3D Eikonal Solvers, Part II: Anisotropic Traveltimes

In anisotropic media the direction of energy propagation is not in general tangent to the wavefront normal. On the other hand, nite dierence eikonal solvers compute the solution based on the traveltime gradient and the wavefront normal. Local convexity of the wavefronts in transverse isotropic (TI) media is studied for the eikonal solver to determine the correct upwind direction of the energy propagation. A second-order essentially non-oscillatory (ENO) scheme is applied to the computation of traveltimes in TI media. To overcome instability inherited in the standard expanding-box schemes, the ENO scheme is implemented incorpo-rating a down-n-out marching and a post sweeping iteration. Various numerical techniques such as the maximum angle condition, the average normal velocity, and a cache-based implementation are adopted to further improve accuracy and eÆciency of the algorithm. It is numerically veried that the resulting algorithm is stable, second-order accurate, and eÆcient. The algorithm has been successfully tested for the computation of traveltimes in heterogeneous synthetic TI models having large contrasts. 1