A fast sweeping method based on coordinate transformation for eikonal equation on unstructured triangular meshes
Xin Chen, Danping Cao, Xin Hua Fu · 2024
Accurate traveltime estimation is essential in seismic and seismology applications, such as traveltime tomography and seismic imaging. When dealing with subsurface models with irregular topographies, unstructured triangular meshes often outperform Cartesian meshes when solving eikonal equations. The fast sweeping method (FSM) is a highly effective approach for calculating traveltime, and it has been successfully applied to triangular meshes as well. However, most existing FSMs cannot directly solve the eikonal equation on an obtuse triangle and require dividing the obtuse angle into two or more new acute angles. This approach greatly increases the difficulty of programming. To overcome this limitation, we propose a novel one, the FSM based on coordinate transformation (FSMCT), to solve eikonal equations on unstructured triangular meshes. The FSMCT can transform any triangular mesh in the physical domain into the canonical reference triangle in the computational domain, and construct a difference scheme within the reference triangle to approximate the partial derivatives in the eikonal equation. The finite-difference method introduced by FSMCT can also effectively discretize the factored eikonal equation in triangular meshes, solve the singularity of point sources, and improve the accuracy of traveltime calculation. Numerical simulations demonstrate the validity and accuracy of the new method for models with irregular topography.