Optimal transport for seismic full waveform inversion

Engquist, Björn; Froese, Brittany D.; Yang, Yunan

doi:10.4310/cms.2016.v14.n8.a9

Cited by 134 publications

(164 citation statements)

References 16 publications

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“…Our work is motivated in part by [7,8,34], where the authors use the quadratic Wasserstein metric to solve Full-Waveform Inversion (FWI) problems. In particular, it is demonstrated that the quadratic Wasserstein metric, as opposed to the L 2 norm, provides an effective measure of the misfit between given data and computed solution.…”

Section: Prior Workmentioning

confidence: 99%

“…Our work extends that of [7,8,34] by considering different inverse problems, a more general noise model, and we use a different Wasserstein metric. See section 4.4 for more detail.…”

Section: Our Contributionmentioning

confidence: 99%

“…The work here is inspired, in part, by the study of seismic imaging inverse problems in [7,8,34]. There the authors measure the misfit between simulated and measured data using the Wasserstein distance squared…”

Section: Comparison With Prior Workmentioning

confidence: 99%

“…To handle the possibly negative distributions, the authors in [7,8,34] introduce the misfit function…”

Section: Comparison With Prior Workmentioning

confidence: 99%

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Diagnosing Forward Operator Error Using Optimal Transport

2019

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We investigate overdetermined linear inverse problems for which the forward operator may not be given accurately. We introduce a new tool called the structure, based on the Wasserstein distance, and propose the use of this to diagnose and remedy forward operator error. Computing the structure turns out to use an easy calculation for a Euclidean homogeneous degree one distance, the Earth Mover's Distance, based on recently developed algorithms. The structure is proven to distinguish between noise and signals in the residual and gives a plan to help recover the true direct operator

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Section: Prior Workmentioning

confidence: 99%

“…Our work extends that of [7,8,34] by considering different inverse problems, a more general noise model, and we use a different Wasserstein metric. See section 4.4 for more detail.…”

Section: Our Contributionmentioning

confidence: 99%

Section: Comparison With Prior Workmentioning

confidence: 99%

“…To handle the possibly negative distributions, the authors in [7,8,34] introduce the misfit function…”

Section: Comparison With Prior Workmentioning

confidence: 99%

See 2 more Smart Citations

Diagnosing Forward Operator Error Using Optimal Transport

2019

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“…If the misfit between the synthetic and observed data is examined from another point of view, a mapping can be considered to exist between them (Ma & Hale, ; Engquist & Froese, ; Métivier et al, ; Yang et al, ). Recently, a novel measure of misfit related to optimal transport was proposed by Engquist and Froese ().…”

Section: Introductionmentioning

confidence: 99%

Passive Adjoint Tomography of the Crustal and Upper Mantle Beneath Eastern Tibet With a W2‐Norm Misfit Function

Dong

Yang

Niu

2019

Geophysical Research Letters

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Full waveform tomography is an effective method to obtain high‐resolution subsurface velocity structures. It is, however, difficult for the conventional L2‐norm‐based inversion to reach the global minimum because of cycle‐skipping problem. In this study, we investigated the feasibility of using the quadratic Wasserstein metric distance (W2 norm) as the misfit function for passive adjoint tomography. We first derived equations of the Fréchet gradient and adjoint source under W2‐norm misfit function. We then conducted numerical experiments to illustrate the effectiveness of the proposed method in avoiding cycle skipping. We finally applied the adjoint tomography to eastern Tibet and obtained a 3‐D velocity model of the lithosphere. The adjoint tomography revealed two low‐velocity channels beneath the NE and SE margins of the Tibetan plateau, which were also observed by previous studies. Our results are consistent with the lower crust flow model that was proposed to explain the deformation occurring at the two margins.

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Optimal Transport Based Seismic Inversion:Beyond Cycle Skipping

Engquist

Yang

2021

Comm Pure Appl Math

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Full‐waveform inversion (FWI) is today a standard process for the inverse problem of seismic imaging. PDE‐constrained optimization is used to determine unknown parameters in a wave equation that represent geophysical properties. The objective function measures the misfit between the observed data and the calculated synthetic data, and it has traditionally been the least‐squares norm. In a sequence of papers, we introduced the Wasserstein metric from optimal transport as an alternative misfit function for mitigating the so‐called cycle skipping, which is the trapping of the optimization process in local minima. In this paper, we first give a sharper theorem regarding the convexity of the Wasserstein metric as the objective function. We then focus on two new issues. One is the necessary normalization of turning seismic signals into probability measures such that the theory of optimal transport applies. The other, which is beyond cycle skipping, is the inversion for parameters below reflecting interfaces. For the first, we propose a class of normalizations and prove several favorable properties for this class. For the latter, we demonstrate that FWI using optimal transport can recover geophysical properties from domains where no seismic waves travel through. We finally illustrate these properties by the realistic application of imaging salt inclusions, which has been a significant challenge in exploration geophysics. © 2021 Wiley Periodicals LLC.

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Optimal transport for seismic full waveform inversion

Cited by 134 publications

References 16 publications

Diagnosing Forward Operator Error Using Optimal Transport

Diagnosing Forward Operator Error Using Optimal Transport

Passive Adjoint Tomography of the Crustal and Upper Mantle Beneath Eastern Tibet With a W2‐Norm Misfit Function

Optimal Transport Based Seismic Inversion:Beyond Cycle Skipping

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