The Wavelet Transform as a Geophysical Signal Processing Tool

T. A. Thompson
Curtin University of Technology, Dept. of Exploration Geophysics, Perth, Western Australia

The wavelet transform decomposes a signal into well-localized timefrequency compartments that display the energy distributions over the time and frequency domains respectively. This makes the wavelet transform and related wavelet analysis techniques (WT) powerful signal analysis tools for characterizing seismic signals with respect to dispersion, attenuation, and the identification of multiple interfering events. By analyzing frequency components at an appropriate resolution, high and low frequencies are well resolved in time and frequency, respectively. This makes wavelets an ideal signal analysis tool for practical seismic signals. The process of multiple generation leads to similarities and patterns in both the location and appearance of multiples. Due to the very nature of their design, wavelets are a powerful tool for characterizing similar behavior and recognizing patterns over a range of time scales.

As seismic imaging techniques increase in sophistication noise (multiple energy in particular), attenuation becomes crucial. An increased understanding of geophysical applications of the WT may promote new data processing methods to image the subsurface in areas where multiples are a major problem. The aim of this research is to develop new processing (in particular demultiple processing) techniques using the wavelet transform. Wavelets have fostered a relatively new and rapidly expanding area of research spanning many scientific disciplines catering for a wide variety of applications. Exploration geophysics is one such discipline where the WT has many potential applications.

AAPG Search and Discovery Article #90902©2001 AAPG Foundation Grants-in-Aid