GEOPHYSICAL RESEARCH, 2016, vol.17, no.3, pp. 60-69. DOI: 10.21455/gr2016.3-5

 UDC 550.334

Abstract  References  Full text (in Russian)


E.A. Rodionov

Russian State Geological Prospecting University, Moscow, Russia 

The orthogonal wavelets with compact support on the positive half-line were defined by W.C. Lang in 1996. Masks of these wavelets are Walsh polynomials. These wavelets have multifractal structure and generate unconditional bases in Lp-spaces for all 1<p<+∞. Lang’s wavelets and their modifications for biorthogonal, non-stationary and periodic cases are used for image processing, compression of fractal signals and evaluating the smoothness of geophysical signals. Based on the geophysical monitoring data, the wavelet-aggregated signals constructed using Lang wavelets are compared with similar signals constructed using Haar and Daubechies wavelets.

The analysis is directed on identification the earthquakes precursors that occurred on Kamchatka and in Northeast China. Results of computational experiments show that for the chosen data Lang wavelets reflect earthquakes precursors better than Haar and Daubechies wavelets. In addition, wavelet measures of coherence are calculated using Haar and Lang wavelets for data on monitoring of speed of a wind over the USA Atlantic coast. 

Keywords: geophysical signals, wavelet-aggregated signal, wavelet measure of coherence, Lang wavelets, earthquake precursors.



Farkov Yu.A., Maksimov A.Yu., Stroganov S.A. On biorthogonal wavelets related to the Walsh functions, Int. J. Wavelets Multiresolut. Inf. Process, 2011, vol. 9, no. 3, pp. 485–499.

Farkov Yu.A., Stroganov S.A. The use of discrete dyadic wavelets in image processing, Izv. Vyssh. Uchebn. Zaved. Mat., 2011, no. 7, pp. 57–66

Farkov Yu.A.  Examples of frames on the Cantor dyadic group, Journal of Mathematical Sciences, 2012, vol. 187, no. 1, pp. 22–34.

Farkov Yu.A., Rodionov E.A. Nonstationary wavelets related to the Walsh functions, American Journal of Computational Mathematics, 2012, no. 2, pp.82–87.

Farkov Yu.A. Constructions of MRA-based wavelets and frames in Walsh analysis. Poincare J. Anal. Appl., 2015, vol. 2. Special Issue (IWWFA-II, Delhi), pp.13–36.

Lang W.C. Orthogonal wavelets on the Cantor dyadic group, SIAM J. Math. Anal., January 1996, vol. 27, no 1, pp.305–312.

Lyubushin A.A. Wavelet-aggregated signal and synchronous peaked fluctuations in problems of geophysicalmMonitoring and earthquake prediction. Izvestiya, Physics of the Solid Earth, 2000, vol. 36, no. 3, pp. 204–213.

Lyubushin A.A. A Robust wavelet-aggregated signal for geophysical monitoring problems. Izvestiya, Physics of the Solid Earth, 2002, vol. 38, no. 9, pp. 745–755.

Lyubushin A.A. Analiz dannyh system geofizicheskogo I ekologicheskogo monitoringa (Data analysis of geophysical and environmental monitoring systems), Moscow: Nauka, 2007.

Lyubushin A.A. Wavelet-aggregated signal in earthquake prediction, Earthquake Res. China. Engl. Ed., 1999, vol. 13, no 1, pp.33–43.

Protasov V.Yu., Farkov Yu.A., Dyadic wavelets and refinable functions on a half-line. Sbornik Mathematics, 2006, vol. 197, no. 10. pp. 1529-1558.

Stroganov S. A. Dyadic wavelets for estimate of smoothness of low-frequency microseismic Oscillations, Geophysical Research, 2012, vol. 13, no.1, pp.60-65.