Publication Date:
2013-06-08
Description:
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.
Print ISSN:
0037-1106
Electronic ISSN:
1943-3573
Topics:
Geosciences
,
Physics
