Efficient traveltime solutions of the acoustic TI eikonal equation
Abstract
Numerical solutions of the eikonal (Hamilton–Jacobi) equation for transversely isotropic (TI) media are essential for imaging and traveltime tomography applications. Such solutions, however, suffer from the inherent higherorder nonlinearity of the TI eikonal equation, which requires solving a quartic polynomial for every grid point. Analytical solutions of the quartic polynomial yield numerically unstable formulations. Thus, it requires a numerical root finding algorithm, adding significantly to the computational load. Using perturbation theory we approximate, in a first order discretized form, the TI eikonal equation with a series of simpler equations for the coefficients of a polynomial expansion of the eikonal solution, in terms of the anellipticity anisotropy parameter. Such perturbation, applied to the discretized form of the eikonal equation, does not impose any restrictions on the complexity of the perturbed parameter field. Therefore, it provides accurate traveltime solutions even for models with complex distribution of velocity and anisotropic anellipticity parameter, such as that for the complicated Marmousi model. The formulation allows for large cost reduction compared to using the direct TI eikonal solver. Furthermore, comparative tests with previously developed approximations illustrate remarkable gain in accuracy in the proposed algorithm, without any addition to the computational cost.
 Authors:
 Publication Date:
 OSTI Identifier:
 22382180
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Computational Physics; Journal Volume: 282; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; ANALYTICAL SOLUTION; ANISOTROPY; COMPARATIVE EVALUATIONS; EIKONAL APPROXIMATION; GAIN; HAMILTONJACOBI EQUATIONS; ISOTROPY; MATHEMATICAL MODELS; NONLINEAR PROBLEMS; NUMERICAL SOLUTION; PERTURBATION THEORY; POLYNOMIALS
Citation Formats
Waheed, Umair bin, Email: umairbin.waheed@kaust.edu.sa, Alkhalifah, Tariq, Email: tariq.alkhalifah@kaust.edu.sa, and Wang, Hui, Email: hui.wang@kaust.edu.sa. Efficient traveltime solutions of the acoustic TI eikonal equation. United States: N. p., 2015.
Web. doi:10.1016/J.JCP.2014.11.006.
Waheed, Umair bin, Email: umairbin.waheed@kaust.edu.sa, Alkhalifah, Tariq, Email: tariq.alkhalifah@kaust.edu.sa, & Wang, Hui, Email: hui.wang@kaust.edu.sa. Efficient traveltime solutions of the acoustic TI eikonal equation. United States. doi:10.1016/J.JCP.2014.11.006.
Waheed, Umair bin, Email: umairbin.waheed@kaust.edu.sa, Alkhalifah, Tariq, Email: tariq.alkhalifah@kaust.edu.sa, and Wang, Hui, Email: hui.wang@kaust.edu.sa. 2015.
"Efficient traveltime solutions of the acoustic TI eikonal equation". United States.
doi:10.1016/J.JCP.2014.11.006.
@article{osti_22382180,
title = {Efficient traveltime solutions of the acoustic TI eikonal equation},
author = {Waheed, Umair bin, Email: umairbin.waheed@kaust.edu.sa and Alkhalifah, Tariq, Email: tariq.alkhalifah@kaust.edu.sa and Wang, Hui, Email: hui.wang@kaust.edu.sa},
abstractNote = {Numerical solutions of the eikonal (Hamilton–Jacobi) equation for transversely isotropic (TI) media are essential for imaging and traveltime tomography applications. Such solutions, however, suffer from the inherent higherorder nonlinearity of the TI eikonal equation, which requires solving a quartic polynomial for every grid point. Analytical solutions of the quartic polynomial yield numerically unstable formulations. Thus, it requires a numerical root finding algorithm, adding significantly to the computational load. Using perturbation theory we approximate, in a first order discretized form, the TI eikonal equation with a series of simpler equations for the coefficients of a polynomial expansion of the eikonal solution, in terms of the anellipticity anisotropy parameter. Such perturbation, applied to the discretized form of the eikonal equation, does not impose any restrictions on the complexity of the perturbed parameter field. Therefore, it provides accurate traveltime solutions even for models with complex distribution of velocity and anisotropic anellipticity parameter, such as that for the complicated Marmousi model. The formulation allows for large cost reduction compared to using the direct TI eikonal solver. Furthermore, comparative tests with previously developed approximations illustrate remarkable gain in accuracy in the proposed algorithm, without any addition to the computational cost.},
doi = {10.1016/J.JCP.2014.11.006},
journal = {Journal of Computational Physics},
number = ,
volume = 282,
place = {United States},
year = 2015,
month = 2
}

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