PROBLEMS OF GEOCOSMOS

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

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