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

Juan Wu,Yangkang Chen,Dong Zhang,Hang Wang,Guangtan Huang,Min Bai

doi:10.1109/access.2020.3026020

Abstract

Five-dimensional (5D) seismic data reconstruction becomes more appealing in recent years because it takes advantage of five physical dimensions of the seismic data and can reconstruct data with large gap. The low-rank approximation approach is one of the most effective methods for reconstructing 5D dataset. However, the main disadvantage of the low-rank approximation method is its low computational efficiency because of many singular value decompositions (SVD) of the block Hankel/Toeplitz matrix in the frequency domain. In this paper, we develop an SVD-free low-rank approximation method for efficient and effective reconstruction and denoising of the seismic data that contain four spatial dimensions. Our SVD-free rank constraint model is based on an alternating minimization strategy, which updates one variable each time while fixing the other two. For each update, we only need to solve a linear least-squares problem with much less expensive QR factorization. The SVD-based and SVD-free low-rank approximation methods in the singular spectrum analysis (SSA) framework are compared in detail, regarding the reconstruction performance and computational cost. The comparison shows that the SVD-free low-rank approximation method can obtain similar reconstruction performance as the SVD-based method but with a large computational speedup.

Highlights

Data reconstruction is extremely important during the entire seismic processing chain due to the fact that our acquired data are never complete and regular in spatial dimensions
The traditional singular value decomposition (SVD) based low-rank approximation method suffers from the bottleneck of computational cost due to many singular value decompositions (SVD) calculations
In order to relieve the computation overburden, we develop an SVD-free low-rank approximation method in this paper

Summary

INTRODUCTION

Data reconstruction is extremely important during the entire seismic processing chain due to the fact that our acquired data are never complete and regular in spatial dimensions. Major issues in low-rank approximation approaches for 5D data interpolation are [53]: (1) high computational cost during SVD process, (2) the inevitable residual noise [19] and (3) the rank inconsistency problem [71]. We discuss an SVD-free low-rank approximation method for efficient and effective reconstruction and denoising of 5D seismic data that contains four spatial dimensions. Where H denotes the level-four block Hankelization/ Toeplitization operator Both missing traces and additive noise increase the rank of the matrix M, which originally possesses low-rank structure. The filtered data can be recovered with random noise attenuated and missing traces reconstructed via properly averaging along the anti-diagonals of the target low-rank approximation matrix MK :. Τ is a tiny increment and ωmax is the maximum value that ω can be

FAST 5D RECONSTRUCTION

SYNTHETIC EXAMPLES

Findings

CONCLUSION