Traveltime calculations for qP, qSV, and qSH waves in 3D tilted transversely isotropic media using fast sweeping method with a Newton method local solver

Abstract

Efficient and accurate traveltime calculations of seismic waves have important applications in tomography, prestack migration, earthquake location, etc. Anisotropy significantly affects the traveltimes of seismic wave. For high-resolution imaging and inversion, it is necessary to consider anisotropy in the traveltime calculations. The fast sweeping method (FSM) does not need to track and store the minimum traveltime point of wavefront, which has important applications in computing the anisotropic first-arrival traveltime. The conventional method that solves a transformed traveltime quartic equation combined with FSM is suitable for general anisotropic media. However, this method involves finding the intervals of roots and solving the quartic equations using bisection algorithm at each iteration, leading to high computational cost and instability for the 3D problems. In our previous work, for the vertical transversely isotropic (VTI) case, we developed an FSM to compute the qP-wave first-arrival traveltimes by analytically solving the simplified quadratic slowness equation in a specific triangular-pyramid stencil. This method greatly improves the computational efficiency. However, for the qP and qSV waves, analytically solving the slowness equation cannot be extended to tilted transversely isotropic (TTI) media. To address this problem, we introduced the Newton method in the triangular-pyramid local solver to quickly solve the TTI slowness equation. For the qSH wave, its slowness equation is quadratic and simple to solve. The proposed method provides an efficient procedure for the traveltime calculations of qP, qSV, and qSH waves in 3D general TTI media. Numerical examples have verified the efficiency and accuracy of the proposed method.