Assessment of optimal transport based FWI: 3D OBC Valhall case study

Pladys, Arnaud; Brossier, Romain; Irnaka, Theodosius Marwan; Kamath, Nishant; Métivier, Ludovic

doi:10.1190/segam2019-3212002.1

Cited by 5 publications

(3 citation statements)

References 21 publications

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“…There are also modeling and numerical errors in the wave simulation as well as noisy data. What makes us confident of the practical value of the techniques discussed here is the emerging popularity in the industry and successful application to real field data, which have been reported [41,43,47]. We include one numerical example to show the robustness of W 2 -based inversion in Section 6 by using a perturbed synthetic source and adding correlated data noise.…”

Section: Introductionmentioning

confidence: 97%

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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Section: Introductionmentioning

confidence: 97%

Optimal Transport Based Seismic Inversion:Beyond Cycle Skipping

Engquist

Yang

2021

Comm Pure Appl Math

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“…There are also modeling and numerical errors in the wave simulation as well as noisy data. What makes us confident of the practical value of the techniques discussed here is the emerging popularity in the industry and successful application to real field data, which have been reported [34,37,32]. We include, however, one numerical example to show the robustness of W 2 -based inversion in Section 3.1 by using a perturbed synthetic source and adding correlated data noise.…”

Section: Introductionmentioning

confidence: 99%

Optimal Transport Based Seismic Inversion: Beyond Cycle Skipping

Engquist

Yang

2020

Preprint

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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 beyond cycle skipping. One is the necessary normalization of turning a seismic signal into probability measure, and the other is 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.

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“…This method is called the graph space optimal transport (GSOT) and presents the main characteristic of preserving the convexity with respect to time shifts (Métivier et al, 2018(Métivier et al, , 2019. GSOT has already been successfully applied to 3D synthetic and field data (He et al, 2019;Pladys et al, 2019;Li et al, 2019;Górszczyk et al, 2019).…”

Section: Introductionmentioning

confidence: 99%

Robust full-waveform inversion with graph-space optimal transport: Application to 3D ocean-bottom cable Valhall data

et al. 2022

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Improving full-waveform inversion to make it more robust to cycle-skipping has been the subject of a large number of studies. From the several families of approaches developed, one of the most documented consists in modifying the least-squares distance defining the discrepancy between observed and calculated data. From all the propositions made to improve and replace the least-squares distance, only a few of them have been applied to field data. One of the methods proposed recently, the graph space optimal transport distance, presents appealing properties for field data applications. This study compares it with the least-squares distance in an analysis performed on the three-dimensional ocean bottom cable data from the Valhall field. This data has already been at the heart of several full-waveform inversion studies, making it a good candidate to evaluate the properties of this new misfit function. We first perform this comparison starting the inversion from the reflection traveltime tomography model used in previous studies. We then perform a second comparison from a crude, linearly varying in-depth one-dimensional velocity model. Starting from this model, least-squares-based full-waveform inversion fails to provide a meaningful estimate of the pressure-wave velocity model due to cycle skipping. We illustrate how the graph-space optimal transport-based full-waveform inversion mitigates this issue. A meaningful estimate of the pressure-wave velocity model is obtained in the zone sampled by both diving and reflected waves, down to almost two kilometers depth. To our knowledge, this is the first application of a graph space optimal transport-based full-waveform inversion to three-dimensional field data.

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Assessment of optimal transport based FWI: 3D OBC Valhall case study

Cited by 5 publications

References 21 publications

Optimal Transport Based Seismic Inversion:Beyond Cycle Skipping

Optimal Transport Based Seismic Inversion:Beyond Cycle Skipping

Optimal Transport Based Seismic Inversion: Beyond Cycle Skipping

Robust full-waveform inversion with graph-space optimal transport: Application to 3D ocean-bottom cable Valhall data

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