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 p-norm (p>2) 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.

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