An adaptive finite-difference method for accurate simulation of first-arrival traveltimes in heterogeneous media

Accurate simulation of first-arrival traveltimes is the foundation of seismic depth imaging and macro velocity model building for full waveform inversion. In this paper, an adaptive finite-difference method based on Gauss-Seidel iterations has been developed to achieve a more accurate calculation of first-arrival traveltimes in heterogeneous media. The plane wave, spherical wave and refracted wave approximations of local eikonal solver are used to simulate the seismic traveltimes, respectively. Then, a novel updating strategy based on Fermat principle is proposed to make the accurate choice of factor and traveltime, adaptively. The new algorithm can guarantee the high accuracy of traveltime simulation at the grid point not only near the source point, but also at a great distance from the source point. With the combination of global fast sweeping method, the traveltime simulation is unconditionally stable and all possible propagating directions of different seismic waves are considered to describe the complex propagating process due to the velocity model with sharp variations. Several numerical examples were solved to demonstrate that the adaptive finite-difference method can fulfill the accurate, efficient and robust simulation of first-arrival traveltimes.