Simultaneous seismic data denoising and reconstruction via multichannel singular spectrum analysis

Abstract

We present a rank reduction algorithm that permits simultaneous reconstruction and random noise attenuation of seismic records. We based our technique on multichannel singular spectrum analysis (MSSA). The technique entails organizing spatial data at a given temporal frequency into a block Hankel matrix that in ideal conditions is a matrix of rank [Formula: see text], where [Formula: see text] is the number of plane waves in the window of analysis. Additive noise and missing samples will increase the rank of the block Hankel matrix of the data. Consequently, rank reduction is proposed as a means to attenuate noise and recover missing traces. We present an iterative algorithm that resembles seismic data reconstruction with the method of projection onto convex sets. In addition, we propose to adopt a randomized singular value decomposition to accelerate the rank reduction stage of the algorithm. We apply MSSA reconstruction to synthetic examples and a field data set. Synthetic examples were used to assess the performance of the method in two reconstruction scenarios: a noise-free case and data contaminated with noise. In both cases, we found extremely low reconstructions errors that are indicative of an optimal recovery. The field data example consists of a 2D prestack volume that depends on common midpoint and offset. We use the MSSA reconstruction method to complete missing offsets and, at the same time, increase the signal-to-noise ratio of the seismic volume.

Exploration of Singular Spectrum Analysis for Online Anomaly Detection in CRNs

“…Wu et al applied SSA for data preprocessing, associating with artificial neural network (ANN), to predict daily rainfall-runoff transformation [15]. Oropeza and Sacchi presented multichannel singular spectrum analysis (MSSA) as a tool for simultaneously denoising and reconstructing seismic data [16]. Moskvina and Zhigljavsky developed an algorithm of change-point detection in time series, based on sequential application of SSA [17].…”

M-Estimate robust PCA for Seismic Noise Attenuation

“…Conventionally, random noise in seismic data are assumed to have a Gaussian distribution, with SNR related to √ N where N is the number of sensors. Assuming noise with Gaussian distribution, rank reduction based methods work pretty well for denoising data [8,9,10,11]. Rank reduction methods work on the assumption that within a small spatio-temporal seismic window, seismic reflections are linear events with different dips (gradients).…”

“…Rank reduction methods work on the assumption that within a small spatio-temporal seismic window, seismic reflections are linear events with different dips (gradients). In these methods [8,9,10,11], data are first transformed to the Fourier domain in the temporal direction (also known as Fx transform [7]) and then for every frequency slice, rank reduction is applied on the Hankel matrix to remove incoherent signals. Cadzow's algorithm [12], popular in array processing, can also be applied for further noise reduction [9].…”

Sharp mantle transition from cratons to Cordillera in southwestern Canada

“…By analyzing radial component receiver functions [Langston, 1979;Ammon, 1991;Cassidy, 1992;Ligorria and Ammon, 1999], we are able to accurately determine the depths of the MTZ discontinuities and thereby estimate the changes in temperature and composition from craton to terranes/Cordillera in western Canada. Singular Spectrum Analysis (SSA) [Cadzow, 1988;Trickett, 2003;Oropeza and Sacchi, 2011] was applied to individual station gathers for noise attenuation and the interpolation of irregularly spaced data, and least squares parabolic Radon transform (PRT) [Sacchi and Ulrych, 1995;Schultz and Gu, 2013] was introduced for more reliable detection and assessment of P-to-S conversions from MTZ discontinuities (e.g., P410s and P660s). The combination of these algorithms and the availability of the regional array provided the basis for an updated model of mantle interfaces beneath southwestern WCSB.…”