Wavefronts of Linear Elastic Waves: Local Convexity and Modeling

Seismic techniques incorporating high frequency asymptotic representation of the 3D elastic Green's function require eecient solution methods for the computation of traveltimes. For nite diierence eikonal solvers, upwind diierences 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 nite diierence eikonal solvers compute the solution based on the traveltime gradients and wavefront normal. Local con-vexity 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 t conveniently. A stable, second-order, shock-capturing, upwind nite diierence scheme is suggested for solving ITI eikonal equations in regular grids in 3D. Numerical experiments are presented to demonstrate the eeciency of the algorithm .