An iterative fast sweeping method for the eikonal equation in 2D anisotropic media on unstructured triangular meshes

Abstract

Computation of traveltimes and raypaths is important for anisotropic tomography inversions. The eikonal-equation-based method outperforms traditional ray methods by producing more accurate results. However, most existing eikonal solvers are formulated on structured regular meshes, which are no longer accurate for models with the presence of irregular topography and subsurface interfaces. To solve the eikonal equation in vertically transversely isotropic (VTI) or tilted transversely isotropic (TTI) models with irregular geometry, we have formulated a new iterative fast sweeping method (FSM) on unstructured triangular meshes. The fixed-point iteration is implemented to capture the high-order nonlinear terms therein, and an FSM on unstructured triangular meshes is implemented to solve the resulting elliptically anisotropic eikonal equation at every iteration. We test the new algorithm for direct arrivals and reflected arrivals, and then we use the calculated traveltimes to track the raypath in VTI/TTI media. Numerical tests demonstrate the validity and accuracy of the new method for models with rough topography and subsurface interface.