Effective diffraction separation using the improved optimal rank-reduction method

Geophysics ◽  
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.

Five-dimensional seismic data reconstruction using the optimally damped rank-reduction method

2020 ◽  
Vol 222 (3) ◽  
pp. 1824-1845 ◽  
Author(s):  
Yangkang Chen ◽  
Min Bai ◽  
Zhe Guan ◽  
Qingchen Zhang ◽  
Mi Zhang ◽  
...  
Keyword(s):  
Seismic Data ◽  
Reduction Method ◽  
Random Noise ◽  
Singular Values ◽  
Adaptive Method ◽  
Frobenius Norm ◽  
Damping Factor ◽  
Rank Reduction ◽  
Large Rank ◽  
Residual Noise

SUMMARY It is difficult to separate additive random noise from spatially coherent signal using a rank-reduction (RR) method that is based on the truncated singular value decomposition (TSVD) operation. This problem is due to the mixture of the signal and the noise subspaces after the TSVD operation. This drawback can be partially conquered using a damped RR (DRR) method, where the singular values corresponding to effective signals are adjusted via a carefully designed damping operator. The damping operator works most powerfully in the case of a small rank and a small damping factor. However, for complicated seismic data, e.g. multichannel reflection seismic data containing highly curved events, the rank should be large enough to preserve the details in the data, which makes the DRR method less effective. In this paper, we develop an optimal damping strategy for adjusting the singular values when a large rank parameter is selected so that the estimated signal can best approximate the exact signal. We first weight the singular values using optimally calculated weights. The weights are theoretically derived by solving an optimization problem that minimizes the Frobenius-norm difference between the approximated and the exact signal components. The damping operator is then derived based on the initial weighting operator to further reduce the residual noise after the optimal weighting. The resulted optimally damped rank-reduction method is nearly an adaptive method, i.e. insensitive to the rank parameter. We demonstrate the performance of the proposed method on a group of synthetic and real 5-D seismic data.

scholarly journals Adaptive rank-reduction method for seismic data reconstruction

2018 ◽  
Vol 15 (4) ◽  
pp. 1688-1703 ◽  
Author(s):  
Juan Wu ◽  
Min Bai
Keyword(s):  
Seismic Data ◽  
Reduction Method ◽  
Singular Values ◽  
Data Reconstruction ◽  
Rank Reduction ◽  
Practical Applications ◽  
Field Environment ◽  
Local Window ◽  
Seismic Data Reconstruction ◽  
Automatic Algorithm

Abstract Seismic data reconstruction plays an important role in the whole seismic data processing and imaging workflow, especially for those data that are acquired from severe field environment and are missing a large portion of the reflection signals. The rank-reduction method is considered to be a very effective method for interpolating data that are of small curvature, e.g. the post-stack data. However, when the data are more complicated, the rank-reduction method may fail to achieve acceptable performance. A useful strategy is to use local windows to process the data so that the data in each local window satisfy the plane-wave assumption of the rank-reduction method. However, the rank in each window requires a careful selection. Traditional methods select a global rank for all windows. We have proposed an automatic algorithm to select the rank in each processing window. The energy ratio between two consecutive singular values is chosen as the criterion to define the optimal rank. We apply this strategy to seismic data interpolation and use both synthetic and field data examples to demonstrate its potential in practical applications.

Hybrid rank-sparsity constraint model for simultaneous reconstruction and denoising of 3D seismic data

Geophysics ◽  
2017 ◽  
Vol 82 (5) ◽  
pp. V351-V367 ◽  
Author(s):  
Dong Zhang ◽  
Yatong Zhou ◽  
Hanming Chen ◽  
Wei Chen ◽  
Shaohuan Zu ◽  
...  
Keyword(s):  
Seismic Data ◽  
Reduction Method ◽  
Superior Performance ◽  
3D Seismic ◽  
Rank Reduction ◽  
Simultaneous Reconstruction ◽  
Reduction Methods ◽  
Sparsity Constraint ◽  
Constraint Model ◽  
3D Seismic Data

We have determined an approach for simultaneous reconstruction and denoising of 3D seismic data with randomly missing traces. The core in simultaneous reconstruction and denoising of 3D seismic data is the choice of constraint method. Recently, there have been two types of popular approaches to choose such a constraint: sparsity-promoting transforms using a sparsity constraint and rank reduction methods using a rank constraint. Although the sparsity-promoting transform enjoys the direct advantage of high efficiency, it lacks adaptivity to a variety of data patterns. On the other hand, the rank reduction method can be adaptively applied to different data sets, but its computational cost is quite high. We investigate multiple constraints for simultaneous seismic data reconstruction and denoising based on a novel hybrid rank-sparsity constraint (HRSC) model, which aims at combining the benefits of the sparsity-promoting transforms and rank reduction methods. Also, we design the corresponding HRSC algorithmic framework to effectively solve our new model via tightly combining a sparsity-promoting transform and a rank reduction method, which is more powerful in simultaneous reconstruction and denoising of 3D seismic data. Our HRSC framework aims at providing an extra level of constraint and, thus, can significantly improve the signal-to-noise ratio (S/N) of the reconstructed results with higher efficiency. Application of the HRSC framework on synthetic and field 3D seismic data demonstrates superior performance in terms of S/N and visual observation compared with the well-known rank reduction method, known as multichannel singular spectrum analysis.

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.

Damped rank-reduction method for simultaneous denoising and reconstruction of 5D seismic data

2016 ◽  
Author(s):  
Yangkang Chen ◽  
Dong Zhang ◽  
Weilin Huang ◽  
Shaohuan Zu ◽  
Zhaoyu Jin ◽  
...  
Keyword(s):  
Seismic Data ◽  
Reduction Method ◽  
Rank Reduction

scholarly journals Five-dimensional seismic data reconstruction using the optimally damped rank-reduction method

2019 ◽  
Vol 218 (1) ◽  
pp. 224-246 ◽  
Author(s):  
Yangkang Chen ◽  
Min Bai ◽  
Zhe Guan ◽  
Qingchen Zhang ◽  
Mi Zhang ◽  
...  
Keyword(s):  
Seismic Data ◽  
Reduction Method ◽  
Data Reconstruction ◽  
Rank Reduction ◽  
Seismic Data Reconstruction

Separation and imaging of seismic diffractions using a localized rank-reduction method with adaptively selected ranks

Geophysics ◽  
2020 ◽  
Vol 85 (6) ◽  
pp. V497-V506
Author(s):  
Hang Wang ◽  
Xingye Liu ◽  
Yangkang Chen
Keyword(s):  
Plane Wave ◽  
Reduction Method ◽  
Seismic Profile ◽  
Low Rank ◽  
Imaging Method ◽  
Seismic Profiles ◽  
Rank Reduction ◽  
Diffraction Profile ◽  
Imaging Result ◽  
Accurate Performance

Seismic diffractions are weak seismic events hidden within the more dominant reflection events in a seismic profile. Separating diffraction energy from the poststack seismic profiles can help infer the subsurface discontinuities that generate the diffraction events. The separated seismic diffractions can be migrated with a traditional seismic imaging method or a specifically designed migration method to highlight the diffractors, that is, the diffraction image. Traditional diffraction separation methods based on the underlying plane-wave assumption are limited by either the inaccurate slope estimation or the plane-wave assumption of the plane-wave destruction filter and thus will cause reflection leakage into the separated diffraction profile. The leaked reflection energy will deteriorate the resolution of the subsequent diffraction imaging result. We have adopted a new diffraction separation method based on a localized rank-reduction (LRR) method. The LRR method assumes the reflection events to be locally low-rank and the diffraction energy can be separated by a rank-reduction operation. Compared to the global rank-reduction method, the LRR method is more constrained in selecting the rank and is free of separation artifacts. We use a carefully designed synthetic example to demonstrate that the LRR method can help separate the diffraction energy from a poststack seismic profile with kinematically and dynamically accurate performance.

An Improved Seismic Data Completion Algorithm using Low-Rank Tensor Optimization: Cost Reduction and Optimal Data Orientation

Geophysics ◽  
2021 ◽  
pp. 1-88
Author(s):  
Jonathan Popa ◽  
Susan E. Minkoff ◽  
Yifei Lou
Keyword(s):  
Fourier Transform ◽  
Singular Value Decomposition ◽  
Seismic Data ◽  
Convex Sets ◽  
Singular Spectrum Analysis ◽  
Singular Value ◽  
Low Rank ◽  
Traditional Methods ◽  
Value Decomposition ◽  
Conjugate Symmetry

Seismic data are often incomplete due to equipment malfunction, limited source and receiver placement at near and far offsets, and missing cross-line data. Seismic data contain redundancies as they are repeatedly recorded over the same or adjacent subsurface regions, causing the data to have a low-rank structure. To recover missing data one can organize the data into a multidimensional array or tensor and apply a tensor completion method. We can increase the effectiveness and efficiency of low-rank data reconstruction based on the tensor singular value decomposition (tSVD) by analyzing the effect of tensor orientation and exploiting the conjugate symmetry of the multidimensional Fourier transform. In fact, these results can be generalized to any order tensor. Relating the singular values of the tSVD to those of a matrix leads to a simplified analysis, revealing that the most square orientation gives the best data structure for low-rank reconstruction. After the first step of the tSVD, a multidimensional Fourier transform, frontal slices of the tensor form conjugate pairs. For each pair a singular value decomposition can be replaced with a much cheaper conjugate calculation, allowing for faster computation of the tSVD. Using conjugate symmetry in our improved tSVD algorithm reduces the runtime of the inner loop by 35% to 50%. We consider synthetic and real seismic datasets from the Viking Graben Region and the Northwest Shelf of Australia arranged as high-dimensional tensors. We compare tSVD based reconstruction to traditional methods, projection onto convex sets and multichannel singular spectrum analysis, and see that the tSVD based method gives similar or better accuracy and is more efficient, converging with runtimes that are an order of magnitude faster than the traditional methods. Additionally, we verify the most square orientation improves recovery for these examples by 10-20% compared to the other orientations.

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