A New Finite Difference Eikonal Equation Solver for Anisotropic Medium

Abstract

The fast sweeping method has been proved very efficient in calculating the first arrivals in isotropic media. In this study, we extend the fast sweeping method to heterogeneous anisotropic medium by adapting the Lax-Friedrichs local scheme. The new fast sweeping method is able to solve the first arrival traveltime field for both qP and qS waves. By comparing the traveltime field to the full-waveform solution, we demonstrate that the iso-surfaces of the time field follow the constant phase of the wave and form a continuous envelope wrapping the wavefront. The iso-surfaces for the shear wave identify two continuous wavefronts one ahead of the other even in the directions where the triplication of qS-wave is developed. The rays for both qP and qS wave can be traced using the slowness vector from the traveltime field and we compared its accuracy with a two-point ray tracing method in a layered model. We show that rays from the traveltime field is nearly identical to the two-point ray tracing results. This new fast sweeping method not only avoids the multipath and shadow zone issues in complex heterogeneous media but also circumvent the multiple shear branch problems due to anisotropy.