Enhanced low-rank matrix estimation for simultaneous denoising and reconstruction of five-dimensional seismic data

Geophysics ◽

10.1190/geo2020-0773.1 ◽

2021 ◽

pp. 1-96

Author(s):

Yapo Abolé Serge Innocent Oboué ◽

Yangkang Chen

Keyword(s):

Seismic Data ◽

Hankel Matrix ◽

Low Rank ◽

The Novel ◽

Proximity Function ◽

Rank Reduction ◽

Matrix Estimation ◽

Useful Signal ◽

Truncated Svd ◽

Noisy Observation

Noise and missing traces usually influence the quality of multidimensional seismic data. It is, therefore, necessary to e stimate the useful signal from its noisy observation. The damped rank-reduction (DRR) method has emerged as an effective method to reconstruct the useful signal matrix from its noisy observation. However, the higher the noise level and the ratio of missing traces, the weaker the DRR operator becomes. Consequently, the estimated low-rank signal matrix includes a unignorable amount of residual noise that influences the next processing steps. This paper focuses on the problem of estimating a low-rank signal matrix from its noisy observation. To elaborate on the novel algorithm, we formulate an improved proximity function by mixing the moving-average filter and the arctangent penalty function. We first apply the proximity function to the level-4 block Hankel matrix before the singular value decomposition (SVD), and then, to singular values, during the damped truncated SVD process. The relationship between the novel proximity function and the DRR framework leads to an optimization problem, which results in better recovery performance. The proposed algorithm aims at producing an enhanced rank-reduction operator to estimate the useful signal matrix with a higher quality. Experiments are conducted on synthetic and real 5-D seismic data to compare the effectiveness of our approach to the DRR approach. The proposed approach is shown to obtain better performance since the estimated low-rank signal matrix is cleaner and contains less amount of artifacts compared to the DRR algorithm.

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Robust reduced-rank filtering for erratic seismic noise attenuation

Geophysics ◽

10.1190/geo2014-0116.1 ◽

2015 ◽

Vol 80 (1) ◽

pp. V1-V11 ◽

Cited By ~ 63

Author(s):

Ke Chen ◽

Mauricio D. Sacchi

Keyword(s):

Gaussian Noise ◽

Seismic Data ◽

Random Noise ◽

Singular Spectrum Analysis ◽

Hankel Matrix ◽

Noise Attenuation ◽

Rank Reduction ◽

Data Set ◽

Reduced Rank ◽

Truncated Svd

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 [Formula: see text] deconvolution, the classical SSA method, and the proposed robust SSA method. The [Formula: see text] 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.

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Effective diffraction separation using the improved optimal rank-reduction method

Geophysics ◽

10.1190/geo2021-0326.1 ◽

2022 ◽

pp. 1-85

Author(s):

Peng Lin ◽

Suping Peng ◽

Xiaoqin Cui ◽

Wenfeng Du ◽

Chuangjian Li

Keyword(s):

Seismic Data ◽

Reduction Method ◽

Singular Values ◽

Vital Role ◽

Singular Value ◽

Low Rank ◽

Small Scale ◽

Frobenius Norm ◽

Rank Reduction ◽

Reduction Methods

Seismic diffractions encoding subsurface small-scale geologic structures have great potential for high-resolution imaging of subwavelength information. Diffraction separation from the dominant reflected wavefields still plays a vital role because of the weak energy characteristics of the diffractions. Traditional rank-reduction methods based on the low-rank assumption of reflection events have been commonly used for diffraction separation. However, these methods using truncated singular-value decomposition (TSVD) suffer from the problem of reflection-rank selection by singular-value spectrum analysis, especially for complicated seismic data. In addition, the separation problem for the tangent wavefields of reflections and diffractions is challenging. To alleviate these limitations, we propose an effective diffraction separation strategy using an improved optimal rank-reduction method to remove the dependence on the reflection rank and improve the quality of separation results. The improved rank-reduction method adaptively determines the optimal singular values from the input signals by directly solving an optimization problem that minimizes the Frobenius-norm difference between the estimated and exact reflections instead of the TSVD operation. This improved method can effectively overcome the problem of reflection-rank estimation in the global and local rank-reduction methods and adjusts to the diversity and complexity of seismic data. The adaptive data-driven algorithms show good performance in terms of the trade-off between high-quality diffraction separation and reflection suppression for the optimal rank-reduction operation. Applications of the proposed strategy to synthetic and field examples demonstrate the superiority of diffraction separation in detecting and revealing subsurface small-scale geologic discontinuities and inhomogeneities.

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Fast dual-domain reduced-rank algorithm for 3D deblending via randomized QR decomposition

Geophysics ◽

10.1190/geo2015-0292.1 ◽

2016 ◽

Vol 81 (1) ◽

pp. V89-V101 ◽

Cited By ~ 33

Author(s):

Jinkun Cheng ◽

Mauricio D. Sacchi

Keyword(s):

Seismic Data ◽

Seismic Profile ◽

Qr Decomposition ◽

Low Rank ◽

Acquisition Time ◽

Vertical Seismic Profile ◽

Rank Constraint ◽

Truncated Svd ◽

Dual Domain ◽

Simultaneous Source

We have developed a fast dual-domain algorithm based on matrix rank reduction for separating simultaneous-source seismic data. Our algorithm operates on 3D common receiver gathers or offset-midpoint gathers. At a given monochromatic frequency slice in the [Formula: see text]-[Formula: see text]-[Formula: see text] domain, the spatial data of the ideal unblended common receiver or offset-midpoint gather could be represented via a low-rank matrix. The interferences from the randomly and closely fired shots increased the rank of the aforementioned matrix. Therefore, we could minimize the misfit between the blended observation and the predicted blended data subject to a low-rank constraint that was applied to the data in the [Formula: see text]-[Formula: see text]-[Formula: see text] domain. The low-rank constraint could be implemented via the classic truncated singular value decomposition (SVD) or via a randomized QR decomposition (rQRd). The rQRd yielded nearly one order of processing time improvement with respect to the truncated SVD. We have also discovered that the rQRd was less stringent on the selection of the rank of the data. The latter was important because we often had no precise knowledge of the optimal rank that was required to represent the data. We adopted a synthetic 3D vertical seismic profile and a real seismic data set acquired at the North Viking Graben to test the performance of the proposed source separation algorithm. The proposed algorithm effectively eliminated the interferences while preserving the desired unblended signal. Especially for the synthetic vertical seismic profile example, experiments were evaluated under different survey time ratios. Our tests indicated that the proposed method could save up to 90% of acquisition time under a self-simultaneous source acquisition scenario.

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Application of Wavelet Analysis in Denoising Seismic Data

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.530-531.540 ◽

2014 ◽

Vol 530-531 ◽

pp. 540-543 ◽

Cited By ~ 1

Author(s):

Qing Yi Liu

Keyword(s):

Wavelet Analysis ◽

Seismic Data ◽

Random Noise ◽

The Novel ◽

Analysis Method ◽

Denoising Method ◽

Standard Methods ◽

Useful Signal ◽

Acceleration Sensors ◽

Optical Acceleration

The random noise is the kind of noise with wide frequency band in seismic data detected by the optical acceleration sensors. The noises influence and destroy the useful signal of the seismic information. There are a lot of methods to remove noise and one of the standard methods to remove the noise of the signal was the fast Fourier transform (FFT) which was the linear Fourier smoothing. In this paper, the novel denoising method based on wavelet analysis was introduced. The denoising results of seismic data with the noise with FFT method and wavelet analysis method, respectively. SNRs of the signal with noise, FFT denoisng and wavelet analysis denoising are-8.69, -1.13, and 8.27 respectively. The results show that the wavelet analysis method is prior to the traditional denoising method. The resolution of the seismic data improves.

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Simultaneous seismic data denoising and reconstruction via multichannel singular spectrum analysis

Geophysics ◽

10.1190/1.3552706 ◽

2011 ◽

Vol 76 (3) ◽

pp. V25-V32 ◽

Cited By ~ 302

Author(s):

Vicente Oropeza ◽

Mauricio Sacchi

Keyword(s):

Spectrum Analysis ◽

Seismic Data ◽

Field Data ◽

Convex Sets ◽

Singular Spectrum Analysis ◽

Hankel Matrix ◽

Reconstruction Method ◽

Rank Reduction ◽

Data Set ◽

Singular Spectrum

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.

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