Combining the multigrid and gradient methods to solve the seismic inversion problem

Saleck, Fatimetou M.; Bunks, Carey; Zaleski, Stéphane; Chavent, Guy

doi:10.1190/1.1822589

Cited by 6 publications

(3 citation statements)

References 1 publication

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“…The method consists of decomposing a problem by scale, followed by the resolution of each scale component by a suitable relaxation operator. More recently, the multigrid method has been applied to distributed parameter estimation problems [1][2][3]14]. The results showed that iterative inversion methods performed much better when employed with a decomposition by scale.…”

Section: Introductionmentioning

confidence: 95%

A wavelet multiscale method for the inverse problems of a two-dimensional wave equation

Han

2004

Inverse Problems in Science and Engineering

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This article considers the problem of estimating the velocity in a two-dimensional acoustic wave equation. The wavelet analysis is introduced and a wavelet multiscale method is constructed, based on the idea of hierarchical approximation. The inverse problem is decomposed into a sequence of inverse problems which rely on the scale variables and are solved successively according to the size of scale from the longest to the shortest. And in every inversion, at different scales, the regularized Gauss-Newton method is used, which is stable and fast, until the parameter of the primary inverse problem is found. The results of numerical simulations indicate that the method is a widely convergent optimization method (in some cases it may be global), and exhibits the advantages of conventional methods on computational efficiency and precision.

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Section: Introductionmentioning

confidence: 95%

A wavelet multiscale method for the inverse problems of a two-dimensional wave equation

Han

2004

Inverse Problems in Science and Engineering

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“…Another effort to mitigate the cycle-skipping problem is to apply a multiscale seismic waveform inversion method (Kolb et al, 1986;Lindgren et al, 1989;Saleck et al, 1993), which gradually inverts from low-wavenumber to high-wavenumber structures. Bunks et al (1995) propose a multigrid waveform inversion method based on frequency decomposition by three operators.…”

Section: Introductionmentioning

confidence: 99%

Alternating first-arrival traveltime tomography and waveform inversion for near-surface imaging

Sun

Zhang

2017

GEOPHYSICS

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Near-surface seismic imaging often plays a significant role in producing quality data processing results for the deep subsurface in land and shallow marine environments.First-arrival traveltime tomography is a common approach for near-surface imaging due to its high efficiency and simplicity. However, the method faces issues of missing hidden layers and resolving the structures with low resolution. On the other hand, waveform inversion should offer better solutions for dealing with these issues but may suffer from the cycle-skipping problem. We intend to use the advantages and reduce the disadvantages of the two methods by developing a new strategy of alternately applying traveltime tomography and waveform inversion through iterations.First-arrival traveltime tomography applies a wavefront raytracer and a nonlinear inversion approach. Waveform inversion is a multiscale approach in which a wavelet transform is applied in the data domain to better handle the cycle-skipping problem.By alternating the two inversions rather than performing a joint inversion, we reduce the memory requirements and avoid non-physical scaling problems between the two approaches. Using one synthetic and two real data examples, we demonstrate that alternating inversions minimize two separate objective functions at the same time and constrain the near surface structures fairly well compared with the waveform inversion method alone. For the field examples, the new method avoids generating the obvious artifacts and provides results consistent with the geology analysis of those areas.

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“…Moving on to inversion applications, Saleck et al [2] combined multigrid and gradient methods to solve 2D acoustic wave equation. In such cases, solving a nonlinear optimization problem requires a discretization of the problem followed by numerical integration.…”

Section: Introductionmentioning

confidence: 99%

A Parallel Multigrid Solver For Block-Tridiagonal Stencil Matrices Derived From Acoustic Wave Equation On Large Finite Difference Grids

Carrion¹,

Catabriga²,

Coutinho³

et al. 2017

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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Abstract. In this work we present efficient numerical solvers for large linear systems originated from a second-order finite difference discretization of three-dimensional acoustic wave problems in the frequency domain. We consider Geometric Multigrid strategies combined with the well known Conjugate Gradient and Red-Black SOR algorithms. Our method is designed for parallel execution on shared-memory platforms using the OpenMP paradigm. The experiments show that the parallel Conjugate Gradient method applying Multigrid as a preconditioner offers the best results in terms of CPU time and number of iterations.

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Combining the multigrid and gradient methods to solve the seismic inversion problem

Cited by 6 publications

References 1 publication

A wavelet multiscale method for the inverse problems of a two-dimensional wave equation

A wavelet multiscale method for the inverse problems of a two-dimensional wave equation

Alternating first-arrival traveltime tomography and waveform inversion for near-surface imaging

A Parallel Multigrid Solver For Block-Tridiagonal Stencil Matrices Derived From Acoustic Wave Equation On Large Finite Difference Grids

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