A Method of Detecting Seismic Singularities Using Combined Wavelet with Fractal

Abstract

A new method of utilizing combined wavelet with fractal to detect seismic singularities is proposed aiming at improving the detecting precision. Firstly the fractal property of seismic wave is comprehensively investigated based on its power spectrum analysis, and the conclusion is made that seismic wave is of self-affine fractal property only in several higher frequency bands. This not only provides the theoretic foundation for reasonably applying fractal to seismic wave analysis, but also reveals the shortage of employing single integrated fractal dimension to detect seismic singularities. Secondly an algorithm of frequency and time-ordered non-decimated wavelet packet transform is put forward to produce excellent platform for fractal analysis of seismic wave. On the basis of the above two aspects, a wavelet-fractal based method for detecting seismic singularities is developed, which consists of three successive steps: seismic wave is decomposed into multi-scale coefficient sequences, and then fractal-parameter space of seismic profile is constructed depending on the correlation dimension analysis of effective scale coefficient sequences, in the end, singular parameters are identified and they indicate the seismic singularities. An engineering example shows that the proposed method outperforms the existing wavelet and fractal concerned methods in rationality and practicability, so it provides a new approach for parameterized accurate seismic geophysical prospecting.