Hybrid fast sweeping methods for anisotropic eikonal equation in two-dimensional tilted transversely isotropic media
First- and second-order hybrid fast sweeping methods are presented for computing the first-arrival travel time of qP, qSV and qSH waves in two-dimensional tilted transversely isotropic media. The computations are based on solving the factored anisotropic eikonal equation after applying a factorization to solve the original equation outside of the neighborhood of the source. The traveltime and its gradient are computed by a first-order method that has first-order accuracy. This superconvergence property is utilized to design a second-order fast sweeping method based on a linear discontinuous Galerkin formulation. The method possesses all the desired properties of the usual fast sweeping method, i.e., efficiency, accuracy, and convergence guaranteed by monotonicity by imposing the appropriate enforcement of the causality condition. The second-order method serves as a post-processing procedure of the first-order method and is based on a linear discontinuous Galerkin formulation. Numerical experiments verify the efficiency of the proposed methods. Numerical solutions computed by the Lax-Friedrichs fast sweeping methods for Hamilton-Jacobi-type equations are also presented to compare with the methods developed in this paper.
scientific article; zbMATH DE number 7259459
scientific article