A new 5D seismic reconstruction method based on a Parallel Square Matrix Factorization algorithm

Abstract

Multidimensional seismic data reconstruction can be viewed as a low rank matrix or tensor completion problem. Different rank-reduction approaches can be employed to perform seismic data interpolation and denoising. For these methods, the computational cost and reconstruction quality are two important aspects that must be carefully considered. In this paper, we present a new fast and economic tensor completion method named Parallel Square Matrix Factorization (PSMF). We apply the algorithm to the ubiquitous 5D seismic data regularization problem. 5D reconstruction entails reconstructing a series 4th-order multilinear arrays (tensors) in the frequency domain. For this purpose we transform the data to the frequency domain and 4D spatial volumes in midpoint-offset are reshaped into matrices. Rank-reduction of these matrices is at the core of our reconstruction algorithms. We show that properly reshaping the data tensor into almost square matrices lead to an improved tensor completion algorithm. We demonstrate the effectiveness of the proposed approach via synthetic examples and by a data set from Western Canadian Sedimentary Basin.