Residual statics estimation by sparsity maximization

Abstract

Residual statics estimation in complex areas is one of the main challenging problems in seismic data processing. It is well known that the result of this processing step has a profound effect on the quality of final reconstructed image. A novel method is presented to compensate for surface-consistent residual static corrections based on sparsity maximization, which has proved to be a powerful tool in the analysis and processing of signals and related problems. The method is based on the hypothesis that residual static time shift represents itself by noise-like features in the Fourier or curvelet domain. Residual time shift corrections are then retrieved by optimizing the sparsity in these domains. Here, the statics model is considered as a maximizer of [Formula: see text]-norm ([Formula: see text]) of the data coefficients in the sparse domain, and a fast and efficient algorithm is presented to iteratively solve the corresponding nonlinear optimization problem. Applications on synthetic and real data show very high performance of the presented algorithm.