A topography-dependent eikonal solver for accurate and efficient computation of traveltimes and their derivatives in 3D heterogeneous media

Accurate and efficient computation of traveltimes and their spatial gradients for 3D heterogeneous media are essential in many areas of seismology, such as traveltime/slope tomography and quantitative migration. A popular method of obtaining this information is to solve the eikonal equation using the finite difference (FD) scheme. However, the complex surface of the Earth causes numerical complications when applying FD methods based on rectangular grids. To overcome this problem taking into account the topographic effect, we make use of the 3D topography-dependent eikonal equation (TDEE) from the idea of a 3D surface-flattening scheme with curvilinear grid-based FD methods, which could transform irregular surfaces in the physical domain into regular surfaces in the computational domain. Unfortunately, solving the TDEE in 3D starting from the initial point-source condition needs to overcome the point-source singularity, we formulate the 3D factored TDEE based on the factoring principle. Furthermore, to numerically solve the 3D original TDEE, as well as the factored TDEE, we introduce a lock sweeping method, which avoids the problem of repetitive computation in the fast sweeping method. Several numerical examples demonstrate the efficiency of the new lock scheme in terms of computation time and gain in the accuracy of the 3D factored TDEE solver for the calculation of traveltimes and their derivatives. This provides a good choice for the calculation of traveltimes and their spatial derivatives using models with irregular surfaces, which means greater potential for seismic data processing under complex topographical conditions.