*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)**

**LANG WAVELETS FOR PROBLEMS OF GEOPHYSICAL MONITORING**

*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 L^{p}-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.

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