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.

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.

scholarly journals An Alternative Adaptive Method for Seismic Data Denoising and Interpolation

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Zilin Lu ◽  
Nuan Xia ◽  
Liang Sun ◽  
Wenxing Xu ◽  
Guangcheng Zhang ◽  
...  
Keyword(s):  
Seismic Data ◽  
Energy Intensity ◽  
Reduction Method ◽  
Random Noise ◽  
Complex Surface ◽  
Adaptive Method ◽  
Rank Reduction ◽  
Energy Entropy ◽  
The Difference ◽  
Field Area

Seismic data denoising and interpolation are generally essential steps for reflection processing and imaging workflow especially for the complex surface geologic conditions and the irregular acquisition field area. The rank-reduction method is a valid way for the attenuation of random noise and data interpolation by selecting the suitable threshold, i.e., the rank of the useful signals. However, it is difficult for the traditional rank-reduction method to select an appropriate threshold. In this paper, we propose an adaptive rank-reduction method based on the energy entropy to automatically estimate the rank as the threshold for seismic data processing and interpolation. This method considers the energy entropy into the traditional rank-reduction method. The energy entropy of signals can be used to indicate the energy intensity of a signal component in the total energy. The difference of the energy entropy between the useful signals and random noise is perceived as a measurement for selecting the appropriate threshold. Synthetic and field examples indicate that the proposed method can well achieve the attenuation of random noise and interpolation automatically without the estimation of the ranks and demonstrate the feasibility of the new adaptive method in seismic data denoising and interpolation.

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.

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

Geophysics ◽  
2020 ◽  
pp. 1-143
Author(s):  
Yapo Abolé Serge Innocent Oboué ◽  
Wei Chen ◽  
Hang Wang ◽  
Yangkang Chen
Keyword(s):  
Singular Value Decomposition ◽  
Seismic Data ◽  
Moving Average ◽  
Random Noise ◽  
Singular Value ◽  
Truncated Singular Value Decomposition ◽  
Rank Reduction ◽  
Residual Noise ◽  
Value Decomposition

We have developed a new method for simultaneous denoising and reconstruction of 5-D seismic data corrupted by random noise and missing traces. Several algorithms have been proposed for seismic data restoration based on rank-reduction methods. More recently, a damping operator has been introduced into the conventional truncated singular value decomposition (TSVD) formula to further remove residual noise, the presence of which disturbs the quality of the seismic results. Despite the success of the damped rank-reduction (DRR) method when the observed data have an extremely low signal-to-noise ratio (SNR), random noise is still a limiting factor for obtaining perfect quality of the result. Therefore, how to accurately solve the simultaneous denoising and reconstruction problem with high fidelity is still challenging. We assume that introducing only the damping operator into the TSVD formula is not enough to remove the random noise and restore the useful signal well. Here, by combining the soft thresholding operator and the moving-average filter, we first develop a new operator, which we call soft thresholding moving-average (STMA) operator. Then, by introducing the STMA operator into the DRR framework, we develop a new algorithm known as the robust damped rank-reduction (RDRR) method, which aims at mixing the advantages of the STMA operator and the damping operator. The STMA operator is applied to the Hankel matrix after damped truncated singular value decomposition (DTSVD) to better remove the residual noise. Examples of the proposed approach on synthetic and field 5-D seismic data demonstrate the better performance in terms of the visual examination and numerical test compared with the DRR approach. The proposed method aims at producing an effective low-rank filter and, thus, can perfectly enhance the SNR of the simultaneously denoised and reconstructed results with higher accuracy.

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

5D de-aliased seismic data interpolation using non-stationary prediction error filter

Geophysics ◽  
2021 ◽  
pp. 1-92
Author(s):  
Yangkang Chen ◽  
Sergey Fomel ◽  
Hang Wang ◽  
shaohuan zu
Keyword(s):  
Seismic Data ◽  
Prediction Error ◽  
Reduction Method ◽  
Signal To Noise Ratio ◽  
Data Interpolation ◽  
Computationally Efficient ◽  
Rank Reduction ◽  
Frequency Space ◽  
Time Space ◽  
Ill Posed

The prediction error filter (PEF) assumes that the seismic data can be destructed to zero by applying a convolutional operation between the target data and prediction filter in either time-space or frequency-space domain. Here, we extend the commonly known PEF in 2D or 3D problems to its 5D version. To handle the non-stationary property of the seismic data, we formulate the PEF in a non-stationary way, which is called the non-stationary prediction error filter (NPEF). In the NPEF, the coefficients of a fixed-size PEF vary across the whole seismic data. In NPEF, we aim at solving a highly ill-posed inverse problem via the computationally efficient iterative shaping regularization. The NPEF can be used to denoise multi-dimensional seismic data, and more importantly, to restore the highly incomplete aliased 5D seismic data. We compare the proposed NPEF method with the state-of-the-art rank-reduction method for the 5D seismic data interpolation in cases of irregularly and regularly missing traces via several synthetic and real seismic data. Results show that although the proposed NPEF method is less effective than the rank-reduction method in interpolating irregularly missing traces especially in the case of low signal to noise ratio (S/N), it outperforms the rank-reduction method in interpolating aliased 5D dataset with regularly missing traces.

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.

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