Robust reduced-rank filtering for erratic seismic noise attenuation

Geophysics ◽  
2015 ◽  
Vol 80 (1) ◽  
pp. V1-V11 ◽  
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.

Simultaneous seismic data denoising and reconstruction via multichannel singular spectrum analysis

Geophysics ◽  
2011 ◽  
Vol 76 (3) ◽  
pp. V25-V32 ◽  
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.

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

Geophysics ◽  
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.

A fast reduced-rank interpolation method for prestack seismic volumes that depend on four spatial dimensions

Geophysics ◽  
2013 ◽  
Vol 78 (1) ◽  
pp. V21-V30 ◽  
Author(s):  
Jianjun Gao ◽  
Mauricio D. Sacchi ◽  
Xiaohong Chen
Keyword(s):  
Spatial Data ◽  
Toeplitz Matrix ◽  
Seismic Data ◽  
Random Noise ◽  
Computational Cost ◽  
Reconstruction Method ◽  
Rank Reduction ◽  
Lanczos Bidiagonalization ◽  
Reduced Rank ◽  
Block Toeplitz Matrix

Rank reduction strategies can be employed to attenuate noise and for prestack seismic data regularization. We present a fast version of Cadzow reduced-rank reconstruction method. Cadzow reconstruction is implemented by embedding 4D spatial data into a level-four block Toeplitz matrix. Rank reduction of this matrix via the Lanczos bidiagonalization algorithm is used to recover missing observations and to attenuate random noise. The computational cost of the Lanczos bidiagonalization is dominated by the cost of multiplying a level-four block Toeplitz matrix by a vector. This is efficiently implemented via the 4D fast Fourier transform. The proposed algorithm significantly decreases the computational cost of rank-reduction methods for multidimensional seismic data denoising and reconstruction. Synthetic and field prestack data examples are used to examine the effectiveness of the proposed method.

Deep denoising autoencoder for seismic random noise attenuation

Geophysics ◽  
2020 ◽  
Vol 85 (4) ◽  
pp. V367-V376 ◽  
Author(s):  
Omar M. Saad ◽  
Yangkang Chen
Keyword(s):  
Seismic Data ◽  
Signal To Noise Ratio ◽  
Random Noise ◽  
Singular Spectrum Analysis ◽  
Synthetic Data ◽  
Seismic Signal ◽  
Denoising Autoencoder ◽  
Levels Of Abstraction ◽  
Data Set ◽  
Effective Manner

Attenuation of seismic random noise is considered an important processing step to enhance the signal-to-noise ratio of seismic data. A new approach is proposed to attenuate random noise based on a deep-denoising autoencoder (DDAE). In this approach, the time-series seismic data are used as an input for the DDAE. The DDAE encodes the input seismic data to multiple levels of abstraction, and then it decodes those levels to reconstruct the seismic signal without noise. The DDAE is pretrained in a supervised way using synthetic data; following this, the pretrained model is used to denoise the field data set in an unsupervised scheme using a new customized loss function. We have assessed the proposed algorithm based on four synthetic data sets and two field examples, and we compare the results with several benchmark algorithms, such as f- x deconvolution ( f- x deconv) and the f- x singular spectrum analysis ( f- x SSA). As a result, our algorithm succeeds in attenuating the random noise in an effective manner.

Damped multichannel singular spectrum analysis for 3D random noise attenuation

Geophysics ◽  
2016 ◽  
Vol 81 (4) ◽  
pp. V261-V270 ◽  
Author(s):  
Weilin Huang ◽  
Runqiu Wang ◽  
Yangkang Chen ◽  
Huijian Li ◽  
Shuwei Gan
Keyword(s):  
Spectrum Analysis ◽  
Seismic Data ◽  
Random Noise ◽  
Singular Spectrum Analysis ◽  
Superior Performance ◽  
Damping Factor ◽  
Signal Subspace ◽  
Noise Attenuation ◽  
Random Noise Attenuation ◽  
Singular Spectrum

Multichannel singular spectrum analysis (MSSA) is an effective algorithm for random noise attenuation in seismic data, which decomposes the vector space of the Hankel matrix of the noisy signal into a signal subspace and a noise subspace by truncated singular value decomposition (TSVD). However, this signal subspace actually still contains residual noise. We have derived a new formula of low-rank reduction, which is more powerful in distinguishing between signal and noise compared with the traditional TSVD. By introducing a damping factor into traditional MSSA to dampen the singular values, we have developed a new algorithm for random noise attenuation. We have named our modified MSSA as damped MSSA. The denoising performance is controlled by the damping factor, and our approach reverts to the traditional MSSA approach when the damping factor is sufficiently large. Application of the damped MSSA algorithm on synthetic and field seismic data demonstrates superior performance compared with the conventional MSSA algorithm.

Denoising seismic data using the nonlocal means algorithm

Geophysics ◽  
2012 ◽  
Vol 77 (1) ◽  
pp. A5-A8 ◽  
Author(s):  
David Bonar ◽  
Mauricio Sacchi
Keyword(s):  
Seismic Data ◽  
Random Noise ◽  
Seismic Energy ◽  
Real Data ◽  
Spatial Proximity ◽  
Data Sets ◽  
Noise Attenuation ◽  
Nonlocal Means ◽  
Reflection Seismic ◽  
Generally True

The nonlocal means algorithm is a noise attenuation filter that was originally developed for the purposes of image denoising. This algorithm denoises each sample or pixel within an image by utilizing other similar samples or pixels regardless of their spatial proximity, making the process nonlocal. Such a technique places no assumptions on the data except that structures within the data contain a degree of redundancy. Because this is generally true for reflection seismic data, we propose to adopt the nonlocal means algorithm to attenuate random noise in seismic data. Tests with synthetic and real data sets demonstrate that the nonlocal means algorithm does not smear seismic energy across sharp discontinuities or curved events when compared to seismic denoising methods such as f-x deconvolution.

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