An Efficient Method for Calculating Raypaths of First-Arrival Traveltimes in Transversely Isotropic Media

Raypath tracing is a commonly used technique in geophysics, employed to simulate and analyse seismic wave propagation paths from source to receiver in complex media. In isotropic media, raypaths can be obtained by tracing from the receiver point along directions perpendicular to the wavefront towards the source point, based on the Fermat principle, because in isotropic media, the ray direction aligns with the ray gradient direction. In an anisotropic medium, the ray direction generally differs from the ray gradient direction, rendering the conventional tracing method inaccurate. Solving raypaths using Hamilton's canonical equations is a powerful method. However, in anisotropic media, the complex dependence of wave velocity on the propagation direction complicates the Hamiltonian function, significantly increasing computational complexity. To address this problem, we have derived a scheme based on the relationship between the group velocity vector and the slowness vector in anisotropic media. Firstly, the slowness vector is derived from the traveltime obtained through the eikonal equation, followed by the computation of the group velocity vector. Then, the raypath is determined by tracing back from the receiver point using the group velocity components to the source point. The efficiency and accuracy of our approach are validated through three numerical experiments.