzθ 

z θ S 

− − 

0 = 0 

2 2 2 2 

⎢γ 

a + ℜθ 

′ ⎜ 

⎟ 

S ⎜ 

m + a z + + 2 2 2 ⎟⎥W 

(17) 

dz 

γ a + m ℜθ 

′ z ⎢⎣ 

⎝ 

a + m ℜ ′ 

S d 

γ γ θ S ⎠⎥⎦ 

in z. It is to be solved subject to the boundary conditions 

dW0 

2 

2 

W0=0 at z=0, im − a zγW0 

= 0 at z = 1− s , (18, 19) 

dz 

which follow from (15) and (16) for Pr=1. 

399


Our local (Busse 1970 type) asymptotic analysis of (17-19) results in the critical parameters values listed in 

Table I. In geophysical contest, the cases with Qo > 1 , Qi 

= 1, 

Qo 

= 0 ) instability 

b 0.05 0.1 0.2 0.3 0.35 

Asymptotic results, Pr = 1000 : 

3 

3 

3 

3 

3 

ℜ cr 1 . 073× 

10 1 . 068× 

10 1 . 035× 

10 1 . 018× 

10 1 . 007× 

10 

ω 3.113 3.187 3.227 3.278 3.294 

cr 

s 0.5846 0.5853 0.5884 0.5914 0.5921 

cr 

m 0.4971 0.5002 0.5017 0.5095 0.5114 

cr 

The results of Table II show that there is no strong dependence of the critical values ω cr and ℜ cr on 

the dimensionless inner core radius b. Independent on E (due to (10) and (11)) critical compositional values 

of Rayleigh and frequency numbers also demonstrate simple Pr-scaling 

400


ω cr ( Pr) 

≅ const, 

( ) 0 , Pr R Pr ℜ cr ≅ 

R 0 = const 

in this larger Prandtl number case. This simplification becomes possible for two reasons. Firstly, the inner 

rigid core is relatively small and, secondly, the change of the relative (integrated) convective efficiency is 

also small for our b≤0.35 inspite of the sharp buoyancy source rise ~b -3 at the inner boundary. 

The real dimensional value of compositional power flux Qi~b 2 strongly depends on the inner core 

radius and rises sharply as b grows up to a certain critical radius that is slightly greater than one in the current 

Earth value (see Starchenko 2003 for details). When the radius of the inner core is small (consequently Qi, is 

small too), the Rayleigh number of flow is also small. Thus, it is hard to excite the compositional convection 

when the inner core is relatively small because the critical Rayleigh numbers in Table III are too large. 

Small thermal Prandtl numbers. 

To describe thermal convection we neglect the non-adiabatic input heat flux and set Qi=0. Then for given 

Qo>0, we may set Qo=1 in (4) as before as long as redefine the Rayleigh number to be 

2 2 −1 

R = 4π 

Qo 

( αgor 

o ) TCP 

/ κν with the original value of Qo. 

The relative efficiency of such convection is determined by the integral IS from (8). In the case of 

pure thermal convection we can safely stay in the small Prandtl number limit because the typical thermal 

diffusion coefficient κ is larger than viscosity ν. See e.g. Braginsky and Roberts (1995) who have suggested 

this molecular thermal Prandtl number Pr≈0.1 for the Earth’s outer liquid core. 

We solve the complete system (20) with boundary conditions (21) and (22) for this small Prandtl 

number case. For various Prandtl numbers, our local results for this system are listed in Table III. We can 

conclude from Table III that the critical Rayleigh number for almost adiabatic thermal convection becomes 

smaller as the radius of the inner core increases. Possibly this help to maintain thermal convection even 

during the later stages of the planetary evolution when the internal radioactive heat sources become too 

weak. 

Table III. Critical parameters for thermal ( Pr


negative and ~b 3 that we could relate to the strong dependence of the critical Rayleigh number on the inner 

core radius b (see Table III). 

Thus, we may well attribute the difference between compositional and thermal cases to the 

difference between the z-derivatives shown in (23). 

Discussion and conclusions. 

In Introduction we argued that the widely used Boussinesq approximation is not applicable for studies of 

convection in deep planetary interiors. Nevertheless, the adiabatic approximation is commonly employed to 

describe the spherically symmetric structure of the deep convective interiors of all the known planets and 

moons. However, the almost adiabatic approximation has rarely been used to describe convection, in spite of 

the fact that this approximation was originally proposed specifically for these kinds of objects. 

We treat section 2 and the first one-third of section 3 as just summary to the well-known but unfortunately 

rarely used almost adiabatic approach. Slightly more general addition to this approach is developed in the 

last two-third of section 3. We do not set any restriction until the condition (25) that is the only serious 

assumption in our approach. However, it is obvious that this condition is less restrictive comparing to any 

one used before, especially for the terrestrial planets. 

Our equations (1-3) are exactly identical to the Boussinesq equations. That we consider as an 

advantage because previously well-developed methods could be used to solve them. However, the physical 

meaning of our equations is much clearer comparing to the Boussinesq equations due to use of entropy as a 

thermodynamic variable instead of non-correct super-adiabatic Boussinesq-type temperature. Besides, our 

system has integral (5) and boundary (6-7) conditions that considerably differ from the conditions that are 

commonly used in all known applications of Boussinesq approximation and its modifications. The buoyancy 

source (4) is most important for the convection. It depends only on non-adiabatic heat fluxes at the 

boundaries. Generally, the buoyancy sources of almost adiabatic convection are rather non-uniform in the 

deep interiors of the planets and moons. However, such non-uniform buoyancy driving can be determined by 

the boundary conditions for heat and compositional power alone. Not only does it make the almost adiabatic 

system more accurate but also makes it simpler than the Boussinesq system, which typically requires input 

information throughout the entire convective volume. In application to marginal stability in the Earth-type 

terrestrial planets and moons, we have found their critical Raleigh-type numbers, frequencies and forms of 

marginal convection. 

We have modeled the marginal stability of the compositional-thermal turbulent geo-convection with 

Prandtl number unity. Extremely large critical Rayleigh numbers appear in this case when thermal 

convection opposes the compositional convection in some regions of the core. Such opposition possibly 

occurs in some terrestrial planets in their later evolutionary stages. 

We have investigated the onset of compositional convection in the large compositional Prandtl 

number limit and have found rather small variations of the critical frequency and other threshold parameters. 

Large critical Rayleigh numbers in this case lead to the relatively small supercritical values, which are 

typical for modern numerical dynamo modeling. Especially severe conditions are to be expected for marginal 

instability when the inner rigid core is small. It means that the increasing importance of compositional 

buoyancy, as time proceeds, can make the time when the compositional geodynamo started to operate closer 

to our epoch. 

Finally, we have modeled the onset of thermal planetary convection in the limit of small molecular 

Prandtl number. It was found that value of the critical Rayleigh number sharply decreases with growth of the 

inner core radius. This property can help to support the thermal convection even during the later stages of the 

planetary evolution when the internal radioactive heat sources become too weak. 

This work was supported by the President of Russian Federation grant MK-2846.2008.5. 

Reference. 

Braginsky, S. I. and Roberts, P. H. (1995), Equations governing convection in the Earth's core and the 

geodynamo. Geophys. Astrophys. Fluid Dynamics, 79, 1–97. 

Busse, F. H. (1970), Thermal instabilities in rapidly rotating system. J. Fluid Mech., 44, 441–460. 

Glatzmaier, G. A. and Roberts, P. H. (1996), An anelastic evolutionary geodynamo simulation driven by 

compositional and thermal convection. Physica D, 97, 81–94. 

Spiegel, E. A. and Veronis, G. (1960), On the Boussinesq approximation for a compressible fluid. Astrophys. 

J., 131, 442–447. 

Starchenko, S. V. and Jones, C. A. (2002), Typical velocities and magnetic field strengths in planetary 

interiors. Icarus, 157, 426-435. 

Starchenko, S. V. (2003), Gravitational differentiation of liquid cores of planets and natural satellites. 

Russian Journal of Earth Sciences, 5 (6), 431-438. 

402


A�ALYTIC CO�VECTIO� SOLUTIO� A�D THE EARTH’ TYPE 

PLA�ETARY MAG�ETISM 

S.V. Starchenko 1 and A.M. Soward 2 

1 IZMIRAN, Troitsk, Moscow oblast,142190, Russia, e-mail: sstarchenko@mail.ru 

2 University of Exeter, Exeter, EX4 4QE, UK, e-mail: soward@maths.ex.ac.uk 


Abstract. The planetary convection and magnetic instabilities driven by thermal or/and 

compositional power had been investigated in their natural limit of very small transport 

coefficients. We modeled the instability of the combined compositional-thermal turbulent geoconvection. 

When thermal convection is in opposition to compositional convection, extremely thin 

convection instability layer is possible at the inner boundary of the planetary liquid spherical shell, 

while the rest of the shell is stably stratified. This might happen for a terrestrial planet during its 

later stage of evolution. For the Prandtl number unity we succeed to find an analytic semi-steady 

solution for the case with strong instability concentrated near the inner rigid core of a planet. This 

could effectively be applied to modern Mercury, while to the Earth, Venus and Mars at the 

correspondent stage in their evolution. 

We solve rotating convection problem originated by Roberts (1968) and Busse (1970) that is hybrid of Jones 

et al. (2000) and Dormy et al. (2004) problems. The Jones internal heating constituent is actually cooling and 

stabilizing, whereas the Dormy differential heating remains destabilizing. The combined thermal driving 

gives rise to an unstable thin layer adjacent to the inner core (of width 0


Depending on height z functions are here: w is vertical velocity, ψ is potential for the other velocity 

components, θ is Archimedean buoyancy due to thermal and compositional effects. One dimension (1D) 

system (3) contains the following 3D+time parameters: ω is complex eigenvalue that real part is growth rate, 

while imaginary part is frequency; m is scaled azimuth wave number; R is scaled Rayleigh number, P is 

Prandtl number. 

We shall consider only the modes with w antisymmetric about the equator z=0, because it is the physically 

realized solution with smallest critical Rayleigh number Busse (1970). Thus, we need only consider one-half 

of the spherical domain using non-penetrating boundary condition w=0 at z=0 and 

3 Asymptotic solutions and conclusions 

z 1− s 

2 

= . 

We are looking for the solution of system (3) concentrated near origin with very small ε


type of convection with related weak and irregular magnetism could work inside some Earth’s type satellites 

as well. 

Acknowledgments: This work was supported by RFBR grants: 06-05-65162 and 07-05-90006. 

References 

Busse, F. H. (1970) Thermal instabilities in rapidly rotating system, J. Fluid Mech., 44, 441–460. 

Dormy, E., Soward, A. M., Jones, C. A., Jault, D. and Cardin, P. (2004) The onset of thermal convection in 

rotating spherical shells, J. Fluid Mech., 501, 43-70. 

Jones, C. A., Soward, A. M. and Mussa, A. I. (2000) The onset of thermal convection in a rapidly rotating 

sphere, J. Fluid Mech., 405, 157-179. 

Roberts, P. H. (1968) On the thermal instability of a rotating fluid sphere containing heat sources, Phil. 

Trans. R. Soc. Lond. A, 263, 93-117. 

Starchenko, S. V. and Jones, C. A. (2002) Typical velocities and magnetic field strengths in planetary 

interiors, Icarus, 157, 426-435. 

Starchenko, S. V. (2003) Gravitational differentiation of liquid cores of planets and natural satellites, Russian 

Journal of Earth Sciences, 5 (6), 431-438. 

Starchenko, S. V., Kotelnikova, M. S. and Maslov, I. V. (2006) Marginal stability of almost adiabatic 

planetary convection, Geophys. Astrophys. Fluid Dynamics, 100, 397-428. 

405


THE DILATANCY-DIFFUSION MODEL: NEW PROSPECTS 

V.G. Bakhmutov, A.A. Groza 

Institute of Geophysics, National Academy of Science, Ukraine 

e-mail: groza@igph.kiev.ua 

Abstract. The earthquake generation process is considered as noise-induced transition of 

thermodynamic system. The general basis for different physical models of earthquake preparation 

(dilatancy-diffusion, dry dilatancy, stick-slip, phase transition) is proposed. It is shown that the 

appearance of «long tail» in aftershock distribution (Omori law) is a result of stochasticity of 

relaxation process. 

The dilatancy-diffusion (DD) model history begins since 1973, when Scholtz at al. published the paper 

“Earthquake prediction: a physical basis” [11]. The DD-scenario of earthquake generation process was 

proposed in this paper. At present time optimistic hope of DD-model has been changed by pessimistic 

estimation – is the model applicable to real conditions of earthquakes preparation? The reason is internal 

contradictions of the model. 

In the present paper we attempt to remove some problems, and moreover, to propose the basis for 

integration of DD-model with alternative models of earthquake preparation in which diffusion of fluids is not 

considered as the main factor (such as dry dilatancy models and stick-slip model). 

Let us begin with consideration of DD-scenario. 

1. THE DILATANCY-DIFFUSION MODEL. According to the model the earthquake generation 

process consists of the following stages: 

Stage 1 – increasing of elastic strain. 

Stage 2 - elastic strain eventually causes rocks to dilate (increase in volume) when stress on rocks = 50% 

of the rock strength. Open fractures develop with minor seismicity. 

Stage 3 - influx of water into open fractures increases fluid pressure. This lowers the rock strength and 

facilitates rupture. 

Stage 4 - Rupture occurs and fluid pressure and stress on rocks is released. 

Stage 5 - Aftershocks activity. 

The crust earthquake dilatant-diffusion model is based on incontestable physical phenomena: dilatancy 

and diffusion. At first glance there are not serious problems in DD-scenario. But it is not agree with real 

conditions. Let us investigate effects of dilatancy and diffusion in details. 

Dilatancy. The dilantancy is the inelastic increase in volume associated with the opening of small cracks 

in the material by shear deformation. 

The excellent example of dilatancy process can be seen if to put a leg on wet sand on a sea coast. The 

sand around the leg for some time becomes unsaturated - pressure on the sand surface has broken a dense 

packing of sand grains, and as a sequence led to undersaturation by water as a result of the porosity local 

increase. 

This example is resulted here to pay attention on some circumstances. 

� Obviously, the dilatancy is an essentially non-equilibrium phenomenon. In this connection there appears 

a problem about assumptions that should be accepted to describe a non-equilibrium system. It is 

important that in the “sand-water” system or in any other dilatant medium hydrostatic (lithostatic) 

pressure is not the same function of state variables, as in equilibrium. Equally the thermodynamic 

potentials can not be a function only on equilibrium state variables. The full analysis of system dynamics 

must include time dependence of thermodynamic variables (in particular, energy and entropy). 

Thus, the description of dilatation process should be based on dynamic equations. 

� The above obvious example indicates definitely the object of research. This is reservoir-induced 

earthquakes. 

� Kiyoo Mogi [8] has paid attention to the fact that in focal areas of strongest earthquakes the seismic 

activity decreases in the same way, and at the same time seismic activity increases in neighboring 

regions (so-called ring-type form of seismicity). But just such form of seismicity is characteristic for 

reservoir-induced earthquakes. 

The essential condition of the development of earthquake preparation process in DD-scheme is faster 

formation of dilatant zone at stage II in comparison with filling of newly formed cracks by water from 

406


neighboring areas. Due to pressure growth before earthquake cracks open in the crust, pressure of pore 

fluids, filling these cracks, drops, so the crust strength temporarily increases (dilatancy hardening), and 

therefore seismic activity in hearth areas decreases. 

The dilatancy hardening is determined by Coulomb-Mohr law: 

(1) � � c � f ( � � p) 

, 

where � is shearing stress; c is the cohesion shear stress; f is friction coefficient; � normal stress, equal 

to geostatic pressure; p is pressure of pore water. 

However this law is static and does not take into account the process dynamics. Laboratory experiments 

prove that effect of dilatancy hardening for such rocks as granite and basalt may be essential only if 

deformation rate is more that 10 -7 sec -1 , that significantly higher than the deformation rate typical for natural 

conditions (10 -10 � 10 -14 sec -1 [5]). 

Diffusion. In DD-scenario the underground fluids diffuse to a dilatant zone at stage III. Water inflow 

from neighboring areas will lead to increase of pore pressure and, hence, will reduce rocks effective strength. 

Increasing of fluid pressure in DD-scenario is considered as one of the factors predetermining rocks fracture. 

The catastrophic destruction occurs within a short time interval after water inflow. During this interval 

foreshocks occur. 

At first glance diffusive filling of newly formed dilatant cracks by water from neighboring areas seems 

to be quite logical. 

But there are a number of serious problems in this connection: 

� The microscopic investigations on the samples of the rocks (granites, basalts) show that essential part of 

dilatant cracks has order of microns, that is, much smaller then the grains size. It is obvious that water 

cannot penetrate to micro-cracks. 

� During preparation of earthquakes direct measurements show that deformation magnitude is ε ~10 -6 . 

Obviously, the order of relative changes of underground water levels will be the same � H � �H 

. From 

this estimation it follows, that for observed variations of underground fluids levels (10-15 cm) during 

crust earthquakes preparation, thickness of the water-bearing layer should be about 100 km that is more 

than thickness of the earth crust in several times. 

Thus, the deformation of water-bearing horizons cannot directly cause levels variations. 

� The dilatancy is irreducible process. In this connection it is not clear the cause of water levels (surface) 

restoration after earthquakes. 

� It is absolutely impossible in context of DD-mechanism to explain the observational increasing of wells 

debit at the simultaneous drop water level in neighboring areas. 

2. DILATANCY and UNDERGROUND FLUIDS DYNAMICS. From DD-scenario it follows, that 

main properties of rocks at the period of earthquakes preparation must essentially vary, reflecting the process 

of development of dilatancy. Thus, the task consists in investigation how the change of filtering environment 

properties is reflected on the fluid dynamics. This problem was investigated in details [6]. If the initial 

permeability of environment (k ) increases by � k than stationary piezometric head H is defined from 

2 �k 

2q 

H � 2 hH 

� � x � const . 

k k 

�H 

h 

Here q � � � k( 

z) 

dz is water flow, h is part of underwater horizons, where increases permeability. 

�x 

z�0 

Comparing the flows for initial level H 0 and for level H H H � � 

� 0 , for small value 

�k 

k 

h 

H0 

we have 

�k 

� H � � h . 

k 

Negative value of � H shows decreasing in H � level with respect to the initial value H 0 , that agrees with 

the tendency of drop underground water level during earthquake preparation. It is interesting that amplitude 

of variations is not dependent (in the first approximation) actually on the initial level height. However, the 

growing of permeability due to directly deformation is not essential (as mentioned above). The question is to 

clarify if there are additional causes of permeability. 

407


Experimental studying of elastic impulses influence on water-permeability of rock. It was established 

[10] that 

� Elastic waves intensify mass transfer in the system “water-rocks”. 

� For impulse force the increasing of coefficients of rocks permeability is in several times more, than for 

continuous regime. 

� The higher initial permeability, the more increasing permeability effect. 

� The effectiveness of influence by elastic acoustic impulses on rocks permeability reduces with increasing 

of temperature. 

With the found effect authors of [10] have connected increasing of water levels and increasing of wells 

debits. But as we have showed above, permeability increasing (even for a part of water stratum) must lead to 

level decreasing. But the debit will rise (for some conditions). 

The effect was explained [10] by destruction of bound water films in pores as a result of boundary layer 

turbulization in pores. However such mechanism is improbable since it needs a high intensity acoustic 

impulses. 

In our opinion the effect of permeability increasing is connected with decreasing (variances) of surface 

tension. The indirect testimony of such point of view is reducing effect with increasing temperature. In the 

same time it is known similar behaviour of surface tension. This gives us some reason to link effect with 

variances of surface tension and variances of discontinuity surface under influence of elastic impulses. 

Experimental studying of elastic impulses influence on gas emission from rock. The effect of 

radioactive gas (radon, toron) emission from rocks under action of ultrasonic was established in [3]. One of 

the reasons is transition of gas from bound state to free state. Under the elastic impulses impact adsorption 

forces, that for normal conditions hold gas on the pore walls, has been broken, and gas passes to the free 

state. Here we have direct reference to the role of surface tension. 

It is necessary to add that ultrasonic impulses divide up gas bubbles that not only promote gas emission 

(both from frame and from liquid phase) but also essentially accelerate gas diffusion. 

On this basis it is possible to explain radon anomalies observed before earthquakes. 

3. The SURFACE TENSION and PORE PRESSURE VARIANCES. According to DD-scenario 

pores volume increases at stage II that leads to undersaturation of dilatant zone. In the case of incomplete 

saturation, water fills pores partially, that leads to films formation, meniscuses and appearance of capillary 

pressure. 

Thus the question about variations of pore pressure is inseparable from variations of surface tension. In 

this connection there appears the question about surface tension and meniscus curvature, their equilibrium 

with wetting films (on the boundary with gas phase). 

The main relation is 

2� 

Pint 

� Pext 

� . 

r 

If the form of tension surface is changed, then P � Pext 

) dr � r dP � 2d� 

. If besides 

( int 

int 

d Pint 

d� 

r � 2 � Pext 

� Pint 

, 

d r d r 

then equilibrium is instable. 

Due to fluctuations the surface tension� is changed by the value, equal to � � , then for newly formed 

surface, we receive 

�� 

2� 

Pint 

� � Pext 

� . 

r r 

It follows that reducing of the surface tension is equivalent to increasing of internal pressure. Since � � 

arises almost instantly, the pressure changes by step. 

If effective capillary radius changes simultaneously with surface tension, then we receive 

2� 

d� 

(2) 

P � P � � . 

int ext r d r 

Thus, by heuristic way we come in suti to the well-known Gibbs relation [2]. 

Up to here we have discusses surface liquid tension. But such approach can be applied to alternative 

models of earthquakes preparation (to DD-model) where fluids diffusion is not considered as the main factor. 

408


Stick-slip models explain earthquake by mechanical instability of existing fault as a result of sudden 

decreasing of friction between its sides. Increasing of compressing pressure is favorable to step moving 

(stick-slip) whereas temperature increasing transfers contacting blocks in conditions of stable sliding. It is 

known that under vibration effect things can slide even on horizontal surface. Temperature increasing, as has 

been noted above, is equivalent to surface tension decreasing. 

In dry dilatancy models it is supposed localization of (instable) deformation in a narrow zone of future 

(macro-) fracture. In this case the difference between pressures in layer and external pressure is 

d s 

Pint � Pext 

� � . 

dV 

Here ds dVint 

is derivative of surface area with respect to volume (compare with (2)). The pressure 

difference can be both positive and negative. Positive difference prevents thinning-down of the layer under 

action of external forces, negative value leads to thinning-down of layer to a thickness for which pressure 

becomes positive, up to fracture of a layer. 

Remark. From here, besides, it follows that drop of pore pressure can lead not only to hardening 

(according to (1)), but also to the contrary process - additional cracking. 

This approach allows us to change the equation (1) to the form 

(3) � � 

d� eff 

dt 

d � d ( � s) 

� d � d ( � s) 

� 

� � 

� 

� 

� � � 

� . 

dt 

� dV 

� dV 

� dt 

� 

4. NOISE-INDUCED TRANSITION IN THERMODYNAMIC SYSTEMS. For any heterogeneous 

system we can provide Gibbs energy gain in the form 

d i i 

G � �S 

dT 

�V 

dP 

� � ds � sd� 

� � � n � � dq 

Here arrows indicate the five possible processes of surface energy transformation into: Gibbs energy; heat; 

mechanical energy; chemical energy; electric energy. 

We can give the following physical meaning for the surface energy transformation: 

� ds is fluctuations of entire system in earthquake generation process; sd� is internal noise. 

In such approach the earthquake generation process can be considered as noise-induced transition of 

thermodynamic system. 

Remark. Here we don’t consider electrokinetic effects, however, their role may be significant in 

earthquake generation process. Usually electrokinetic effects in porous media are dealt with in the 

assumption that � � E � 0 

� 

and � � E � 0 

� 

. In above context geomagnetic storms can be considered as 

� 

� �B 

external noise. Then � � E � � . Thus pore pressure variances can be generated by not only internal 

�t 

processes but also by external processes. 

5. RESERVOIR-INDUCED EARTHQUAKES. It is known many reservoir-induced earthquakes [4]. 

Among them are: Kariba, Rhodesia-Zambia, 1963, M = 5.8; Kremasta, Greece, 1966, M = 6.3; and Koyna, 

India, 1967 M = 6.5 (up to M=7 by different authors). 

Let us consider the seismicity associated with the Shivaji Sagar Lake formed by the Koyna dam is 

considered to be a classic example of earthquake activity triggered by reservoirs. Seismicity at Koyna shows 

remarkable correlations with the filling cycles in the reservoir. It is believed that the pore pressure changes 

induced by the reservoir reduce the strength of the rocks leading to failure along a major fault zone in the 

vicinity of the dam. 

The Koyna earthquake (1967). The Koyna Dam and the Koyna Reservoir formed by it are located on 

the western side of India, about 200 kilometers south of Bombay. The project is comprised of an 800 meter 

long, 110 meter high concrete dam. The reservoir is 103 meters high and has a water capacity of 2.8 billion 

cubic meters. The dam was built in 1962, and infilled with water in 1963. On December 11, 1967 at 4:21 

local time, an earthquake with an approximate magnitude of 6.5 - 7.0 shook the region in and around the 

dam. A focal depth of 8 to 10 kilometers was assigned (various agencies have assigned this earthquake 

different focal depths anywhere from 9 to 32 kilometers). 

409 

int


On the picture - forshock-aftershock activity associated with Koyna earthquake 1967 year. 

The earthquake was followed numerous aftershocks which have hyperbolic time-distribution (the famous 

empirical Omori law (1894)): 

�� 

N ( t) 

~ t . 

The empirical Gutenberg-Richter law is 

obeys the law 

�� 

N(E)~E . On the other hand relaxation of mechanical systems 

E � E0 

�e 

Thus there is a contradiction. Aftershocks decay faster at early times and then much more slowly. 

It is, so-called, «long-tail» distribution. 

What is the reason of such phenomenon? 

Before answering this question let us consider a «excitation -dissipation» system 

dE 

� ( e � d ) E . 

dt 

Then in accordance with Gutenberg-Richter law 

d N 

d t 

t 

� 

τ 

. 

N 

� �( 

e � d ) N � . 

� 

Here � relax is own (internal) time of relaxation. 

Then N( 

E) 

� const � E 

�c 

1 

, where c � 1� 

. It follows that c � const if and only if 

( e � d) 

� 

e d relax const � � � ) ( . 

Generally it is not true. That is why b � coefficient 

varies in relation log N � a � b M. 

relax 

6. THE PHENOMENOLOGICAL EVIDENCE OF OMORI LAW. In above context it is logically 

suppose that 

d N N 

� � . 

dt 

� (t) 

The question is: In what way do random fluctuations of � (t) 

govern system dynamics? 

Let us assume that values � (t) 

at various times mutually independent. If � (t) 

has normal distribution 

0 

R t ( 

R 

t dt 

in every moment t , then � also has Gauss distribution. Since 

� ) 

�� 

t �� 

� �� 

� � 

�� R �� 

t 

dt 

N N0 

exp 

0� 

( ) 

then N has log-normal distribution. In this connection it should be noted that in practice it is difficult to 

distinguish log-normal distribution from hyperbolical distribution. It often leads to incorrect interpretation of 

statistical data (see discussion in [7]). 

410 

R 

R 

relax 

R


We will proceed from the assumption that average amplitude of fluctuations is proportional to 

fluctuations describe by Gaussian-distributed value � t ( 0; 

D) 

(details see in [9]). Then 

N and 

d N 

dt 

N 

� � � � � 

� ( t) 

t 

N . 

In this case probability density will have on of two forms: 

R 

It follows that the solution of the stochastic equation for N will have the similar form. The appearance of 

local minimum in aftershocks distribution shows that exponential decay of aftershocks is the least probable 

event. The most probable should be jumps (jerks) of aftershocks. Thus overshoots of N are the result of 

stochastic relaxation. Just stochasticity of relaxation process leads to appearance of «long tail» in aftershock 

distribution. The reorganization of relaxation process is an example of noise-induced transitions. 

It is clear that forshocks distribution should also have jumps. In fact we observe just such behaviour (see 

the picture above). 

7. PROSPECTS. The consistent examination of the DD-scenario has led us to investigation of the role 

of surface tension variations in earthquakes generation process. Prospects are not in the future development 

of DD-model but in integration of DD-model with alternative models of earthquake generation process in 

which diffusion of fluids is not considered as the main factor - dry dilatancy models and stick-slip models. 

The integration should be based on the Gibbs thermodynamic theory. The basis of the Gibbs theory of 

capillarity is the concepts of discontinuity surface and surface tension. The Gibbs energy can change not only 

due to surface area variations but also due to internal fluctuations of surface tension. Thus the problem is to 

investigate noise-induced transitions in thermodynamic systems. 

References. 

1. Brace W.F., Byerlee J.D. (1966), Stick-slip as a mechanism of earthquake, Science, 153, 990-992. 

2. Gibbs J.W. (1982), Thermodynamics, Nayka, Moskow, 536 p., [in Russian]; Gibbs J.W. (1878), Trans. 

Conn. Acad., v. 3, p. 343. 

3. Gratzinsky V. at al. (1967), On radioactive gas emission from rocks under action of ultrasonic, Physics of 

Earth, № 10, 91-94, [in Russian]. 

4. Gupta H., Rastogi B.(1976), Dams and Earthquakes. Elsevier Publishing. 

5. Earthquake prediction (1983), No. 3, Donish, Dushanbe, 226 p., [in Russian]. 

6. Makarenko V., Groza A. (1991), Earthquake Precursors and Acoustic Fields, The Journal of Geophysics, 

No. 1, v. 13, pp.3-14., [in Russian] 

7. Mandelbrot B. (1982), The Fractal Geometry of Nature. New York: W. H. Freeman and Co. 

8. Mogi K. (1985), Earthquake Prediction, Academic Press. 

9. Nicolis G., Prigogine I., Self-organization in nonequilibrium system, A Wiley-Interscience Publication. 

10. Tzarev V., Kuznetzov O. (1978), Experimental study of physical-chemical processes in rocks at small 

elastic deformations, [in Russian], Physics of the Earth, № 6, 94-101. 

11. Scholz C.H., Syke L.R., Aggarwal Y.P (1973), Earthquake prediction: a physical basis, Science, 181, 

803-809. 

411


ABOUT NON-LINEAR DYNAMICS APPLIED TO DEPTH FRACTURES, 

CONRTOLLING HIGH SEISMICITY AREAS IN DAGHESTAN 

A.M. Boykov 

Institute of Geothermal Problems of Daghestan Scientific Centre of RAS, Makchatchkala, 367030, 

Russia, e-mail: buamama@yandex.ru 

Abstract. Seismogenerating fractures are revealed in the surface temperature field by means of 

anomalies of heat space survey. These anomalies are rather the processes of preparing for the 

earthquakes. Our heat model of subvertical inter block zone for analysis of seismogene dynamics 

corresponds Foothills fracture, which controls zones of high seismicity. Geological characteristics 

of this fault correspond in details to a well-known seismodynamic model I.A.Volodin. This model 

as well as the Foothills fracture, contains a zone of narrow plates, alternating with the fissures. The 

fracture-resonator is the source of non-linear diffraction of Fraunhofer regarding the waveguide 

seismic field. The seismic activation, whose source is the fracture-resonator of the seismic energy 

is added by prolonged actions of seismic pulses in the limits of influence of the earthquakes 

centers zones. The heat cosmic survey in the regime of observation is perfectly able, as it follows 

from the given above, to have a sense of forcast. Therefore it is reasonable to carry it out with 

these purposes in the Daghestan region in the future. 

Seismogenerating fractures are revealed in the surface temperature, field by means of anomalies of heat 

space survey (See fig.1). These anomalies are rather the processes of preparing for the earthquakes. These 

Fig.1. Fragment of the map of the Caucasus earthquakes epicenters (the author – A.A.Godzikovskaya – 

February 21, 2001). The black arrow points the disposition of the anomaly fragment of the cosmic survey 

radiation temperatures, which we used to calculate the width of the Foothills fracture. (The anomaly extents 

along the route of the Foothills fracture. The cosmic survey was made at night 21.07.98 at 3:07 Moscow 

Time. The survey data processing was done by the method of lower frequency filtration with radius 

R=0,7 km. The smoothing of the obtained data was done by the Gauss method – in the area from the centre 

of picsel). 

412


anomalies reflect sections of shift, compression or tension of rocks, as well as of jointing and higher 

permeability zones, which are developed along depth faults. Our heat model of subvertical inter block zone 

for analysis of seismogene dynamics [1] corresponds Foothills (in other words, Pshekish-Tirnaus) fracture, 

which controls zones of high seismicity. This fracture is traced for 300 km from the south to the North and 

presents itself a zone of narrow plates, falling under the monocline construction. Fissures along the plates in 

the depth come close into one vertical fracture. This fracture splits the frontal part of the Daghestan wedge 

and forms an almond–shaped structure. The focal point of the Daghestan earthquake 1970 is connected with 

it (M=6,6; H=13 km; Jo=96). 

Geological characteristics of this fault correspond in details to a well-known seismodynamic model 

I.A.Volodin [2]. Model is built in 2 variants of passive and active fractures as eradiating sources. This model 

is elaborated by means of using mechanism of Fraunhofer non-linear diffraction. The united vertical fracture 

in the depth forms an intensive eradiating resonator – the source of non-linear diffraction of the wave seismic 

field [2, p.149-157]. 

The I.A.Volodin model as well as the Foothills fracture, contains a zone of narrow plates, alternating with 

the fissures. The differences are mainly in the fall of the Foothills fracture, between the two tectonic blocks 

of the crystal base but not under “the monocline construction” as in the model [2, p.155]. “The faults limiting 

these plates, are coming close at the depth into united vertical fracture, in the I.A.Volodin model are the 

similar. Together they form an intensive, eradiating resonator, “which selects from the common disturbance 

field longitude along orthogonal direction according boundaries of fracture harmonics with integer numerical 

relations between the fracture width and wave length” [2, p.150]. The resonator is the source of non-linear 

diffraction of Fraunhofer regarding the waveguide seismic field which is described by the asymptotic 

formula. The indicated intensity of resonator is manifested “in the dynamic of landscape… in the erosion 

activity of the soils, caused by the background high frequency vibration, which in the first approximation can 

be regarded proportional to it. This makes it possible to regard, that the diffraction pattern, described by the 

formula…, will be really presented in the aero-space photographs (Our Italics – А.B.) as an assemblage, 

packet of lineaments, parallel to the direction of the fracture in the crystal foundation. The analysis of 

distances between them by means of using this formula allows defining the radiation intensity and the depth 

of the source. This, as a result, can be interpreted as the location of the fracture and some it’s qualitative 

characteristics” [2, p.154]. 

Derivation of the design formulae for such model [2, p.151-155] was made by I.A.Volodin on the basis of 

introducing coordinate system, orthogonal to the direction of the fracture. 

The wave field of disturbance weakly changes in the direction of the fracture that is independence 

condition from the third coordinate is introduced. This formulation of problem is a consequence of the 

transverse wave model [2, p.107-108], where the equation with coordinates: X2 – along the foundation 

orthogonal to the fracture, Y1 – in the vertical direction along the earth’s radius is examined. The equation is 

reduced to the following form [2, p.152]: 

i2k∂A/∂X2 + ∂ 2 A/∂Y1 2 + k 2 b|A| 2 A = 0, (1) 

where the amplitude of the transverse waves A2 = A {See[2], p.107, formula (2.38) – A.B.}, k – the wave 

number of asymptotical number field (of the plane seismic wave), b – arbitrary constant, determined as 

velocity of solution of the seismic field in reference to the non-linear equation of Shredinger describing 

solution effects. From the formula (1) is determined the space configuration of intensity I wave field, 

proportional to the square of its amplitude, for this purpose is used asymptotical formula which describes 

non-linear diffraction of Fraunhofer of the wave field on the slots with parameters A0 and S, having the view 

[2, p.152]: 

dI/dφ = (k/πb)ln{(k 2 φ 2 /4 + a 2 )/(k 2 φ 2 /4 + a 2 cos 2 [s(k 2 φ 2 /4 + a 2 ) 1/2 ]}, (2) 

where parameter a 2 = k 2 b/|A0| 2 /2 is determined by initial conditions, and φ – is an angle between the 

directions of propagation of radiation from the source and earth’s radius. It must be noted, that the diffraction 

formula (2) is true only when the source intensity is weak, specifically under the condition I = s|A0| 2 < IКР, 

where critical meaning of intensity IКР = π 2 /(2sbk 2 ). 

The lines of field intensity antinodes on the diurnal surface are determined from the formula of diffraction 

as lines, which derivative of intensity of waveguide seismic field is equal to zero. When X – a distance along 

the earth’s surface in the direction orthogonal to the fracture, and H – is the depth of the radiation source 

413


from the fracture (the level, where the fracture as an active resonator ends). Then the average step in the 

packet of lineaments is determined by the equation [2, p.154]: 

2s(k 2 φ 2 /4 + a 2 ) 1/2 = mπ ⇒ X0 = H[(πm/2sk) 2 – 2b|A0| 2 ] 1/2 = H[λm/4s) 2 – 2b|A0| 2 ] 1/2 , (3) 

where λ – wave length of the seismic radiation of the fracture–resonator, m – lineament number in the 

packet. 

Intensity I is identified with linear density of seismic radiati0n energy by the fracture – resonator. Then 

the evident expression for the average step in the packet of lineaments is recorded as [2, p.155]: X0 = 

(Hm/2n)(1 – I/Ikp) 1/2 . The critical intensity value Ikp = π 2 /(2sbk 2 )= λ/8nb, n – the number of wave – length in 

the width of the fracture. The distance X0 is equal to zero at the critical intensity. This means absence of 

packet of lineaments in the section of the studied area. Fracture quality as resonator becomes higher for 

modality values with the minimum number n. This can be confirmed passing to statistic characteristics. The 

main mode at n = 1 is represented in the landscape in practice most evidently. The mode at n = 2 is expressed 

weaker. The distance X0 between the lineaments can be calculated at the both mode values by formula [2, 

p.155]: X0 = (H/2)(1 – I/Ikp) 1/2 , Xo = (H/4)(1 – Ikp) 1/2 . 

But I.A.Volodin theory is not completed for practical use of formulae in predictive target, where the bases 

are cosmic survey materials. It must be noted geometrical characteristics of the fracture can be calculated 

with the help of given formulae. The inside structure of the fracture–resonator can be also made more 

precise. This by itself is important indeed. But it is a subordinate result within the framework of our theme. 

But analysis of large-scale photographs is necessary even for our goals. This needs separate finance, because 

such cosmic photos are paid. Moreover additional land researches are absolutely necessary for determining 

the number of other parameters in the rated formulae of I.A.Volodin, for example, studying of microseisms 

at the surface, and so on. 

So today we can only state existence of the theory of mechanism of seismic generation by the deep 

fractures, which reveal on the maps, of heat cosmic surveys. This seismic generation is identically explained 

from the position of the theory of seismic fields. This physic-mathematic model construction is very 

important for our research in perspective. The I.A.Volodin model as its author points out [2, p.152]: “makes 

it possible to interpret some results, obtained by remote methods. Traces of the described processes (wave 

collapses in the seismic field – A.B.) are reflected on the diurnal surface, as on the screen, on which the 

established seismic fields are printed”. Manifestations of seismic activity on the earth’s surface over the deep 

seismic generating fault of the Foothills type will be reflected, as it follows from the fact, in the temperature 

field according to the data of heat cosmic survey. But quantitative estimation of these fault parameters will 

be possible by these design formulae only under condition if the values of attendant seismic parameters of 

the wave length λ type and depth of extent of fracture-resonator H are exactly known. Determination of their 

exact numerical values is difficult to carry out for execution of practical calculations, though their 

approximate determination seems possible. 

Nevertheless, the quantitative interpretation was done by us according to the data of numbering of heat 

cosmic survey result. This was done on the example of the temperature anomaly longitudinally the Foothills 

fracture route (See fig. 2) with the help of the program GetData Graph Digitiser 2.24 with the transfer of the 

numbering results into km. The numbering with the use of the program made it possible to calculate the 

approximate zone width of this seismic generation fracture. The fracture zone is identified with sharply 

selecting on the colour image of the cosmic photograph area of intensity of this radiation temperature 

anomaly with ΔT ≈ 2,7 0 C along all extent of the fault from the North to the South. The width of the Foothills 

fracture longitudinally anomaly fluctuates according to numbering data from 8 km in the northern part of the 

fracture (See fig.2) to 2 km in the southern. The Foothills fracture has according to the heat cosmic survey 

data the maximum width in the epicenter area of earthquakes. This zone is regarded as the zone of prolonged 

seismic activity. The minimum width of the anomaly is far from this zone in the south, where the fracture 

can be difficult to note. 

This conclusion corresponds to our theoretical ideas given above. The seismic activation, whose source is 

the fracture-resonator of the seismic energy is added by prolonged actions of seismic pulses in the limits of 

influence of the earthquakes centers zones. The width of the reflecting fault anomaly is caused by jointing 

which is tailplane of the fault. It is determined according to our heat model of the fault [1], the whole zone of 

the dynamic influence of the fault. The formation of the radiation temperature anomaly area takes place 

above the rock discontinuity zone, in which jointing of the fault takes part, that is the whole zone of the fault 

dynamic influence. 

414


The heat cosmic survey in the regime of observation is perfectly able, as it follows from the given above, 

to have a sense of forecast. Therefore it is reasonable to carry it out with these purposes in the Daghestan 

region in the future. 

Fig.2. The anomaly of radiation temperatures according to the data of the cosmic survey along the route of 

the Foothills fracture and the fragment of this anomaly (at the bottom) in latitude of Makchatchkala. The 

simple black arrows (in the upper part) point the route of the deep Foothills fracture. The black arrow with 

two points (at the bottom) indicates the width of the anomaly fragment in the range of colors to calculate the 

width of the fracture. 

The studies are carried out at support of RFFI (grant 06-05-96610, regional contest "South of Russia"). 

References: 

1. Boykov, A.M. (2007), The Heat Model of Subvertical inter Block Zone for Seismogene Dynamics 

Analysis, in: “Seismic Monitoring and Studies of Daghestan Geodinamic and Middle Caspian Water 

Area”, World Scientific Publ. №1, Makchatchkala, “Epoch” Publishing House, 159-170. 

2. Volodin, I.A. (1999), Non-linear Dynamic of Geological Medium, Moscow, GUP, “WIMI”, pp. 230. 

415


WAVE DISTRIBUTION OF ANISOTROPY OF ELASTIC PROPERTIES OF 

ROCK SAMPLES COLLECTED ALONG SECTION FROM THE SURFACE 

Il’chenko V.L. 

Geological Institute of the Kola SC RAS, Russia, 184209, Apatity, Fersmann str., 14. 

E-mail: vadim@geoksc.apatity.ru 

Results of investigations of elastic properties of metamorphic rock oriented samples collected from 

the surface of a part of the Central Kola megablock along the 22 km long profile are presented. 

Indexes of rock elastic properties anisotropy by spreading velocities of P- and S-waves have been 

measured. Spatial position of elastic symmetry elements of samples have been determined and 

compared with rock bedding elements. It was established that there is an inverse dependence 

between values of anisotropy of sample elastic properties and relative altitudes of the sampling 

points. It was established that distribution of anisotropy of elastic properties of rocks is individual 

for each geoblock, confirming the author’s hypothesis on a presence of wave component in totality 

of forces supervising geodynamic evolution of the lithosphere. It is shown that dynamic influence 

on the rock in scale of a geoblock, entailing changes in spatial position of its elastic symmetry 

elements is selective and conservative. 

. 

Introduction. It is considered that crystal basements of platform formations of the lithosphere and, in 

particular, crystal shields are solid and stable areas, the most perspective and suitable, as well, for burial of 

highly toxic waste [Laverov and all, 2000]. Crystal platform basements and shields are distinguished by 

complex-folded structure and variation of petrographic composition of rocks along the section at a small set 

of rock varieties (gneisses and gneissic granites prevail in our case), that is historically stipulated by 

processes of development of these geological objects. Besides this, such areas are characterized by low 

seismicity and ancient age of rocks. The ancient age assumes accumulation of a plenty of information caused 

by various kinds of geochemical and stress influence on rocks and rock complexes. All possible sorts of 

influence on rock are reflected in its metamorphic degree, and physical characteristics in many respects 

depend on its stress-deformed state, direct reflection of which is anisotropy of elastic properties of rocks. 

For revealing of diagnostic features of index of elastic properties anisotropy (B) total comparison of the SD-3 

core samples and its surface analogues was carried out (fig.1). 

Fig.1. Comparison of core 

samples and surface analogues 

by index of elastic anisotropy B. 

Value of index B: 1 – 0-0.05, 2 

– 0.05-0.1, 3 – 0.1-0.15, 4 – 

0.15-0.20, 5 – 0.20-0.25, 6 – 

0.25.-0.30, 7 – 0.30-0.35, 8 – 

0.35.-0.40, 9 – 0.40-0.45, 10 – 

0.45-0.50, 11 – 0.50-0.55, 12 – 

0.55-0.60, 13 – 0.60-0.65, 14 – 

0.65-0.70. Solid line – index B 

for core samples, dotted line 

– for surface samples. 

The section opened by the Kola Superdeep borehole (SD-3) is the most studied by anisotropy of elastic 

properties (and other physical characteristics) in the Central-Kola megablock is [8]. After work under the 

IGCP-408 project which purpose was comparison of SD-3 core with its rocks-analogues from the surface by 

all accessible scientific methods [Inaugural …, 1998], some new conclusions have been drawn. One of them 

is that distribution of the core by a degree of anisotropy of elastic properties is described by the graph of 

dumping oscillations, whence follows, that in set of the parameters controlling geodynamics of the given 

416


megablock, a wave component enters [Il’chenko, 2004]. For samples-analogues from the surface the same 

dependence was described by a curve similar to the graph of quasi-exponentional function (Fig.1). At the 

same time the version was suggested that such distinction can be caused by way of sampling - non-uniform 

distribution of sampling surface points through enough extensive area (from the SørVaranger province in 

Norway to Ura-guba of the Murmansk block) while SD-3 core has been tested along the section with a step 

of about 100 m and "was strung" on a trajectory of the well that is equivalent to sampling along straight 

profile. 

Technique. During field works under the project supported by the Russian Foundation of Basic Recearches 

(project № 03-05-64169) and as the completion of the work which have not been finished during carrying 

out the IGCP-408 project, oriented samples have been collected from Archean frame of the Petchenga 

structure (110 samples). Samples were taken every 200 m along the profile line more than 22 km long 

(Fig.2). From the West to the East this profile intersects the Eastern part of the Liinakhamary block and 

almost the whole Suormuss block (components of the Central-Kola megablock). 

Fig.2. Scheme of sampling 

profile location. 1 – Archean 

biotite gneisses, migmatites and 

amphibolites of Liinakhamary 

(I) and Suormuss (II) blocks, 2 – 

Archean granitogneisses and 

enderbites of the Murmansk 

(III) block, 3 – Riphean 

sediments, 4 – faults, 5 – profile 

line. 

Samples of rock-analogues from 

the surface were collected 

proportional in quantity and 

quality (by structure and mineral 

composition) to the number of studied core-samples from the SD-3. Then samples of the cubic form were 

made of them and analyzed by acoustopolariscopic method [Gorbatsevich, 1995]. 

After acoustopolariscopic investigations on three pairs of sample sides and determination of velocities of Pwaves 

spreading and according to the revealed projections of elements of elastic symmetry – S-waves 

spreading, the matrix (Vij) of velocity values was made: 

V11 

V12 

V13 

Vij= V21 

V22 

V23 

, (1) 

V V V 

31 

32 

Where V11, V22, V33 – P-wave velocities in 1,2,3 (X,Y,Z) directions respectively, and V12,V13,V21,V23,V31, V32 – 

S-wave velocities, where the first index typed by an interlinear font designates sounding direction, and the 

second – a direction of an elastic symmetry element which coincided with a plane of polarization of source 

and receiver oscillations during measurements. 

Then index of anisotropy В was calculated for each pair of sides. For example, for the side 1 index В is 

equal: 

B1=2(V12-V13)/(V12+V13). (2) 

Indexes В2 and B3 for the sides 2 and 3 were calculated using values V21, V23, V31, V32 respectively. The 

parameter of anisotropy of a sample is a geometrical average of anisotropy factors for each side: 

B=√(B 2 1+B 2 2+B 2 3). (3) 

Indexes of anisotropy by P-waves are calculated as deviator [9] of values Vii in the quasi-matrix: 

1 2 

2 

2 

A p = ( V11 

−Vcp 

) + ( V22 

−Vcp 

) + ( V33 

−Vcp 

) × 100% 

, (4) 

Vcp 

where Vср = (V11 + V22 + V33)/3 – is the mean P-wave spreading velocity in a sample. 

417 

33


For all samples geological rock begging parameters (azimuth and angle of dip) and variations of spatial 

position of the main plane of elastic symmetry (azimuth and angle of dip) have been measured. The 

estimation and analysis of distinctions by an azimuth of dip and an angle of dip between geological rock 

bedding elements and spatial position of their elastic symmetry planes have been carried out. 

Results of the work. The profile, along which the described samples have been collected, is sublatitudinal 

and reflects reduction of the surface erosion degree from the West to the East. It is emphasized by variations 

of complexity of a relief and uplifting of a relief above sea level to the East (Fig.3а). The uplifting begins 

sharply enough after a sector of sampling №№64-71 which approximately corresponds to the fault (suture) 

zone separating the Liinakhamary block from the Suormuss. 

Fig.3. Comparison of the relief (а) with indexes of anisotropy В for rock samples along the profile (b). 

By results of acoustopolariscopic study indexes of anisotropy of elastic properties B (Fig.3b) have been 

calculated. Despite of heterogeneity of petrographic composition (frequent change of rocks) along the 

profile, there is a tendency on the graph to reduction of anisotropy indexes in samples from the West to the 

East. With that, anisotropy indexes from the West to the East have wavy character of variation. In the 

Liinakhamary block the first "wave" is reflected in elastic anisotropy of samples №№1-32, the second - 

№№32-64. Waves of the Liinakhamary block have a "length" (distance between the adjacent minima) of 

approximately 6.5 km and "amplitude" (value of index B) with the maximal value within the limits of 35-45 

%. In the Suormuss block it is also possible to distinguish two "waves": the first in the interval №№64-85, 

the second - №№85-106, that assumes waves with "length" of about 2.2 km and "amplitudes" for variations 

of index B in 20-30 %. The estimation of the whole number of samples by index B of anisotropy has shown 

the presence of wavy distribution with dumping (Fig.4), similar to the distribution obtained earlier at 

418


anisotropy analysis of the SD-3 core samples (Fig.1). On the sector of samples №№64-71 there is a change 

of western "motive" by eastern. From here follows, that in spite of belonging to the united Central-Kola 

megablock, Liinakhamary and Suormuss blocks are independent self-oscillatory systems [Ivanyuk and all., 

1996] and each of them developed in its own wave regime [Il’chenko, 2004]. 

Fig.4. Distribution of samples collected along the profile Petchenga – 

Suormusyarvi by index of anisotropy B. Values for index B are the same 

as at Fig. 1. 

Coincidence of bedding elements of a rock (its structure) with elastic 

symmetry plane position assumes that such rock either was in a constant 

stress field the whole time of its existence, or possesses indestructible 

strength and rigidity which tectonic processes in no way can affect. The 

latter is extremely doubtful taking into consideration an ancient age of 

analyzed rocks (by different estimations from 2.6 to 2.9 Ga [Bayanova 

and all., 2002]). Nevertheless, about 25 % of the studied samples have 

shown coincidence of bedding elements of elastic symmetry plane with 

bedding elements and structure of geological bodies from which these 

samples have been collected. From here follows, that selectivity of 

geodynamic processes influence on rocks in separate geoblock boundaries 

remained constant during the period of their existence. 

Discussion. The carried out comparison (Fig.1, 4) shows that there is an 

essential distinction between elastic anisotropy of the SD-3 core and its 

analogues from the surface. Wave character of this diagram confirms a 

hypothesis on a wave nature of layering of geological objects [Il’chenko, 2002]. 

Wave character of layering can be considered from another point of view, if to present a layering wave as a 

complex sound tone or complex oscillation which can be divided into simple harmonics - the overtones 

having their own frequency characteristic [The course…, 2002]. Such set of frequencies, or an acoustic 

spectrum, has lineal character (Fig.5). 

Fig.5. Fig. 5. An acoustic spectrum of the note 

(taken on a piano), which represents complex 

oscillation [The course…, 2002]. 

Putting an analogy between figures 1,3 and 4, one 

can assume, that the division of the SD-3 core and 

rock-samples from surface into spectra by index 

of elastic anisotropy is caused by constant 

influence of complex oscillatory process on the 

lithosphere, when each overtone of this process has naturalized somehow in some of the investigated 

samples. 

Conclusions 

1. Comparison of values of elastic properties anisotropy of samples with relative altitudes of sampling points 

has shown a presence of inverse correlation. In most cases, the higher the sampling point is above sea level, 

the less the sample is anisotropic, otherwise, the higher is the index of elastic properties anisotropy of a rock, 

the more it is subjected to destructive exogenous influence, and vice versa. 

2. Individual (for each block) character of wavy distribution of anisotropy of elastic properties of rocks in 

the adjacent geoblocks (Liinakhamarski and Suormusski) confirms a hypothesis [Il’chenko, 2004] on a wave 

component presence in the whole complex of forces supervising geodynamic evolution of geoblocks. 

419


3. By research of variations of spatial position difference of elastic symmetry elements and geological 

bedding elements of samples it is established, that internal dynamic development of the studied geoblocks 

occurred selectively and this selectivity, apparently, had conservative character. 

This investigation was made with support of RFBR grants: №№-00-05-64057, 03-05-64169, 07-05-00100 

and INTAS-01-0314. 

R E F E R E N C E S 

Bayanova T.B., Pozhilenko V.I., Smol’kin V.F. & all. Catalogue of geochronological data along north-east 

part of Baltic Shild. (Supplement №3 to monograph «Geology of ore areas of Murmansk region.- Apatity: 

Kola Res.Centre of RAS. 2002. P.53. (in Russian) 

Gorbatsevich F.F. Acoustopolariscopy of rocks. Apatity, 1995, 204 p. (in Russian) 

Il’chenko V.L. On controlling role of wave influence in stratification of geological objects (experimental 

data). Intern. Conf. on Problems of Geocosmos. St.-Petersburg, 2002, pp.136-137. 

Il’chenko V.L. On presence of wave-component in variations of elastic properties anisotropy of Kola 

Superdeep core samples. //Abstracts of XV session of Russian acoustic society. V.1.М.: GEOS, 2004, p.313- 

316. (in Russian) 

Inaugural meeting of IGCP project N408: comparison of composition, structure and physical properties of 

rocks and minerals in the Kola Superdeep borehole (KSDB) and their homologues on the surface //Episodes. 

1998. V.21. N4. P.266. 

Ivanyuk G.Ju., Goryainov P.M., Egorov D.G. Introduction into non-linear geology (the experience of the 

adaptation of the self-organisation theory to geological practice). Apatity: Kola Res.Centre of RAS. 1996. 

P.185. (in Russian) 

Kola Superdeep. Scientific Results and Research Experience. - М.:«ТЕCHNОNEFTEGAZ», 1998.–260 p. 

(in Russian) 

Laverov N.P., Velichkin V.I., Omel’yanenko B.I. & all. New approach to underground keeping of high 

radio-activ wastes of Russia //Geoecology. 2000. №-1. P.3-12. (in Russian) 

The course of Physics. The textbook for HIGH SCHOOLS. //Remizov A.N., Potapenko A.Ya.–Moscow: 

Drofa, 2002.-720 p. (in Russian) 

Gorbatsevich F.F., Golovataja O.S., Il’chenko V.L. et al. Elastic properties of some rock samples along the 

section of the Kola Superdeep borehole (SD-3), determined under atmospheric pressure and in situ // Fisika 

Zemli. 2002. №-7. P. 46-55 (in Russian). 

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UPPER SOLID CORE’S FABRIC CONSTRAINED BY PKiKP CODA 

OBSERVATIONS 

D.N. Krasnoshchekov, V.M. Ovtchinnikov 

Institute of Dynamics of Geospheres, Leninsky pr. 38 korp. 1, Moscow 119334 Russia, 

e-mail:krasnd@idg.chph.ras.ru 

Abstract. We analyze reflections from the Earth’s inner core boundary (ICB) and coda waves 

following the reflections (PKiKP) on array records of underground nuclear explosions. The 

observed codas after reflections with ray paths diverse in crust, mantle and outer core, and nearby 

bounce points show similar shape, frequency content, intensity and duration, and feature 

uncorrelated reflected waveforms as if originating from local discontinuities buried down to 600 

km below the ICB, inclined by up to 30° and having acoustic impedance up to 2%. We interpret 

the observations in terms of misaligned anisotropic iron crystals up to 10 km in size that constitute 

the upper IC, cause PKiKP coda through scattering and reflections on their boundaries, and 

contribute to ICB patchiness. The IC fabric’s image observed as PKiKP coda appears to be time 

stationary in 20 years span, so not confirming noticeable differential rotation of the IC. 

Ferrous or almost ferrous [Alfe et al., 2002] inner core of the Earth plays an important role in 

geodynamo theory, mineralogy and studies of condensed matters, whereas seismology is the only source of 

direct measurements of its properties and structural peculiarities. Although IC is believed to be a result of 

gradual few billion years long crystallization process, it is rather heterogeneous than a single crystal of iron 

[Vidale and Earle, 2002]. The IC fabric is possibly radial diverse [Cormier and Li, 2002], and estimates of 

sizes of anisotropic hexagonal close-packed (hcp) and face-centered cubic (fcc) iron crystals vary from 

hundreds of meters to few tens kilometers [Vidale and Earle, 2002; Cormier and Li, 2002; Bergman, 1998]. 

Fabric variations such as changes in crystallographic alignment or supposed increase in crystal size with 

depth often constitute physical grounds for hypothesizing IC heterogeneities of various scale lengths. The 

global ones include hemispherical variations [Tanaka and Hamaguchi, 1997], and seismic boundaries at IC 

radii from 300 to 1100 km. The latter were recently assumed as anisotropic discontinuities due to change in 

magnitude [Song and Helmberger, 1998] or orientation [Ishii et al., 2002] of anisotropy, or in the form of 

first- or second-order jumps in the IC properties due to change in attenuation values about 600 km below the 

ICB [Li and Cormier, 2002], changes in composition of iron alloy [Lin et al., 2002], or existence of a 

shallow partial melt zone [Sumita and Yoshida, 2003]. Unlike global heterogeneities generally indifferent to 

the crystal size, regional IC peculiarities such as 20 to 40 km thick layer at the top of the IC below Asia 

[Stroujkova and Cormier, 2004] or proposed complex anisotropy in the upper 80 km of the IC below Africa 

[Yu and Wen, 2007] should rely on a finer texture featured in the upper portion of the IC. Lots of the above 

results have been inferred from inversion of teleseismic waveforms refracted in or near the IC, so less 

controversy [Leyton et al., 2005] and more robust results on IC stratigraphy and aggregate properties would 

be expected, if both refracted and precritically reflected seismic data for the specific IC region were jointly 

analyzed. In addition, a discrepancy between IC models based on normal modes predicting anisotropic 

portion of the IC above its more isotropic center [Tromp, 1993] as opposed to isotropic layer residing on 

anisotropic bulk IC derived from body-wave data is subject to reconciliation. Meanwhile, appealing to finescale 

heterogeneities recently inferred from PKiKP coda observations [Vidale and Earle, 2002; Koper et al., 

2004] sets the issue of discrimination between the IC texture and its perturbations. The study [Cormier and 

Li, 2002] of PKIKP waveforms inverted for a model of IC attenuation due to forward scattering by threedimensional 

heterogeneous fabric finds a significant contribution of scattering to aggregate IC attenuation 

and admits both mechanisms – scattering due to inclusions in the outermost IC and scattering on velocity 

perturbations due to changes in alignment of crystallographic axes across the boundaries of anisotropic 

crystals. Single scattering theories were also used when modeling PKiKP coda [Leyton and Koper, 2007] 

[Leyton and Koper, 2007] to show it is predominantly due to IC heterogeneities, while contributions from 

other parts of the seismic path are less important. In the same time we can’t disregard reverberations in the 

ICB region [Poupinet and Kennett, 2004] as another mechanism to form the PKiKP coda wavetrain. Finally, 

changes in PKiKP coda waves tracked over a time period of 3 years [Vidale et al., 2000] yielded an estimate 

of the IC differential rotation rate making 0.2 degree per year, given the coda results from the IC scattering 

on fine-scale heterogeneities. Here we revisit the issue of fine structure of the IC and possible time 

dependence of its seismic image on daylight surface using a new dataset of precritical PKiKP coda waves 

421


recorded after the Chinese and USSR underground nuclear explosions (UNEs) at distances from 6 to 94 

degrees. 

The collected dataset includes digital records of short-period and broadband vertical channels of 

array and three-component stations. Characteristics of the selected channels were essentially similar in the 

frequency range 0.7 – 7 Hz and supported reliable registration of weak seismic waveforms with amplitudes 

below 0.1 nm. We analyzed data provided by ordinary seismic arrays of receivers that recorded an explosion, 

and data integrated into an array of sources, where same test site explosions closely conducted and separated 

by few years were recorded by a three-component station (see Fig. 1, Table 1 and Appendix. Data and 

Methods). In contrast to earthquakes, availability of ground truth information on explosion parameters 

(locations, origin times, depths, etc.) makes the resulting estimates unbiased by seismic source uncertainties. 

The processing included linear and phase-weighted stacking and methods of frequency-wavenumber (f-k) 

analysis applied in a sliding window to the array data (See Appendix). We present mainly beams and coda 

decay curves obtained from linear processing as distinct from more commonly invoked envelopes. Although 

both coda decay curves and envelopes convey essentially the same physical information (i.e. a set of 

instantaneous amplitudes), the former ones seem to be more intelligible physically and adequate 

mathematically as they require no evaluation of Gilbert transform normally correct only for infinite signals. 

Table 1. Epicentral distances for source-receiver paths 

from Figure 1. 

Path # Source Receiver Distance (°) 

1 STS BRVK 6.2 

2 LNTS KURK 11.5 

3 STS KEV 31.3 

4 LNTS FINES 41.8 

5 STS COL 59.9 

6 LNTS YKA 73.8 

7 LNTS ASAR 77.2 

8 STS LON 82.1 

9 LNTS PDAR 94.2 

Fig. 1. Locations of Semipalatinsk (STS) and Lop Nor (LNTS) Test Sites, 

three-component stations (BRVK, COL, KEV, LON) and seismic arrays 

(ASAR, FINES, KURK, PDAR, YKA) mutually connected by Great Circle 

Paths. Open dots are PKiKP reflection points’ projections on daylight surface. 

The analyzed time period of traces spans at least half an hour past the origin time, providing 

comparison between different seismic phases for an event. The inner core related effects due to propagation, 

reflection or scattering are extractable from the wavefield passages following the PKiKP arrival whose travel 

time varies between 992 and 1084 s for the above distances. Such passages often feature steady growth in 

amplitudes detected on the coda decay curves and beams in a narrow or full seismic frequency range. We 

find PKiKP codas at all distances observable independently of the parent phase being frequently not 

detectable but followed by a distinct coda or being very intensive with no or weak coda to come (Fig. 2 and 

A2). Such behavior is predictable from precritical PKiKP reflection coefficient remaining well below 0.01 as 

compared to the energy transmitted into the IC (Fig. 3). We find both smoothly decaying codas after a sharp 

PKiKP onset and so called “spindle-shaped” ones that feature growth and decay parts with its’ maximum 

coming tens of seconds after the PKiKP arrival (either observable above noise or not). The detected PKiKP 

codas show no clear tendency to change its frequency content with distance or regionally. The shown curves 

were estimated after pre-filtering between 2 and 4 Hz, while the low frequency bound of PKiKP coda 

observability varied between 1.3 and 2 Hz not tending to grow with distance increase. Such changes, for 

example, could have complied with Born approximation predicting higher frequency PKiKP coda’s content 

for shorter distances. In terms of regional similarity paths #3 and #4 are worth notice as closely probing the 

IC below Europe and showing the opposite PKiKP coda forms, while paths #3 and #7 produce good 

similarity despite geographical diversity of their ray paths. 

Traces #1 and #2 are particularly suitable for comparing coda decay curve’s passages that follow 

core related phases on the same trace. They are possibly the first [Koper et al., 2004] credible narrow angle 

reflections featuring close pierce/reflection points of PcP and PKiKP all through the ray path and lack of P 

scattered to PKP on core-mantle boundary topography or in D’’. We detect no coda triggered after PcP, 

while appropriate PKiKP codas are weak and short despite the impulsive parent phase capable of causing 

422


strong scattering in D’’. This fairly minor contribution to PKiKP coda from shells above the ICB to a lesser 

degree can be confirmed by absence of PcP codas from the decay curves estimated for other distances of the 

dataset. Finally, as to relation between the parent phase and its coda, we note long spindle-shaped coda after 

barely visible PKiKP in path #5, and almost identical PKiKP codas observed in paths #8 and #9 in spite of 

weak and strong PKiKP waveforms detected at the head accordingly. Thus propagation of direct PKiKP 

through D’’ and upper Earth’s shells turned out to be weak alternative to formation of PKiKP coda in the 

inner core, while contribution from P scattered to PKP on the source or receiver side may be more 

significant, especially at longer distances. However, this mechanism was recently shown [Leyton and Koper, 

2007] to be invalid for PKiKP coda, at least for the case of single scattering and the adopted assumptions, 

whereas heterogeneities in the outermost 350 km of the IC were favored to cause the PKiKP coda. 

Fig. 2. Seismic coda decay curves estimated for paths 

#2 (A), #3 (B), #4 (C) and #7 (D). Δ - epicentral 

distance. 

Fig. 3. ICB reflection/transmission coefficients. The 

upper black and gray curves correspond to waves 

PKIKP and PKJKP transmitted into the IC as P and S, 

accordingly, and the bottom black is for PKiKP. 

Fig. 4. Overlaid PKiKP coda doublets and beams plotted aligned on predicted 

PKiKP arrival (zero time). 

Unfortunately, the published envelope modeling [Leyton and Koper, 2007] is non-unique in terms of 

scattering mechanisms and gives no clue as to whether we can discard reverberative PKiKP coda generation 

theory and hypothesized discontinuities within the IC either local or global. In attempt to distinguish between 

different physical scenarios of PKiKP coda generation, we first analyze fine structure of PKiKP coda 

423


wavefield formed in essentially the same region of the IC and propagated differently through the rest of the 

ray path. In particular, we trace amplitude, slowness and back azimuth of PKiKP coda oscillations by using 

slowness diagrams calculated in a sliding window and arranged in a movie, and then compare PKiKP coda 

“doublets” to reveal the outermost IC structure. The processing was applied to pairs of PKiKP codas 

observed in paths #1 and #2, #5 and #6, #8 and #9 that have close epicentral distances and PKiKP reflection 

points on the IC surface divided by approximately 173, 47 and 17 km, accordingly (Fig. 1). Except for paths 

#1 and #2, pairs of seismic codas were normalized to the first arrival’s jump from the noise level and then 

were plotted overlaid with aligning onto the PKiKP arrival (Fig. 4). On one hand we find duplicated forms 

and similar durations of PKiKP codas corresponding to close PKiKP reflection points regardless of ray 

path’s diversity and slight changes in epicentral distances, which indicates we very likely evidence two 

independent measurements of aggregate characteristics of the IC probed by two nearby paths. On the other 

hand, each coda doublet exhibits a unique fine structure if compared to its counterpart. The detected PKiKP 

codas include a set of low slowness arrivals dominating for 0.7 – 1.2 s, coming from the source azimuth and 

having amplitudes sometimes few times as big as direct PKiKP (see excerpts with linear beams in Fig. 4). To 

preclude misidentification with crust reverberations capable of producing similar arrivals with low slowness 

and acceptable azimuth, we inspected coda passages after P and PcP where available and found no signs of 

such oscillations. The maxima of slowness diagrams remain for the most part close to the values of back 

azimuth and slowness predicted for reflections from discontinuities in the IC all through the PKiKP coda 

lasting tens of seconds. Although PKiKP coda pattern was not expected to coincide in each pair, we could 

expect that longstanding strong arrivals comparable to or exceeding the parent phase in amplitude would 

correlate or match any reasonable travel time curve of a wave reflected/refracted in the IC. This scenario 

would correspond to the presence of a local large-scale reflector or inclusion characterized by distinct 

velocity perturbation. Instead, we observe the stochastic pattern of unmatched arrivals appearing to originate 

from local discontinuities buried down to 600 km below the ICB, inclined by up to 30° and having acoustic 

impedance up to 2%. The assumed pairwise past PKiKP arrivals observed in doublets never matched jointly 

any travel time curve for a model with a reflector parallel to the ICB, giving residuals between 7 and 20 s. 

Such arrivals are detected within 35, 75 and 85 s after PKiKP in panes A, B and C of Fig. 4 accordingly. No 

waveforms with azimuth and slowness close to that expected for PKiKP and dominating at least 0.5 s are 

detected afterwards where the beams fade back to seismic noise, which yields rough estimation of minimal 

PKiKP coda duration for the above cases. 

The reported PKiKP coda features indicate its scattering origination from IC texture, and reveal the 

presence of anisotropic reflectors that result presumably from velocity perturbations due to significant 

changes in alignment of crystallographic axes crossways the boundaries of large anisotropic iron crystals. 

We also find weak correlation of waves generated on such larger elements of the IC texture, especially if 

compared to precursors due to D’’ heterogeneities some of which were recently revealed with remarkable 

precision [Cao and Romanowicz, 2007]. Thus the classical space stationary scattering medium with 

inclusions/impurities of any nature is less preferable to constitute the outermost IC scattering fabric than a 

cellular structure of misaligned anisotropic iron crystals. And the crystal size variability can reach a factor of 

100 – from 10 km based on the frequency content of PKiKP coda waveforms (above 1.3 Hz) and IC seismic 

velocities (more than 10 km/s), to few hundred meters from lab experiments [Bergman, 1998]. Such grainy 

pattern complies with a model for IC texturing where younger crystals of the outermost IC exhibit higher 

disorder and stronger intrinsic anisotropy about 12% [Steinle-Neumann et al., 2001], and consequently 

agrees with weak seismic anisotropy in the uppermost IC evidenced by Song and Helmberger [1995]. 

Unfortunately, getting reasonable estimates of IC scattering attenuation from fitting the observed PKiKP 

codas with an exponential model function is hampered by strong trade-off between the above wide range of 

scale-lengths, velocity perturbations and choice of autocorrelation function. The trial Q fits varied between 

75 and 450, showed no regional consistency and clear depth dependence. For instance, the appropriate Q 

estimates made a factor of 3 for the similar distance paths #3 and #4 that probed the IC in the same region 

below Europe. This possibly results from using single scattering [Wu and Aki, 1985] in place of multiple, 

and necessity to use Dirac autocorrelation function for the assumed grainy model instead of exponential. 

The observed spatially complicated pattern of the IC texture was also tested for changes in calendar 

time by comparing its images or PKiKP codas divided by 20 years. For this purpose, two Semipalatinsk 

source arrays for time periods 1966 – 1972 and 1985 – 1989 were formed. Given the rotation rate of 0.2 

degrees per year, the outermost IC heterogeneities would move by more than 80 km for the case. Except for 

anisotropy effects, such movements are effectively comparable to the path changes that provide significant 

differences in coda decay curves and beams for the above PKiKP coda doublets. However, PKiKP beams 

divided by 20 years (Fig. 5) show good correlation of passages corresponding to steady back azimuth and 

424


slowness close to that expected for PKiKP. To define time error bounds that made about 0.12 s, we 

calculated beams for bootstrap-type resampled arrays [Koper and Pyle, 2004] and estimated travel time error 

for past PKiKP waveforms survived but decorrelated due to array resampling. An example of such a beam 

(Fig. 6) shows worse correlation of the parent phase and increased decorrelation of the following ones – at 

997th, 1000th and 1005th seconds. Poorly known details of the IC texture preclude firm conclusions as to 

whether IC differential rotation exists, but the observed robust pattern of PKiKP beams during 20 years hints 

the IC texture underlying PKiKP coda is rather time stationary than subject to rotation. 

Fig. 5. PKiKP beams estimated for earlier (black) and later (gray) 

Semipalatinsk source arrays. 

Fig. 6. PKiKP beams estimated for earlier (blue), later (magenta) 

and resampled (gray) arrays of Semipalatinsk explosions. 

Finally we note that presumed strong variability in crystal size and higher crystallographic disorder 

in the uppermost IC may contribute to changeability of ICB reflecting conditions and hence PKiKP 

properties [Krasnoshchekov et al., 2005] simply by presence of large misaligned iron grains on the top of the 

IC. 

References 

Alfe D., M. J. Gillan, L. Vocadlo, J. Brodholt, G. D. Price (2002), The ab-initio simulation of the Earth’s 

core, Philos. Trans. R. Soc. London, Ser. A 360, 1227-1244. 

Bergman, M.I. (1998), Estimates of the Earth’s inner core grain size. Geophys. Res. Lett. 25, 1593-1596. 

Cao, A., B. Romanowicz (2007), Hemispherical transition of seismic attenuation at the top of the Earth’s 

inner core, Earth Planet. Sci. Lett. 255, 22-31. 

Cormier V.F., X. Li (2002), Frequency-dependent seismic attenuation in the inner core – 2. A scattering and 

fabric attenuation, J. Geophys. Res. 107(B12), 2362, doi:10.1029/2002JB001796. 

Ishii, M., A.M. Dziewonski, J. Tromp, G. Ekstrom (2002), Joint inversion of normal-mode and body-wave 

data for inner-core anisotropy, J. Geophys. Res. 107(B12), doi:10.1029/2001JB000713. 

Koper, K.D., J.M. Franks, M. Dombrovskaya (2004), Evidence for small-scale heterogeneity in Earth’s inner 

core from global study of PKiKP coda waves, Earth Planet. Sci. Lett. 228, 227-241. 

Koper, K., M. L. Pyle (2004), Observations of PKiKP/PcP amplitude ratios and implications for Earth 

structure at the boundaries of the liquid core, J. Geophys. Res. 109, B03301, 

doi:10.1029/2003JB002750. 

Krasnoshchekov, D.N., P.B. Kaazik, V.M. Ovtchinnikov (2005), Seismological evidence for mosaic 

structure of the surface of the Earth's inner core, Nature 435, 483-487. 

Leyton, F., K. Koper (2007), Using PKiKP coda to determine inner core structure: 1. Synthesis of coda 

envelopes using single-scattering theories, J. Geophys. Res. 112, B05316, doi:10.1029/2002JB004369. 

Leyton, F., K. Koper, L. Zhu, M. Dombrovskaya (2005), On the lack of seismic discontinuities within the 

inner core, Geophys. J. Int. 162, 779-786. 

Li, X., V.F. Cormier (2002), Frequency-dependent seismic attenuation in the inner core. J. Geophys. Res. 

107(B12), 2361, doi:10.1029/2002JB001795. 

Lin, J.F., D.L. Heinz, A.J. Campbell, J.M. Devine, G. Shen (2002), Iron-Silicon Alloy in Earth’s Core? 

Science 295, 313-315. 

Poupinet, G., B.L.N. Kennett (2004), On the observation of high frequency PKiKP and its coda in Australia, 

Phys. Earth Planet. Inter. 146, 497-511. 

Song, X., D.V. Helmberger (1995), Depth dependence of anisotropy of Earth’s inner core, J. Geophys. Res. 

100, 9805-9816. 

Song, X., D.V. Helmberger (1998), Seismic evidence for an inner core transition zone, Science 282, 924. 

Steinle-Neumann, G., L. Stixrude, R. Cohen, O. Gulseren (2001), Elasticity of iron at the temperature of the 

Earth’s inner core. Nature 413, 57-60. 

Stroujkova, A., V.F. Cormier (2004), Regional variations in the uppermost 100 km of the Earth’s inner core, 

J. Geophys. Res. 109, B10307, doi:10.1029/2004JB002976. 

425


Sumita, I., S. Yoshida (2003), Earth’s core: Dynamics, Structure, Rotation (American Geophysical Union, 

Washington, DC, pp. 213 – 231. 

Tanaka, S., H. Hamaguchi (1997), Degree one heterogeneity and hemispherical variation of anisotropy in 

the inner core from PKP (BC)-PKP (DF) times, J. geophys. Res. 102, 2925-2938. 

Tromp,J. (1993), Support for anisotropy of the Earth’s inner core from free oscillations. Nature 366, 678. 

Vidale,J.E., D.A. Dodge, P.S. Earle (2000), Slow differential rotation of the Earth’s inner core indicated by 

temporal changes in scattering, Nature 405, 445-448. 

Vidale J.E., P.S. Earle (2000), Fine-scale heterogeneity in the Earth’s inner core, Nature 404, 273-276. 

Waldhauser, F., D. Schaff, P. G. Richards, W.-Y. Kim (2004), Lop-Nor revisited: Underground Nuclear 

Explosions, Bulletin of the Seismological Society of America, 94, No. 5, 1879–1889. 

Wu, R., K. Aki (1985), Elastic wave scattering by a random medium and the small-scale inhomogeneities in 

the lithosphere, J. Geophys. Res. 90, 10261-10273. 

Yu, W., L. Wen (2007), Complex seismic anisotropy in the top of the Earth’s inner core beneath Africa, J. 

Geophys. Res., 112, B08304, doi:10.1029/2006JB004868. 

Appendix. Data and Methods 

There were processed data from 5 seismic arrays ASAR, FINES, KURK, PDAR and YKA that 

registered Chinese explosions dated June 8, 1996, May 15 and August 17, 2005 [Waldhauser et al., 2004], 

and four source arrays incorporating vertical records of stations BRVK, COL, KEV, LON that recorded 29, 

13, 10 and 23 Semipalatinsk explosions accordingly (Fig.1). The source arrays incorporate same instrument 

records and comply with plane wave approximation in terms of their aperture (Fig. A1). The configurations 

and Array Response Functions (ARF) for the resulting source arrays obtained from integrating vertical 

components of three-component records are given in Fig. A1. The presented ARFs are estimated as slowness 

diagrams calculated for “white noise” with Gaussian amplitude distribution supplied to all channels of the 

array. The calculated ARF for source arrays recorded by BRVK, COL and LON show excellent 

characteristics, and the source array recoded at KEV features no “side lobes” for the actual azimuth to 

station. 

Before main processing, all data were visually inspected for presence of glitches, abnormal locally 

dominating amplitudes or zero traces that frequently result in false arrivals on the sum trace or other output 

plots. Additionally, to adjust for slightly different magnitude of events incorporated into a source array (5.9 < 

mb < 6.1), scaling factors normalizing to P or cross-correlated PcP waveforms in the array were applied to 

individual traces. The effective scaling factors varied between 0.85 and 1.2. Array records were then 

bandpass filtered using a Butterworth three-pole zero-phase octave filter with one of the following octaves 1 

– 2 Hz, 1.4 – 2.8 Hz, 2 – 4 Hz, 2.4 – 4.8 Hz, 2.8 – 5.6 Hz. The information on dominating oscillation in a 

predefined time window was obtained from the slowness diagram calculated in two-dimensional cartesian 

system of slowness vectors Sx and Sy, where beam power in the predefined time window was defined as 

r.m.s. amplitude with linear beams. Except for paths #1and #2 (see Table 1), where slowness diagrams were 

calculated with bounds –0.2 to 0.2 s/km due to low velocity of first arrival, all the diagrams were estimated 

between –0.1 and 0.1 s/km using an increment of 0.0008 s/km for both slowness components. Slowness 

diagrams were evaluated both in the “absolute time” mode and P-relative which meant aligning of array 

traces on the first arrival of a P wave by means of a cross-correlation technique prior to stacking and 

application of f-k analysis. Such P-relative slowness diagrams provide better accuracy, as they are 

independent of UNE’s origin times and possible errors of station clocks. We then chart a coda decay curve 

which is essentially a set of slowness diagrams’ maxima calculated in a sliding window: 

⎪⎧ 

t+ τ n 

2 

⎤ ⎪⎫ 

2 

−1 

⎡ −1 

F ( t) 

= max⎨τ 

∫ ⎢n 

∑ f ( t'−kri 

) ⎥ dt'⎬ 

, 

k ⎣ i= 

1 ⎦ 

⎪⎩ 

τ 

where f(t-kri) – seismogram at array receiver “i”, n – number of receivers in the array, k – wave vector, ri – 

radius vector to the receiver, τ - predefined time window in seconds. Figure A2 shows coda decay curves 

estimated in the frequency band 2 – 4 Hz using 1 second sliding window. To track slowness and azimuth of 

arriving coda oscillations in time, we compose a movie whose frames are successive slowness diagrams. 

Fig. A1. Configurations and Array Response Functions for source arrays formed out of Semipalatinsk explosions recorded at stations 

BRVK, COL, KEV and LON (from top to bottom accordingly). Dates of explosions are given in the dd.mm.yyyy format. Reference 

points’ coordinates in configuration maps from top to bottom are: (49.942° N; 78.871° E), (49.924° N; 78.820° E), (49.916° N; 

78.807° E) and (49.923° N; 78.838° E): 

426 

⎪⎭


427


Fig. A2. Seismic coda decay curves estimated for paths #1 through #9 from Table 1. Except for the upper row, PKiKP arrival time 

correspond to zero time mark. Four bottom coda decay curves are normalized to the first arrival’s jump from the noise level. 

428


AVALANCHE-LIKE NUCLEATION OF CRACKS THROUGH FRACTURE 

KINETICS 

I.V. Kuznetsov 1 , V.V. Kuznetsov 2 

1 Lavrentyev Institute of Hydrodynamics, Novosibirsk, Russian Academy of Sciences, Siberian Branch. e-mail: 

kuznetsov_i@hydro.nsc.ru ; 2 Institute of Space Physical Research and Radio Wave Propagation, Russian 

Academy of Sciences, Far Eastern Branch , Kamchatka 

Abstract. Models of evolution of crack ensembles are wide spread in seismologic theory. 

But it is still debated weather acoustic emissions should be used as a precursor of 

seismologic events. In the Griffith's theory of fracture, which is widely exploited in 

seismologic models, it is generally accepted that acoustic emission accompanying a crack 

formation has no influence on the subsequent nucleation of other cracks. The main reason of 

this ignorance is that acoustic stress is insufficient to be taken into account. 

In this report we give several well-known facts and apply them in the theory of fracture. The main 

peculiarity is that lattice long-wave vibrations are responsible for lattice breakdown (fracture). 

Experiments of stressed and seismic data. It is known that acoustic emission can't be ignored in 

predicting of precursor of seismologic events and in control of stressed solid before final breakdown [1]. 

(a) Crack nucleation rate at uniaxial static compression of diabase. (b) Geoacoustic signals observed 

at Kamchatka before earthquake labeled by arrow. 

Thermodynamic instabilities of crystal lattise. 

1. Zhurkov's formula. The empirical formula relating the lifetime, , with stress, , and 

temperature, T, 

429


namely has been developed by S.N. Zhurkov and his coworkers as an equation reflecting the nature 

of the fracture process. The coefficients and entering formula (1) have been given a 

certain physical meaning. The coefficient which is ordinarily close to 10 -12 sec is associated with 

the period of atomic oscillations in solids, and quantity is given the meaning, of an activation 

energy for the fracture process. Experiments have shown it to correlate well with the energy of 

interatomic binding. Coefficient is linked with anharmonicy of crystal lattice. 

It is affirmed that the acoustic emission can't be ignored owing to the S.N. Zhurkov's kinetic theory 

of strength [2]. The key point of kinetic concept of strength is that a fraction of the sample is 

controlled by rupture of chemical bonds being caused by thermal energy fluctuations. Here we try to 

give definitions to atomic vibration modes that could be responsible for crack initiation. 

2. Energy localization. Short wavelength atomic anharmonic vibrations (10 12 – 10 15 Hz) are 

responsible for single atomic bond rupture. This short wavelength atomic vibrations are intrinsic 

localized modes of anharmonic atomic lattice [3]. In short, energy localization leads to that 

displacement of one atomic bond exceeds critical meaning and dislocation is formed. 

3. Spectral dimension. Probably this mechanism of defect formation (instability of intrinsic 

localized modes) is responsible for lattice rheological transformation. During this process 

(prefracture) clusters of vacancies and dislocations are formed. Zhurkovs' experimental formula (1) 

might establish duration of this process. 

In order to characterize lattice transformation "from order to disorder", we need another notion : 

spectral dimension. Spectral dimension d was defined by the asymptotic law [4]: 

ρ(ω) is the density of modes (fractons) with frequency ω. The spectral dimension is the most 

natural extension of the usual Euclidean dimension d to disordered structures as far as dynamic 

processes are concerned. It coincides with d in the case of lattices, but in general, it can assume noninteger 

values between 1 and 3. The spectral dimension represents a useful measure of the effective 

connectedness of geometrical structures on a large scale, because large values of correspond to 

high topological connectedness. Therefore, clusters of vacancies and dislocations decrease spectral 

dimension of crystal lattice. 

4. Peierls' instability in stressed lattice. Long wavelength vibrations (fractons) 

(10 6 — 10 12 Hz) of atomic lattice having fractal dimension are responsible for collective 

rupture of atomic bonds and new crack initiation. 

This fact is not published yet, but can be affirmed by thorough investigation of instability (Peierls' 

instability) of atomic vibration modes of crystal lattice with clusters of vacancies. In [5] Peierls' 

(melting-like) instability, induced by thermal fluctuations, was established in percolating solids 

(solids with porous). 

The reduced dimensionality of stressed lattice with defects (vacancies and dislocations) leads to 

strong long wavelength lattice fluctuations (fractons). As a consequence its positional ordering is not 

truly long-range, the mean-square displacement of the lattice with N sites (atoms, molecules) 

diverges with the sample size (Peierls' instability): 

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when spectral dimension is less than 2 [6]. 

5. Unstable fracton modes. Griffith's crack initiation by thermal fluctuation. 

Due to Peierls' instability, there are unstable vibration modes (fractons) of crystal lattice which 

spectral density is less than two. Fracton can serve as a initiator of Griffith's crack, if its half of 

wavelength exceeds length of critical crack in Griffith's criteria. This idea is very similar to the 

dilaton concept to explain the fracture of solids [7]. 

6. Fracton and phonon nonlinear interaction. 

It is experimentally verified that phonons (extended modes) interact with fractons (localized modes) 

in Cantor-like structure [8]. The large enhancement of nonlinear interaction results from the more 

favorable frequency and spatial matching of coupled modes (fractons and phonons). 

Possibility of avalanche-like nucleation of cracks. It is well-known that opening cracks radiate 

elastic waves (acoustic emission). If we postulate that cracks are initiated by fractons (dilatons) and 

phonons interact with fractons in disordered matter (with clusters of dislocations and vacancies), than 

we can propose of avalanche-like nucleation of cracks: 

a. fracton+phonon —> unstable fracton, 

b. unstable fracton (dilaton) —> opening crack, 

c. opening crack —> emitted phonons. 

Literature 

[1] Kuznetsov, V.V. (2008) Vvedenie v Fiziku Goryachei Zemli. 366 pp. Petropavlovsk-Kamchatsky. 

[2] Zhurkov S.N. (1965) Kinetic concept of strength of solids. Int. J. Fract. Mech. 1. 311–323. 

[3] Burlakov V.M. et. al. (1990) Localized vibrations of homogeneous anharmonic chains. Phys. 

Lett. A 147(2-3) 130-134; Burlakov V. M. (1991) Molecular-dynamics simulation of the decay 

kinetics of uniform excitation of an anharmonic 1D chain. Zh. Eskp. Teor. Fiz. 99. 1526 

[4] Alexander S., Orbach R. (1982) Density of states on fractals : “fractons”. J. Phys. Lett. 43 625- 

631. 

[5] Bikas K. Chakrabarti (1994) Fracture and other breakdown phenomena in disordered solids. 

Lecture Notes in Physics, 437.171-185. 

[6] Burioni R. et. al. (2002) Vibrational thermodynamic instability. Europhys. Lett.58 (6), pp. 806– 

810 

[7] Zhurkov S.N. (1983) Dilaton strength mechanism of rigid bodies, Fiz. Tverd. Tel. 25. 3119-3123. 

[8] Craciun F. et. al. (1992) Direct experimental observation of fracton mode patterns in onedimensional 

Cantor composites.Phys. Rev. Lett. 68(10) 1555 – 1558. 

431


TEMPORAL VARIATIONS IN GEOPHYSICAL FIELDS AS A 

MANIFESTATION OF THE NONLINEAR ROCK PROPERTIES 

O.I. Silaeva 1 , A.V. Ponomarev 2 , A.A. Khromov 3 , S.M. Stroganova 4 , T.I. Rudenko 5 

1 Institute of Physics of the Earth, Moscow, Russia, e-mail: silaeva@ifz.ru; 2 Institute of 

Physics of the Earth, Moscow, Russia, e-mail: avp@ifz.ru; 3 Institute of Physics of the Earth, 

Moscow, Russia; 4 Institute of Physics of the Earth, Moscow, Russia, e-mail: 

stroganova306@mail.ru; 5 Institute of Physics of the Earth, Moscow, Russia 

Abstract. In this study we have conducted research of rock properties changes under explosive 

action by means of ultrasonic pule velocity method and apparent resistivity one. 

At present a conception on a rock model as an open system having a discrete-block structure was 

established. Conception of a rock model as a block medium was put forward by academician Sadovsky. 

Actually a block structure of a massif is revealed at geomorphological surveys and distinctly traced on space 

photographs. [1, 2] 

A research of the medium behavior in time at its destruction (due to explosion or during an 

earthquake, rock shock etc.) has a great scientific and practical significance to estimate rock massif stability 

in a mine, at carriers’ excavation, trenches, underground cavities, canyons, water reservoirs and creation of 

basements of different industrial constructions. In a theoretical paper [3] Rakhmatulin considered 

propagation of deformations due to an explosion in a medium where these deformations exceed elasticity 

limit. He proved that in this case a specified deformation wave will propagate in it which he called an 

unloading wave. This wave is observed by miners during their work in mines with explosions. The 

observations entail great technical difficulties. Therefore, there is an urgent need to obtain data on 

propagation of slow deformational waves related to deformation process of real blocks of rock massifs 

influenced by heavy effects: explosions, rock shocks, earthquakes, reflecting structural reconstruction of a 

massif. We selected two geophysical methods to study a rock massif state occurring at its destruction: a 

seismic one (in ultrasound frequency band) and an electric one (electrical resistance). These methods allowed 

to trace temporal variations of field parameters of seismic and electrical waves related to destruction process 

of the massif due to external effects registering a structural reconstruction of the massif at destruction by 

underground explosions. 

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The experiments were carried out at iron-ore Severo-Peschanskaya mine in the North Urals [4]. The 

Severo-Peschanskaya magnetite deposit represents a blind ore body of complicated form with maximum 

dimensions by a course of pool of 1500 m, a dip of 600 m and capacity around 100 m. Series of large 

crumpling and crushing zones I and II, which are placed in a direct vicinity from basic constructions of the 

industrial site, are caused by intense tectonic activity in a deposit area. In (Fig.1) a schematic cut of the mine 

and of a site of installation of geophysical observation stations at the horizon of 240 m are presented. 

The observation stations, (Fig.2), were placed in such a way that during 5-8 years the two stations, 

the first and the second one which are located close to the ore body should come close to the boundary of the 

destruction zone, at the same time as the last station, the third one, in an area of the main trunk, should be 

located in a «quiet» zone where effect of mining operations should remain a minimum one. 

Rock massif broken by tectonically fractured zones was composed of diorite and porphyrites. The 

observation points were located at distance of 700-800 meters away from the explosions and the ore body at 

the depth of 450 meters. The measurements were made by means of four probes with ultrasonic transducers 

working like electrodes for observations of electrical anisotropy parameters. At each station (Fig.2) four bore 

holes were drilled at the depth of around of 4 m and from the wall of the rock production in a zone of natural 

pressures four probes with ultrasound sensors were installed, the bodies of which were used as electrodes. 

The distance between the holes reached about one meter. The holes were cemented which ensured steady 

contact between sensors and the rock and constancy of measurement base. The base deformation is small [4, 

5] and it may be ignored. This fact allowed to relate all the observed variations of elastic impulse 

propagation time (the velocity of elastic wave propagation) between the sensors and also variations of 

electric resistance, at the account of strain stress state of the massif. It also permitted to monitor temporal 

variations of physical parameters (deformation, elastic wave velocity, electrical resistance etc.). Not only 

variations of the stress state of the massif were evaluated but the deformation process as a single rapturecontinuous 

process was also reconsidered. 

The observations were carried out with intervals of longitudinal wave velocities which was included 

in successive comparison of propagation times of elastic impulse for the base during the observation time. 

The error of determination of elastic impulse propagation time reached ±0,5%.[5]. The electrical 

anisotropy parameter (as analogy with coefficient of electrical anisotropy) K* was determined as difference 

of potentials measured on mutually perpendicular installations in stabilized tone. De-energizing the mine in a 

period of conducting mass explosions decreased noise interference and gave opportunity to observe 

anomalous variations of K* by a value up to 0.06 % [6]. Thus, monitoring by geophysical methods was 

realized with the use of the means of measurement and automating observations available at present. The 

433


geophysical monitoring is an adequate method of research of deformation processes occurring in block 

structures of rock massifs. 

The aim of ultrasonic monitoring was to establish changes in the stress state of the rock massif 

related to geodynamic processes and the process with respect to the mine. Ultrasonic observations (Fig.3) 

showed that time fluctuations of longitudinal wave velocities were observed, and in the X, Y and Z 

directions for all the three observation stations increasing after 1991. It is related to movement of the 

destruction zone towards the main trunk. The fluctuations within 5-8% usually noted at ultrasound 

monitoring are caused by natural fluctuation of the parameters of initial stress state in the Earth crust [7]. The 

observations of slow deformational waves occurring after mass explosions were carried out in the most 

«quiet» period in 1990. 

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The production of mass underground explosion is peculiar by successive explosions of massif in 

bore holes drilled on significant areas. The exploded massif remains in place. During the time of conduction 

of an explosion in a mine all the mechanisms are turned off, the mine is de-energized. 

Breaking of balance in a rock massif as a result of the explosion leads to variations of geophysical 

parameters (anisotropy of velocity and electrical resistance) (Fig.4 and 5) in a significant distance from the 

location of explosion and they are registered several hours later. The velocity of propagation of slow 

deformational wave in this case was about 3 m/min. It testifies that an unloading wave which Rakhmatulin 

calculated is being propagated in a block massif [3]. In this case it is a fact that a block system strives to pass 

into a new stable state. 

435


Thus, complex monitoring observation (ultrasonic and electrometric) revealed the appearance of 

wave-shaped fluctuations of P-wave velocities and anisotropy of apparent resistivity after explosions. The 

time of relaxation was about several hours and probably indicated the transition of medium in the 

equilibrium state. 

Two kinds of anisotropy were observed in these experiments: «static», which associated with 

features of rock massif structure, and «dynamic», associated with temporal variations of geophysical 

parameters due to structural changes under failure. This allows to consider that nonelastic deformations 

spread in rock massif after explosions present waves of « unloading». 

Investigations of temporal behavior and geophysical structure medium after explosions have great 

scientific and practical significance for estimates of rock mass stability in mines, reservoirs excavating, etc. 

Presence of nonelastic manifestations and the tasks of stability of rock massifs and constructions 

located in them occurring in this connection demand that the problems related to the influence of 

peculiarities of structural-tectonic structure of rock massif on mechanical consequences of large scale 

underground explosion [1] should be studied. It is necessary to develop special methods and ways of 

establishing physical-mechanical properties and a stress-strain state of rock massifs. Geophysical monitoring 

is a way of solving these problems. 

References 

1. Sadovsky M.A., Bolchovitinov L.G., Pisarenko V.F. Deformation of Geophysical Medium and 

Seismic Process. M.: Nauka, 1987. P. 100. 

2. Sadovsky M.A., Adushkin V.V., Spivak A.A. On Dimensions of a Zone of Irreversible 

Deformation During the Explosion in Block Medium // Izvestiy USSR Acad. of Sci., Physic of the 

Earth, 1989, N9, P.9-16. 

3. Rachmatulin H.A. Propagation of a Wave of Unloading. PMM, Vol.IX, Iss.1, 1945, P. 91-100. 

4. Sashurin A.D. Displacement of Rocks in the Mines of Ferrous Metallurgy. Ekaterinburg.: IGD UrO 

RAS, 1999, P. 268. 

5. Silaeva O.I., Zamakhaev A.M., Terentiev V.A and Rudenko T.I., Ultrasonic Monitoring of Rock 

Massifs, 1994, Journal of Earthquake Prediction, V.3., PP. 2203-214. 

6. Stopinski V., Ponomarev A.V. Chromov A.A., Irisova E.L., Los W.F., Lekkostup W.S., Ananiev 

V.A. Sledzenie metoda electrycznooporowa prezemieszoza hia sie pola naprezen w deformowanym 

eksploatacja grotworze. Publs. Irst. Geopphys. Pol. Acad. Sc., M-15(235), 1991. P. 301-109. 

7. Silaeva O.I. and Zamakhaev A.M., Time Variations in Parameters of Ultrasonic Oscillations in a 

Tectonic Zone Before the Susamyr Earthquake of 1992-1997. Journal of Earthquake Prediction, 

V. 6, P. 428-437. 

436


COMPARATIVE ANALYSIS OF IONOSPHERIC VARIATIONS BEFORE 

STRONG EARTHQUAKES 

T.V. Gaivoronskaya 

Pushkov Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation RAS 

(IZMIRAN), Troitsk, Moscow Region, 142190, Russia 

e-mail: gansk@izmiran.ru 

Abstract. At two ionospheric stations Petropavlovsk and Magadan the series of deviations of critical 

frequencies foF2 from their moving average values are considered before strong earthquakes. The 

irregular variations at both stations are compared to exclude the identical changes connected with 

geomagnetic disturbances and to reveal seismo-ionospheric effects. It has been found that positive 

deviations are predominated in the time of preparation of strong earthquakes. They become more 

intense with increase of magnitude of earthquakes. 

Introduction 

Anomalies of electronic concentration of the ionosphere at middle latitudes, which are connected with seismic 

activity, are usually less than ionospheric disturbances observed during global geomagnetic storms, therefore 

the seismic effects are quite often difficult to identify. The earthquakes occur both in geomagnetic quiet and 

disturbed periods. It is a note in this connection that geomagnetic storms are global phenomena, whereas 

premonitory ionospheric effects of earthquakes are essentially local. 

In general, characteristics of F2-layer are qualitatively identical at stations if they are located from each other 

on distances no more than 500-700 km. However at such distances one of the stations can be in a zone of 

seismic activity, and another - outside of it, so that seismo-ionospheric disturbances should be marked at the 

first station and to be absent or be less intense at other. In order to reveal seismo-ionospheric disturbances, the 

comparative analysis of data at two stations of radiosounding Petropavlovsk and Magadan has been made. 

Earlier, data at two stations are compared with each other, and daily correlation coefficients of ionospheric 

parameters are calculated. It is received that before strong earthquakes the correlations are quite often broken 

(Gaivoronskaya et al., 2002; Gaivoronskaya, 2005). Now hourly variations of critical frequencies foF2 are 

examined in more detail. 

Methods 

There have been considered ten strong earthquakes in 1992-1994 with magnitudes from М=5.4 up to М=7.5 at 

seismic region - Kamchatka. Zone of active preparation of earthquakes usually covers the area in radius of 200- 

300 km (Bowman et al., 1998; Dobrovolsky et al., 1979), thus the earthquakes with epicenter on distances not 

farther than 250 km from Petropavlovsk-na-Kamchatke have been chosen. 

The ionospheric F2-layer is the most variable of regular layers, and its critical frequency foF2 is one of the 

most accurately measured parameters of ionosphere, therefore that frequency has been taken for analysis of 

data series obtained at stations located near earthquake areas. We have examined the series of ΔfoF2 deviations 

of critical frequencies of F2-layer from their moving average values at two ionospheric stations Petropavlovsk 

and Magadan. Usually the average values are calculated for a month, they are derived from the data for the 

previous and following 15 days. In case of forecasting of seismic events it is necessary to calculate average 

values only for previous period of 15 days when results of radiosounding are known. The hourly irregular 

variations received at two stations Petropavlovsk and Magadan are compared with each other: 

437


ΔfoF2 (P-М) = ΔfoF2 (P) - ΔfoF2 (М) = [foF2 (P) - foF2 (М)] - [C (P) - C (М)], 

C is the moving average value of frequencies on previous 15 days. Thus it is possible to exclude the significant 

ionospheric variations connected with geomagnetic storms, and also some distinctions between average values 

foF2 at two stations. 

Fig. 1 illustrates results of calculations of variations ΔfoF2 (P) at station Petropavlovsk (above) and relative 

variations ΔfoF2 (P-М) by comparison of data of stations Petropavlovsk and Magadan (below). On horizontal 

axis the hours of local time of Petropavlovsk are marked. Irregular variations are calculated within 12 days, 

from 23 February till 5 March 1992, when there are a series of earthquakes, the greatest of which with 

magnitude M = 6.8 was registered on 2 March 1992. A few days before the geomagnetic storm take place. In 

the top figure the significant negative irregular variations connected with geomagnetic storm are visible, while 

at the bottom figure the negative disturbance practically is absent. However at bottom figure the positive 

disturbance 7 day prior to the main seismic shock is noticed. 

Fig. 2 shows another example of relative variations ΔfoF2 (P-М) before an earthquake on 8 June 1993. In that 

case there is a catastrophic earthquake with magnitude М=7.5 and a series of aftershocks. Considerable positive 

deviations are observed before the main shock and one of the aftershocks. 

.foF2(P), MHz 

.foF2(P-M), MHz 

4 

2 

0 

-2 

-4 

-6 

-8 

4 

2 

0 

-2 

-4 

Petropavlovsk 

23 February-05 March 1992 

6.8 6.0 6.3 

0 24 48 72 96 120 144 168 192 216 240 264 288 

Petropavlovsk-Magadan 

23 February-05 March 1992 

6.8 6.0 6.3 

0 24 48 72 96 120 144 168 192 216 240 264 288 

hours LT 

Fig.1. Variations ΔfoF2 (P) at station Petropavlovsk (above) and relative variations 

ΔfoF2 (P-М), received at comparison of data of Petropavlovsk and Magadan (below), 

before earthquake occurred 2 March 1992. 

438


.foF2(P-M), MHz 

3 

1 

-1 

-3 

Petropavlovsk-Magadan 

02-13 June 1993 

7.5 5.1 5.5 5.8 6.3 

0 24 48 72 96 120 144 168 192 216 240 264 288 

hours LT 

Fig.2. Relative irregular variations ΔfoF2 (P-М) at Petropavlovsk as compared with 

Magadan before earthquake on 8 June 1993 with magnitude М=7.5. 

Results 

So only a small part of energy of earthquakes penetrates into ionospheric altitudes, the disturbances of critical 

frequencies foF2 caused by seismic activity are difficult to reveal on the background of daily irregular 

variations, particularly on the background of ionospheric storms. Comparative analysis of data of 

radiosounding at two stations Petropavlovsk and Magadan allows us to exclude the disturbances connected 

with geomagnetic storms and to select seismo-ionospheric effects. 

It is received that 10-12 days before strong earthquakes in 1992-1994 the irregular positive variations are 

predominated at station Petropavlovsk as compared with station Magadan. Calculations show that positive 

deviations become visible in the period preceding strong earthquakes with magnitude M=5.8 and more. 

Positive variations are more expressed with larger magnitude of earthquake. It confirms that the effect is just 

connected with seismic activity. 

References 

Bowman, D.D., G. Quillon, C.G. Sammis, A. Sornette, and D. Sornette (1998), An observation test of the 

critical earthquake concept, Journal of Geophysic Research, 103, 24359-24372. 

Dobrovolsky, I.R., S.I. Zubkov, and V.I. Myachkin (1979), Estimation of the cize of earthquake preparation 

zones, Pure Applied Geophysics, 117, 1025-1044. 

Gaivoronskaya, T.V., and S.A.Pulinets (2002), Analysis of the F2-layer variability in the areas of seismic 

activity, 20 pp., Preprint IZMIRAN, N2 (1145), Moscow. 

Gaivoronskaya, T.V. (2005), Ionospheric variations in seismically active regions, Izvestia, Physics of the Solid 

Earth, 41, N3, 56-60. 

439


COMPARISON OF EXPERIMENTAL AND MODEL Q-BURSTS 

IN TIME DOMAIN 

M. Hayakawa 1 , A.P. Nickolaenko 2 , T. Ogawa 3 , M. Komatsu 4 

1 Department of Electronic Engineering, UEC, Chofu-city, Tokyo, Japan, e-mail: 

hayakawa@whistler.ee.uec.ac.jp 

2 Usikov Institute for Radio-Physics and Electronics, NAS of the Ukraine, Kharkov, Ukraine, e-mail: 

sasha@ire.kharkov.ua 

3 Science Laboratory International, Kamobe, Kochi, Japan, e-mail: ogawasli@I-kochi.or.jp 

4 Polytechnic College Kochi, Noichi, Kochi, Japan, e-mail: koma2@ma.akari.ne.jp 

Abstract. We compare natural extremely low frequency pulses (Q-bursts) with computations of 

analytical time domain solution. The wide band receiver was used in experiment with the upper 

cut-off frequency about 11 kHz. The ball antenna allowed for ELF-VLF records of vertical electric 

field in the fair weather conditions with a unique resolution of 22 kHz sampling frequency. We 

use the uniform Earth – ionosphere cavity model, the linear frequency dependence of propagation 

constant, and we find an excellent agreement between the observation and modeling. 

Introduction and experimental setup 

Term ‘Q-burst’ is related to discrete natural ELF radio pulses detected worldwide and lasting for 0.3 

– 1.5 seconds. These signals originate from powerful lightning strokes whose pulsed amplitude exceeds the 

continuous Schumann resonance (SR) background by a factor ten or greater. Some Q-bursts were related to 

the ‘red sprites’. In the present study we compare the precise electric field measurements in the ELF-VLF 

band with the time domain solution for the uniform Earth–ionosphere cavity [see Nickolaenko, Hayakawa, 

Ogawa, and Komatsu, 2008 for detail]. 

Fig. 1. Frequency response of ELF – VLF receiver. The wide band receiver detects the ELF – VLF pulses, 

and the narrow band filtering corresponds to typical response of a receiver for the global electromagnetic 

(Schumann) resonance studies. 

A ball antenna was istalled at Tochi station (33.3° N, 133.4 ° E) a few kilometers away from the 

center of Kochi City, Japan. Electric fields were observed in the fair weather afternoons covering the four 

seasons since November 2003. The ‘narrow band’ and ‘wide band’ frequency responses of our receiver are 

440


shown in Fig.1. We discuss the wide band data acquired with the 22 kHz sampling rate [Ogawa and 

Komatsu, 2007]. 

Waveforms observed 

Typical waveforms are shown in Fig. 2, which usually corresponded to the source – observer 

distances D close to 20 Mm. These pulses contain the direct and antipodal waves that merge into a W type 

Q-burst. Two kinds (the wide – and narrow–band) of waveforms were acquired, and we use below the wide 

band records for a comparison with model computations. 

Fig.2. A Q-burst of W type in the wide and narrow frequency bands. 

One may conclude by comparing the upper and lower panels in Fig.2 that wide– and narrow 

band waveforms are different. The wide band signal contains the resolved leading and rear parts. 

The first one contains the direct (initial pulse) and antipodal (second pulse) waves forming the W 

pattern. The secondary or rear pulse is a combination of merged round–the–world waves, and it is 

delayed from the first pulse by ~0.16 s. The delay allows for estimating the signal velocity in the 

Earth – ionosphere cavity being about 250 thousands kilometers per second [Ogawa and Komatsu, 

2007]. The fine details of the record are absent in the narrow band channel: individual atmospherics 

become invisible. We know [Nickolaenko, Hayakawa, 2002] that for large source – observer distances 

cavity losses concentrate the pulse spectrum below 100 Hz. Therefore, the waveform modifications although 

being present in the narrow band do not unrecognizably change the waveform. One can identify the W 

pattern at the beginning. The dispersion pertinent to the narrow band filtering provides a greater impact on 

the delayed ELF waveform by turning it into a kind of attenuating sinusoid. 

441


Model 

We compute waveforms directly in the time domain for the uniform Earth – ionosphere cavity 

model. The ‘linear’ propagation constant is used ν ( f ) = ( f − 2) 6 − i f 100 that was found from the 

Schumann resonance cross-spectra measured at large longitudinal separation of two observatories 

[Nickolaenko and Hayakawa, 2002]. Computations were performed with the algorithm accelerating the 

convergence of time series. 

Fig.3. Evolution of E – and H – pulses with the source distance. Signal focusing is obvious around the source 

antipode. 

A flat infinite frequency response of the receiver was assumed. Figure 3 depicts a series of 

pulsed waveforms computed for a set of source – observer distances ranging from 2 to 20 Mm. The 

field increase is clearly seen at the vicinity of antipodal distance of 20 Mm. We used the ‘white’ 

source current moment of a lightning discharge with Ids (f) = 10 8 A*m. The above current moment 

is related to a stroke with the peak current of 25 kA and the channel length of 4 km. Since we 

compare experimental and computational waveforms, the particular source amplitude is 

insignificant. The stroke polarization was positive. Visual comparison of pulse amplitudes indicates 

that the above current moment underestimates the observed value by a factor of up to five, which is 

in agreement with regular Q-bursts observations. 

Comparison of experimental (black) and model (color) data 

Frames below present individual pulses: black lines depict the results observed and the model data 

are shown by the red dotted lines. The time is shown along the abscissa, and the pulse middle sub-peaks were 

aligned to facilitate the comparison. The major feature of all data sets was their high reciprocity. Once the 

442


sub-peaks coincide, the rest of the waveforms became synchronized also, provided that a correct source – 

observer distance was found. 

Pulse No.1. Industrial 60 Hz interference is clearly seen. 

Pulse No.2. A few discrete pulses and a distinct negative slow tail atmospheric are superimposed on the 

waveform of the Q – burst. Industrial interference is noticeable. 

443


Pulse No.3. A positive slow tail atmospheric is combined with the Q – burst together with continuous 60 Hz 

industrial interference signal. 

Pulse No.4. A W type Q – burst arrived from antipodal distance. Direct and antipodal waves almost merge. 

Many ‘short distance’ VLF atmospherics were detected indicating on a high activity of the Asian 

thunderstorm center. 

444


The left ordinates of each frame show experimental amplitude of vertical electric field in all the 

frames. The right ordinate shows the computed amplitude corresponding to the red dotted curves. As one 

may see, the source amplitude used in our computations was underestimated in comparison with 

measurements by a factor of 2 – 5. 

The wide band record in the above frames resolves small ‘regular’ spikes responsible for the 

Schumann resonance background signal. Different kinds of atmospherics occur during the records including 

the ‘slow tails’ denoted in the plots. These signals were not processed during this particular study. Our wide 

band measurements applied an exceptional sampling frequency of 22 kHz, they covered both the slow tail 

(VLF) and the Schumann resonance (ELF) bands, and very pure records were obtained. The high quality of 

experimental records is clear. In particular, the industrial interference at 60 Hz frequency (radiation from 

local power supply lines) is very small. 

Conclusion 

Data presented in this report allow for the following conclusions: 

Experimental and model data are similar: if one aligns the first (arrival) peak, positions of all other 

peaks practically coincide. The pulses have rather sophisticated waveforms, which do not resemble an 

attenuating sinusoid. 

Results of precise ELF – VLF observations correspond to the radio propagation model within the 

uniform Earth – ionosphere cavity having the linear frequency dependence of propagation constant. 

Similarity of model data to observations confirms the accuracy of such a model. 

Insignificant deviations between the plots are easily explained by the finite pulse – to – background 

ratio (~ 10), by an impact of industrial 60 Hz interference, and by the random (hence, unknown) details of 

the spectrum of a parent lightning stroke. 

References 

Nickolaenko, A. P., and M. Hayakawa (2002), Resonances in the Earth-ionosphere Cavity, 380 pp., Kluwer 

Acad., Dordrecht, Netherlands. 

Ogawa, T., and M. Komatsu (2007), Analysis of Q-burst waveforms, Radio Sci., 42, RS2S18, 

doi:10.1029/2006RS003493. 

Nickolaenko, A. P., M. Hayakawa, T. Ogawa, and M. Komatsu (2008), Q-bursts: A comparison of 

experimental and computed ELF waveforms, Radio Sci., 43, RS4014, doi:10.1029/2008RS003838. 

445


FINE STRUCTURE OF ELECTRIC PULSED FIELD 

ABOVE THE BENT STROKE OF LIGHTNING 

I.G. Kudintseva 1 , A.P. Nickolaenko 2 , and M. Hayakawa 3 

1 Karasin National University, Kharkov, Ukraine, 

2 Usikov Institute for Radio-Physics and Electronics, National Academy of Sciences of the Ukraine, 

Kharkov, Ukraine, e-mail: sasha@ire.kharkov.ua 

3 The University of Electro-Communications, Chofu-city, Tokyo, Japan, e-mail: 

hayakawa@whistler.ee.uec.ac.jp 

Abstract. We present the pulsed electric fields computed in the neutral atmosphere above a 

powerful positive lightning stroke with the bent channel containing vertical and horizontal 

sections, each 10 km long. The fine structure of field is demonstrated arising in the space due to a 

combination of delayed pulses arriving from the stroke sections. The electric field distribution 

depends on time and on the stroke orientation with respect to an elevated observer. Characteristic 

size of ‘filaments’ in the transient electric field is about 1 km along the horizontal direction, and it 

reaches a few tens of kilometers in the height. 

Introduction 

The present paper is related to the red sprite phenomena. The detailed description of the 

phenomenon and its model might be found in the review paper by Pasko (2006). A specific feature of 

atmosphere transient luminous events (TLE) is the fine tendril structure of sprites possibly associated with 

the horizontal sections of the parent lightning channel. 

We do not model development of a sprite in the present paper. Instead, we discuss the property 

overlooked in literature: the transient electric field has a structured spatial distribution. We treat the simplest 

possible model of lightning stroke. The ‘engineering model’ of a return stroke is bent (broken) in the middle, 

so that the current wave moves along the Γ–shaped channel: initially it goes upward and afterwards it turns 

horizontally. We demonstrate that such a stroke provides three pulses in the mesosphere. An interference of 

these pulses in space causes a sophisticated structured field distribution. The fine structure of the field may 

induce the bunching of charged particles, which form the filaments of a transient luminous event. 

Model description 

When computing electric pulses in the mesosphere, we use the model of a stroke with the bent 

channel. The stroke channel is 20 km long. Initial, vertical half of the channel is 10 km; it coincides with the 

vertical Z-axis of the Cartesian coordinate system. The Γ–shaped stroke is bent at 10 km altitude and the 

current proceeds horizontally here along the X-axis. We use the ‘engineering model’ with the following 

4 

∑ 

k = 1 

current at the base of a positive stroke: ( t) 

= I ⋅ exp( 

− t ) 

I τ , t ≥ 0. Amplitudes Ik and relevant time 

k 

constants are: I1 = 569 kA, I2 = −460 kA, I3 = −100 kA, I4 = −9 kA, τ1 = 16.6 µs, τ2 = 333.3 µs, τ3 = 0.5 ms, 

V ( t) 

= V ⋅ exp − t τ , Vo = 

and τ4 = 6.8 ms. Current wave propagates along the stroke with the velocity ( ) 

o 

V 

8⋅10 7 m/s, and τV = 0.25 ms. Total length of the channel is 20 km. Initial electric moment is vertical. The 

horizontal current appears when ⎟ ⎛ V ⎞ o 

t > tk 

= τV ln ⎜ , the latter is necessary for reaching the ‘turning’ 

⎝τ 

VVo 

− zk 

⎠ 

altitude zk = 10 km. Reflections from the perfectly conducting ground are also included. 

Radiation component of electric field (components EX, EY, and EZ) was computed for an arbitrary 

point in neutral atmosphere. In the present treatment we find the spatial distribution of electric field above 

the Γ–shaped discharge and demonstrate its fine structure never mentioned in the literature. 

446 

k


Computed results 

Electromagnetic pulse (see Fig.1) originates from the vertical section of lightning and its reflection 

in the ground. Radiation from the horizontal section (the second pulse in Fig.1) appears after the current 

wave turns horizontally (t = 390 µs from the stroke initiation). Finally, the wave reflected from the ground 

provides the third pulse. Particular waveforms were computed at an observer altitude z = 80 km. Shown are 

the “Along” and “Across” positions. The origin of coordinate system is set at the base of the cloud-to-ground 

stroke. The horizontal branch is oriented along X – axis. Position “Across” is in the YZ plane (or x = 0) at a 

horizontal distance 50 km from the stroke base. Position “Along” is in the XZ plane (y = 0) and has the same 

horizontal distance. The abscissa in Fig.1 depicts the time in µs from the stroke initiation. Transient electric 

field is plotted on the ordinate in V/m. Component EX is depicted by the red line, EY – by blue, and EZ – by 

the black line. 

‘ACROSS’ ‘ALONG’ 

z = 80, x = 0, y = 50; z = 80, x = 50, y = 0. 

Fig.1. Pulses radiated by vertical and horizontal sections of the Γ–shaped stroke. 

Pulses from horizontal section are delayed with respect to those arriving from the vertical part of the 

stroke; this is caused by the finite velocity of the current wave. The third pulse corresponds to reflections 

from the ground. It has the opposite sign in comparison with the ‘direct horizontal’ signal. To obtain spatial 

distributions of electric fields, we computed temporal variations at positions ranging from 50 to 100 km 

vertically and from –50 to 50 km horizontally. The EX, EY, and EZ data allowed us to construct the spatial 

dependence of all field components for the fixed time moments. The 2D maps of these 3D distributions 

reflect the pulse interference in space. 

We depict in Fig.2 the ‘motion picture’ of vertical electric field EZ distribution for five particular 

times t ∈ [320; 440] µs varying with the 30 µs step. Two cross-sections are shown: the XZ (Along) and the 

YZ (Across) planes. Fine structure of the field is seen with a general upward progress of the pulsed fronts. 

The filament structure of the field arises from delicate interaction of delayed pulses coming to the elevated 

447


observation point. The model indicates that a powerful stroke with only two sections of current channel can 

form a complicated field structures in mesosphere. Such fields ‘warm up’ fragments of atmosphere thus 

supporting formation, motion, and branching of future sprite filaments. 

Fig.2. Spatial distribution of the EZ field component. 

Plots in Fig.2 indirectly show the ‘doughnut’ radiation pattern from the vertical section of the stroke, 

as might be expected (the red structure in the lower left frame and the crimson structure in the right one). The 

higher rows of plots correspond to the situation when pulses from the horizontal section of stroke reach the 

mesosphere. Particular arrival times depend on the distance and orientation of horizontal branch with respect 

to the observer. Therefore, different ‘hair comb’ distributions arise depending on the field component and the 

448


plane of observation. The positive fields are shown by reddish colors, and negative – by the blue palette. The 

first attract free electrons, while the second repel them. As a result, the atmosphere particles are subjected to 

the field, which might cause free electron bunching. It is worth noting that the field structure strongly 

depends on the position (along or across) of the observer. 

Obviously, electric field in the atmosphere is structured and variable within an arbitrary plane. We 

have shown two planes for the reason that relevant plots are highly symmetric, which is easily understood 

from simple considerations. 

Discussion and conclusion 

We considered spatial structures of transient electric field above a simple bent or Γ–shaped positive 

stroke. A fine constitution of electric field in space arises from the sequential radiation from vertical and 

horizontal sections of the lightning channel. The model was applied of a return stroke having single vertical 

and a horizontal section, each 10 km long. The current waveform and the velocity of current wave in the 

channel were borrowed from usual models of return strokes (e.g., Nickolaenko and Hayakawa, 2002). 

Physics of a bent lightning stroke was not addressed, as this is a separate and a complicated problem itself. 

We note that mere presence of two sections in the stroke channel causes the spatial effects demonstrated 

since a Γ–shaped stroke provides three delayed pulses in the atmosphere. These pulses cause a fine structure 

in space. 

The number of pulses increases when a stroke acquires additional sections. For example, a discharge 

of two vertical and two horizontal segments provides seven pulses. Hence, relevant spatial distributions of 

electric field may become much more complicated even when the horizontal sections remain collinear. It is 

obvious that particular distribution of the field and its temporal variation depend on the stroke morphology 

and on the particulars of current wave progress along the channel. Real strokes, such as ‘spiders’, have many 

sections and branches; these may cause an extremely sophisticated distribution of fields in space. 

A standard explanation of sprite development exploits the quasi-electrostatic field (Pasko, 2006), 

which slowly varies in time and space. In contrast, we turned to the radiation component alone and found 

complicated spatial structures. It is obvious that all the fields – the static, induction and radiation take part in 

the sprite formation. Radiation field decreases with distance as 1 r , but it has a smaller initial value than the 

2 

3 

static and induction fields. The induction and static field decrease faster, as 1 r and 1 r correspondingly. 

All three of them become equal at the distance where kr = 1, 

this is a classical definition of the ‘far zone’. 

By assuming r = 50 km, we find that the equality is held for f = 955 Hz. Hence, the radiation field will 

dominate in the mesosphere, as the spectrum of a typical stroke occupies frequencies much higher than 

1 kHz. 

Influence of atmospheric conductivity was ignored here, as is usually done at ‘high’ frequencies 

(Pasko, 2006). If one accounts for the finite conductivity, the electric field will decrease faster with distance; 

the details will be ‘smoothed’ in time and space, separate filaments might ‘blur’ or ‘merge’ owing to the 

wave dispersion, but the fine structure will not vanish completely. 

We found the downward/upward and sideways driving forces, which are highly structured in space. 

Future modeling should involve the complete fields including the pulsed ones. Incorporated in the motion 

equations, the transient forces will cause focusing of free charged particles on the time scales exceeding the 

pulse duration, as we discuss below. 

Consider a one-dimensional electron beam that moves upward with the velocity U0 = 5000 km/s, that 

corresponds to the particle energy of E = 1.14×10 −10 erg or to ~71 eV. Let a short pulse ∆E of the ∆t duration 

interact with the beam at altitude h0 = 60 km. We assume that the pulse simultaneously reduces the velocity 

e ⋅ ∆E 

by − ∆U 

= − ⋅ ∆t 

of all particles from the interval [h0 − ∆h; h0 + ∆h], and they loose the moment 

me 

∆ p = −∆E 

⋅ e ⋅ ∆t 

. Electrons from altitude interval [h0 − ∆h; h0 + ∆h] will lag behind the median flow, and 

the latter is maintained by the ‘background’ quasi-static field. Thus, a juvenile clustering of particles may 

appear in the beam, which we ignore. Further, a new pulse of opposite (positive) polarity arrives at the same 

altitude interval being delayed by τ = 10 ms. The positive pulse accelerates particles by increasing their 

e ⋅ ∆E 

velocity by ∆ U = ⋅ ∆t 

. 

m 

e 

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In our speculations, the decelerated electrons leave the altitude h0 with the velocity U − ∆U 

, while 

those accelerated have the velocity U + ∆U 

, but they are delayed by the time τ. Obviously, the particles of 

0 

the second group overtake the first group at some altitude above the h0. The vertical coordinate of each group 

varies in time as: z () t h + ( U − ∆U 

)t t = h + U + ∆U 

t −τ 

. They become equal at the 

1 = 0 0 and z2 ( ) 0 ( 0 )( ) 

U0 

+ ∆U 

1+ 

δ 

∆U 

time of bunching tb = τ = τ where δ = . Focusing (bunching) will occur at the height 

2∆U 

2δ 

U0 

1+ 

δ 

H b = h0 

+ τU0 

. One may observe that there is an important model parameter describing the 

2δ 

1 + δ 1 

‘extension’ of time: R = ≈ . This is the ratio of focusing time to the initial retard τ of second 

2δ 

2δ 

electric pulse. 

Let us substitute a particular value of δ = 1/200 velocity modulation or ∆U = 25 km/s, which is quite 

realistic. Indeed, if the characteristic duration of radio pulse is ∆ t = 0.2 µs, the necessary alteration in the 

electron mechanical momentum is ∆ U = e∆E∆t 

. The causative electric pulse has to be of 

m e 

me 

∆U 

∆ E = amplitude or, ∆E = 7 V/m. In other words, an electric pulse of 7 V/m amplitude and of 

e ∆t 

0.2 µs duration modulates the above postulated electron velocity U0 by the factor of 1/200. It is easy to 

calculate now that both groups of electrons will meet at the Hb = 60 + 5 = 65 km altitude, and the encounter 

is shifted in time by tb = Rτ = 1 ms from the onset of the paired electric pulse. Our elementary estimates 

provide quantities perfectly agreeing with the sprite observations. 

Structure of a real lightning stroke is more complicated than that of a simple Γ – shaped model. 

However, the simplest Γ – shaped model readily predicts focusing of free charged particles in the atmosphere 

above the stroke. 

To conclude the paper, we list the main results. 

1. Structured spatial distribution was obtained of the transient electric fields in the 

mesosphere above a Γ – shaped lightning stroke. The fine structure appears even in the simplest 

model containing vertical and a horizontal section. 

2. Characteristic size of filaments in the electric field distribution is about 1 km on the 

horizontal direction and reaches a few tens of kilometers along the vertical. 

3. The spatial distribution originates from the pulse series arriving at an elevated 

observer. Their superposition provides the structured electric field in space. 

4. Transient electric fields are able to cause focusing of free charged particles in the atmosphere. 

Such a mechanism must be included into advanced models of sprite development. 

Reference 

Nickolaenko, A. P., and M. Hayakawa (2002), Resonances in the Earth-ionosphere Cavity, 392 pp., Kluwer 

Acad., Dordrecht, Netherlands. 

Pasko, V.P., (2006). Theoretical modeling of sprites and jets, M. Füllekrug et al (eds.), “Sprites, Elves and 

Intense Lightning Discharges”, 253 – 311, © Springer. Printed in Netherlands. 

450 

0


STRESSES IN ROCK SAMPLES AND ELECTROMAGNETIC 

RELAXATION TIMES 

Lementueva R.A., Gvozdev A.A., Irisova E.L. 

Foundation of the Russian Academy of Sciences Shmidt Institute of Physics of the Earth RAS, 

Moscow, Russia, e-mail: leto@ifz.ru 

Abstract. The results of laboratory studies made on rock samples and models are given in the 

work. Samples were exposed to mechanical loading by means of press. The method of free 

relaxation of absorption current has been applied. Curves of the dependence of the decrement of 

absorption current on time have been obtained at different values of mechanical stress. The curves 

are not characterized by one, but a number of relaxation times-short and long. Short times changes 

are pronounced at the increase of stresses, but long relaxation times increase greatly. It is evident 

that the increase of relaxation times is connected with the formation of micro-cracks in the sample. 

The formation of the main crack leads to the streak decrease of long relaxation time. Thus 

relaxation times of absorption current characterize the change in the system of cracks. The results 

of the investigations can be applied in the development of new methods of natural studies in 

seismology. 

Introduction 

One of actual problems in geophysics is studying a process of destruction of rocks and changes of the 

geophysical fields observable during the formation of cracks. In a zone of preparing destruction there is a 

complex intense condition which leads to the generation and germination of cracks. In such zones significant 

anomalies of various geophysical fields are expected to develop. Fast and slow relaxation processes in electric 

fields at deformation of rocks are studied poorly. Practically mechanisms of occurrence of polarizability in 

complex stress conditions are not studied. In a number of works (A.V. Ponomarev and G.A. Sobolev) it was 

marked that the change of a seeming resistance is an effective precursor of preparing destruction of a file of 

rocks. However till now completely there are not clear the nature of anomalies and places of the most 

probable displays. Especially intensive processes of variations of resistance can develop close to 

nonhomogenities where there are the strongest concentration of pressure. The purpose of the given work is 

reception of the new information on polarizability of rocks, revealing of possible mechanisms of occurrence 

and a relaxation of charges in laboratory experiments. 

Methods 

Rocks can be presented as an imperfect dielectric with losses in parallel connected resistance and 

capacity. The general current arising under the action of an electric field, it is possible to present it as the sum 

defined by the formula: 

I = I3 + I0 + Ia , 

where I - general current through the dielectric, I3 - current of charge, I0 - residual current, Ia - current 

gradually weakening in due course. It is named reversible current of absorption, and the phenomenon of its 

occurrence - dielectric absorption (Sidorov, V.A.). Falling off of a current in due course can be described by 

means of a set of exhibitors and to present by the formula: 

Ia = 

A An τ 

− t − t t 

τ1 τ 

− 

2 

n 

0 + + ..... 

1 

Ae e e 

Thus, when studying a current of absorption (Ia) it is necessary to measure the rate of recession of the 

curve of polarizability. This method is known as a method of free relaxation of a current of absorption in 

absence of an external circuit (Sidorov, V.A.). 

For studying recession of a current of absorption from natural (pirophillit, sandstone, and others) and 

modeling (concrete) materials, different samples were made (fig.1). Samples of the rectangular form were 

451


made by the size 10х7х5 cm. Models of large-scale samples (fig. 1d) reached the size 200х70х50 cm. Cores 

had the sizes: height: 6- 7 cm, diameter: 5 cm. 

For loading we applied the press of 50 ton (Troitsk). Within 1-2 days before loading the measurements 

of background curves of recession of a current of absorption were spent at F=0, and average curve Ia = f (t) 

was under construction. In cycles loading measurements were carried out at stages of constant loadings, and 

before the measurement the sample or model were exposed to constant pressure within 3-4 minutes. The same 

process was repeated at other loading. On a surface of samples from pirophillit, limestone, and sandstone, 

measuring electrodes MN were fixed which were established in a stratified zone of lamination and a predicted 

zone of concentration of pressure. In the top and bottom parts of the sample there are current gauges A and B 

made of graphite paste; transitive resistance of contact to the sample was less than 2 kOm for models from 

concrete. 

Fig.1. Models. a - a core, b - a sample of the rectangular form, c - a sample of the rectangular form with 

concentrators, d - a large-scale sample from concrete. 

The model from concrete with the additive of a graphite dust was applied. In this case, the influence of 

a mineralization on the behavior of electric parameters was studied at loading. On large-scale model process 

of a relaxation of a current of absorption in a zone of asperity of blocks was studied at development of a 

condition of instability (Fig. 1d). On this sample in the work of R.A. Lementueva, V.I. Ponjatovskaya, E.I. 

Irisova, and V.A. Popov variations of various geophysical fields were investigated. In the given work it is 

experimentally shown that the process of a relaxation of current Ia is possible to study in a local site of the 

large-scale sample, in the case of break of asperity with the movement of the fault. 

Samples were humidified and contained 3 - 5 % of moisture. That provided a condition of rocks close 

to the natural one. 

452


Studying of electric processes was spent on the equipment described by Komarov, V.A. for method of 

caused polarization (ВП). The scheme of measuring installation presented in fig. 2, includes: MSVP device 

(Bobrovnikov, L.Z., L.I. Orlov, and V.A. Popov), batteries, the switchboard of a current, ballast resistance 

(Rk) and milliampermeter (mА). Gauges M and N (of “Radelkis”) were fixed to lateral surfaces of the sample 

by means of plugs from plexiglas. The stability of own potentials of electrodes is 0.1 - 0.2 mV. 

Fig.2. Scheme of measurements. 

The technique of supervision consists in the following. In the beginning natural electric potentials 

( Δ U0) between each pair of gauges N-M1 and N-M2 have been measured. Then through the sample an 

impulse of the stabilized current (I) runs of duration of 15 s with an amplitude 20 mА. At the passing of the 

impulse of current potentials ΔU were registered between the same pairs of gauges. 

After switching-off of current I = 20 мА potentials of the caused polarization (ΔUвп) were measured in 

0.25, 0.5, 1, 2, 7, 11, and 22 s. Laboratory installation allowed registration of potentials in time оf 1 upto 100 

sec. And by that limits of registration (t → 200 sec) extended. It is visible that the process of recession of a 

current of absorption Ia = Iaехр (- Δt 

) is characterized for various relaxations times (1, 2,. .n). 

τ 

The quantitative estimation of the observable phenomenon in an interval ( Δ t) can be received 

ln Ia = ln I0 — Δt 

τ . 

Having defined the time of relaxation, it is possible to speak about a degree of polarizability of 

environment, because it is known that τ = RC , С~ε , ε — dielectric permeability of environment. 

Results 

Curves of recession of a current of absorption depending on loading for various samples are shown in 

fig.3. The analysis of experimental data shows that curves of reduction of a current of absorption in due 

course, received at various mechanical pressure have an expotential appearance. As the received curve in halflogarithmic 

scale, is also similar to an exhibitor (instead of a straight line), we observe a number of processes 

of relaxation with various τ. In the received dependences of a current of the absorption presented in fig. 3а, b, 

c, d, it is possible to allocate conditionally fast and slow processes of relaxation. The first time of relaxation is 

defined, when Ia falls down in-е-time. In the field of “slow” (τi ≥ 20s) delay of relaxation was observed at 

increase of loading (F). At change of F (MPa) τi increased or decreased, depending on variation of loading on 

the sample. 

453


Curves of recession of a current of absorption depending on time at various loadings for various samples. a - 

rectangular sample from pirofillit, b - rectangular sample from limestone, c - model from the concrete mixed 

with a graphite dust, d - sample from concrete with concentrators of pressure; 1 – state before loading, 5 – 

state after loading. 

454


The change of loading Fmax up to 0, both τ1 and τ2 decreased (“fast” and “slow” relaxations). The stated 

laws of behavior of curves are well visible in fig. 3а (the sample from pirophillit) and 3b (the sample from 

limestone). Similar dependences have been observed for cores from sandstone. Curves are presented of model 

from the concrete mixed with a graphite dust (fig. 3c) and with concentrators of pressure (fig. 3d). 

Fig.3е. Attenuation of a current of absorption depending on time of large-scale model from concrete. 

Characteristics of the curve Ia for these models constructed in half-logarithmic scale is similar for 

pirophillit, however constants of time τ1 and τn of the relaxation are less and after loading removal (F→0) it is 

almost a straight line. 

Development of a status of instability in zone of modeled break as shown in the experiments 

[Lementueva, R.A., V.I.Ponjatovskaya, E.I.Irisova, and V.A. Popov], is in a direct communication with the 

process of accumulation of deformations under the influence of a tension and structural changes in the 

environment. It, in turn, is reflected in the character of dependence Ia = f (t). 

Experiments with large-scale model from concrete are presented in fig. 3е. In fig. 3e results of recession 

Ia for one pair gauges N – M1 are presented. At occurrence of a local break in asperity it is visible that there is 

an accelerated process of relaxation Ia (Fig. 3e, curve 2). However loading increase (curve 3) results in 

increase of time of relaxation. Durability of asperity in this time interval has increased because of a 

congestion destroyed parts of the material in the fault. Failure of asperity with advancement on a break is 

characterized by a curve 4 with character change exponent dependences at the point t = 11s. Current Ia falls 

down at first very slowly and curve — 4 shows that the state before of destruction of asperity is characterized 

by the big times of relaxation. Thus, as well as in the previous experiments, in a local deformable zone at 

modeling of a status of instability in a fault occurrence of big times of relaxation before the asperity failure is 

noted. There is a long steady polarization. 

455


Conclusions 

Results are presented of research of electrophysical characteristics of rocks under the influence of 

mechanical loadings on samples. The applied method of free relaxation of a current of absorption has allowed 

us to reveal the basic distinctions in behavior of a current of absorption Ia at micro- and macrodestruction of 

samples and models of rocks and at development (in model from concrete) statuses of mechanical instability 

in the environment. Relaxation time (τn) is a key parameter of process of an establishment and disappearance 

of volume polarization of rocks. On the basis of the resulted schedules acceleration of process of relaxation 

can testify to the occurrence of considerable infringements in the environment of rocks. Occurrence of big 

times of relaxation testifies that in a deformation zone there is an essential destruction, or the beginning of the 

main crack is formed. The constant relaxation τ in the absorption current is the characteristic of environment 

in the given time interval and can be used for the description of polarizability of rocks in various stages of 

loading. Definition τi on a curve constructed in half-logarithmic scale, allows us to calculate in each time 

interval times τn relaxations Ia. The received results, probably, will promote understanding of the processes 

which are taking place at destruction of rocks and for improvement of techniques of geophysical 

measurements. 


The work was partly supported by the grant RFFI № 06-05-64888-a. 

References 

Ponomarev, A.V., and G.A.Sobolev (2003), Earthquakes Physics and Precursors, Nauka, Moscow, 270 pp. 

(in Russian) 

Sidorov, V.A. (1987), About electric polarizability of non-uniform rocks, Izvestia Russian Academy of 

Sciences, Physics of the Solid Earth. No 10, 58–64. 

Lementueva, R.A., V.I. Ponjatovskaya, E.I. Irisova, and V.A. Popov (2007), Results of ultrasonic diagnostic 

and electrometric measurements at modeling of a fault of complex structure, Geophysical Researches, 7, 

65–73 (in Russian) 

Komarov, V.A. (1980), Electroinvestigation by a method of the caused polarization, Nedra, Leningrad, 90 pp. 

(in Russian) 

Bobrovnikov, L.Z., L.I. Orlov, and V.A. Popov (1986), Multichannel station of a method of the caused 

polarization, In: Electroprospecting Equipment: Handbook, Nedra, Moscow, 79–85 (in Russian) 

456


OPPORTUNITIES OF USING OF ELECTROMAGNETIC SIGNAL OF 

LIGHTNING DISCHARGES FOR THE REMOTE SENSING OF SEISMIC 

ACTIVITY 

V.A. Mullayarov 1 , V.I. Kozlov 1 , A.V. Ambursky 1 

1 Yu.G. Shafer Institute of Cosmophysical Research and Aeronomy SB of RAS, Yakutsk, 677980, Russia, 

e-mail: mullayarov@ikfia.ysn.ru 

By using of earthquake events in the Kamchatka region the opportunity of using electromagnetic 

signals of lightning discharges (atmospherics) for the remote sensing of seismic activity is 

considered. Variations of the amplitude of atmospherics, propagating in subionospheric waveguide 

above areas of earthquake epicentres reflect changes in the structure of electron concentration in the 

lower ionosphere occurring under the influence of litospheric processes. 

The characteristic attributes of variations preceding strong seismic events with no deep focus, 

(electromagnetic precursors of earthquakes) are revealed. The application of algorithm to the 

extended set of observational data for the winter periods of 2004-2006 has shown that the possibility 

of a short-term prediction of such earthquake events can reach 60 %. The reasons of "false alarms" 

(probability of 25 %) are not yet revealed. 


As is known the ionospheric variations were often associated with the seismic activity (Liu et el., 2000, 

Silina et al., 2001, Pulinets et al., 2004). They appeared a few days or hours before the seismic shocks of large 

intensity. These effects of seismic phenomena on ionospheric parameters were accompanied by changes in radio 

station signals whose paths are over quake epicenters (Gokhberg et al., 1989, Molchanov and Hayakawa, 1998, 

Rozhnoi et al., 2004, Soloviev et al., 2004). The nature of these changes depends on the signal frequency, path 

length, and on the conditions alone the path. At the same time there are natural sources of VLF emissions that 

can be used for probing the areas of seismic activity. Electromagnetic emissions during lightning discharges 

(atmospherics) are the most widespread and most suitable natural sources for this purpose. Although 

electromagnetic signals deriving from thunderstorm sources are substantially non-stationary, a sufficiently large 

flow of atmospherics should facilitate the acquisition of statistically significant results. 

In this work we examine the elementary algorithm of defining of alert days by a "blindly" retrospective 

analysis of amplitude variations in VLF signals caused by thunderstorms propagating above the earthquake 

epicenters in the Kamchatka region and recorded in Yakutsk (ϕ = 62º N, λ = 129.7º E). 

2. Methods 

The influence of processes of a preparing earthquake on the level of VLF-signals received in Yakutsk will 

take place, if the area of earthquake corresponds to the first Fresnel zones above the path "a storm source - point 

of signal receiving". The size of Fresnel zones F is determined by the distance d and wave length λ as F = (λ n 

d1d2/d) 1/2 , where d = d1+d2, d1 is the distance from a point up to a source, d2 is the distance from a point up to the 

receiver, n is the ordinal number of zone. 

Therefore for each chosen earthquake we defined the azimuth and distance up to Yakutsk by which we 

determined the first Fresnel zones. We choose those atmospherics whose azimuths correspond to the calculated 

Fresnel zones. And a minimal distance up to sources (discharges) must exceed the distance up to earthquakes by 

25 %. The average atmospherics amplitude received within an hour (average quantity is of the order 1000 and 

more) is determined. Preliminarily the signal amplitudes are led to the amplitude of one distance (a distance up 

to a seismic center), using as a first approximation the dependence of factor of attenuation, inversely 

proportional to a squared distance. 

3. Results 

Fig. 1 shows the variations of the hourly averaged amplitude of electromagnetic signals of lightning 

discharges - atmospherics, which has been already published for the Koryak event of strong earthquake 

(magnitude 7.6) that occurred on 20.04.06 (20th of April) at 23:35:05 UT. The azimuth on the Koryak seismic 

457


center is 76.3 degree, and the distance is 1953 km. The feature of this earthquake was that the great number of 

aftershocks was observed, and the high magnitude was up to 6.5. Variations of average atmospherics amplitude 

in the interval 06-26.04.2006 determined for night (a) and day time (b) hours are presented. The preliminary 

maximum of night atmospherics amplitude was observed on 10.04.06, 10 days before the earthquake, and the 

minimum - was on 16.04.06 (4 days before the earthquake). The effect of earthquake was displayed the next day 

after the event as a significant peak of atmospherics amplitude, exceeding the minimum level by a factor of 3. In 

the level of day time atmospherics the effect of earthquake is expressed even in the greater degree - the excess of 

the previous level was exceeded by a factor of 10. The day amplitude after that peak did not decrease, and night 

amplitude dropped on 3rd day, then it has again increased a little. Such behaviour of amplitude can be connected 

with a significant aftershocks' magnitude. 

The short-term (1-2-day) strengthening of amplitude of atmospherics, passing "precisely" above the future 

epicenter (within limits of the first Fresnel zone) was observed 10 days prior to the earthquake. Maximum in the 

distribution correspond to the earthquake azimuth (76 degree, Fig. 2). 

Fig.1. Variations of the mean night 

amplitude of the atmospherics received 

from the various azimuths before and 

during Koryak earthquakes 20-22.04.06. 

Fig.2. The azimuth distribution of the night 

amplitude of atmospherics at 10 days 

before the earthquake (20.04.06). 

Then, after the minimum within 3-4 days before the earthquake there was an increase in amplitude which 

has reached the maximum on the next day after the earthquake. The effect of earthquake (the increase of the 

atmospherics amplitude) was observed in an enough wide area corresponding to sizes of the fifth (and more) 

consequent Fresnel zones. 

The similar picture of behaviour of average atmospherics amplitude has been observed in a significant part 

of events of strong earthquakes. Results of consideration of amplitude variations of VLF-signal of the storm 

nature which are passing above areas of earthquakes with magnitude of more than 5, show that despite nonstationary 

state of their sources, their amplitude drops 3-6 days before earthquakes with its subsequent 

458


restoration by the day of events. The effect is similar to signal amplitude variations of low-frequency radio 

stations. 

It allows us to consider such behaviour as typical and try to formulate one of the possible elementary 

(primitive) algorithms for the detection of earthquake precursor. A steady increase of atmospherics amplitude 

within 4 days was defined as "alert" periods - or, really, the total increase of amplitude for such period must 

exceed the mean-square value of amplitude variations for the previous five days multiplied by a correcting factor 

(it has been calculated, that it equals 3). 

Such an algorithm has been checked up on the Kamchatka peninsula region. Without using of the 

earthquakes catalogue at the first stage by data of atmospherics received in Yakutsk for winter periods of 2004- 

2006 according to the considered algorithm the possible "alert" days of earthquakes have been defined. The 

azimuth 120º (from the northern direction), corresponding to the "center" of Kamchatka has been chosen as the 

most probable azimuth on seismic centers (within the limits of fifth Fresnel zone). 

The analysis of atmospherics amplitude variations for the specified period has shown 8 "alert" days which 

according to the algorithm can be interpreted as a precursor of earthquakes. Then these alert days were compared 

with the earthquake catalogue with magnitude more than 4.5, really occurred on the Kamchatka peninsula or in 

the nearest region. In Fig. 3 the earthquake epicenters are presented, where "+" represents the earthquakes with 

"alert" and "o" - represents the earthquakes with no "alert". One can see, the centers of earthquakes during the 

analyzed period were mainly located in two areas, one of which is closer to the chosen direction of atmospherics 

arrival. In this area practically all earthquakes have "alert" (5 of 7 days). At the same time, in the other region far 

from the selected direction of atmospherics arrival, only two alerts were defined. The recalculation of 

atmospherics amplitude in case when the azimuth corresponds to the direction of the second area of earthquakes 

gives an increase in probability of correct alerts. 

Fig. 3. Location the epicenters of 

earthquake with M > 4.3 at Kamchatka 

region for winter 2004-2006. The line is 

the direction from st. Yakutsk to “center” 

of Kamchatka peninsula. 

4. Discussion 

Thus, a control "blindly" ("in the dark") retrospective analysis using the elementary algorithm of defining 

alert days by average atmospherics amplitude has shown that the probability of such short-term forecast of 

earthquakes can be up to 60-70 %. 

Unfortunately, except the omitted earthquakes during the considered period the algorithm has defined 3 

false alerts. To find the possible reasons of such false alerts the Kamchatka volcano activity in these days and 

geomagnetic disturbances have been considered. Any specific activity of volcanoes has not been observed. Ар 

index is used as the parameter describing geomagnetic disturbances. The behaviour of average values of Ар 

index in the previous days by the moment's false alerts, is presented in Fig. 4 where a zero day corresponds to 

false alert days. One can see that the false alerts are generated on the 4th day after Ар maximum and they can be 

connected with such character of magnetic planetary disturbances. However, if we construct the picture of 

behaviour Ар (using the statistical superposed method) for all considered earthquakes (Fig. 5), then it is seen that 

against the background of quasi-periodic variations of Ар the event of earthquakes falls on the second day after 

the maximum of Ар index. 

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Thus, false alert days do not differ from events of earthquakes from the point of view of geomagnetic 

disturbances. So, we think that geomagnetic disturbances cannot be used to explain the false alert days. At the 

same time we see that the event of earthquakes were perhaps closely connected to geomagnetic disturbances. 

Fig.4. The behaviour of average values of 

Ар index in the previous days to the 

moments of 3 false alerts. 

Fig.5. The behaviour Ар (by the statistical 

superposed method) for all considered 

earthquakes. 


Results of consideration of amplitude variations of VLF-signal of the storm nature which are passing 

above areas of earthquakes with magnitude of more than 5, show that despite non-stationary state of their 

sources, their amplitude drops 3-6 days before earthquakes with its subsequent restoration by the day of events. 

The similar picture of behaviour of average atmospherics amplitude has been observed for a significant part of 

events of strong earthquakes. The effect is similar to signal amplitude variations of low-frequency radio stations. 

It allows us to consider such behaviour as typical and try to formulate one of the possible primitive 

algorithms for the detection of earthquake precursor. Such an algorithm has been checked on the Kamchatka 

peninsula region by data of atmospherics received in Yakutsk for winter periods of 2004-2006. A control 

"blindly" retrospective analysis using of the elementary algorithm of defining alert days by average atmospherics 

amplitude has shown that the probability of such short-term forecast of earthquakes is 60-70 %. 

References 

Gokhberg, M. B., Gufeld, I. L., Rozhnoi, A. A., Marenko, V. F., Yampolshy, V. S., and Ponomarev, E. A. 

(1989), Study of seismic influence on the ionosphere by superlong wave probing of the Earth-ionosphere 

waveguide. Phys. Earth Planet. Inter., 57, 64–67. 

Liu J.Y., Chen Y.I., Pulinets S. A., Tsai Y.B., and Chuo Y.J. (2000), Seismo-ionospheric signatures prior to M ≥ 

6 Taiwan earthquakes. Geophys. Res. Lett., 27, 3113-3116. 

Molchanov, O. A., and Hayakawa, M. (1998), Subionospheric VLF signal perturbations possibly related to 

earthquakes. J. Geophys. Res., 103, 17489–17504. 

Pulinets S. A., Gaivoronska T. B., Contreras A. Leyva, and Ciraolo L. (2004), Correlation analysis technique 

revealing ionospheric precursors of earthquakes. Natural Hazards and Earth System Sciences, 4, 697–702. 

Rozhnoi, A., Solovieva, M. S., Molchanov, O. A., and Hayakawa, M. (2004), Middle latitude LF (40 kHz) phase 

variations associated with earthquakes for quiet and disturbed geomagnetic conditions, Phys. Chem. Earth, 29, 

589–598. 

Silina A. S., Liperovskaya E. V., Liperovsky V. A., and Meister C.-V. (2001), Ionospheric phenomena before 

strong earthquakes. Natural Hazards and Earth System Sciences, 1, 113–118. 

Soloviev, O.V., Hayakawa, M., Ivanov, V.I., and Molchanov, O.A. (2004), Seismo-electromagnetic 

phenomenon in the atmosphere in terms of 3D subionospheric radio wave propagation problem, Phys. Chem. 

Earth, 29, 639–647. 

460


The anomalous resonance was observed during the period from the afternoon on March 24 to the 

morning on March 31. 

Figures 6 shows the largest anomalous resonance of the Bx component observed at 06:00 – 11:55 

L.T. on March 25, 2007, just before and after the earthquake. There is a strong anomalous resonance in Bx 

component marked with “C”, but there is no obvious anomaly in By component differently from the case of 

the 2004 Mid-Niigata Prefecture earthquake. Therefore we make a histogram of phase differences between 

By and Bx at the all frequency ranges from 19.53 Hz to 21.48 Hz. It is just the same as Figure 4. We can 

conclude this resonance is usual Schumann resonance (n=3). 

Next we analyzed the distribution of the frequency with the maximum intensity of anomalous 

strong resonance of Bx component, marked with “C”. The median frequencies of maximum intensity are 

18.06 Hz, 18.16 Hz, and 18.26 Hz, which are about 2 Hz lower than the typical frequency of Schumann 

resonance (n=3), being the same as the case of the 2004 Mid-Niigata Prefecture earthquake. The phase 

difference between By and Bx at the median frequencies (18.06 Hz, 18.16 Hz, and 18.26 Hz) is the same as 

Fig.5. 

As mentioned above, the temporal changes of the intensity of the anomalous resonances are almost 

the same between the anomalous Schumann resonance (n=3: 20 Hz) and another anomalous resonance 

(16.21 Hz and 18.35 Hz). Let us suppose that the intensity change of these anomalous resonances (20 Hz, 

16.21 Hz, and 18.35 Hz) was precursor of the earthquake and caused by the propagation anomaly in the 

ionosphere and/or atmosphere disturbed by any energy source from the epicentral region. 

In the case of the 2007 Noto Hantou earthquake, the third mode of the Schumann resonance is not 

so strong and the bandwidth is broad. This Schumann resonance arrived from the broad direction centered at 

20° - 25° by goniometer method. On the other hand, the anomalous resonance at the frequency centered at 

18.16 Hz has a strong intensity and a narrow bandwidth, and its resonant frequency is 2 Hz lower than the 

conventional frequency of n=3. This anomalous resonance is found to be very similar to the anomalous 

resonance observed before the 2004 Mid-Niigata Prefecture earthquake (lower strong resonance shown in 

Figure 3). 

However, the generation mechanism of this anomalous resonance is quite unknown and there is no 

convincing theory at the moment to explain both cases of the 2004 Mid-Niigata earthquake and the 2007 

Noto Hantou earthquake. However, there exists one possible generation mechanism of these anomalous 

ULF-ELF resonances (Sorokin et al., 2003). 

5. Conclusion 

We have observed the anomalous excitation of the Schumann resonances possibly associated with 

earthquakes since 1999 at Nakatsugawa station in Gifu prefecture in Japan (Hayakawa, et al., 2005; Ohta et 

al., 2006). In this paper we analyzed the anomalous Schumann resonance and an additional anomalous 

resonance observed before the 1999 Chi-Chi earthquake, the 2004 Mid-Niigata Prefecture earthquake and 

the 2007 Noto Hantou earthquake. The characteristics of anomalous resonances are: 

1. The intensity of a particular mode of the Schumann resonance increased before the large earthquake near 

the observation station, and decreased after the occurrence of earthquake. 

2. An excitation of another anomalous resonance was also observed at the frequency shifted by about 2 Hz 

from the typical frequency of the Schumann resonance. This anomalous resonance had a high Q factor and 

a strong intensity. 

3. Since the temporal changes of the intensity of the anomalous Schumann resonance and another anomalous 

resonance were almost the same, there is a possibility that another anomalous resonance was closely 

related with the Schumann resonance. However, we need to consider any convincible generation 

mechanism of anomalous resonances in future. 

4. There is a possibility that another anomalous resonance was received at Nakatsugawa as the induced 

magnetic field from the epicentral region (Sorokin et al. 2003). However, these anomalous resonances 

465


VARIATIONS OF VLF SIGNALS RECEIVED ON DEMETER SATELLITE 


IN ASSOCIATION WITH SEISMICITY 

A. Rozhnoi 1 , M. Solovieva 1 , Molchanov O. 1 

1 Institute of the Earth Physics, RAS, Bolshaya Gruzinskaya 10, Moscow, Russia, 

e-mail:rozhnoi@ifz.ru 

Abstract. We present two methods of the global ionosphere diagnostics using VLF signals received 

on board the DEMETER satellite in association with two cases of strong seismic activation. The 

method of reception zone changes reveals an evident effect before and during the great Sumatra 

earthquake with long-time duration of the order of one month. The result leads to the conclusion on 

the size of perturbation area of the order of several thousands kilometers. Disadvantage of this 

method is in its difficulty to separate preseismic and postseismic effects. In contrast, the difference 

method allows us to overcome this difficulty and it shows the appearance of preseismic effect for 

several days for seismic activation near Japan. However, we need such an analysis for reliability in 

regular satellite data to be checked by ground reception of subionospheric VLF signals. It is not so 

obvious that both of these satellite and ground effects are excited by the same generation 

mechanism on the ground. So, these look as complementary. 

During the last 10-20 years there have been attracted noticeable attention in the effects of ionospheric plasma 

related to seismicity, with keeping in mind both possibilities to use them for earthquake forecast and to study 

the fundamental problem of lithosphere-ionosphere coupling. There are two directions of this research. The 

first is in-situ observation of those effects, i.e. satellite observation. Numerous papers have already been 

published on such observations (see the reviews by Parrot et al., 1993; Molchanov et al., 2002). The second 

direction is far-distant remote sounding of the ionospheric perturbations in connection with seismic events by 

means of electromagnetic signals. Results of VLF sounding in different frequency bands have been 

published in many papers (Gufeld, et al., 1992; Hayakawa, et al., 1996; Molchanov and Hayakawa, 1998; 

Rozhnoi et al., 2004; Horie et al., 2007). 

We are going to discuss here the reception of VLF transmitter signals on board the DEMETER satellite. 

Such a reception was undertaken on many satellites for the investigation of VLF wave propagation and VLF 

wave interaction with ionospheric plasma (e.g. Inan and Helliwell, 1982; Molchanov, 1985). However, in the 

application of VLF signals to long-time seismic effects we need a special data processing both on board the 

satellite and on the ground in addition to the reception itself. Therefore it can be considered as a new method 

of ionospheric sounding in association with seismicity. 

2. Satellite VLF Data 

Here we will discuss only the data of electric field from a powerful Australian NWC (19.8 kHz) transmitter. 

As the main characteristic of a VLF signal, we compute the signal to noise ratio (SNR) as follows: 

SNR=/Amin, where is an average amplitude spectrum density in the frequency band including the 

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transmitter frequency F0 and Amin is the minimum value outside of the signal band..Due to large longitudinal 

distances between adjacent orbits (about 2500 km at the middle latitudes) we need the averaging period of, at 

least, 3-4 weeks in order to obtain statistically significant results and longitudinal spatial resolution of 

100-200 km. It dictates a selection of rather long periods of seismic activity related to very strong 

earthquakes or to a series of large earthquakes. We need to average the signal over fast variations and try to 

seek for slow changes in the reception zones during seismically active periods. We discuss two methods for 

revelation of the seismic influence: analysis of changes in reception zones for finding the large-scale space 

variation and analysis of SNR differences for finding of temporal variation during seismic activation. 

3. Change in reception zone 

As an example we analyse the reception zone of the NWC transmitter in relation to a strong earthquake 

activity near Sumatra which started with a great seismic shock on December 26, 2004 (magnitude M = 9). 

There were several strong shocks with following weaker ones until January 3, 2005 and the aftershock series 

continued until the summer of 2005 with new explosions of activity on March 28, 2005 (M=8.7, so-called 

Sumatra-2 earthquake) and on July 24, 2005 (M= 7.5). Fig. 1 shows the area of Sumatra activity and two 

reference zones with rather weak seismic activity during this period. 

Fig. 1. Seismic activity during the period from October 1, 

2004 to December 31, 2005. A triangle indicates the place 

of NWC transmitter, positions of the strong earthquakes 

with M> 6.6 are shown by solid circles, and the area of 

Sumatra activity is outlined by an open circle. Reference 

zones with rather weak seismic activity are outlined by 

circles with the numbers 2 and 3. 

We use DEMETER data during the period of more than 

one year from October 24, 2004 to December 31, 2006. In 

order to find a possible EQ influence we divide the 

observation period into the intervals with duration of 30 

working days, taking into account the missing days and 

keeping about the same volume of recording points. Then 

we compare the reception in the different time intervals 

both in the Sumatra area and in the reference zones. In 

such a way some seasonal variations can be expected. So we computed values averaged over the 

central part of the NWC transmitter reception zone for each month from October 2004 to August 2006 and 

found a small seasonal variation of the order of 25% with an increase in the winter time. Therefore we 

analyse the normalized SNR values: Sn = SNR/ and calculate the ratio p = N(Sn 1)/N0, where N0 is 

the total number of recording points and N(Sn 1) is the number of points with increased value Sn 1 inside 

the Sumatra area or inside the reference zones. The result is presented in Fig. 2. We conclude an essential 

depression of VLF signal intensity during the period of November-December 2004 only above the Sumatra 

468


area, which is probably connected with the preparation of seismic activity in this area. 

4. Difference method 

We use the method for correlated analysis of VLF subionospheric signals from transmitters located in Japan 

(JJY and JJI) and in Australia (NWC) that were measured at the ground stations and on board the 

DEMETER satellite. So we develop the satellite data processing which is similar to the processing of data at 

the ground station (Rozhnoi et al., 2004). 

Fig.2. Ratio of reception points with strong signals 

(Sn 1 ) to the total number of recording points 

inside the Sumatra area (second panel from 

above) and inside the reference zones (shown in 

Fig.1, first and third panels) together with 

magnitude difference (M-7) of the great 

earthquakes inside the Sumatra area (forth panel) 

and seismic energy released (fifth panel). 

For ground observation we use a residual signal of 

phase dP or amplitude dA defined as the difference 

between the observed signal and the average of 

quiet days of the current month. For satellite 

observation we calculate a “reference surface” 

(model) over the region of interest as a function of 

longitude and latitude. In this study, a simplified 

approach to compute this surface was used. The 

method consists in averaging all the data available 

in the considered region, regardless of the global 

disturbances, in particular, of the magnetic activity. 

The length of this period was selected equal to 2 

months in order to be not affected by the seasonal variations. The method of the local polynomial 

interpolation was used to build the reference surface with a longitude and latitude resolution of 0.32 ° . Using 

the reference surface, at any time and for any longitude and latitude, it is possible to define the residial VLF 

signal as the difference between the measured amplitude S (t, longitude, latitude) and the reference value Sm 

(longitude, latitude). 

We present here a comparison of satellite and ground reception during July-September 2005. There were 

several large EQs (M 6.2) at the area of Japan in this period, which occur inside or close to the sensitivity 

zone of our ground reception and inside of the satellite reception zone for NWC transmitter (19.8 kHz). 

Positions of these EQs are shown in Figure 3a for the ground reception and in Figure 3b for satellite 

reception (right rectangle). Additionally for the control of satellite reception we select another rectangle that 

is also inside of the reception zone but it is free from seismic activity (left rectangle in Fig. 3b). 

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A comparison of results of the satellite and ground observations is presented in Fig.4. Here we show the 

differences averaged over night time for the ground reception and differences averaged along the orbit 

crossing the seismic or reference area depicted in Fig. 3. By paying attention to the hatched regions, we 

notice an evident decrease in VLF signal both on the ground and on the satellite in association with 

seismicity. 

(a) (b) 

Fig. 3 (a) Map of earthquakes with M≥6.0 during the period of July-September, 2005. Sensitivity zones for 

the ground reception of Japan transmitters are shown by red line, NWC and NPM transmitters - by dash 

lines; (b) Reception zone of the NWC transmitter during the period of July-September, 2005 (model) 

registered on the satellite DEMETER together with the positions of large EQ epicenters. Red circles – EQ in 

sensitivity zone of wavepath JJY-PTK. The selected area for the analysis of VLF signal reception above 

Japan is outlined by A) rectangle on the right, and the control rectangle B) that is free from earthquake 

activity is shown on the left. 

5. Discussion 

We have presented two methods of the global ionosphere diagnostics using VLF signal received on board a 

satellite in association with two cases of strong seismic activation. The method of changes in reception zone 

reveals an evident effect before and during great Sumatra earthquakes with long-time duration of the order of 

one month. The result leads to the conclusion on the size of perturbation area of the order of several 

thousands kilometers, which is found to be in good agreement with the suggestion by the ground-based 

subionospheric VLF propagation (NWC-Japan path) (Horie et al., 2006). The disadvantage of this method is 

in its difficulty to separate preseismic and postseismic effects. In contrast, the difference method allows us to 

overcome this difficulty and shows the appearance of significant preseismic effect for several days for 

seismic activation near Japan. However, we need such an analysis for reliability in regular satellite data and 

in the check by ground reception of subionospheric VLF signal. It is not obvious that both the effects are 

excited by the same generation mechanism at the ground, so that those methods are complementary to each 

other. 

In general the methods of diagnostics discussed here have perspective to be global due to the world-wide 

470


positioning of powerful VLF transmitters and satellite reception. However, they have specific disadvantage 

because they require a rather long time period of analysis due to large longitudinal distances between 

satellite orbits. Above a fixed area in the same local time the satellite appears only once a day. As the result, 

we need, at least, one month period of registration for the longitudinal spacing of about 1000km. 

Fig.4. VLF signal differences in the ground observation for the wave paths: JJI-Kamchatka, JJY-Kamchatka, 

NWC-Kamchatka and NPM-Kamchatka and averaged satellite VLF signal differences observed on board the 

DEMETER from the reception of NWC transmitter: the solid line for the data above Japan, and dash-dot line 

for the data aside of Japan area (see Fig. 3b). Two panels below are Dst variations and EQ magnitude 

values. 

As a mechanism of the observed effects, we suggest the following: 

- Of course such a long-time and large-scale perturbation in the ionosphere cannot be produced by a seismic 

shock itself (duration of minutes) and we need to suppose some long-lasting agent, which influences the 

ionosphere around the date of an earthquake. 

- We believe that this initial agent is an upward energy flux of atmospheric gravity waves (AGW) which are 

induced by gas-water release from earthquake preparatory zone (e.g. Liperovsky et al., 2000; Molchanov, 

2004). 

- Penetration of AGW waves into the ionosphere leads to the modification of natural (background) 

ionospheric turbulence, especially for space scales ~ 1-3 km and wave numbers kT~ 10 -4 -10 -3 m -1 . This 

weak but reliable effect is revealed from direct satellite observations (Molchanov et al., 2004; Hobara et al., 

2005). 

- Resonant scattering of the VLF signals is possible on the following condition of the frequency- wave 

471


number synchronism : 0= s + T , k0 = ks+ kT, where 0, k0 are for the incident VLF wave, T, 

kT are for the turbulence and s, ks are for the scattering waves. It can be found that the amplitude of 

incident wave A0 decreases exponentially during the course of propagation through the perturbed medium: 

A0~ exp(- nATH), where n is the coefficient of nonlinear interaction, and H is the length of interaction 

region. In our case of VLF signals: T


SEISMIC TRAVELLING IONOSPHERE DISTURBANCES AT F2-REGION IN 

TIME OF HELIOGEOPHYSICAL DISTURBANCES 

N.P. Sergeenko, M.V. Rogova, A.V. Sazanov 

Pushkov Institute of Terrestrial magnetism, Ionosphere and Radio waves propagation, 

Troitsk, Moscow region, 142190, Russia, e-mail: serg@izmiran.ru 

Abstact. The properties of travelling ionospheric disturbances (TID) (their horizontal sizes are 1~ 

4 thousand kms, excesses from the background are 15-30 %), formed in F2 layer as a result of 

preparation of the strong earthquake in time of heliogeophysical perturbations are explored. The 

inhomogeneities arise 10-15 h before earthquakes and move horizontally with a transonic speed on 

distances of a few thousand kms up to round – the - world trajectories focused approximately 

along an arc of a major circle, transmitted above an epicenter region. Select of macro-scale 

irregularities was caused by spatial - time differences of dynamics of F2-layer of the ionosphere in 

time of the heliogeophysical disturbances from dynamics of quasi-causative seismic macroscale 

ionospheric inhomogeneities. 

The complex analysis of the arrays of critical frequencies of F2 - layer of the ionosphere (foF2) of 

a world network of automatic ground ionospheric stations of vertical sondage was carried out. As a 

result of these examinations, the geophysical patterns of ionospheric effects incipient at 

superimposition of macroscale inhomogeneities and ionospheric disturbances of solar and 

magnitospheric origin were synthesized. 

INTRODUCTION 

This work is devoted to the study of the possibilities of detection of traveling disturbances (TIDs) of 

seismic origin in the main peak of ionosphere at the time of heliogeophysical disturbances. The sizes of 

irregularities reach 1~3 thousand kms, lifetimes exceed 10 4 sec, and moving distances are 10~15 thousand kms, 

the speeds are approximate to sonic velocity. It was also established that the formation of TID precedes 10~15 

hrs to the moment of catastrophic earthquakes with magnitude М ≥ 6 and localization ~1 thousand kms from the 

epicenter of the earthquake (Kalinin and Sergeenko, 2002; Kalinin et al, 2003; Sergeenko and Kharitonov, 

2005). Perturbations of electron concentration, commensurable in sizes and contrast range with seismic TIDs, 

but completely different character of temporal and spatial changes, can appear on the conditions of ionospheric 

storms and substorms. Below we review features of occurrence of TID in quiet and disturbed heliogeophysical 

conditions. 

DATA ANALYSIS 

Files of values of relative variation of critical frequencies of F2 layer of the ionosphere by the global 

network of ionospheric stations of vertical sounding δfoF2 were used in the analysis as a main source of 

information about seismic TID: δfoF2 = (foF2- foF2m)/foF2m , foF2m – moving median [Gaivoronskaya et al., 

1971). {δfoF2} are used for detection and numerical characterization of ionosphere disturbances (Zevakina et 

al., 1990). It does not depend on multiplicative errors of representation foF2 due to the use of various scales at 

stations of vertical sounding, gives "protection" against inadequate influence of major "emissions" and excludes 

regular seasonal and daily variability. 

The seismic TIDs are selected as a local irregularity with extreme value (δfoF2)max ≥15 % at the middle 

latitudes and (δfoF2)max ≥10 % at low latitudes. It is also supposed that during of 2~3 hours diversion should be 

more than 10 %. Kp, Dst, and AE indices were used for the description of geomagnetic situation. 

The quite conditions. 

In fig. 1a we can see an example of variations δfoF2(t) for different ionospheric stations for the earthquake, 

which occurred at Alyaska on 09.03.1985 (ϕ=66,6N; λ=150,5W; t0=14 h 08 m UT; M=6,2), a vertical line marks 

473


the moment of the earthquake, an oblique line represents variant of propagation of signals most likely related to 

a developing earthquake. The appearing disturbances before the earthquake travel to Asia, Indian ocean and up 

to La Renion ionosphere station. The first signals are registered ∆t = -13 hours ahead of time. Amplitudes of 

signals are δfoF2(t) > 20 %. According to the data in fig. 1c, positive impulses appeared on quiet geomagnetic 

background: Kp ≤ 2, AE


Northen America at the left part of this figure. The variations of geomagnetic indices are presented in fig. 3c 

which testify that 01.03.1985 the moderate geomagnetic disturbance (Dstmax ~ -50 nT, Kpmax=6) was observed. 

Fig.2 δfoF2(t) variations at different ionospheric stations for the Caribbean earthquake on 16.03.1985 

The substorm has also taken place at ~5 h UT on disturbance background. The δfoF2(t) data in fig. 3b 

testify a biphase ionosphere disturbance in the F2 layer. All diagrams contain clear positive perturbations with 

amplitude 15~30 % and duration 5~7 hrs and in day local time beginning (5 h UT) on the first day of the 

geomagnetic disturbance. Approximately at 18 h LT the perturbation has transformed in a negative phase at all 

stations. It is obvious that when observed simultaneously on ionospheric stations located at various latitudes and 

longitudes the positive phase of ionosphere storm cannot be identified as seismic precursor, though they have 

happened in "the necessary" time. 

However, fig.3а illustrates the δfoF2(t) data on a chain of stations from Manila and Vanimo, posed in a 

region of forthcoming earthquake, through domestic stations in the Asia and Europe (Irkutsk, Tomsk, 

Sverdlovsk, Gorky, Moscow), posed approximately 5 thousands kms from the earthquake epicenter, up to north 

Africa station Ouagadougou. The positive impulses - harbingers of earthquake have appeared in a region of 

epicenter ~13 hrs before the beginning earthquake. The time delays of their occurrence at the relevant stations 

specify an apparent velocity of their travel ~1000 kms/hrs. In fig. 3c dotted line indicated a possible direction of 

a motion of these TIDs. 

In fig. 3а the chain of δfoF2(t) impulses with duration 3~4 hrs was observed both in day time, and in 

evening local time, while the positive phase of a biphase ionosphere disturbance usually occurs only in day time 

(06~18 hrs LT) and last not less than 7~8 hrs (Zevakina et al., 1990). 

475


Fig.3 δfoF2(t) variations at different ionospheric stations for the Indonesian earthquake on 1.03.1985 

DISCUSSION 

Situations are presented when apparent TIDs in F2 layer of the ionosphere are presumably linked with 

developing earthquake. We have given examples when they arose in quiet conditions, in conditions of isolated 

substorm on the backgrounds of quiet ionosphere and during ionosphere storm with positive initial phase. 

Undoubtedly, the above given examples do not cover entire spectrum of ionosphere variations. 

The changes of electron concentration of F2 layer from storm to storm are significant in the sense that two 

storms never existed with the same behavior of ionosphere parameters. The basic approach to select macro-scale 

irregularities consists of the use of differences in dynamics of ionosphere variations, characteristic for disturbed 

heliogeophysical conditions and in dynamics of TIDs, inconvertible under the shape and velocity of a motion, 

but with the casual moments of occurrence. Identifications of the dynamics of TIDs require processing data for 

the territories of hundreds of thousand square kms. 

Basic differences between TIDs and effects of magnetosphere perturbations in F2 layer are: 

♦During an ionosphere substorm electron concentration is incremented as a result of activity of zonal and 

meridian electric fields as well as under IGW in the day time after preliminary decrease (Brunelly and 

Namgaladze, 1988). The trajectories of movement of TIDs coincide with the arcs of the major circle, whereas 

the perturbations, which arise as a result of IGW generation during a substorm, are usually spread from high 

latitudes to low in a meridian direction. IGW generation is delayed by 1 hr with respect to the AE-index; 

♦Ionosphere storm represents a continuous process lasting from several hours to several days. Parameter 

variations have global character. In the absence of AE outbursts, positive impulses recorded in δfoF2(t) on the 

background of negative storm phase can be related to seismic TIDs. Positive perturbations of electron 

476


concentration can be observed during ionosphere storms at the transitional and low latitudes; as well as at the 

midlatitudes in the early stages ionosphere storm, if this storm begins at a day time. 

CONCLUSION 

The above reviewed situations demonstrate that diagnostics of seismic TIDs is quite possible in many 

cases, as there are essential differences in the character of time and spatial changes allowing us to distinguish 

these disturbances from perturbations of solar and magnetosphere origin. However data configurations that are 

submitted in figs. 1~3, are not possible for all earthquakes. One of the reasons is in actual properties of a 

network of ionosphere stations - nonuniform spatial arrangement and, naturally, only on land. Other difficulties 

are the detection of TIDs on the background of other disturbances in the ionosphere. It is represented that this 

short-term harbinger could be the essential block in blanket algorithm of the seismic-ionosphere forecast. 

REFERENCES 

Kalinin, U.K., Sergeenko, N.P. (2002), Mobile solitary macroinhomogeneities appearing in the ionosphere 

several hours before catastrophic earthquakes. Doklady of Russian Akademy of Sciences / Earth Science 

Section, 387(1), 105-107. 

Kalinin, U.K., Romanchuk, A.A., Sergeenko, N.P. Shubin, V.N. (2003) The large-scale isolated disturbances 

dynamics in the main peak of electronic concentration of ionosphere. Journal of Atmospheric and Solar 

Terrestrial Physics, v.65, issue 11-13, 1175-1177. 

Sergeenko, N.P., A.L. Kharitonov (2005) Short-time magnetosphere – ionosphere predictors of catastrophe 

earthquakes. Investigations of Earth from Space. №6, 61-68. (Russian) 

Gaivoronskaya T.V., Sergeenko N.P., Udovich L.A. (1971) Deviations of critical frequencies of F layer from 

median values, in Ionospheric disturbances and their influence on a radio communication, Moscow, Nauka, 

55-73 (Russian) 

Zevakina, R.A., N.P., Sergeenko, E.M.Zgulina, G.N. Nosova (1990) Text-book of short-time forecast of 

ionosphere, 71 pp, Materials of the World Data Center B. (Russian) 

Brunelly B.E., Namgaladze A.A. (1988) The Physics of Ionosphere, 527 pp. (Russian) 

477


TESTING OF THE METHOD FOR THE CONVERSION OF THE MT 

APPARENT RESISTIVITY CHANGES INTO THE RELATIVE CHANGES 

IN THE ROCK ELECTRICAL RESISTIVITY 

USING THE 2D MODEL OF THE GEOELECTRIC STRUCTURE 

Marina E. Sholpo 

SPbF IZMIRAN, Russian Academy of Sciences, Muchnoy 2, St.Petersburg, 191023, Russia, 

e-mail: msholpo@mail.ru 

Abstract. A method for direct conversion of observed variations in magnetotelluric apparent 

resistivity ρa into relative variations in the resistivity of elements of a well-studied geoelectric 

structure is tested on a 2-D model structure of Petropavlovsk geodynamical polygon. It is shown 

that (1) the study of the frequency and spatial dependences of the sensitivity of ρa to changes in the 

resistivities of the structure elements allows us to choose the optimal observation regime and (2) 

the application of the proposed method makes it possible to define relative changes in the rock 

resistivity with sufficient accuracy. 

The MT apparent resistivity is extensively investigated at present as a possible prognostic parameter in many 

geodynamic research areas. But it is clear that these researches can hardly be effective, if the source of the 

variations in the apparent resistivities ρa is unknown. If we have in mind that the cause of variations in ρa is 

the changes in the rock resistivity (that is the seismic- electrical effect of first kind) then the direct relative 

variations in the resestivity of elements of a geoelectric structure are a more effective prognostic indicator 

compared to observed variations in the magnetotelluric apparent resistivity. In this connection the method for 

the separation of the contributions of individual elements of the geoelectric structure to the variations in the 

apparent resistivity is proposed. It is the method for the estimation of the relative variations in the 

resistivities ρi of some elements of the geoelectric structure responsible for variations in ρa.. It reduces to the 

construction and solution of the following system of equations: 

∏ xi aij = сj, j = [1, m]. 

i 

Here i is the number of the structure element ( it is comfortable to give to this number the value of the 

structure element resistivity in Ω m), xi = ρi2 /ρi1 is the relative change in the resistivity of the ith element of 

the structure, aij = εiav(Tj) is the [ρi1, ρi2]-averaged sensitivity of ρa to changes in the resistivity of the ith 

element of the structure at the electromagnetic field period Тj, cj=ρa2j /ρa1j , were ρa1j and ρa2j are the apparent 

resistivities at two different moments at the jth period, and m is the number of the periods used. (We remind 

the reader that the sensitivity of ρa to changes in the resistivity of the ith element of the structure is defined 

here as a value that determines the relation between relative variations in the resistivity of the ith element of 

the structure and the corresponding relative variations in the apparent resistivity: εi (ρi,Tj) = dlogρa/dlogρi = 

(dρa/ρa)/ (dρi/ρi) [Sholpo, 2003].) Taking the logarithm of these equations, we obtain the system of linear 

equations. The solution of the latter involves no fundamental difficulties if the values ρa1, 2 are determined 

with a sufficient accuracy in the entire range of required periods. The main problem in the realization of this 

method is the correct determination of the aij = εiav (Tj) using numerical modeling of a well-studied 

geoelectric structure. 

The results of testing of this method on a 1D model structure were published in [Sholpo, 2006]. This 

article is dedicated to its testing on a 2D structure. 

Testing of the proposed method was performed using 2D model of Petropavlovsk geodynamical 

polygon (Kamchatka). The geoelectric model of this polygon includes three deep and a few surface high 

conductive elements (Fig.1. The numbers within the model are electrical resistivities in Ω m). 

Figure 2 presents spatial dependences of maximal values of the function εi(√ T) calculated for i = 8, 

10, 20, 30 at the number of points of profile AA. Taking into account the investigation purpose and using 

these dependences it is possible to determine the best place for MT monitoring. 

478


A x, km A 

depth, km 

Fig. 1. Geoelectric structure of the earth crust at Petropavlovsk geodynamical polygon (Kamchatka) 

1.2 

0.8 

0.4 

0.0 

ε i max 

20 

30 

0 40 80 

8 

10 

x km 

Fig. 2. Spatial dependences of maximal values of the function εi(√T) on the profile AA 

i = 8, 10, 20, 30 – the numbers of the structure elements and its resistivities in Ω m 

ε8 --------------------------------- √T = 3.5 - - - - - - - - - - √T = 5 

ε10 --------------------------------- √T = 14 - - - - - - - - - - √T =17 

ε20 --------------------------------- √T = 12 - - - - - - - - - - √T =17 

ε30 --------------------------------- √T = 1 

At the same time it is necessary to study the frequency responses εi in the different points of the profile, 

because the possibility of the separation and the accuracy of the estimation of contributions of the individual 

elements of the geoelectric structure are dependent on the correlation between the periods of its maximums. 

Thanks to that it is possible to determine the optimal frequency interval. Figure 3 presents the frequency 

responses of ρa sensitivity to variations in the resistivity of four structure elements for the profile points with 

x = 37, 45, 60km. 

479


1.0 

0.5 

0.0 

1.0 

0.5 

0.0 

1.0 

0.5 

0.0 

ε i 

20 

1E-4 1E-3 1E-2 1E-1 1E+0 

10 

20 

x = 47 km 

1E-4 1E-3 1E-2 1E-1 1E+0 

10 

20 

10 

x = 37 km 

1E-4 1E-3 1E-2 1E-1 1E+0 

8 

8 

8 

x 

fHz 

f Hz 

= 60 km 

Fig. 3. The frequency responses of the ρa sensitivities to variations in the resistivities 

of the structure elements for three points of the profile AA: x = 37, 45, 60 km 

i = 8, 10, 20, 30 – the numbers of the structure elements and its resistivities in Ω m 

The results of the method testing at these points for two variants of changes in the resistivities of three 

deeps elements are given in Table 1. The matrices of the coefficients aij were calculated for these points. It 

should be noted that the matrix A is the characteristic of the given point placed on the surface of the given 

structure. It can be calculated once for all if geoelectric structure is studied well enough to perform numerical 

modeling. Owing to that the conversion of apparent resistivity changes into relative changes in rock 

resistivity can be easily produced. 

In Table 1 ρi1 and ρi2 are the resistivities of the ith structure element at two different moments; (ρi2/ρi1)r 

– the real relative changes in the resistivities of the ith element; (ρi2/ρi1)c – the values calculated using the 

tested method; δ% – the relative error of (ρi2/ρi1)c; ”noise” – the errors introduced into the apparent 

resistivities ρa1 and ρa2; εi max – the maximal value of the function εi(Tj) at the present points. To construct the 

columns of free terms of system of linear equations bj = lg cj = lg (ρa2/ρa1), the values ρa1 and ρa2 are 

calculated for the sets of given values ρi1 and ρi2 for the optimal interval of periods Tj using the program by 

Vardaniants. To make the model problem even more realistic, the errors typical of the accuracy of the 

present-day MTS studies (3-5 %) are introduced into the values ρa1 and ρa2. As can be seen from Table 1 the 

variations in the resistivity of 20th element are determined rather roughly at the all points. This could be 

expected because ε20max is small and at the point x=37 km the frequency response maximums of ε10(Tj) and 

ε20(Tj) are located at close frequencies (Fig.3). Because of this the relative changes in resistivity of 10th 

element are determined at this point with the greater errors as at others. The point x = 47 km is most 

favorable for the investigations of 10th and 8th elements but at this point the errors δ20 are also too great. To 

observe the variations in the resistivity of the 20th element it is reasonable to choose the observation point at 

the beginning of the profile, for example at x=14.5. Here it is possible to neglect the influence of the 8th 

element and to solve the system of linear equations for two unknowns (Table 2). Thus, in present case it is 

480 

30 

30 

30 

f 

Hz


impossible to observe the changes in the resistivity of all three deep structure elements with the sufficient 

accuracy using only one observation point. 

Table 1. Results of the testing of the method at three points of the profile AA( x = 37, 45, 60 km ) 

for two variants of the changes in the resistivity of three structure elements 

1 Variant 1 Variant 2 

2 i 10 8 20 10 8 20 

3 ρi1 Ω m 9 7 15 10.5 7 22 

4 ρi2 Ω m 11 9 25 9.5 9 18 

5 (ρi2/ρi1)и 1.222 1.286 1.667 .905 1.286 .818 

6 x = 37 km, ε10 max = 0.75, ε8 max = 0.20, ε20 max = 0.25 

7 (ρi 2/ρi 1)э 1.287 1.189 1.484 .873 1.324 .898 

δ% 5.3 7.6 11.0 3.5 3.0 9.8 

8 δ%(noise 3%) 20 13.4 38 13.3 7.7 75 

9 x = 47 km, ε10,max = 0.77, ε8,max = 0.91, ε20,max = 0.17 

10 (ρi 2/ρi1)э 1.234 1.260 1.673 .899 1.298 .825 

δ% 0.9 2.1 0.3 0.5 0.9 0.9 

11 δ%(noise 3%) 2.8 1.8 17 1.4 1.2 7.1 

12 δ%(noise 5%) 7.6 1.6 37.8 7.1 1.7 23 

13 x = 60 km, ε10,max = 0.74, ε8,max = 0.51, ε20,max = 0.14, 

14 (ρi2/ρi1)э 1.219 1.229 1.753 .904 1.311 .812 

δ% 0.2 4.4 5.2 0.1 2.0 0.7 

15 δ%(noise 3%) 2.9 4.4 10.5 3.1 3.0 20 

16 δ%(noise 5%) 6.0 5.0 23.5 6.0 2.8 32 

Table 2. Defining of the changes in the resistivity of 20th structure elements 

by the observations at the point x = 14.5 km 

i 10 8 20 

(ρi2/ρi1)и .905 1.286 .818 

εi max .45 .0038 .40 

(ρi 2/ρi 1)э 

δ% 

δ% 

(noise 3%) 

( ρi 2 /ρi 1)э 

δ% 

δ% 

(noise 3%) 

0.906 

1.685 

0.799 

0.1 

31 

2.3 

6.6 281 12.4 

0.882 

0.859 

2.5 

4.9 

4.9 10.1 

481


To investigate the influence of the surface layer on the results of the estimations of the values of the 

relative variations in the resistivities ρi there was studied a model where to three deep elements the fourth 

one with the number i = 30 was added (see Fig.1). The results of the calculations of the values ρi2/ρi1 at the 

point x = 47 km for the changes in the resistivity of four structure elements are given in Table 3. As is seen 

the introduction into the model of the surface element capable of time- change of its resistivity does not 

increase the errors of the determining of the relative variations in the resistivity of the deep structure 

elements, which is evidently the consequence of the isolated position of the frequency response maximum of 

ε30 (Fig.3). 

Table 3. Results of the testing of the method at the point x = 47 km in case of the changes 

in the resistivities of four structure elements. 

I 10 8 20 30 

ρi1 Ω m 10.5 7 22 20 

ρi2 Ω m 9.5 9 18 40 

(ρi2/ρi1)и .905 1.286 .818 2 

εi max .77 .91 .17 .51 

(ρi 2/ρi 1)э 

δ% 

δ% 

(noise 3%) 

.903 

.2 

1.303 

1.3 

.812 

.7 

2.05 

2.5 

4.4 1.8 21.9 2.7 

Conclusions 

(1) To choose the regime of observations of variations in the rocks conductivity suitable for the investigation 

aim it is needed to study the frequency and spatial dependences of the sensitivities εi(T, x) using numerical 

modeling of a well-studied geoelectric structure. 

(2) The application of the proposed method in optimal points of observation allows us to estimate values ρi2 / 

ρi1 with accuracy sufficient for monitoring of relative changes in the electrical conductivity of rocks. 

References 

Sholpo, M.E. (2003), Magnetotelluric monitoring of variations in the electrical resistivity of a conducting 

layer: numerical modeling. Physics of the Solid Earth, Vol. 39, No. 2, 112-117. 

Sholpo, M.E. (2006), Monitoring of relative changes in the electrical conductivity of rock from 

observations of the magnetotelluric apparent resistivity (numerical modeling). Physics of the Solid Earth, 

Vol. 42, No. 4, 323-329. 

482


Introduction 

FRACTAL CHARACTERISTICS OF ULF EMISSIONS 

REGISTERED IN THE HIGH LATITUDE 

SEISMIC-QUIET REGION OF SPITSBERGEN ISLAND 

N.A. Smirnova, A.A. Isavnin 


nsmir@geo.phys.spbu.ru 

Abstract. ULF frequency range (f = 0.001-5Hz) is now considered as a promising one for manifestation 

of electromagnetic earthquake precursors. To support the registration of ULF emissions in seismicactive 

areas, and to exclude magnetospheric effects from the lithospheric ones, the reference stations in 

seismic quiet but magnetic active regions are required. Here we are starting to analyze the magnetic 

field data obtained with high resolution (10 Hz sampling rate) in the high latitude seismic-quiet region 

of Spitsbergen Island (Barentsburg station, Φm=76° N; Λm=115°). Fractal analysis of the ULF data has 

been fulfilled using Higuchi method and Burlaga-Klein approach. The first preliminary results of the 

fractal analysis are presented. Variations of the fractal dimensions of the ULF emissions time series are 

considered along the local time. The possible physical interpretation of the results obtained is suggested. 

A possibility of using the Barentsburg observatory as a reference station in seismo-electromagnetic 

research is discussed. 

One the most important tasks in geophysics is the study of precursors of earthquakes. Nowadays it is known that 

earthquakes are related to weak seismogenic ULF emissions (see Hayakawa and Fujinawa (eds), 1994). But the 

problem of analyzing these signals is that they are strongly screened by ULF emissions of the magnetospheric 

origin (Smirnova, 1999). So the analysis may be strict only during the calm “space weather” time. In this work 

we are starting to analyze the magnetic field data in the high latitude seismic-quiet region of Spitsbergen Island. 

This region is situated at the cusp latitude – the most sensitive area to magnetic field disturbances. Because of its 

extremely high sensitivity to the solar wind conditions it can be used as a reference station for the research of 

seismogenic electromagnetic emissions. 

There is also an important task to monitor the position and size of the cusp area. 

Experimental data 

In Fig.1 you can see a principle scheme of the magnetosphere of the Earth. There are two cusp areas in the 

magnetosphere corresponding to two poles of the dipole field of the Earth. Each of the cusps is situated between 

closed and opened magnetic field lines. It is clear that dependent on the solar wind conditions the geographical 

position of the station can fall into the zone of opened or closed magnetic field lines. So it is important to learn 

out if the station is situated in the cusp during the 

analyzed period of time (the magnitude gap of 

cusp area is very narrow). For this aim we will 

use the Tsyganenko model of magnetosphere to 

project the cusp area on the Earth's surface 

according to parameters of the solar wind. 

Comparing the magnetic field behavior during the 

periods when the station falls into the projection 

of the cusp area on the Earth's surface with 

parameters of solar wind we will exclude the 

fluctuations of the magnetic field caused by 

inhomogenities in the solar wind. After such 

filtering we will obtain the magnetic field data 

with most of fluctuations in ULF frequency range 

Fig.1. The scheme of the Earth's magnetosphere. One can 

see the polar cusps between opened and closed magnetic 

field lines (the so-called points of bifurcation). 

caused by lithospheric effects, not magnetospheric. Analyzing such “clean” data and confronting it in time with 

registered lithospheric events and finding correlation parameters between them could give us some sort of 

483


prediction mechanism. 

In this work we are giving preliminary results of data analysis showing the possibility of filtering magnetic field 

data from the magnetospheric effects. 

Until recent times few measurements were held at the cusp latitudes and most of them were recorded with low 

resolution such as 1/60Hz. Using such data we couldn't resolve ULF-range effects in the magnetosphere of the 

Earth. In this work we are starting to analyze for the first time the magnetic field data with frequency of 10Hz 

obtained from the Barentsburg observatory – high latitude station with coordinates 78°N, 14°W (local time 

UTC+1 hour) and magnetic coordinates Φm=76°N, Λm=115°. Currently we have available data for the January 

2008. An example of the magnetic record at Barentsburg (H-, D- and Z- components) for the chosen date – 5 th 

January 2008 is presented in Fig.2. 

Methods of data analysis 

Fig.2. The magnetic field data for the 5 th January 

2008 obtained at the Barentsburg observatory. The 

x-axis denotes local time (LT). One can see two 

rather strong distrubances near 21:00 LT and 00:00 

LT. 

We use two fractal methods of spectrum analysis in our research. These are Higuchi method (Higuchi, 1988, 

1990) and Burlaga & Klein method (Burlaga and Klein, 1986). Here we present a short discription of each of 

them. 

1. Higuchi method. 

Consider a set data X(n) with fixed sampling rate. K new time series can be obtained from these data using 

formula: 

X k 

m 

⎧ 

⎛ ⎡N −m 

⎤ ⎞⎫ 

= ⎨X(m), 

X(m+ 

k), X(m+ 

2k ), ... , X ⎜m 

+ ⎢ ⋅ k ⎟⎬ 

⎩ 

⎝ k ⎥ 

⎣ ⎦ ⎠⎭ 

Then we can get the length of the curves representing the obtained time series as: 

⎛⎡N 

−m⎤ 

⎜ 

⎢⎣ k ⎥⎦ ⎜ 

Lm(k) 

= ⎜ ∑ 

⎜ i= 

1 

⎜ 

⎝ 

| X(m+ 

ik) − X(m+ 

(i −1) 

⋅k) 

| 

Finally we find the total length of the curve depending on k as 

L(k) 

⎞ 

⎟ 

N −1 

⎟ 1 

⋅ ⎟⋅ 

⎡N −m⎤ 

k 

⋅k 

⎟ 

⎢ 

⎣ k ⎥ 

⎦ ⎟ 

⎠ 

(m = 1, 2, ... , k) 

−D 

If L( 

k ) ∝k 

then the time series X(n) is considered to be a fractal one with dimension D. 

= 

k 

∑ 

m= 

1 

484 

L 

k 

m 

(k)

2. Burlaga & Klein method. 

The main difference between the Burlaga & Klein method and the Higuchi method lies in their operation of 

averaging the time series before calculating the curve length. If assume k = 3 then the curve lengths are: 

L BK 


( 3) 

As the k interval becomes larger the curve length defined by Burlaga & Klein method tends to be shorter, 

although the fractal dimension D tends to be larger than the real value. 

So it is clear that the Higuchi method is better suited for analyzing time series with low resolution. This is 

especially actual in the case of ULF emissions with frequences lying in the range 

In our work we use the magnetic field data with resolution 10 Hz obtained in Barentsburg, Spitsbergen. Such a 

high resolution allows us to investigate appropriately the fractal properties of ULF emissions in the frequency 

range from f=0.001 Hz up to f=1-2 Hz. We have applied the Higuchi method of data processing to obtain more 

stable values of scaling exponents and fractal dimensions of the ULF emission time series. 

Results 

⎧ 

⎨ 

⏐ ⏐X 

= 

⎩⏐ 

⎧ X 

3 = ⎨ 

⎩ 

( ) 

L H 

( 4) 

+ X ( 5) 

+ X ( 6) 

X ( 1) 

+ X ( 2) 

+ X ( 3) 

X ( 7) 

+ X ( 8) 

+ X ( 9) 

X ( 4) 

+ X ( 5) 

+ X ( 6) 

3 

⎫ 

− ⏐ 

+ ⏐ 

− 

⏐ 

+ …⎬ 

/ 3 

3 ⏐ ⏐ 3 

3 ⏐ ⎭ 

5 − X 2 + | X 6 − X 3 | | X ( 7) 

− X ( 4) 

| + | X ( 8) 

− X ( 5) 

| + | X ( 9) 

− X ( 6) 

| ⎫ 

+ 

+ …⎬ 

/ 3 

3 

3 

⎭ 

| ( 4) 

− X ( 1) 

| + | X ( ) ( ) | ( ) ( ) 

485 

10 10Hz 

3 − 

÷ 

Here we present the results of our analysis of the 

magnetic field data for the 5 th January 2008. To 

find out how fractal dimension varies during the 

24-hour period we calculated the dynamics of 

fractal dimension (see Fig.3). 

We held our calculation using the following 

algorithm. For every 10 th -minute interval we 

compose the corresponding time series of the H-, 

D- and Z- component variations, each of which is 

contains 6000 points (taking into account the 10Hz 

resolution). Then we apply the Higuchi method to 

the obtained time series beginning from the current 

timestamp. So given that, every horizontal stroke 

on our plots denotes 10 minutes gap between 

calculations. 

From Fig.3 one can see the pronounced daily 

dynamics of the ULF emissions fractal dimensions 

in all of the three magnetic components (H, D, and 

Z). There are several extremums in those 

dynamics, the most of which correspond to the 

critical times (00:00, 03:00, 06:00, 09:00, etc.). 

But also there are extremums, which are not 

concerned with daily rotation of the Earth. These 

peculiarities might show the movement of the 

station between zones with opened and closed 

magnetic field lines and also they can reflect the 

interaction of the magnetosphere with solar wind 

(or both effects mixed). 

Fig.3. The dynamics of fractal dimension 

calculated for the H- (top), D- (middle), and Z- 

(bottom) components of ULF emissions registered 

at Barentsburg station on 5 th January 2008. The 

Higuchi method was used for this calculation.


Discussion and conclusions 

From the results obtained we see the convenience of fractal methods for study of the behavior of the ULF 

emission source system. We see that fractal dimension of the ULF emissions time series in its dynamics “feels” 

the changes in magnetosphere such as terminators and other fluctuations of magnetic field and reflects them as 

extremums. The next step of our research is to consider the correlation between the dynamics of the ULF 

emissions fractal dimensions and solar wind parameters and exclude variations caused by magnetospheric 

effects. 

To get the more definite conclusions concerning the origin of the extremums revealed, it is necessary to monitor 

the position and size of the cusp. For such a forthcoming research we will use the Tsyganenko model 

(http://geo.phys.spbu.ru/~tsyganenko/Geopack-2008.html), which allows us to calculate the projection of the 

cusp on the Earth's surface. That will give us a possibility to relate appropriate peculiarities in the ULF emissions 

fractal dynamics with moment of ingress of the Barentsburg station into the entire cusp region. 


We thank Polar Geophysical Institute for provided data of Barentsburg station and especially Yury Katkalov – 

the developer of the DMS (the database system for collecting and processing geophysical data). 

The work was supported by RF President Grant “Leading Scientific School” 1243.2008.5 and Program 

RNP.2.2.2.2.2190 of Russian Ministry of Education “Intergeophysica”. 

References 

Burlaga L.F. and L.W. Klein (1986), Fractal structure of the interplanetary magnetic field, J. Geophys. Res., 91 

(A1), 347-350. 

Hayakawa M. and Y. Fujinawa (eds, 1994), Electromagnetic Phenomena Related to Earthquake prediction, 677 

pp.,Terra Scientific Publishing Companym Tokyo, Japan 

Higuchi, T. (1988), Approach to an Irregular Time Series on the Basis of Fractal Theory, Physica D, 31, 277- 

283. 

Higuchi, T (1990): Relationship between the Fractal Dimension and the Power-low Index for a Time Series: a 

Numerical Investigation, Physica D, 46, 254-264. 

Smirnova, N. (1999), The peculiarities of ground-observed geomagnetic pulsations as the background for 

detection of ULF emissions of seismic origin, in: Atmospheric and Ionospheric Electromagnetic Phenomena 

Associated with Earthquakes, edited by M. Hayakawa, Terra Sci. Pub. Co., Tokyo, 215-232. 

Tsyganenko, N.A. (2008), http://geo.phys.spbu.ru/~tsyganenko/Geopack-2008.html 

486


PECULIARITIES OF THE ULF EMISSION FRACTAL 

CHARACTERISTICS OBTAINED AT THE STATIONS OF 210 GM 

A.A. Varlamov, N.A. Smirnova 


nsmir@geo.phys.spbu.ru 

Abstract. Magnetic records (1Hz sampling rate) of the 5 stations (Guam, Moshiri, Paratunka, 

Magadan and Chokurdakh) located from equatorial region to auroral zone approximately along the 

same geomagnetic meridian (210 MM) have been analyzed using Higuchi method of fractal analysis. 

The period of 22 months (October 1992 – July 1994) that embodies the date of the strong Guam 

earthquake of 8 August 1993 has been considered. Comparison of the ULF emission scaling 

parameters (spectral indexes β and fractal dimensions D) obtained at different latitudes has been 

fulfilled. Dependence of β and D on Kp index of geomagnetic activity has been separately analyzed for 

each of 24 local time intervals. The results obtained are considered on the basis of the SOC (Selforganized 

criticality) concept. A possibility of using the data of the 210 GM stations as reference 

materials for the Guam seismic active area is discussed. 

Introduction 

In a series of papers by Smirnova and Hayakawa (see References), the specific dynamics of fractal 

characteristics of ULF emissions registered at the Guam observatory in relation to the strong Guam earthquake 

of 8 August 1993 has been reported. Namely the spectral exponents β were decreasing and the corresponded 

fractal dimension D was increasing when approaching the date of the Guam earthquake. It is also revealed that 

scaling parameters of the ULF time series are influenced by geomagnetic activity. So the local seismoelectromagnetic 

phenomena are screened by magnetospheric effects, which are of more global character. To 

distinguish between these effects the data from reference stations are necessary in addition to the Guam data. 

Here we consider coordinated magnetic records (1Hz sampling rate) of the 5 stations located approximately at 

the Guam geomagnetic meridian (210 MM stations). The purpose is to compare the fractal properties of ULF 

emissions along meridian profile and try to answer the question which station could be used as a Guam reference 

point in seismio-electromagnetic research. 

Experimental Data 

Magnetic records (ΔН, ΔD, ΔZ – components) used for our analysis were obtained at the 210 MM stations 

by means of ring-core-type fluxgate magnetometers with sampling rate 1 second. The chain of stations includes 

Chokurdakh (CHD), Magadan (MGD), Paratunka (PTK), Moshiri (MSR), Guam (GAM) and covers a wide 

range of latitudes from auroral zone to the equator (see the Table 1) 

Table 1. The list of the stations used for analysis 

Abbreviation geographic geomagnetic 

GAM 13.58° N 144.87° E 5.61° N 215.55° E 

MSR 44.37° N 142.87° E 37.28° N 213.55° E 

PTK 52.94° N 158.25° E 46.17° N 226.02° E 

MGD 59.97° N 150.86° E 53.49° N 218.75° E 

CHD 70.62° N 147.89° E 64.66° N 212.14° E 

The observation period covers 20 months from October 1992 to July 1994 This period embodies the date of 

a strong M8 Guam earthquake of 8 August 1993: depth = 60 km, Φ=12.98° N, Λ= 144.80° E. An example of the 

typical record obtained at Paratunka is given in Fig. 1. In this study we have analyzed the data in each of the 24 

daily 1-hour intervals. In the insertion to Fig. 1, one can see the enlarged 1-hour record (ULF emission) for 16- 

17 UT. So each analyzed time series, which represents ULF emission in 1-hour interval, contains 3600 points. 

We apply fractal methods to analyze scaling (fractal) characteristics of ULF emissions and study their dynamics 

in each location in relation to geomagnetic activity as well as in relation to the strong Guam earthquake of 8 

August 1993. 

487


Fig. 1 An example of the typical magnetic record, (Paratunka, 15/10/92) 

Fractal approach 

Now it is recognized that the extended dissipative dynamical systems evolve naturally to the state of selforganized 

criticality (SOC). The SOC state is characterized by high sensitivity of the system to any external 

perturbations and a fairly broad energy spectrum of dissipation events. The Earth’s magnetosphere and 

lithosphere were shown to exhibit this type of behavior. The fingerprints of the SOC state are fractal 

organization (power-law distributions) of the output parameters in both space and time domains (scale-invariant 

structures and flicker-noise or 1/f fluctuations). Hence we can use fractal methods for analysis of spatiotemporal 

scaling characteristics of the magnetospheric and lithospheric emissions. 

Three methods of fractal analysis have been considered: 1) PSD method (Feder, 1989; Turcotte, 1997); 

2) Burlaga-Klein method (Burlaga and Klein, 1986); 3) Higuchi method (Higuchi, 1988, 1990). Time series can 

be considered as fractal ones in the chosen frequency range, if its PSD (power spectra density) S(f) follows the 

power law at those frequencies: S(f) ~ 1/f β Spectral exponent β, and fractal dimension D, characterize the rate 

of irregularity of the time series. β and D are connected via the Berry equation (Berry, M.V. ,1979 ): D = (5 - β ) 

/ 2. The more advanced fractal approach is Higuchi method. It gives more stable values of fractal dimensions. 

The method is based on the estimation of length of fractal curve X(N). We consider the ULF data with sampling 

rate of 1s as a time sequence X(1), X(2), …, X(N). From given time series k new time series are constructed, 

defined as follows: 

N m 

X X( 

m), 

X ( m k), 

X ( m 2k), 

..., X m k ( m 1, 

2, 

..., k) 

k 

Then we estimate the length of the curves, which represents the new time series for each k: 

k ⎧ 

⎛ ⎡ − ⎤ ⎞⎫ 

m = ⎨ + + ⎜ + 

⎢ ⎥ 

⋅ ⎟⎬ 

= 

⎩ 

⎝ ⎣ ⎦ ⎠⎭ 

⎛ ⎡ N −m 

⎤ 

⎞ 

⎜ ⎢ 

k 

⎥ 

⎟ 

⎣ ⎦ 

N 1 1 

Lm 

( k) 

⎜ 

− 

= X ( m ik) 

X ( m ( i 1) 

k) 

⎟⋅ 

⎜ ∑ + − + − ⋅ ⋅ 

i 1 

⎡ N − m⎤ 

⎟ 

= 

k 

⎜ 

⎢ 

⋅k 

⎟ 

⎝ 

⎣ k ⎥ 

⎦ ⎠ 

N − 1 

where ⎡ N − m ⎤ is a normalizing factor. Then the total length of curve is defined as follows: 

⎢ 

⋅ k 

⎣ k ⎥ 

⎦ 

k 

∑ Lm 

( k ) 

m = 1 

< L( 

k ) > = 

k 

And finally, we plot versus k (ex. k=1, 2, …, 10). 

−D 

If L( 

k) 

∝ k and scales linearly in log-log presentation then 

we can consider this time series as fractal ones and estimate 

fractal dimension from the slope of curve (see Fig. 2). 

Fig. 2. Examples of the calculation of the ULF emission 

fractal dimension using Higuchi method. 

488


Results 

1. Dynamics of the ULF emissions fractal dimensions at the stations along 210 geomagnetic meridian. 

489 

We have obtained 24 sets of the results representing 

dynamics of the ULF emissions fractal dimensions 

along the 210 MM profile in each 1-hour daily 

interval. One example of such dynamics for 11-12 UT 

interval is shown in Fig. 3. 

One can see the following peculiarities: 

1) Daily fluctuations of D exhibit chaotic dynamics at 

each of the 5 stations of 210MM. It is difficult to 

understand whether such fluctuations are random ones 

or represent deterministic chaos. Those fluctuations 

may contain the influence of the magnetospheric, 

ionospheric, lithospheric, processes as well as effects of 

the man-made origin. 

2) Averaging over ± 5 days (running average values of 

D) exhibits some features of deterministic behavior. 

Namely the distinct modulation of D with periods near 

27 days is outlined, which corresponds to rotation of 

the Sun around its axes. So it is definitely a 

magnetospheric effect that is confirmed by the 

corresponding variations of Kp-index (see the bottom 

panel). 

3) Going to the longer time variations of D, one can 

reach the effect revealed earlier in the reference papers. 

Namely that is gradual increase of the ULF emissions 

fractal dimension before the Guam earthquake of 8 

August 1993 (marks by an arrow). That may be an 

earthquake precursory effect. According to our analysis 

this effect is more pronounced in the H-component of 

Guam, and it just vanishes in the Moshiri, Paratunka 

and Magadan data. What about Chokurdakh, lots of 

gaps in the data do not allow us to trace such a 

tendency. 

4) The modulation by the 27-day period is the most 

pronounced in the auroral zone (Chokurdakh), where it 

is manifested in the H, D and Z components. At the 

other stations, which are situated inside the 

plasmasphere, the modulation is observed in the H and 

D components, and never in Z-component. As to the 

Guam station, which is situated in the region of 

equatorial electrojet, such a modulation is seen also in 

Z component 

5) The range of variations of D (see H-component) is 

wider at the stations of auroral zone (Chokurdakh) and 

equatorial electrojet region (Guam) in comparison with 

inside-the-plasmasphere stations (Magadan, Paratunka, 

Moshiri). 

Fig. 3. Dynamics of D along 210 MM. Thin curves - 

daily values, the thick ones - ± 5 day running average 

value.


2. Dependence of the ULF emissions fractal dimensions from Kp index of geomagnetic activity 

Chokurdakh 

Magadan 

Paratunka 

Moshiri 

Guam 

490 

Some results to study the correlations 

between fractal dimensions of ULF 

emission time series and the Kp – 

index of geomagnetic activity are 

presented in Fig. 4. From the left part 

of Fig. 4 one can see that fractal 

dimensions of the ULF emissions 

time series decrease with increasing 

of magnetic activity at all stations, 

but the rates of the decrease are 

different at different stations and in 

different time intervals. The 

dependence of D on Kp is the most 

pronounced in the auroral zone 

(Chokurdakh), and it is rather smooth 

at the middle latitudes (Magadan and 

Paratunka). Near the equator (Guam) 

it becomes again sharper. From the 

right part of Fig. 4 one can see daily 

variation of the correlation 

coefficients between D and Kp. This 

variation is more regular in the 

middle latitudes (Magadan, Paratunka, 

Moshiry) with a pronounced 

maximum near 15 UT and minimum 

around 4 UT. As to the auroral zone 

and equatorial region (Chokurdakh 

and Guam) the maximum is not so 

pronounced there, and it is spread 

over the time interval 10-20 UT. But 

the minimum is also around 4 UT, 

which corresponds to local time near 

the noon (14 LT). So we may 

conclude that the evening, night and 

early morning hours are preferable 

for studying magnetospheric effects 

whereas the noon hours are the most 

suitable for analysis of lithospheric 

effects. 

Fig. 4. 

At the left - examples of the plots 

representing fractal dimensions of the 

ULF time series (H-component, 11- 

12 UT) versus Kp-index for all 

stations. 

At the right - daily variations of the 

correlation coefficient between D and 

Kp along meridian profile (the Hcomponent).


Discussion and conclusions 

We have obtained rather pronounced dynamics of the ULF emission fractal dimension D along 210 MM 

profile, which reflects the global magnetospheric effects as well as some local processes at each of the 5 stations. 

One can see magnetospheric effects from the thick lines (± 5 days running average values of D) in Fig. 3 as a 

modulation of D with the same period near 27 days. That is a characteristic period of the Sun rotation, and it is 

clearly seen from the corresponding modulation of the Kp index of geomagnetic activity at the bottom panel in 

Fig. 3. In the horizontal components H and D, this effect is pronounced at all the stations, but in the vertical 

component Z, it is more visible near the projection of characteristic electrojet locations: auroral electrojet - 

Chokurdakh station, and equatorial electrojet – Guam station. At the stations situated inside the plasmasphere, 

which are Magadan, Paratunka and Moshiri, the modulation of the 27-days period is practically disappeared in 

Z-component. So in order to exclude magnetospheric effects from the horizontal components of the Guam 

station, all the other stations of 210 MM are appropriate. But to exclude magnetospheric effects from the vertical 

component of the Guam station, the station Chokurdakh belonging to auroral zone is more recommendable, if 

there is no other reference station situated near auroral electrojet projection. As to the preferable local hours for 

analyzing lithospheric effects, the noon hours (near 4 UT or 14 LT) are the most suitable, since influence of 

geomagnrtic activity on the fractal properties of ULF emissions is depressed near the noon hours (see Fig. 4). 

The following conclusions have to be done from the analysis fulfilled. 

1. Our analysis shows that the results of the fractal analysis of the data from 210 MM chain of stations may give 

a support to the results of the Guam station data analysis when we attempt to distinguish between 

magnetospheric and lithospheric effects. 

2. Since magnetospheric effects are of global character, they give the correlated part in the results obtained at all 

the stations. Lithospheric effects could be of individual and local character at each of the station. So we have to 

manage how to remove the correlated part from the raw 210 MM results. Now we are working in this direction. 

3. We understand that our results are of preliminary character, and they need to be checked and confirmed on the 

other independent materials. Nevertheless we may conclude that the peculiarities revealed can be used as control 

factors in the forthcoming investigations of the earthquake precursory signatures based on the analysis of scaling 

(fractal) characteristics of ULF emissions. 


The work was supported by RF President Grant “Leading Scientific School” 1243.2008.5 and Program 

RNP.2.2.2.2.2190 of Russian Ministry of Education “Intergeophysica”. We thank Prof. M. Hayakawa and 

Prof. K. Yumoto for the experimental data of 210 MM. 

References 

Hayakawa, M., T. Ito, and N. Smirnova (1999), Fractal analysis of ULF geomagnetic data associated with the 

Guam earthquake on August 8, 1993. Geophys. Res. Lett., 26, 2797-2800 

Higuchi T. (1988), Approach to an irregular time series on the basis of the fractal theory, Physica D, 31, 277-283 

Higuchi, T (1990), Relationship between the Fractal Dimension and the Power-low Index for a Time Series: a 

Numerical Investigation, Physica D, 46, 254-264. 

Smirnova, N. (1999), The peculiarities of ground-observed geomagnetic pulsations as the background for 

detection of ULF emissions of seismic origin, in Atmospheric and Ionospheric Electromagnetic Phenomena 

Associated with Earthquakes, edited by M. Hayakawa, Terra Sci. Pub. Co., Tokyo, 215-232. 

Smirnova, N., M. Hayakawa, and K. Gotoh (2004), Precursory behavior of fractal characteristics of the ULF 

electromagnetic fields in seismic active zones before strong earthquakes, Phys.Chem. Earth, 29, 445-451. 

Turcotte, D.L. (1997), Fractals and Chaos in Geology and Geophysics, 398 pp., Cambridge University Press, 

Cambridge, New York, Melbourne, 2nd edition. 

491


SIMULATIONS OF THE EQUATORIAL IONOSPHERE RESPONSE TO THE 

SEISMIC ELECTRIC FIELD SOURCES 

Zolotov O.V. 1 , Namgaladze A.A. 1 , Zakharenkova I.E. 2 , Shagimuratov I.I. 2 , 

Martynenko O.V. 1 

1 Murmansk State Technical University, Murmansk, 183010, Russia, 

e-mail: ZolotovO@gmail.com, NamgaladzeAA@mstu.edu.ru; 

2 West Department of IZMIRAN, Kaliningrad, Russia, 

e-mail: Zakharenkova@mail.ru 

Abstract. The results of computer simulations of the equatorial ionosphere response to the additional 

electric fields of presumably seismic origin have been presented and discussed. The effects are the 

equatorial anomaly reduction (or increase in some cases) with trough deepening and symmetric 

shifting of the double-peak TEC (and NmF2) maxima from the earthquake epicenter. The obtained 

results have been compared with GPS (Global Positioning System) IGS network data for the Peru 

earthquake of 26 September, 2005. The presented numerical results well reproduce observed features 

of the equatorial ionosphere behaviour before strong earthquakes. 

Introduction 

It has been proposed that earthquakes are preceded by electromagnetic signals penetrating into the ionosphere 

and detectable from ground- and space-based measurements. Many papers are reported on anomalous 

ionospheric TEC (total electron content) disturbances as earthquake precursors generated by additional electric 

charges of a single sign, namely, positive (Pulinets, 1998; Pulinets et al., 2003; Pulinets and Boyarchuk, 2004; 

Liu et al., 2004). 

This paper presents the results of the computer Upper Atmosphere Model (UAM) simulations of the equatorial 

ionosphere response to the hypothetic seismic electric field sources of different spatial configurations. We 

previously made similar numerical simulations described in the paper (Zolotov et al., 2008) but for the midlatitudinal 

cases. This work is a further development of that investigation but for the low-latitudinal sectors 

where F-region ionospheric plasma is strongly driven by the electric field. The obtained results are compared 

with the TEC differential maps for the Peru earthquake of September 26, 2005 derived from the GPS TEC data 

of the IGS (International GNSS Service) network (Dow et al., 2005). 

Observations 

Fig. 1 presents differential TEC (%) maps for September 20-28, 2005 calculated relative to the background quiet 

conditions on the basis of GPS TEC IGS network data. For details on features of the TEC disturbances see 

(Zakharenkova et al., 2008). Fig. 2 shows the geomagnetic activity for September, 2005. It is clear that such 

activity cannot generate investigated local large-scale disturbances in the TEC of the ionosphere. 

Simulations and model results 

Numerical experiments were carried out by means of the first-principle global 3D Upper Atmosphere Model 

(UAM) (Namgaladze et al., 1988, 1991, 1998). The UAM model describes the thermosphere, ionosphere and 

plasmasphere of the Earth as a unite system by means of numerical integration of the corresponding timedependent 

three-dimensional continuity, momentum and heat balance equations for neutral, ion and electron 

gases as well as the equation for the electric field potential. It calculates electric fields both of thermospheric 

dynamo and magnetospheric origin and seismogenic electric fields as well. 

The upper atmosphere states, presumably foregone by strong earthquakes, were modeled by means of switchingon 

additional electric field sources (Fig. 3) in the UAM electric potential equation solved numerically jointly 

with all other UAM equations (continuity, momentum and heat balance) for neutral and ionized gases. These 

sources of different kinds and spatial configurations were switched on at the near-epicenter area and maintained 

as constant during 24 model hours. Two types and eight spatial configurations are taken into considerations: 

492


(1) the dipole that consists of a pair of positive and negative potentials at the western and eastern boundaries of 

the near-epicentral area (Fig. 3, dip1); (2) the dipole elongated in the meridianal direction for ~1500 km (Fig. 3, 

dip2); (3) the point monopole charge that consists of one positive charge at the epicenter (Fig. 3, mono1); (4) the 

fulfilled rectangular regions of positive charges (Fig. 3, mono2-mono3); (5) positive charged (equipotent) 

straight lines of different directions (Fig. 3, mono4-mono6). 

ϕ 30 

02 UT 

ϕ 30 

02 UT 

ϕ 30 

02 UT 

20 

20 

20 

10 

10 

10 

0 

0 

0 

-10 

-10 

-10 

-20 

-20 

-20 

-30 

-30 

-30 

-40 

-40 

-40 

-50 

-90 -80 -70 -60 λ 

-50 

-90 -80 -70 -60 λ 

-50 

-90 -80 -70 -60 λ 

20.09 

21.09 22.09 

02 UT 02 UT 02 UT 

ϕ 30 

ϕ 30 

ϕ 30 

20 

20 

20 

10 

10 

10 

0 

0 

0 

-10 

-10 

-10 

-20 

-20 

-20 

-30 

-30 

-30 

-40 

-40 

-40 

-50 

-50 

-90 -80 -70 -60 λ 

-50 

-90 -80 -70 -60 λ -90 -80 -70 -60 λ 

23.09 24.09 25.09 

ϕ 30 

02 UT 

ϕ 30 

02 UT 

ϕ 30 

02 UT 

20 

20 

20 

10 

10 

10 

0 

0 

0 

-10 

-10 

-10 

-20 

-20 

-20 

-30 

-30 

-30 

-40 

-40 

-40 

-50 

-90 -80 -70 -60 λ 

EQ day 

-50 

-90 -80 -70 -60 λ 

-50 

-90 -80 -70 -60 λ 

26.09 27.09 28.09 

-40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100 

% 

Fig. 1. TEC diff. (%) maps at 02 UT for September 20-28, 2005 relative to the none-disturbed conditions. Black 

spot – the earthquake epicenter position. 

Kp 

Ap 

Dst, nT 

0.5 

0 

1 

1.5 

2 

2.5 

3 

3.5 

4 

4.5 

5 

01 08 15 22 EQ 29 

40 

35 

30 

25 

20 

15 

10 

5 

0 

01 08 15 22 EQ 29 

50 

0 

-50 

-100 

-150 

-200 

01 08 15 22 EQ 29 

Fig. 2. Dst-, Ap- and Kp- indexes for the September, 2005. EQ – the earthquake day. 

493


Fig. 3. Numerical grid and additional electric field sources: plus for positive sources, minus – for negative ones, 

grey points – not modified nodes. 

Fig. 4. Latitudinal variations of the electric potential (top left panel), the eastern component of the electric field 

(top right panel) and corresponding TEC variations (%) (bottom panel). Red line (top panels) stand for the 

none-disturbed level. 

494


Calculated latitudinal and longitudinal electric field variations and corresponding TEC variations relative to the 

background quiet conditions are presented graphically in Figs. 4-5. 

Fig. 5. Longitudinal variations of the eastern electric field (bottom panel) and corresponding TEC (%) 

disturbances (top panel) for earthquake modeled (left) and magnetically conjugated (right) points. 

Figs. 4-5 show that magnitudes of the eastward electric field are less than 5-6 mV/m for simulated data both for 

the epicenter and magnetically conjugate areas. The symmetry of the potential and electric field concerning the 

geomagnetic equator is caused by the ideal conductivity of the ionospheric plasma along the geomagnetic field 

lines and, accordingly, by their electric equipotentiality. The corresponding TEC (%) disturbances reach 80% 

and more. 

Variations of the TEC disturbances for the low-latitude region (Figs. 4-5) have the form and the structure of the 

equatorial anomaly (“trough”). The increase of the eastward electric field leads to the deepening of the equatorial 

anomaly minimum (“trough” over the magnetic equator in the latitudinal distribution of electron density) due to 

the intensification of the fountain-effect. The dipole-like and single sign (positive) additional electric field 

495


sources generate similar disturbances in the TEC of the ionosphere (in contrary to the mid-latitudinal cases). The 

noticeable difference is the magnitude of these variations: the dipole-like sources generate deeper equatorial 

trough. The amplitude of the peaks (the “camel case” maxima) remains nearly the same or slightly greater. That 

behaviour agrees well (at least qualitatively) with the presented Peru earthquake of 26 September, 2005 TEC 

variations (Fig. 1) detected at the earthquake near-epicenter area for a few days before and after the main shock. 

The work was supported by grant No. 08-05-98830 of the Russian Foundation for Basic Research. 

References 

Dow J.M., Neilan R.E., Gendt G. (2005), The International GPS Service (IGS): Celebrating the 10th 

Anniversary and Looking to the Next Decade, Adv. Space Res., Vol. 36, No. 3, pp. 320-326. 

doi:10.1016/j.asr.2005.05.125. 

Liu J.Y., Chuo Y.J., Shan S.J., Tsai Y.B., Pulinets S.A. and S.B. Yu (2004), Pre-earthquake ionospheric 

anomalies monitored by GPS TEC, Annales Geophysicae, 22, pp. 1585 -1593. 

Namgaladze A.A., Korenkov Yu.N, Klimenko V.V, Karpov I.V, Bessarab F.S, Surotkin V.A, Glushchenko T.A, 

Naumova N.M. (1988), Global model of the thermosphere-ionosphere-protonosphere system, Pure and App. 

Geophys., Vol. 127, No. 2/3, pp. 219-254. 

Namgaladze A.A., Korenkov Yu.N., Klimenko V.V., Karpov I.V., Surotkin V.A., Naumova N.M. (1991), 

Numerical modelling of the thermosphere-ionosphere-protonosphere system, Journal of Atmospheric and 

Terrestrial Physics, Vol. 53, N. 11/12, pp. 1113-1124. 

Namgaladze A.A., Martynenko O.V., Namgaladze A.N. (1998), Global model of the upper atmosphere with 

variable latitudinal integration step, International Journal of Geomagnetism and Aeronomy, 1 (1), pp. 53-58. 

Pulinets S.A. (1998), Seismic activity as a source of the ionospheric variability, Adv. Space Res., Vol. 22, No. 6, 

pp. 903-906. 

Pulinets S.A., Legen’ka A.D., Gaivoronskaya T.V. and Depuev V.Kh. (2003), Main phenomenological features 

of ionospheric precursors of strong earthquakes, Journal of Atmospheric and Solar-Terrestrial Physics, 

Vol. 65, pp. 1337-1347. 

Pulinets S.A. and Boyarchuk K. (2004), Ionospheric Precursors of Earthquakes, Springer, Berlin, Germany. 

Zakharenkova I.E., Shagimuratov I.I., Tepenitzina N.Yu., Krankowski A. (2008), Anomalous Modification of 

the Ionospheric Total Electron Content Prior to the 26 September 2005 Peru Earthquake, Journal of 

Atmospheric and Solar-Terrestrial Physics, doi:10.1016/j.jastp.2008.06.003. 

Zolotov O.V., Namgaladze A.A., Zakharenkova I.E., Shagimuratov I.I., Martynenko O.V. (2008), Modeling of 

the ionospheric earthquake precursors generated by various electric field sources, Proceedings of the XXIX 

General Assembly of URSI, Chicago, USA, HP-HGE.21. 

496

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