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-Q filtering.