Seismic pattern recognition by method of wavelet analysis

S.S.Kharintsev, M.Kh.Salakhov, A.Yu.Vorobyev

Kazan State University

Kremlevskaya str., 16, Kazan, Russia, 420008

In this work we develop an approach for detecting nonlinearity in chaotic dynamical systems using the higher order statistics and wavelet analysis. A special attention is paid to the consideration of three-wave interaction in a quadratically coupled medium. The knowledge of nonlinearities allows one to extract order parameters both for reconstruction of a dynamical system and for the study of transient processes between oscillatory regimes. To demonstrate a power of this approach we verify the latter for real data coming from the seismology. We show that the higher order statistics can be used effectively in combination with the wavelet transform to analyze a bound frequency composition of the wave process in the vicinity of the critical point. We intend to demonstrate that high frequency part of the wave evolution spectrum is determined by the higher harmonics of the dominate waves. This means a particular phase relationship between each high-frequency mode and the dominant frequency mode. Thus, the bicoherence of any pair of frequency modes becomes nonzero. The wavelet-based higher order statistics can be successfully used for pattern recognition and fault events prediction in nonlinear dynamical systems.

Over the last two decades, the higher order statistics has been successfully used by many researchers for studying nonlinear effects in the different applications. This technique allows one to look beyond the conventional power spectrum estimation to extract information regarding, in the first turn, phase relations. Certainly, higher order statistics technique has more wide possibilities. In particular, it provides to suppress additive colored Gaussian noise of unknown power spectrum, extract information due to deviations from Gaussinity and detect and characterize nonlinear properties in signals as well as identify nonlinear systems.

љWe consider particular cases of higher order spectra - the third-order spectrum, so called bispectrum (by definition, this is the Fourier tansformation of the third-order statistics) and the trispectrum (the fourth-order statistics) of a stationary signal. Traditionally, when the higher order statistics is used in signal processing the emphasis is placed on the second, third and fourth moments and/or cumulants and their respective Fourier transform (power spectrum, bispectrum and trispectrum).

Here we apply the bi- and tri-spectral wavelet transformation for analyzing the real seismic data. We are trying to solve the following problems: 1) strong earthquake forecasting, 2) differentiation of small earthquake from technogenic explosion.

Finally we can conclude that the wavelet based higher order statistics is a powerful instrument for small earthquake and man made explosion and large earthquake forecasting.