A hybrid method for calculating seismic wave first-arrival traveltimes in two-dimensional models with an irregular surface

A hybrid method is developed for the calculation of seismic wave first-arrival traveltimes in two-dimensional models with an irregular free surface. The method is based on a combination of the classical eikonal equation (CEE) and the topography-dependent eikonal equation (TDEE); the latter applies only to the part of the explored domain that includes the non-flat surface, while the first equation applies anywhere outside this domain. CEE is solved using a fast-sweeping method, and TDEE is solved after discretizing the numerical Hamiltonian using the Legendre transform and applying the upwind fast-sweeping method. For the implementation of the hybrid method and the appropriate application of CEE and TDEE, we sort the contact mode between spatial sub-domains into three types and give an explanation about the working routine adopted for each one. Several numerical experiments considering different models, mesh sizes, seismic source positions and partition styles demonstrate that the proposed hybrid method can effectively address seismic modeling problems involving undulated free surfaces, keeping the same precision as TDEE but with a fairly rapid convergence. This proves that the hybrid method is a powerful tool for practical applications aimed at obtaining high-quality images of earth structures.