A Robust Scheme for Sparse Reflectivity Recovering from Uniformly Quantized Seismic Data

This article proposes an innovative scheme for recovering sparse reflectivity series from uniformly quantized seismic signals. In this scheme, the statistically less affected impulses by the quantization error are assigned higher weights than the ones with a larger error. First, the orthogonal matching pursuit (OMP) algorithm is applied on a quantized seismic trace to obtain a set of conservative estimates of the reflectivity impulses. Second, the quantization error is formulated as a systematic uncertainty within a neighborhood of the obtained conservative estimates from the OMP. Finally, a robust worst case (RWC) deconvolution method is developed to recover an improved estimate of the reflectivity impulses. The proposed scheme significantly increases the robustness and enhances the recovered reflectivity impulses obtained by the OMP algorithm. This is substantiated by experiments on both synthetic and real seismic data. Specifically, the falsely or overly estimated impulses are significantly suppressed, and the robustness to the change of the quantization interval is enhanced.