Adjoint-state eikonal-equation-based traveltime tomography on unstructured triangular meshes

Seismic traveltime tomography is one of the primary and effective methods to image the Earth’s interior structure. Although traveltime tomography is widely used in near-surface velocity modeling, it remains challenging in the presence of complex topography and internal interfaces. The complex topography and interior interfaces can be described by the unstructured triangular mesh’s flexibility. Therefore, an adjoint-state traveltime tomography based on unstructured triangular meshes is developed to estimate irregular subsurface material properties. The adjoint-state method is an effective tool to obtain the gradient of the misfit function due to its low memory requirement. First, a new fast sweeping method based on the unstructured triangular meshes for the factored eikonal equation is developed to obtain the accurate first-arrival traveltime field. Second, to obtain the gradient of the misfit function by the adjoint-state method, the adjoint-state equation based on the unstructured triangular meshes needs to be solved additionally. We design an upwind finite volume scheme to discretize and solve it. In the optimization process, we adopt the nonlinear conjugate gradient method to update the model parameters. Finally, a series of numerical examples is given, which shows the reliability of adjoint-state eikonal-equation-based seismic traveltime tomography on unstructured triangular meshes.