Wavelet analysis in problems of the near-to-earth space

1Lazorenko, OV, 2Lazorenko, SV, 3Chernogor, LF
1Kharkiv National University of Radio Electronics of the Ministry of Education and Science of Ukraine, Kharkiv, Ukraine
2International Slavic University, Kharkiv, Ukraine
3V.N. Karazin National University of Kharkiv, Kharkiv, Ukraine
Kosm. nauka tehnol. 2005, 11 ;(5-6):022-029
Publication Language: Russian
Both wavelet analysis and Fourier analysis were applied to solve some problems of the near-to-Earth space physics. As an example an investigation of some properties of the solar activity time variations described by sunspot numbers was carried out with the use of these analyses. Similar investigations were performed for the time variations of the Dst-index from 1957 to 2001 and for the time variations of the Karazin Kharkiv National University magnetometer-fluxmeter signals from 1999 to 2003. The wavelet analysis is represented by the continuous wavelet transform and the traditional Fourier analysis is denoted by the dynamic spectra. The parameters of the disturbances appearing in the near-to-Earth space were estimated. High efficiency of the wavelet analysis was pointed out. The methods of the wavelet analysis and Fourier analysis were shown to be mutually complement.
1. Astaf’eva N. M. Wavelet analysis: basic theory and some applications. Uspehi fiz. nauk, 166 (11), 1145—1170 (1996) [in Russian].
2. Bezverkhnii V. A. Developing the wavelet-transform method for analysis of geophysical data. Izv. AN. Ser. Fizika atmosfery i okeana, 37 (5), 630—635 (2001) [in Russian].
3. Garmash K. P., Lazorenko O. V., Pazura S. A., Chernogor L. F. Earth’s Magnetic Field Fluctuations During the Severe 1999 Geospace Storm. Radio Physics and Radio Astronomy, 8 (3), 253— 264 (2003) [in Russian].
4. Garmash K. P., Leus S. G., Pazura S. A., et al. Statistics of Terrestrial Electromagnetic Field Fluctuation. Radio Physics and Radio Astronomy, 8 (2), 163—180 (2003) [in Russian].
5. Gorbatenko V. P., Ippolitov I. I., Kabanov M. V., et al. Analysis of the structure of repetitive occurrence in time series of atmospheric circulation patterns and thunderstorms. Optika atmosfery i okeana, 15 (8), 693—706 (2002) [in Russian].
6. Grigorenko E. I., Lazorenko S. V., Taran V. I., Chernogor L. F. Wave disturbances in the ionosphere accompanied the solar flare and the strongest magnetic storm of September 25, 1998. Geomagnetizm i Aeronomiia, 43 (6), 770—787 (2003) [in Russian].
7. Dremin I. M., Ivanov O. V., Nechitailo V. A. Wavelets and their uses. Uspehi fiz. nauk, 171 (5) 465—501 (2001) [in Russian].
8. D’yakonov V. P. Wavelets: From Theory to Practice, 448 p. (SOLON- R, Moscow, 2002) [in Russian].
9. Ivanov V. V., Rotanova N. M. Wavelet analysis of the profile of magnetic anomalies obtained from the MAGSAT satellite data. Geomagnetizm i Aeronomiia, 40 (2), 78—83 (2000) [in Russian].
10. Ivanov V. V., Rotanova N. M., Kovalevskaya E. V. The wavelet analysis as applied to the study of geomagnetic disturbances. Geomagnetizm i Aeronomiia, 41 (5), 610—618 (2001) [in Russian].
11. Ippolitov I. I., Kabanov M. V., Loginov S. V. Application of wavelet transform to analysis of interannual fluctuations of solar activity and surface air temperature in Tomsk. Optika atmosfery i okeana, 14 (4), 280—285 (2001) [in Russian].
12. Kleimenova N. G., Kozyreva O. V., Shott J.-J. Wave geomagnetic response of the magnetosphere to an interplanetary magnetic cloud that approached the Earth on July 14-15,2000 (a Bastille Day Event). Geomagnetizm i Aeronomiia, 43 (3), 321—331 (2003) [in Russian].
13. Kravchenko V. F., Rvachev V. A. Wavelet systems and their applications for signal processing. Zarubezhnaya radioelektronika, No.4, 3—20 (1996) [in Russian].
14. Kravchenko V. F., Rvachev V.A., Rvachev V. L. Mathematical methods for signal processing based on atomic functions. Radiotehnika i jelektronika, 40 (9), 1385—1406 (1995) [in Russian].
15. Lazorenko O. V., Lazorenko S. V., Chernogor L. F. Application of Wavelet Analysis to Problem of Ultra-Wideband Signal Detection on Noise Background. Radio Physics and Radio Astronomy, 7 (1), 46—63 (2002) [in Russian].
16. Lazorenko O. V., Lazorenko S. V., Chernogor L. F. The application of wavelet analysis to problems of cosmic physics and cosmic radio physics. Kosm. nauka tehnol., 9 (Suppl. 2), 91—96 (2003) [in Russian].
17. Novikov I. Ya., Stechkin S. B. Basic constructions of wavelets. Fundamental'naja i prikladnaja matematika, 3 (4), 999—1028 (1997) [in Russian].
18. Rvachev V. L., Rvachev V. A. Nonclassical methods of approximation theory in boundary value problems, 350 p. (Naukova Dumka, Kiev, 1979) [in Russian].
19. Rozhnoy A. A., Kleimenova N. G., Kozyreva O. V., et al. Nighttime midlatitude variations in the LF (40 kHz) signal parameters and Pi3 geomagnetic pulsations. Geomagnetizm i Aeronomiia, 43 (4), 553—560 (2003) [in Russian].
20. Rotanova N. M., Bondar' T. N., Ivanov V. V. Time changes in secular geomagnetic variations. Geomagnetizm i Aeronomiia, 42 (5), 708—720 (2002) [in Russian].
21. Rotanova N. M., Bondar T. N., Ivanov V. V. Wavelet analysis of secular geomagnetic variations. Geomagnetizm i Aeronomiia, 44 (2), 276—282 (2004) [in Russian].
22. Chui Ch. K. An Introduction to Wavelets: Transl. from Eng., 412 p. (Mir, Moscow, 2001) [in Russian].
23. Alexandrescu M., Gibert D., Hulot G., Le Mouel J.-L., Saracco G. Detection of geomagnetic jerks using wavelet analysis. J. Geophys. Res., 100, 12557—12572 (1995).
24. Alperovich L., Zheludev V. Wavelet transform as a tool for detection of geomagnetic precursors of earthquakes. Phys. Chem. Earth, 23 (9-10), 965—967 (1998).
25. Buonsanto M. J. Ionospheric Storms. A Review. Space Sci. Rev., 88, 563—601 (1999).
26. Chernogor L. F., Lazorenko O. V., Lazorenko S. V. Wavelet Analysis and Ultra-Wideband signals. Radio Physics and Radio Astronomy, 7 (4), 471—474 (2002).
27. Daubechies I. Ten lectures on wavelets, CBMS-NSF conference series in applied mathematics, 410 p. (SIAM Ed., 1992).
28. Frick P., Galyagin D., Hoyt D., et al. Wavelet analysis of solar activity recorded by sunspot groups. Astron. and Astrophys., 328, 670—681 (1997).
29. Holschneider A. Wavelets: an analysis tools, 423 p. (Cambridge, 1995).
30. Mallat S. A Wavelet Tour of Signal Processing, 2nd ed., 671 p. (Academ. press, 1999).

31. Mohino E., Heraiz M., Kazimirovsky E. Application of wavelet analysis to quasi-2-day oscillation occurrence in the time variations of f0F2. Internat. J. Geomagnetism and Aeronomy, 4 (3), 215—220 (2003).