Wavefronts of linear elastic waves: local convexity and modeling

Abstract

Seismic techniques incorporating high frequency asymptotic representation of the 3D elastic Green’s function require efficient solution methods for the computation of traveltimes. For finite difference eikonal solvers, upwind differences are requisite to sharply resolve discontinuities in the traveltime derivatives. In anisotropic media, the direction of energy propagation is not in general tangent to the wavefront normal, while finite difference eikonal solvers compute the solution based on the traveltime gradients and wavefront normal. Local convexity of the wavefronts in transverse isotropic (TI) media is proved to show that wavefront normal determines the upwind direction of the energy propagation. The eikonal equations for the traveltimes in TI media of a generally inclined symmetry axis (ITI) are derived in a way that the eikonal solvers fit conveniently. A stable, second-order, shock-capturing, upwind finite difference scheme is suggested for solving ITI eikonal equations in regular grids in 3D. Numerical experiments are presented to demonstrate the efficiency of the algorithm.