Robust Low-Rank Reconstruction of Seismic Data

Seismic reconstruction is an essential preprocessing step aimed at recovering missing traces and suppressing incoherent noise. The low-rank (LR) method has been demonstrated to be one of the most effective methods for seismic data reconstruction. This method considers the seismic data reconstruction as a matrix completion problem, assuming that noise-free seismic signals can be represented as an LR matrix. Incoherent noise and missing traces contribute to increasing the matrix rank. Consequently, seismic reconstruction can be accomplished by a rank-reduction operation. For successful LR reconstruction, it is ideal if incoherent noise closely follows a Gaussian distribution and missing traces are as randomly distributed as possible. However, these conditions are challenging to meet in field seismic acquisition due to dependencies on operational equipment and environmental factors. Field seismic data often contain erratic noise and exhibit regular patterns of missing traces, leading to instability in LR reconstruction and limiting its practical application. In this study, we propose a robust version of LR reconstruction, which can accurately estimate the seismic signals from noisy and undersampled seismic data and is insensitive to the erratic noise and the spatial aliasing caused by regular undersampling. We present a detailed algorithmic framework for this robust LR method and validate it through comprehensive analyses of various seismic data examples. Our results demonstrate that the proposed robust LR method can reconstruct both regularly and irregularly undersampled seismic data and exhibits a good noise immunity to strong and erratic noise.