Calculating traveltimes in 2D general tilted transversely isotropic media using fast sweeping method

Abstract

Traveltime calculations play an important role in the field of exploration seismology, such as traveltime tomography and seismic imaging and so on. Seismic anisotropy poses a challenge for traveltime calculation, because anisotropic eikonal solvers are more complex than the isotropic counter part. To solve the eikonal equations in 2D tilted transversely isotropic (TTI) media, we have developed a fast algorithm combine with fast sweeping method to compute the first arrival traveltimes of quasi-P (qP)-, quasi-SV (qSV)-, and quasi-SH(qSH)-waves. For the qP- and qSV-waves, we analyzed the quartic coupled slowness surface equation derived from the Christoffel equation. Then, we constructed a local solver to relate traveltime and slowness. We found that in the local solver, one component of the slowness vector is known and the corresponding slowness equation is monotonic. This provides a strong basis for the fast iterative algorithm we proposed, where we use the Newton method to solve the qP- and qSV-wave slowness equation to determine the related traveltimes. For the qSH wave, the slowness equation is quadratic and simple to solve. Numerical experiments demonstrate that the proposed method can obtain accurate traveltimes for simple and complicated 2D TTI models.