An improved mesh generation scheme for the wavefront construction method

Wavefront construction is an effective tool for the rapid calculation of ray fields in anisotropic media. The method explicitly tracks the propagation of a wavefront through a model, mapping it to a computational mesh that is interpolated when accuracy criteria based on paraxial ray methods are violated. Takeoff angles are used often to define the initial ray directions, but uniform sampling in the two angles leads to oversampling of the ray field in the direction of the axis. Such sampling can lead also to numerical instability associated with vanishing derivatives with respect to the azimuthal angle. We suggest a new wavefront mesh definition using the cubed-sphere mesh, which is a coordinate system used to solve partial differential equations in spherical geometries. When using this mesh, ray directions are assigned by mapping points on a regular discretization of the faces of a cube surrounding the source to corresponding rays. This scheme produces a nearly uniform distribution of rays with minimal effort and using the cubed-sphere coordinates as ray parameters to calculate partial derivatives completely eliminates the singularities that arise when takeoff angles are used as ray parameters. Numerical results for quantities related to seismic amplitudes confirm that this new mesh does provide more stable and reliable results.