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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]
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Database: Engineering Source
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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]
ISSN:00371106
DOI:10.1785/0120120199