Robust damped rank-reduction method for simultaneous denoising and reconstruction of 5D seismic data

Abstract

We have developed a new method for simultaneous denoising and reconstruction of 5D seismic data corrupted by random noise and missing traces. Several algorithms have been developed for seismic data restoration based on rank-reduction (RR) methods. More recently, a damping operator has been introduced into the conventional truncated singular-value decomposition (TSVD) formula to further remove residual noise, the presence of which disturbs the quality of the seismic results. Despite the success of the damped RR (DRR) method when the observed data have an extremely low signal-to-noise ratio (S/N), random noise is still a limiting factor for obtaining a perfect quality of the result. Therefore, how to accurately solve the simultaneous denoising and reconstruction problem with high fidelity is still challenging. We assume that introducing only the damping operator into the TSVD formula is not enough to remove the random noise and restore the useful signal well. By combining the soft thresholding (ST) operator and the moving-average (MA) filter, we have developed a new operator, which we call the STMA operator. Then, by introducing the STMA operator into the DRR framework, we have developed a new algorithm known as the robust DRR method, which aims at mixing the advantages of the STMA operator and the damping operator. The STMA operator is applied to the Hankel matrix after damped TSVD to better remove residual noise. Examples of our approach on synthetic and field 5D seismic data demonstrate the better performance in terms of the visual examination and numerical test compared with the DRR approach. Our method aims at producing an effective low-rank filter and, thus, can perfectly enhance the S/N of the simultaneously denoised and reconstructed results with higher accuracy.