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

Geophysical Prospecting

Chen

2020

Self Cite

Based on the fact that the Hankel matrix constructed by noise-free seismic data is low-rank, low-rank approximation (or rank-reduction) methods have been widely used for removing noise from seismic data. Due to the linear-event assumption of the traditional low-rank approximation method, it is difficult to define a rank that optimally separates the data subspace into signal and noise subspaces. For preserving the most useful signal energy, a relatively large rank threshold is often chosen, which inevitably leaves residual noise. To reduce the energy of residual noise, we propose an optimally damped rank-reduction method. The optimal damping is applied via two steps. In the first step, a set of optimal damping weights is derived. In the second step, we derive an optimal singular value damping operator. We review several traditional low-rank methods and compare their performance with the new one. We also compare these low-rank methods with two sparsity-promoting transform methods. Examples demonstrate that the proposed optimally damped rank-reduction method could get significantly cleaner denoised images compared with the state-of-the-art methods.

“…It can be derived that the damping formula (equation ()) also holds for equation () but with the damping threshold matrix expressed as

boldΓ = {\overset{σ}{true}}^{K} {((), Σ_{N}^{Q})}^{- K},

where the subscript

N

denotes a sufficiently large rank parameter, as required by the derivations detailed in Chen et al . (2020). The resulted final form of the optimally DRR (ODRR) method then can be expressed as

\hat{boldS} = {boldU}_{N} P \hat{boldW} {boldΣ}_{N} {boldV}_{N}^{normalH} .

…”

Section: Theorymentioning

confidence: 99%

“…Because of the insensitivity, one can use a sufficiently large

N

Section: Theorymentioning

confidence: 99%

Seismic signal enhancement based on the low‐rank methods

Huang

Geophysical Prospecting

Chen

2020

Self Cite

“…Most of these methods have good processing effect on non‐regular data but need to set threshold functions manually, which requires rich experience, and the reconstruction result is poor when the seismic data contain spatial frequency aliasing. (4) Reconstruction of seismic data uses low‐rank matrix (Gao et al., 2013; Lopez et al., 2016; Oboue & Chen, 2021) and is now developed to five‐dimensional seismic data reconstruction (Chen et al., 2016; Chen et al., 2019; Wu et al., 2020). The disadvantage of this kind of method is that the computational cost grows exponentially with the increase of data dimension, which requires higher requirements for the computer hardware.…”

Section: Introductionmentioning

confidence: 99%

Seismic data reconstruction using Bregman iterative algorithm based on compressed sensing and discrete orthonormal wavelet transform

Geophysical Prospecting

Zhang

2022

Due to the limitations of the actual acquisition environment in the field, especially in ocean bottom seismometer (OBS) acquisition, the acquired seismic data are often irregular and incomplete, which affects the subsequent data imaging, interpretation and hydrocarbon‐bearing reservoir prediction. The interpolation reconstruction algorithm based on the compressive sensing theory can reconstruct the data without the limitation of Nyquist sampling interval. However, the reconstruction accuracy and effect are different for different sparse representations of the data. On the basis of compressed sensing theory, we propose a Bregman iterative seismic data reconstruction method based on the sparse decomposition of discrete orthonormal Coiflets and Symlets wavelet transforms. First, the discrete orthonormal matrix is constructed by using the above two wavelet functions to make the original seismic data sparse, then the Bregman iterative algorithm is used to reconstruct the sparse coefficients in the discrete wavelet domain, and finally the recovery matrix is used to reconstruct the seismic data. The discrete orthonormal Coiflets and Symlets wavelet transforms have good sparse representation ability and can compensate for the problem that discrete Fourier transform cannot well sparse representation of the data. After numerical experiments on horizontal‐layered model, Marmousi2 model and actual data, it is verified that the proposed method can reconstruct the missing seismic data under the regular observation system and under the irregular observation system with non‐uniform OBS distribution. Furthermore, this method can hardly bring the interference of random noise, and the reconstruction result is of high accuracy.

“…Although simultaneous 5D seismic data reconstruction and denoising via low-rank approximation becomes more attractive recently, there are still many challenges within this framework. Major issues in low-rank approximation approaches for 5D data interpolation are [53]: (1) high computational cost during SVD process, (2) the inevitable residual noise [19] and (3) the rank inconsistency problem [72].…”

Section: Introductionmentioning

confidence: 99%

“…[67] proposed empirical low-rank approximation, in which the multi-dip data are decomposed to multiple single-dip data so that the optimal rank (e.g., one) can be applied to each local window. More recently, [72] developed an adaptive rank thresholding method to make the damped rank-reduction method suitable for local processing.…”

Section: Introductionmentioning

confidence: 99%

Fast and Robust Low-Rank Approximation for Five-Dimensional Seismic Data Reconstruction

Zhang

et al. 2020

IEEE Access

Self Cite

Five-dimensional (5D) seismic data reconstruction becomes more appealing in recent years because it takes advantage of five physical dimensions of the seismic data and can reconstruct data with large gap. The low-rank approximation approach is one of the most effective methods for reconstructing 5D dataset. However, the main disadvantage of the low-rank approximation method is its low computational efficiency because of many singular value decompositions (SVD) of the block Hankel/Toeplitz matrix in the frequency domain. In this paper, we develop an SVD-free low-rank approximation method for efficient and effective reconstruction and denoising of the seismic data that contain four spatial dimensions. Our SVD-free rank constraint model is based on an alternating minimization strategy, which updates one variable each time while fixing the other two. For each update, we only need to solve a linear least-squares problem with much less expensive QR factorization. The SVD-based and SVD-free lowrank approximation methods in the singular spectrum analysis (SSA) framework are compared in detail, regarding the reconstruction performance and computational cost. The comparison shows that the SVD-free low-rank approximation method can obtain similar reconstruction performance as the SVD-based method but with a large computational speedup.