A discontinuous Galerkin fast-sweeping eikonal solver for fast and accurate traveltime computation in 3D tilted anisotropic media

Bouteiller, Philippe Le; Benjemaa, Mondher; Métivier, Ludovic; Virieux, Jean

doi:10.1190/geo2018-0555.1

Cited by 18 publications

(10 citation statements)

References 73 publications

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“…While Le Bouteiller et al . (2019) considered tilted orthorhombic anisotropy, the elliptical Eikonal

scriptH

reduces to

{scriptH}_{EVTI} false(\nabla t (x), boldx false) = A false(boldx false) \nabla_{x} t {(x)}^{2} + B false(boldx false) \nabla_{z} t {(x)}^{2} - 1,

where spatially dependent quantities

A

and

B

are defined by

({, \begin{matrix} A false(boldx false) = v_{v}^{2} false(boldx false) false(1 + 2 ε (x) false) = v_{h}^{2} false(boldx false), \\ B false(boldx false) = v_{v}^{2} false(boldx false) . \end{matrix})

…”

Section: Methodsmentioning

confidence: 99%

“…We propose to pursue these investigations on FATT in 2D anisotropic media by taking benefit of the recent work of Le Bouteiller et al . (2019) who have developed a highly efficient and very accurate traveltime computation approach in anisotropic media based on the fast‐sweeping method and a discontinuous Galerkin based (DG) Eikonal solver. This level of accuracy can be crucial when high contrasts are at stake.…”

Section: Introductionmentioning

confidence: 99%

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Matrix‐free crosshole elliptical‐anisotropy tomography: parametrization analysis and ground‐penetrating radar applications in carbonates

Salcedo

Garambois

Bouteiller

et al. 2020

Near Surface Geophysics

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A novel traveltime tomographic approach is applied to anisotropic media, limited to 2D geometry at present. A general anisotropic Eikonal solver based on a discontinuous Galerkin method is combined with an efficient adjoint formulation for multiparameter least-squares inversion. This new approach is tested considering synthetic crosshole ground-penetrating radar data. The configuration of the groundpenetrating radar survey is inspired by a real experiment done on layered carbonate media disturbed by the presence of a deep gallery, which induces a localized high-electromagnetic contrast. This made it possible to define a well-adapted general workflow in this context. We notably show that, under the elliptical anisotropic assumption, the parametrization based on vertical and horizontal velocities provides less biased results than those obtained by considering the vertical velocity and the relevant Thomsen parameter. The initial vertical and horizontal velocity models are identical and built from an isotropic inversion. The presence of the high-contrast gallery generates a weak diffraction pattern, which is taken into account in our tomography approach. It also creates potential artefacts due to the model discretization, which are mitigated by a model regularization term within the definition of the misfit function. This general workflow is then applied to the real experiment dataset. The vertical and horizontal velocity images provide similar structures as those previously obtained by isotropic full waveform inversion, complemented by an image of a rather weak elliptical anisotropy.

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“…While Le Bouteiller et al . (2019) considered tilted orthorhombic anisotropy, the elliptical Eikonal

scriptH

reduces to

{scriptH}_{EVTI} false(\nabla t (x), boldx false) = A false(boldx false) \nabla_{x} t {(x)}^{2} + B false(boldx false) \nabla_{z} t {(x)}^{2} - 1,

where spatially dependent quantities

A

and

B

are defined by

({, \begin{matrix} A false(boldx false) = v_{v}^{2} false(boldx false) false(1 + 2 ε (x) false) = v_{h}^{2} false(boldx false), \\ B false(boldx false) = v_{v}^{2} false(boldx false) . \end{matrix})

…”

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Matrix‐free crosshole elliptical‐anisotropy tomography: parametrization analysis and ground‐penetrating radar applications in carbonates

Salcedo

Garambois

Bouteiller

et al. 2020

Near Surface Geophysics

Self Cite

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show abstract

“…Originally introduced in isotropic settings [Zha05], the fast sweeping method has been extended to 2D elliptic anisotropy [TCOZ03], 2D TTI symmetry [LCZ14], 3D TTI symmetry [PWZ17] with a third-order Lax-Friedrich fast sweeping scheme. It also got extended to 3D TOR symmetry [WYF15] treated as an iterative problem on elliptic anisotropy, and more recently [LBBMV19] for the 3D TOR symmetry with high order accuracy. Other iterative methods include the adaptive Gauss-Siedel iteration [BR06], or the buffered fast marching method [Cri09], which can both handle some amount of anisotropy.…”

Section: Introductionmentioning

confidence: 99%

Single Pass Computation of First Seismic Wave Travel Time in Three Dimensional Heterogeneous Media With General Anisotropy

et al. 2021

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We present a numerical method for computing the first arrival travel-times of seismic waves in media defined by a general Hooke tensor, in contrast with previous methods which are limited to a specific subclass of anisotropic media, such as "tilted transversally isotropic" (TTI) media or "tilted orthorhombic" (TOR) media [WYF15, LBBMV19]. Our method proceeds in a single pass over the discretized domain, similar to the fast marching method, whereas existing methods for these types of anisotropy require multiple iterations, similar to the fast sweeping method. We introduce a new source factorization model, making it possible to achieve third-order accuracy in smooth media. We also validate our solver by comparing it with the solution of the elastic wave equation in a 3D medium with general anisotropy.

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“…The complications associated with using fast marching for the anisotropic eikonal equation have resulted in a preference for the fast sweeping method (FSM). However, the higher-order nonlinear terms in the anisotropic eikonal equations require computationally expensive procedures, such as using an iterative fast sweeping algorithm (Waheed et al, 2015) or using the Discontinuous-Galerkin (DG) fast sweeping method (Le Bouteiller et al, 2019).…”

Section: Introductionmentioning

confidence: 99%

“…We first construct an approximation space using a feed-forward neural network and then train the network, by imposing a loss function defined by the anisotropic eikonal equation, to yield traveltime solutions for the corresponding anisotropic medium. By doing so we avoid the need to use computationally costly procedures due to the high-order nonlinear terms in the anisotropic eikonal equation, such as the fixed-point iterative scheme of Waheed et al (2015) or the DG method of Le Bouteiller et al (2019). Furthermore, once the network is trained for a particular source location for a given anisotropic model, training it for a new source location and a modified model requires significantly less computational effort.…”

Section: Introductionmentioning

confidence: 99%

Anisotropic eikonal solution using physics-informed neural networks

Waheed

Haghighat

Alkhalifah

2020

SEG Technical Program Expanded Abstracts 2020

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Traveltimes are essential for seismic applications ranging from imaging to tomography. Traveltime computations in anisotropic media, which are better representative of the true Earth, require solving the anisotropic eikonal equation. Numerical techniques to solve the anisotropic eikonal equation are known to suffer from instability and increased computational cost compared to the isotropic case. Here, we employ the emerging paradigm of physics-informed neural networks to solve the anisotropic qP-wave eikonal equation. By minimizing a loss function formed by imposing the validity of the eikonal equation, we train a neural network to produce traveltime solutions that are consistent with the underlying partial differential equation. We observe considerably higher accuracy compared to the first-order finite-difference solution using the fast sweeping method. We also show that once the network is trained for a particular source location in a given anisotropic model, the traveltimes for a new source location and/or an updated model can be computed much more efficiently using the pre-trained network. This feature is particularly attractive as it can speed up seismic imaging and inversion applications significantly.

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A discontinuous Galerkin fast-sweeping eikonal solver for fast and accurate traveltime computation in 3D tilted anisotropic media

Cited by 18 publications

References 73 publications

Matrix‐free crosshole elliptical‐anisotropy tomography: parametrization analysis and ground‐penetrating radar applications in carbonates

Matrix‐free crosshole elliptical‐anisotropy tomography: parametrization analysis and ground‐penetrating radar applications in carbonates

Single Pass Computation of First Seismic Wave Travel Time in Three Dimensional Heterogeneous Media With General Anisotropy

Anisotropic eikonal solution using physics-informed neural networks

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