Incoherent Noise Suppression of Seismic Data Based on Robust Low-Rank Approximation

Abstract

Incoherent noise is one of the most common noise widely distributed in seismic data. To improve the interpretation accuracy of the underground structure, incoherent noise needs to be adequately suppressed before the final imaging. We propose a novel method for suppressing seismic incoherent noise based on the robust low-rank approximation. After the Hankelization, seismic data will show strong low-rank features. Our goal is to obtain the stable and accurate low-rank approximation of the Hankel matrix and then reconstruct the denoised data. We construct a mixed model of the nuclear norm and the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{1}$ </tex-math></inline-formula> norm to express the low-rank approximation of the Hankel matrix constructed in the frequency domain. Essentially, the adopted model is an optimization for the subspace similar to the online subspace tracking method, thus avoiding the time-consuming singular value decomposition (SVD). We introduce the orthonormal subspace learning to convert the nuclear norm to the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{1}$ </tex-math></inline-formula> norm to optimize the orthonormal subspace and the corresponding coefficient. Finally, two optimization strategies—the alternating direction method and the block coordinate descent method—are applied to obtain the optimized orthonormal subspace and the corresponding coefficient for representing the low-rank approximation of the Hankel matrix. We perform incoherent noise attenuation tests on synthetic and real seismic data. Compared with other denoising methods, the proposed method produces small signal errors while effectively suppressing the seismic incoherent noise and has a high computational efficiency.