Seismic time-frequency spectral decomposition by matching pursuit

TLDR

Matching pursuit decomposes seismic traces into wavelets that match their time‑frequency signatures, typically using Morlet wavelets to capture energy attenuation and velocity dispersion, with wavelet scale controlling time width and frequency bandwidth. The study aims to use the resulting time‑frequency spectrum for lithological analysis, such as detecting gas reservoirs. The method first performs a preliminary estimate followed by a localized refinement of wavelet selection, employing complex‑trace attributes and analytical expressions, and then removes wavelets with extreme scales to suppress spikes and sinusoid functions from the spectrum. The analysis confirms that the low‑frequency shadow of a carbonate gas reservoir persists, while high‑frequency amplitudes are compensated by inverse filtering.

Abstract

A seismic trace may be decomposed into a series of wavelets that match their time-frequency signature by using a matching pursuit algorithm, an iterative procedure of wavelet selection among a large and redundant dictionary. For reflection seismic signals, the Morlet wavelet may be employed, because it can represent quantitatively the energy attenuation and velocity dispersion of acoustic waves propagating through porous media. The efficiency of an adaptive wavelet selection is improved by making first a preliminary estimate and then a localized refining search, whereas complex-trace attributes and derived analytical expressions are also used in various stages. For a constituent wavelet, the scale is an important adaptive parameter that controls the width of wavelet in time and the bandwidth of the frequency spectrum. After matching pursuit decomposition, deleting wavelets with either very small or very large scale values can suppress spikes and sinusoid functions effectively from the time-frequency spectrum. This time-frequency spectrum may be used in turn for lithological analysis—for instance, detection of a gas reservoir. Investigation shows that the low-frequency shadow associated with a carbonate gas reservoir still exists, even high-frequency amplitudes are compensated by inverse-[Formula: see text] filtering.