Multiresolution Chirp-Modulated W-Transform

Abstract For seismic characterization of reservoirs, it is necessary to extract the time-frequency characteristics hidden in time-domain data for effective use in processing and interpretation. In the time-frequency analysis algorithm of the chirp-modulated W-transform (CW-transform), the spread of the analysis kernel is the primary factor controlling the resolution of the power spectral density. We have proposed a multi-resolution CW-transform that improves the localization of the power spectral density and extends the capability of time-frequency algorithms in delineating reservoirs and thin layers. We have also proposed multiplying CW-transforms with different resolutions, to produce a highly localized and well-resolved power spectral density. The resultant spectrum can be regarded as the geometric mean of the spectra estimated with different scaling factors. Compared with the arithmetic mean, this approach is more robust and noise resistant, resulting in higher resolution and greater energy concentration. We have investigated the application of statistical properties of the time-varying spectrum to indicate the presence of gas-bearing reservoirs. We have conducted experiments demonstrating that the multi-resolution CW-transform can be successfully used to estimate a time-frequency spectrum with high energy concentration and has great potential for application in the seismic characterization of complex reservoirs.