Fast sweeping algorithm for accurate solution of the TTI eikonal equation using factorization

Handle URI:
http://hdl.handle.net/10754/625057
Title:
Fast sweeping algorithm for accurate solution of the TTI eikonal equation using factorization
Authors:
bin Waheed, Umair; Alkhalifah, Tariq Ali ( 0000-0002-9363-9799 )
Abstract:
Traveltime computation is essential for many seismic data processing applications and velocity analysis tools. High-resolution seismic imaging requires eikonal solvers to account for anisotropy whenever it significantly affects the seismic wave kinematics. Moreover, computation of auxiliary quantities, such as amplitude and take-off angle, rely on highly accurate traveltime solutions. However, the finite-difference based eikonal solution for a point-source initial condition has an upwind source-singularity at the source position, since the wavefront curvature is large near the source point. Therefore, all finite-difference solvers, even the high-order ones, show inaccuracies since the errors due to source-singularity spread from the source point to the whole computational domain. We address the source-singularity problem for tilted transversely isotropic (TTI) eikonal solvers using factorization. We solve a sequence of factored tilted elliptically anisotropic (TEA) eikonal equations iteratively, each time by updating the right hand side function. At each iteration, we factor the unknown TEA traveltime into two factors. One of the factors is specified analytically, such that the other factor is smooth in the source neighborhood. Therefore, through the iterative procedure we obtain accurate solution to the TTI eikonal equation. Numerical tests show significant improvement in accuracy due to factorization. The idea can be easily extended to compute accurate traveltimes for models with lower anisotropic symmetries, such as orthorhombic, monoclinic or even triclinic media.
KAUST Department:
Physical Sciences and Engineering (PSE) Division
Citation:
Bin Waheed U, Alkhalifah T (2017) Fast sweeping algorithm for accurate solution of the TTI eikonal equation using factorization. GEOPHYSICS: 1–43. Available: http://dx.doi.org/10.1190/geo2016-0712.1.
Publisher:
Society of Exploration Geophysicists
Journal:
GEOPHYSICS
Issue Date:
10-Jun-2017
DOI:
10.1190/geo2016-0712.1
Type:
Article
ISSN:
0016-8033; 1942-2156
Sponsors:
The numerical tests presented in this paper are reproducible and available under the open source software package Madagascar (Fomel et al., 2013). We are grateful to all developers and contributors of the package.
Additional Links:
http://library.seg.org/doi/10.1190/geo2016-0712.1
Appears in Collections:
Articles; Physical Sciences and Engineering (PSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorbin Waheed, Umairen
dc.contributor.authorAlkhalifah, Tariq Alien
dc.date.accessioned2017-06-19T09:21:45Z-
dc.date.available2017-06-19T09:21:45Z-
dc.date.issued2017-06-10en
dc.identifier.citationBin Waheed U, Alkhalifah T (2017) Fast sweeping algorithm for accurate solution of the TTI eikonal equation using factorization. GEOPHYSICS: 1–43. Available: http://dx.doi.org/10.1190/geo2016-0712.1.en
dc.identifier.issn0016-8033en
dc.identifier.issn1942-2156en
dc.identifier.doi10.1190/geo2016-0712.1en
dc.identifier.urihttp://hdl.handle.net/10754/625057-
dc.description.abstractTraveltime computation is essential for many seismic data processing applications and velocity analysis tools. High-resolution seismic imaging requires eikonal solvers to account for anisotropy whenever it significantly affects the seismic wave kinematics. Moreover, computation of auxiliary quantities, such as amplitude and take-off angle, rely on highly accurate traveltime solutions. However, the finite-difference based eikonal solution for a point-source initial condition has an upwind source-singularity at the source position, since the wavefront curvature is large near the source point. Therefore, all finite-difference solvers, even the high-order ones, show inaccuracies since the errors due to source-singularity spread from the source point to the whole computational domain. We address the source-singularity problem for tilted transversely isotropic (TTI) eikonal solvers using factorization. We solve a sequence of factored tilted elliptically anisotropic (TEA) eikonal equations iteratively, each time by updating the right hand side function. At each iteration, we factor the unknown TEA traveltime into two factors. One of the factors is specified analytically, such that the other factor is smooth in the source neighborhood. Therefore, through the iterative procedure we obtain accurate solution to the TTI eikonal equation. Numerical tests show significant improvement in accuracy due to factorization. The idea can be easily extended to compute accurate traveltimes for models with lower anisotropic symmetries, such as orthorhombic, monoclinic or even triclinic media.en
dc.description.sponsorshipThe numerical tests presented in this paper are reproducible and available under the open source software package Madagascar (Fomel et al., 2013). We are grateful to all developers and contributors of the package.en
dc.publisherSociety of Exploration Geophysicistsen
dc.relation.urlhttp://library.seg.org/doi/10.1190/geo2016-0712.1en
dc.rightsArchived with thanks to GEOPHYSICSen
dc.titleFast sweeping algorithm for accurate solution of the TTI eikonal equation using factorizationen
dc.typeArticleen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.identifier.journalGEOPHYSICSen
dc.eprint.versionPost-printen
dc.contributor.institutionDepartment of Geosciences, Princeton University, Princeton, NJ 08544, USA..en
kaust.authorAlkhalifah, Tariq Alien
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