Analysis of optimal transport and related misfit functions in full-waveform inversion

Yang, Yunan; Engquist, Björn

doi:10.1190/segam2017-17754089.1

Cited by 25 publications

(37 citation statements)

References 22 publications

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“…where Lip 1 is the space of 1-Lipschitz functions on (x r , t). The latter strategy has shown interesting properties for mitigating the cycle skipping issue in FWI, and also yields the possibility to directly account for 2D shot-gathers through optimal transport, beyond the trace-by-trace comparison on which are based other current optimal transport implementations (Qiu et al, 2017;Yang and Engquist, 2018). The main drawback of the KR approach is the loss of convexity with respect to large time shifts due to the direct computation of the W 1 distance for non-positive data through its dual formulation.…”

Section: Presentation Of the Case Studymentioning

confidence: 99%

“…The application of OT to seismic data therefore relies on specific adaptations. A first approach consists in transforming the data into positive quantities and normalizing it prior being compared through OT (Engquist and Froese, 2014;Qiu et al, 2017;Yang et al, 2018b;Yang and Engquist, 2018). A second approach, which we have promoted, consists in considering a special instance of the OT distance, based on the 1-Wasserstein distance, which can be extended naturally to the comparison of non-positive data (Métivier et al, 2016a,b,c).…”

Section: Introductionmentioning

confidence: 99%

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A graph space optimal transport distance as a generalization of L ^p distances: application to a seismic imaging inverse problem

et al. 2019

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Optimal transport distance is an appealing tool to measure the discrepancy between datasets in the frame of inverse problems, for its ability to perform global comparisons and its convexity with respect to shifted patterns in the compared quantities. However, solving inverse problems might require to compare signed quantities, while the optimal transport theory has been developed for the comparison of probability measures. In this study we propose to circumvent this difficulty by applying optimal transport to the comparison of the graph of the data rather than the data itself. We investigate this approach in the frame of seismic imaging, where each channel of the oscillatory data is interpreted as a discrete point cloud. We demonstrate that the corresponding misfit function can be computed through the solution of series of linear sum assignment problem (LSAP), while, based on the adjoint state technique, its gradient can be computed from the assignment solution of these LSAP. We illustrate how this approach yields a convex misfit function in the frame of seismic imaging using the full waveform. We show how an efficient strategy, based on a specific LSAP solver, the auction algorithm, can be designed. We illustrate the interest of the approach on a realistic 2D visco-acoustic seismic imaging problem. The proposed strategy relaxes the constraint on the accuracy of the initial model, outperforming the conventional least-squares approach and a previously proposed optimal transport based approach. The computational time increases by only a few percents compared with the least-squares approach, opening the way to applications to 3D field data in the near future.

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Section: Presentation Of the Case Studymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A graph space optimal transport distance as a generalization of L ^p distances: application to a seismic imaging inverse problem

et al. 2019

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“…In order to facilitate avoidance of cycle-skipping pitfalls, several authors have proposed alternative norms (e.g. Warner and Guasch 2016;Jiao et al, 2015;Vigh et al, 2017;Schuster 2017;Yang and Engquist 2018;Wang et al, 2018). In addition to the choice of the norm, we also need to distinguish between the use of the transmitted (refracted) and the reflected wavefields.…”

Section: Model Building Strategymentioning

confidence: 99%

A strategy for regional-scale FWI in the salt provinces offshore Brazil

Fruehn¹,

Greenwood²,

ODriscoll³

et al. 2019

Proceedings of the 16th International Congress of the Brazilian Geophysical Society&Expogef

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“…The normalized integral method defines a new objective function for reconstructing the background velocity model by using the normalized time integral of the squared waveform data to replace the conventional synthetic and observed data (Chauris et al, ; Donno et al, ). The L2 distance is replaced by the optimal transport distance to enhance the convexity of the FWI objective function (Engquist & Froese, ; Engquist et al, ; Métivier et al, , , , ; Yang & Engquist, ; Yang et al, ). Envelope inversion (EI) uses the envelope to extract the ultralow‐frequency information that is contained in the seismic data to build the background velocity model (Bozdağ et al, ; Chi et al, , ; Luo & Wu, ; Wu et al, ; Yuan et al, ).…”

Section: Introductionmentioning

confidence: 99%

“…Esser et al () developed a regularization method by applying total variation constraints to the adaptive waveform inversion misfit function to obtain a highly resolved salt model. FWI using the optimal transport distance achieved good performance in the salt structure inversion (Métivier et al, ; Yang & Engquist, ; Yang et al, ).…”

Section: Introductionmentioning

confidence: 99%

Multiscale Direct Envelope Inversion: Algorithm and Methodology for Application to the Salt Structure Inversion

Chen

2019

Earth and Space Science

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For the full‐waveform inversion, obtaining a globally optimal solution is difficult when the seismic data do not contain sufficient low‐frequency information and the inversion object is a salt structure with a large‐scale salt dome. The large salt dome presents difficulty for the inversion of the salt structure; however, it also confers a convenience that can be utilized: A large salt dome makes the events in the seismic record sparse and isolated. We use the envelope to obtain the arrival time of the events in the seismic data and apply multiscale strategies to extract the low‐frequency information of the seismic data that relates to the long‐wavelength components of the subsurface. In calculating the gradient, the envelope Fréchet derivative is used to take advantage of the multiscale envelope for the characteristics of the salt structure. Therefore, the multiscale direct envelope inversion using the window‐averaged envelope and the direct envelope Fréchet derivative is proposed. To further improve the computational efficiency and inversion quality of the multiscale direct envelope inversion, several auxiliary strategies are proposed: A joint misfit function is designed to make the inversion method more adaptable, and an offset weighting factor is introduced to implement the multioffset inversion method to improve the inversion quality of subsalt. We analyze the antinoise performance of the multiscale direct envelope inversion. The SEG/EAGE salt model is used to test the application effect of the multiscale direct envelope inversion. The antinoise ability and insensitivity to low‐frequency data of the method are verified in the numerical experiments.

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Analysis of optimal transport and related misfit functions in full-waveform inversion

Cited by 25 publications

References 22 publications

A graph space optimal transport distance as a generalization of L ^p distances: application to a seismic imaging inverse problem

A graph space optimal transport distance as a generalization of L ^p distances: application to a seismic imaging inverse problem

A strategy for regional-scale FWI in the salt provinces offshore Brazil

Multiscale Direct Envelope Inversion: Algorithm and Methodology for Application to the Salt Structure Inversion

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Analysis of optimal transport and related misfit functions in full-waveform inversion

Cited by 25 publications

References 22 publications

A graph space optimal transport distance as a generalization of L p distances: application to a seismic imaging inverse problem

A graph space optimal transport distance as a generalization of L p distances: application to a seismic imaging inverse problem

A strategy for regional-scale FWI in the salt provinces offshore Brazil

Multiscale Direct Envelope Inversion: Algorithm and Methodology for Application to the Salt Structure Inversion

Contact Info

Product

Resources

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A graph space optimal transport distance as a generalization of L ^p distances: application to a seismic imaging inverse problem

A graph space optimal transport distance as a generalization of L ^p distances: application to a seismic imaging inverse problem