Parallel matrix factorization algorithm and its application to 5D seismic reconstruction and denoising

Abstract

Tensors, also called multilinear arrays, have been receiving attention from the seismic processing community. Tensors permit us to generalize processing methodologies to multidimensional structures that depend on more than 2D. Recent studies on seismic data reconstruction via tensor completion have led to new and interesting results. For instance, fully sampled noise-free multidimensional seismic data can be represented by a low-rank tensor. Missing traces and random noise increase the rank of the tensor. Hence, multidimensional prestack seismic data denoising and reconstruction can be tackled with tools that have been studied in the field of tensor completion. We have investigated and applied the recently proposed parallel matrix factorization (PMF) method to solve the 5D seismic data reconstruction problem. We have evaluated the efficiency of the PMF method in comparison with our previously reported algorithms that used singular value decomposition to solve the tensor completion problem for prestack seismic data. We examined the performance of PMF with synthetic data sets and with a field data set from a heavy oil survey in the Western Canadian Sedimentary Basin.

An open-source Matlab code package for improved rank-reduction 3D seismic data denoising and reconstruction

“…The other category of rank reduction methods encompasses techniques that are based on dimensionality reduction of multi-linear arrays or tensors. In this case, the multichannel seismic data is viewed as a multi-linear array, and dimensionality reduction techniques are directly applied to the multi-linear array (Gao et al, 2015). For example, Kreimer and Sacchi (2012) adopt the high-order singular value decomposition (HOSVD) to solve the 5D seismic data reconstruction problem in the frequency-space domain.…”

Fast and Robust Low-Rank Approximation for Five-Dimensional Seismic Data Reconstruction

“…While most random noise attenuation approaches utilize the signal predictability, the irregularity of seismic data can directly influence this predictability and result in unsatisfactory denoising performance. Because of these mutual influences mentioned above between random noise suppression and data reconstruction, simultaneous reconstruction and denoising approaches are widely studied in [42], [43], [44], [45], [46] and [47]. Among all these approaches, low-rank approximation methods are most commonly studied.…”

“…[43] introduced a fast rank reduction approach along four spacial dimensions based on Lanczos bidiagonalization. Instead of accelerating low-rank approximation for multi-level Hankel/Toeplitz matrix, [47] presented a tensor completion based fast algorithm via parallel matrix factorization to speed up the 5D interpolation process. Recently, [56] developed a parallel square matrix factorization method for efficient 5D data reconstruction without SVD calculation, which however could be difficult to implement.…”

An Alternative Adaptive Method for Seismic Data Denoising and Interpolation

“…us, we can reduce the rank to suppress the random noise and reconstruct seismic data. Many attempts using the rank-reduction method have been developed to deal with seismic interpolation problems in publications (e.g., [36][37][38]). Multichannel singular spectrum analysis (MSSA) [28,39,40] is a popular way to attenuate the random noise.…”