Efficient traveltime solutions of the acoustic TI eikonal equation

Handle URI:
http://hdl.handle.net/10754/564030
Title:
Efficient traveltime solutions of the acoustic TI eikonal equation
Authors:
Waheed, Umair bin ( 0000-0002-5189-0694 ) ; Alkhalifah, Tariq Ali ( 0000-0002-9363-9799 ) ; Wang, Hui
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 higher-order 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.
KAUST Department:
Earth Science and Engineering Program; Physical Sciences and Engineering (PSE) Division; Environmental Science and Engineering Program; Earth Sciences and Engineering Program
Publisher:
Elsevier BV
Journal:
Journal of Computational Physics
Issue Date:
Feb-2015
DOI:
10.1016/j.jcp.2014.11.006
ARXIV:
arXiv:1311.4203
Type:
Article
ISSN:
00219991
Sponsors:
We thank KAUST for financial support. We are also grateful David Ketcheson for useful discussions on the direct solver. We also thank BP for releasing the benchmark synthetic model.
Additional Links:
http://arxiv.org/abs/arXiv:1311.4203v1
Appears in Collections:
Articles; Environmental Science and Engineering Program; Physical Sciences and Engineering (PSE) Division; Earth Science and Engineering Program

Full metadata record

DC FieldValue Language
dc.contributor.authorWaheed, Umair binen
dc.contributor.authorAlkhalifah, Tariq Alien
dc.contributor.authorWang, Huien
dc.date.accessioned2015-08-03T12:29:05Zen
dc.date.available2015-08-03T12:29:05Zen
dc.date.issued2015-02en
dc.identifier.issn00219991en
dc.identifier.doi10.1016/j.jcp.2014.11.006en
dc.identifier.urihttp://hdl.handle.net/10754/564030en
dc.description.abstractNumerical 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 higher-order 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.en
dc.description.sponsorshipWe thank KAUST for financial support. We are also grateful David Ketcheson for useful discussions on the direct solver. We also thank BP for releasing the benchmark synthetic model.en
dc.publisherElsevier BVen
dc.relation.urlhttp://arxiv.org/abs/arXiv:1311.4203v1en
dc.subjectAnisotropyen
dc.subjectEfficient traveltime solutionsen
dc.subjectEikonal equationen
dc.subjectFast sweeping methoden
dc.subjectTilted transverse isotropyen
dc.titleEfficient traveltime solutions of the acoustic TI eikonal equationen
dc.typeArticleen
dc.contributor.departmentEarth Science and Engineering Programen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.contributor.departmentEnvironmental Science and Engineering Programen
dc.contributor.departmentEarth Sciences and Engineering Programen
dc.identifier.journalJournal of Computational Physicsen
dc.identifier.arxividarXiv:1311.4203en
kaust.authorWaheed, Umair binen
kaust.authorAlkhalifah, Tariq Alien
kaust.authorWang, Huien
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.