A depth-variant wavelet extraction method based on the orthogonal matching pursuit for direct inversion

Abstract

The results of pre-stack depth migration reflect subsurface structures directly. However, it is an urgent geophysical problem that how to deal with this non-stationarity exhibited by depth-domain seismic data and achieve high precision reservoir prediction. To address this issue, we develop a depth-variant wavelet extraction method based on the orthogonal matching pursuit and attain direct inversion of the depth-domain acoustic impedance using the depth-variant wavelets. First, the parameters of source wavelets estimated by complex seismic trace analysis are utilized to construct the overcomplete dictionary. Secondly, the overcomplete dictionary is used to decompose the depth-domain seismic traces by orthogonal matching pursuit. Thirdly, we extract the depth-variant Ricker wavelets from the decomposed optimal atoms. Test of examples demonstrates that the proposed depth-variant wavelet method has high accuracy. The synthetic seismogram obtained by the proposed method has high Pearson correlation coefficients of 99%, which verifies that our method is feasible and accurate. Next, a depth-domain impedance trend constraint is introduced into the objective function of the conventional basis pursuit inversion to enhance the lateral continuity. Finally, the objective function with impedance trend constraint is solved by basis pursuit for depth-domain acoustic impedance. We test the direct depth-domain acoustic impedance inversion method on the synthetic and field data, which indicates that our method has high accuracy and robustness. The mean relative error of its inversion result is only 0.9% for the noise-free example and about 5% for the strong noisy example. Therefore, our method can be effectively applied to the seismic-well calibration and seismic impedance inversion in the depth domain. And it has powerful potential in reservoir characterization, fluid prediction and attribute extraction in the depth domain. Additionally, the energy distribution features of the Ricker wavelet are derived and analyzed, which can guide the application of the Ricker wavelet in seismic signal analysis.