Robust reduced-rank filtering for erratic seismic noise attenuation

Abstract

Singular spectrum analysis (SSA) or Cadzow reduced-rank filtering is an efficient method for random noise attenuation. SSA starts by embedding the seismic data into a Hankel matrix. Rank reduction of this Hankel matrix followed by antidiagonal averaging is utilized to estimate an enhanced seismic signal. Rank reduction is often implemented via the singular value decomposition (SVD). The SVD is a nonrobust matrix factorization technique that leads to suboptimal results when the seismic data are contaminated by erratic noise. The term erratic noise designates non-Gaussian noise that consists of large isolated events with known or unknown distribution. We adopted a robust low-rank factorization that permitted use of the SSA filter in situations in which the data were contaminated by erratic noise. In our robust SSA method, we replaced the quadratic error criterion function that yielded the truncated SVD solution by a bisquare function. The Hankel matrix was then approximated by the product of two lower dimensional factor matrices. The iteratively reweighed least-squares method was used to approximately solve for the optimal robust factorization. Our algorithm was tested with synthetic and real data. In our synthetic examples, the data were contaminated with band-limited Gaussian noise and erratic noise. Then, denoising was carried out by means of f-x deconvolution, the classical SSA method, and the proposed robust SSA method. The f-x deconvolution and the classical SSA method failed to properly eliminate the noise and to preserve the desired signal. On the other hand, the robust SSA method was found to be immune to erratic noise and was able to preserve the desired signal. We also tested the robust SSA method with a data set from the Western Canadian Sedimentary Basin. The results with this data set revealed improved denoising performance in portions of data contaminated with erratic noise.

Iteratively re‐weighted and refined least squares algorithm for robust inversion of geophysical data

“…When the contaminant noise shows a heavy‐tailed distribution, the ℓ 2 ‐norm metric of misfit can lead to a bad estimate due to its sensitivity to outliers. A more robust ℓ 1 ‐norm metric has been preferred for seismic inversion, but it leads to a non‐quadratic cost function (Claerbout and Muir ; Scales, Gersztenkorn and Treitel ; Guitton and Symes ; Ji ; Gholami and Sacchi ; Chen and Sacchi , ; Ibrahim and Sacchi ).…”

Robustf‐xprojection filtering for simultaneous random and erratic seismic noise attenuation

“…Robust estimation (inversion) has been used in geophysics for seismic deconvolution (Claerbout and Muir 1973;Taylor, Banks, and McCoy 1979;Gholami and Sacchi 2012), travel-time tomography (Scales and Gersztenkorn 1988;Bube and Langan 1997), full-waveform inversion (Crase et al 1990;Ha, Chung, and Shin 2009;Brossier, Operto, and Virieux 2010;Aravkin, van Leeuwen, and Herrmann 2011), velocity analysis (Guitton and Symes 2003;Li, Zhang, and Claerbout 2012), simultaneous source separation (Ibrahim and Sacchi 2014), and matrix rank reduction-based erratic noise removal and interpolation (Chen and Sacchi 2013;Chen 2013;Chen and Sacchi 2015). The main contribution of this paper is the introduction of a robust inversion methodology to the problem of estimating projection filters for seismic noise suppression.…”

Coherent noise suppression by learning and analyzing the morphology of the data

“…The DL methods have proven to perform well for denoising seismic data (Beckouche and Ma, 2014;Liang et al, 2014;Yu et al, 2015Yu et al, , 2016Zhu et al, 2015;Turquais et al, 2017). Another data-driven method, the Cadzow filtering method (Trickett, 2002(Trickett, , 2008, also called singular spectrum analysis (SSA) (Sacchi, 2009;Chen and Sacchi, 2015), uses rank reduction for denoising. This method embeds each frequency slice of the data into a Hankel matrix, mutes the low singular values, and averages the antidiagonal elements.…”