A High-order Fast Sweeping Method for Calculating Quasi-P Traveltimes in 2D TTI Media

The fast sweeping method is a potential robust approach for performing seismic anisotropic raytracing. It propagates a wavefront by sweeping different directions to cover all possible wave directions. There is no need to maintain a sorted wavefront in fast sweeping method, thus the computational cost approximates to O(N) ops instead of O(NlogN) ops, where N is the total number of grids. The fast sweeping method has been widely used for isotropic raytracing. Although some efforts have been made to apply the method for anisotropic raytracing by solving static Hamilton-Jacobi equations, they are not straightforward for TTI media. In this study, we propose a high-order fast sweeping method to calculate quasi-P traveltimes in TTI media. We derive an analytical solution of the fourth-order polynomial equation in terms of slowness in the local solver. Our method does not assume weak anisotropy and is an accurate solution of the quasi-P traveltime in a general TTI medium.