Debiasing of seismic reflectivity inversion using basis pursuit de-noising algorithm

Li, Chuanhui; Liu, Xuewei; Yu, Kaiben; Wang, Xiangchun; Zhang, Fanchang

doi:10.1016/j.jappgeo.2020.104028

Cited by 14 publications

(11 citation statements)

References 30 publications

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“…Relevant to the problem under consideration, [16] adopted FISTA for reflectivity inversion. Further studies by [17] and [18] adopted FISTA along with debiasing steps of LS inversion and "adding back the residual", respectively, to improve amplitude recovery after support estimation using FISTA.…”

Section: A Prior Artmentioning

confidence: 99%

“…Also, 1 -norm regularization results in a biased estimate of x [20], [21], [22]. In their application of FISTA to the seismic reflectivity inversion problem, [17] and [18] observed an attenuation of reflection coefficient magnitudes. They adopted post-processing debiasing steps [23] to tackle the bias introduced due to the 1 -norm regularization.…”

Section: A Prior Artmentioning

confidence: 99%

See 1 more Smart Citation

DuRIN: A Deep-unfolded Sparse Seismic Reflectivity Inversion Network

Mache,

Pokala,

Rajendran

et al. 2021

Preprint

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We consider the reflection seismology problem of recovering the locations of interfaces and the amplitudes of reflection coefficients from seismic data, which are vital for estimating the subsurface structure. The reflectivity inversion problem is typically solved using greedy algorithms and iterative techniques. Sparse Bayesian learning framework, and more recently, deep learning techniques have shown the potential of data-driven approaches to solve the problem. In this paper, we propose a weighted minimax-concave penalty-regularized reflectivity inversion formulation and solve it through a modelbased neural network. The network is referred to as deepunfolded reflectivity inversion network (DuRIN). We demonstrate the efficacy of the proposed approach over the benchmark techniques by testing on synthetic 1-D seismic traces and 2-D wedge models and validation with the simulated 2-D Marmousi2 model and real data from the Penobscot 3D survey off the coast of

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Section: A Prior Artmentioning

confidence: 99%

Section: A Prior Artmentioning

confidence: 99%

DuRIN: A Deep-unfolded Sparse Seismic Reflectivity Inversion Network

Mache,

Pokala,

Rajendran

et al. 2021

Preprint

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show abstract

“…Chai et al (2014) invented a l 1 -norm regularized sparse reflectivity inversion method used for nonstationary seismic data. Li et al (2020) improved the estimation accuracy of seismic reflectivity inversion using l 1 -norm regularization by introducing a debiasing step of 'adding back the residual'.…”

Section: Introductionmentioning

confidence: 99%

Sparse seismic reflectivity inversion using an adaptive fast iterative shrinkage‐thresholding algorithm

Liu

2022

Geophysical Prospecting

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Seismic reflectivity inversion using l1‐norm regularization produces sparse solutions by applying an l1‐norm constraint. The fast iterative shrinkage‐thresholding algorithm is one of the most effective methods to solve l1‐norm regularized inversion problems. A large number of iterations are commonly required in the fast iterative shrinkage‐thresholding algorithm because its solution converges slowly towards the sparse solution. To improve its convergence rate, we introduce a modifying strategy for the traditional fast iterative shrinkage‐thresholding algorithm. When implementing the soft‐thresholding operator, the thresholding value is adaptively adjusted by assigning the reciprocal of the solution in the previous iteration as a weight to the thresholding value of the current iteration. In this way, small variables in the solution produce large coefficients applied to the thresholding value, which causes small variables to quickly converge to zero. The adaptive fast iterative shrinkage‐thresholding algorithm shows significantly improved computational efficiency and accuracy compared to the traditional fast iterative shrinkage‐thresholding algorithm. It produces good results for both numerical and field examples of l1‐norm regularized seismic reflectivity inversion.

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“…Zhang and Castagna [9] solved the 1 -norm constrained reflectivity inversion problem through basis-pursuit inversion (BPI) [10], using a wavelet dictionary of odd and even reflectivity pairs. The fast iterative shrinkage-thresholding algorithm (FISTA) [11] has been employed for reflectivity inversion [12] along with an amplitude recovery boost through debiasing steps of least-squares inversion [13] and "adding back the residual" [14]. The 1 -norm, although convex, is not the best sparsity constraint for reflectivity inversion, and the accurate estimation of the sparsity of seismic reflections is challenging [15], [16].…”

Section: Introductionmentioning

confidence: 99%

“…Further, 1 -norm regularization underestimates the high-amplitude components and introduces a bias in the estimate of the sparse code x [17], [18], [19]. Both [13] and [14] observed the attenuation of reflectivity magnitudes due to the 1 -norm regularization term and adopted a post-processing debiasing step [20].…”

Section: Introductionmentioning

confidence: 99%

NuSPAN: A Proximal Average Network for Nonuniform Sparse Model -- Application to Seismic Reflectivity Inversion

Mache¹,

Pokala²,

Rajendran³

et al. 2021

Preprint

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We solve the problem of sparse signal deconvolution in the context of seismic reflectivity inversion, which pertains to high-resolution recovery of the subsurface reflection coefficients. Our formulation employs a nonuniform, non-convex synthesis sparse model comprising a combination of convex and non-convex regularizers, which results in accurate approximations of the 0 pseudo-norm. The resulting iterative algorithm requires the proximal average strategy. When unfolded, the iterations give rise to a learnable proximal average network architecture that can be optimized in a data-driven fashion. We demonstrate the efficacy of the proposed approach through numerical experiments on synthetic 1-D seismic traces and 2-D wedge models in comparison with the benchmark techniques. We also present validations considering the simulated Marmousi2 model as well as real 3-D seismic volume data acquired from the Penobscot 3D survey off the coast of Nova Scotia, Canada.

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Debiasing of seismic reflectivity inversion using basis pursuit de-noising algorithm

Cited by 14 publications

References 30 publications

DuRIN: A Deep-unfolded Sparse Seismic Reflectivity Inversion Network

DuRIN: A Deep-unfolded Sparse Seismic Reflectivity Inversion Network

Sparse seismic reflectivity inversion using an adaptive fast iterative shrinkage‐thresholding algorithm

NuSPAN: A Proximal Average Network for Nonuniform Sparse Model -- Application to Seismic Reflectivity Inversion

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