PROBLEMS OF GEOCOSMOS

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