Seismic spectral sparse reflectivity inversion based on SBL-EM: experimental analysis and application

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Abstract In this paper, we propose a new method of seismic spectral sparse reflectivity inversion that, for the first time, introduces Expectation-Maximization-based sparse Bayesian learning (SBL-EM) to enhance the accuracy of stratal reflectivity estimation based on the frequency spectrum of seismic reflection data. Compared with the widely applied sequential algorithm-based sparse Bayesian learning (SBL-SA), SBL-EM is more robust to data noise and, generally, can not only find a sparse solution with higher precision, but also yield a better lateral continuity along the final profile. To investigate the potential of SBL-EM in a seismic spectral sparse reflectivity inversion, we evaluate the inversion results by comparing them with those of a SBL-SA-based approach in multiple aspects, including the sensitivity to different frequency bands, the robustness to data noise, the lateral continuity of the final profiles and so on. Furthermore, we apply the mean square error (MSE), residual variance (RV) of seismograms and residual energy (RE) between the frequency spectra of the true and inverted reflectivity model to highlight the advantages of the proposed method over the SBL-SA-based approach in terms of spectral sparse reflectivity inversion within a sparse Bayesian learning framework. Multiple examples, including both numerical and field experiments, are carried out to validate the proposed method.