Improved fast marching methods with application in traveltime tomography

Seismic wave speed and anisotropy provide essential constraints on the Earth’s internal velocity structure and deformation history. The propagation of the seismic wave can be modeled by a Hamilton system in the forward modeling. Then the best fit depth-dependent anisotropy is obtained by the optimal solution of an inverse problem. The numerical accuracy of solving the inverse problem has a significant impact on the resolution and quality of the final tomographic images. The classical monotone upwind schemes are efficient and accurate in solving the forward problem modeled by a static convex Hamilton system, for example the fast marching method, since they compute the timetable following the causal property of wave propagation. However, in anisotropic media, when velocity is directional dependent, the fast marching method computes the timetable with the simplex containing the negative gradient vector whereas the traveltime should be computed with the simplex containing the characteristics. One way to improve the accuracy while maintaining the efficiency is to apply the multi-stencils scheme since it computes the arrivaltime along several staggered stencils with a better directional coverage. Another problem is the existence of source singularity for seismic wave simulation where the viscosity solution of the Hamilton–Jacobi–Bellman (HJB) equation can only achieve first order convergency at source even higher order scheme has been applied. This problem is solved by applying factorization to the original eikonal equation which separates the solution into a known initial timetable with source singularity and a smooth updated factor. If the initial table has enough accuracy around the source, theoretically we can obtain any order of accuracy and convergency by factorization. Thirdly, this dijkstra-like algorithm remains a sorting strategy which is time consuming and limits its potential to apply in Single Instruction Multiple Data (SIMD) streaming architecture. Inspired by previous research, in this PhD project, we propose an iterative method which updates several points in parallel. The proposed method can achieve any order of accuracy and convergency for anisotropic media and we apply it for both local and regional seismic tomography. For anisotropic tomography, we develop a new ray tracing technique with the novel eikonal solver. The numerical tests show that for some situations, our ray tracing technique can obtain more accurate results than isotropic ray tracing technique. Besides the ray based tomographic method, we also come up with an adjoint-state traveltime tomography method which avoids ray tracing and solves the inverse problem in a global optimization sense. Rather than accumulating the misfits of individual records, the novel method solves an adjoint-state field which involves the density information of ray trajectories and integrates the whole domain to obtain a global misfit. We apply both methods in some seismologically active regions to study the subducting process, magmatism and volcanism by inverting the highquality manually-picked datasets. Those applications demonstrate that the new methods are reliable tools in producing seismic anisotropy images to study the ongoing tectonic dynamics in the seismogenic zones.Doctor of Philosoph