A Fast Sweeping Scheme for Calculating P Wave First-Arrival Travel Times in Transversely Isotropic Media with an Irregular Surface
Seismic wave propagation shows anisotropic characteristics in many sedimentary rocks. Modern seismic exploration in mountainous areas makes it important to calculate P wave travel times in anisotropic media with irregular surfaces. The challenges in this context are mainly from two aspects. First is how to tackle the irregular surface in a Cartesian coordinate system, and the other lies in solving the anisotropic eikonal equation. Since for anisotropic media the ray (group) velocity direction is not the same as the direction of the travel-time gradient, the travel-time gradient no longer serves as an indicator of the group velocity direction in extrapolating the travel-time field. Recently, a topography-dependent eikonal equation formulated in a curvilinear coordinate system has been established, which is effective for calculating first-arrival travel times in an isotropic model with an irregular surface. Here, we extend the above equation from isotropy to transverse isotropy (TI) by formulating a topography-dependent eikonal equation in TI media in the curvilinear coordinate system, and then use a fast sweeping scheme to solve the topography-dependent anisotropic eikonal equation in the curvilinear coordinate system. Numerical experiments demonstrate the feasibility and accuracy of the scheme in calculating P wave travel times in TI models with an irregular surface.