A compressed data approach for image-domain least-squares migration

We consider the problem of image-domain least-squares migration based on efficiently constructing the Hessian matrix with sparse beam data. Specifically, we use the ultra-wide-band phase space beam summation method, where beams are used as local basis functions to represent scattered data collected at the surface. The beam domain data are sparse. One can identify seismic events with significant contributions so that only beams with non-negligible amplitudes need to be used to image the subsurface. In addition, due to the beams' spectral localization, only beams that pass near an imaging point need to be taken into account. These two properties reduce the computational complexity of computing the Hessian matrix - an essential ingredient for least-squares migration. As a result, we can efficiently construct the Hessian matrix based on analyzing the sparse beam domain data.

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Image domain least-squares migration with a Hessian matrix estimated by non-stationary matching filters

Journal of Geophysics and Engineering ◽

10.1093/jge/gxz098 ◽

2019 ◽

Vol 17 (1) ◽

pp. 148-159 ◽

Cited By ~ 2

Author(s):

Song Guo ◽

Huazhong Wang

Keyword(s):

Least Squares ◽

Numerical Experiments ◽

Field Data ◽

Hessian Matrix ◽

Computational Cost ◽

Image Deblurring ◽

Data Set ◽

Image Domain ◽

Slow Convergence ◽

Least Squares Migration

Abstract Assuming that an accurate background velocity is obtained, least-squares migration (LSM) can be used to estimate underground reflectivity. LSM can be implemented in either the data domain or image domain. The data domain LSM (DDLSM) is not very practical because of its huge computational cost and slow convergence rate. The image domain LSM (IDLSM) might be a flexible alternative if estimating the Hessian matrix using a cheap and accurate approach. It has practical potential to analyse convenient Hessian approximation methods because the Hessian matrix is too huge to compute and save. In this paper, the Hessian matrix is approximated with non-stationary matching filters. The filters are calculated to match the conventional migration image to the demigration/remigration image. The two images are linked by the Hessian matrix. An image deblurring problem is solved with the estimated filters for the IDLSM result. The combined sparse and total variation regularisations are used to produce accurate and reasonable inversion results. The numerical experiments based on part of Sigsbee model, Marmousi model and a 2D field data set illustrate that the non-stationary matching filters can give a good approximation for the Hessian matrix, and the results of the image deblurring problem with combined regularisations can provide high-resolution and true-amplitude reflectivity estimations.

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A fast least-squares migration with ultra-wide-band phase-space beam summation method

Journal of Physics Communications ◽

10.1088/2399-6528/ac261d ◽

2021 ◽

Author(s):

Ram Tuvi ◽

Zeyu Zhao ◽

Mrinal Kanti Sen

Keyword(s):

Phase Space ◽

Least Squares ◽

Wide Band ◽

Summation Method ◽

Ultra Wide Band ◽

Least Squares Migration

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Migration deconvolution using domain decomposition

Geophysics ◽

10.1190/geo2020-0352.1 ◽

2021 ◽

pp. 1-61

Author(s):

Luana Nobre Osorio ◽

Bruno Pereira-Dias ◽

André Bulcão ◽

Luiz Landau

Keyword(s):

Domain Decomposition ◽

Least Squares ◽

Iterative Algorithms ◽

Image Resolution ◽

Image Domain ◽

Hessian Operator ◽

Incomplete Coverage ◽

And Migration ◽

Least Squares Migration ◽

Data Frequency

Least-squares migration (LSM) is an effective technique for mitigating blurring effects and migration artifacts generated by the limited data frequency bandwidth, incomplete coverage of geometry, source signature, and unbalanced amplitudes caused by complex wavefield propagation in the subsurface. Migration deconvolution (MD) is an image-domain approach for least-squares migration, which approximates the Hessian operator using a set of precomputed point spread functions (PSFs). We introduce a new workflow by integrating the MD and the domain decomposition (DD) methods. The DD techniques aim to solve large and complex linear systems by splitting problems into smaller parts, facilitating parallel computing, and providing a higher convergence in iterative algorithms. The following proposal suggests that instead of solving the problem in a unique domain, as conventionally performed, we split the problem into subdomains that overlap and solve each of them independently. We accelerate the convergence rate of the conjugate gradient solver by applying the DD methods to retrieve a better reflectivity, which is mainly visible in regions with low amplitudes. Moreover, using the pseudo-Hessian operator, the convergence of the algorithm is accelerated, suggesting that the inverse problem becomes better conditioned. Experiments using the synthetic Pluto model demonstrate that the proposed algorithm dramatically reduces the required number of iterations while providing a considerable enhancement in the image resolution and better continuity of poorly illuminated events.

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Image-Domain Least-Squares Migration for RTM Surface-Offset Gathers

10.3997/2214-4609.201900827 ◽

2019 ◽

Author(s):

W. Dai ◽

Z. Xu ◽

X. Cheng ◽

K. Jiao ◽

D. Vigh

Keyword(s):

Least Squares ◽

Image Domain ◽

Least Squares Migration

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A fast image domain least squares migration method with local data target approach

10.1190/segam2020-3423961.1 ◽

2020 ◽

Author(s):

Ram Tuvi ◽

Zeyu Zhao ◽

Mrinal K. Sen

Keyword(s):

Least Squares ◽

Local Data ◽

Image Domain ◽

Migration Method ◽

Least Squares Migration

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Least-squares migration with a blockwise Hessian matrix: A prestack time-migration approach

Geophysics ◽

10.1190/geo2018-0533.1 ◽

2019 ◽

Vol 84 (4) ◽

pp. R625-R640 ◽

Cited By ~ 2

Author(s):

Bowu Jiang ◽

Jianfeng Zhang

Keyword(s):

Least Squares ◽

Field Data ◽

Hessian Matrix ◽

Total Variation Regularization ◽

Data Sets ◽

Reflection Point ◽

Inverse Approach ◽

Time Migration ◽

Prestack Time Migration ◽

Least Squares Migration

We have developed an explicit inverse approach with a Hessian matrix for the least-squares (LS) implementation of prestack time migration (PSTM). A full Hessian matrix is divided into a series of computationally tractable small-sized matrices using a localized approach, thus significantly reducing the size of the inversion. The scheme is implemented by dividing the imaging volume into a series of subvolumes related to the blockwise Hessian matrices that govern the mapping relationship between the migrated result and corresponding reflectivity. The proposed blockwise LS-PSTM can be implemented in a target-oriented fashion. The localized approach that we use to modify the Hessian matrix can eliminate the boundary effects originating from the blockwise implementation. We derive the explicit formula of the offset-dependent Hessian matrix using the deconvolution imaging condition with an analytical Green’s function of PSTM. This avoids the challenging task of estimating the source wavelet. Moreover, migrated gathers can be generated with the proposed scheme. The smaller size of the blockwise Hessian matrix makes it possible to incorporate the total-variation regularization into the inversion, thus attenuating noises significantly. We revealed the proposed blockwise LS-PSTM with synthetic and field data sets. Higher quality common-reflection-point gathers of the field data are obtained.

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