A Generalized Seismic Attenuation Compensation Operator Optimized by 2-D Mathematical Morphology Filtering

Abstract

In this work, a Robust Worst-Case (RWC) estimation is presented for recovering sparse reflectivity series from uniformly quantized seismic signals. First, the <i>Orthogonal Matching Pursuit</i> (OMP) algorithm is applied on a quantized seismic trace. A set of conservative estimates of the reflectivity impulses and a dimension-reduced system are accordingly obtained. Second, the error induced by the quantization is modeled as a systemic uncertainty in a multiplication way. This modeling imposes a greater model uncertainty on the estimated reflectivity impulses with small values and vice versa. Finally, a RWC deconvolution scheme is designed for the dimension-reduced system. Among those roughly estimated impulses from the OMP algorithm, the ones statistically less affected by the quantization process are assigned with higher confidence weights and the ones statistically with higher magnitudes of quantization error are assigned with lower confidence weights. By rescaling the quantization error, the proposed scheme significantly increases the robustness of the solution to the quantization error and hence better improves the visual saliency of seismic signals than that of the OMP algorithm. This scheme is tested on both synthetic and real seismic data and the performance is evaluated by compared to that of the OMP algorithm. The results shows that the new scheme significantly outperforms the OMP algorithm by observing the following two aspects: first, the falsely or overly estimated impulses are significantly suppressed in the RWC estimation compared with that of the OMP algorithm, and second, the RWC estimation exhibits enhanced robustness to the change of the quantization interval.