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A High-Order Fast-Sweeping Scheme for Calculating First-Arrival Travel Times with an Irregular.

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Title: A High-Order Fast-Sweeping Scheme for Calculating First-Arrival Travel Times with an Irregular.
Authors: Haiqiang Lan1 lanhq@mail.iggcas.ac.cn, Zhongjie Zhang1
Source: Bulletin of the Seismological Society of America. Jun2013, Vol. 103 Issue 3, p2070-2082. 13p.
Subjects: High-order derivatives (Mathematics), Fast sweeping methods (Mathematics), Surface topography, Eikonal equation, Curvilinear coordinates, Approximation theory
Abstract: Topography-dependent eikonal equation (TDEE) formulated in a curvilinear coordinate system has been recently established and is effective for calculating first-arrival travel times in an Earth model with an irregular surface. In previous work, the Lax-Friedrichs sweeping scheme used to approximate the TDEE viscosity solutions was only first-order accurate. We present a high-order fast-sweeping scheme to solve the TDEE with the aim of achieving high-order accuracy in the travel-time calculation. The scheme takes advantage of high-order weighted essentially nonoscillatory (WENO) derivative approximations, monotone numerical Hamiltonians, and Gauss Seidel iterations with alternating-direction sweepings. It incorporates high-order approximations of the derivatives into the numerical representation of the Hamiltonian such that the resulting numerical scheme is formally high-order accurate and inherits fast convergence from the alternating sweeping strategy. Extensive numerical examples are presented to verify its efficiency, convergence, and high-order accuracy. [ABSTRACT FROM AUTHOR]
Copyright of Bulletin of the Seismological Society of America is the property of Seismological Society of America and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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An: 88325431
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  Data: A High-Order Fast-Sweeping Scheme for Calculating First-Arrival Travel Times with an Irregular.
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  Data: <searchLink fieldCode="AR" term="%22Haiqiang+Lan%22">Haiqiang Lan</searchLink><relatesTo>1</relatesTo><i> lanhq@mail.iggcas.ac.cn</i><br /><searchLink fieldCode="AR" term="%22Zhongjie+Zhang%22">Zhongjie Zhang</searchLink><relatesTo>1</relatesTo>
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  Data: <searchLink fieldCode="JN" term="%22Bulletin+of+the+Seismological+Society+of+America%22">Bulletin of the Seismological Society of America</searchLink>. Jun2013, Vol. 103 Issue 3, p2070-2082. 13p.
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  Data: <searchLink fieldCode="DE" term="%22High-order+derivatives+%28Mathematics%29%22">High-order derivatives (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Fast+sweeping+methods+%28Mathematics%29%22">Fast sweeping methods (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Surface+topography%22">Surface topography</searchLink><br /><searchLink fieldCode="DE" term="%22Eikonal+equation%22">Eikonal equation</searchLink><br /><searchLink fieldCode="DE" term="%22Curvilinear+coordinates%22">Curvilinear coordinates</searchLink><br /><searchLink fieldCode="DE" term="%22Approximation+theory%22">Approximation theory</searchLink>
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  Data: Topography-dependent eikonal equation (TDEE) formulated in a curvilinear coordinate system has been recently established and is effective for calculating first-arrival travel times in an Earth model with an irregular surface. In previous work, the Lax-Friedrichs sweeping scheme used to approximate the TDEE viscosity solutions was only first-order accurate. We present a high-order fast-sweeping scheme to solve the TDEE with the aim of achieving high-order accuracy in the travel-time calculation. The scheme takes advantage of high-order weighted essentially nonoscillatory (WENO) derivative approximations, monotone numerical Hamiltonians, and Gauss Seidel iterations with alternating-direction sweepings. It incorporates high-order approximations of the derivatives into the numerical representation of the Hamiltonian such that the resulting numerical scheme is formally high-order accurate and inherits fast convergence from the alternating sweeping strategy. Extensive numerical examples are presented to verify its efficiency, convergence, and high-order accuracy. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Bulletin of the Seismological Society of America is the property of Seismological Society of America and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1785/0120120199
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 13
        StartPage: 2070
    Subjects:
      – SubjectFull: High-order derivatives (Mathematics)
        Type: general
      – SubjectFull: Fast sweeping methods (Mathematics)
        Type: general
      – SubjectFull: Surface topography
        Type: general
      – SubjectFull: Eikonal equation
        Type: general
      – SubjectFull: Curvilinear coordinates
        Type: general
      – SubjectFull: Approximation theory
        Type: general
    Titles:
      – TitleFull: A High-Order Fast-Sweeping Scheme for Calculating First-Arrival Travel Times with an Irregular.
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            NameFull: Haiqiang Lan
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            NameFull: Zhongjie Zhang
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          Dates:
            – D: 01
              M: 06
              Text: Jun2013
              Type: published
              Y: 2013
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              Value: 103
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              Value: 3
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            – TitleFull: Bulletin of the Seismological Society of America
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