Calculation of group velocity with application for traveltime computation in 3D VTI media using the fast sweeping method

ABSTRACT Traveltime computation is an effective way to simulate seismic wave propagation in isotropic and anisotropic media. It often requires the phase and group velocities along a ray direction. The phase and group velocities are not functions of the ray direction, but functions of the slowness direction, which motivates the need for efficient numerical approaches for computing the slowness direction. A generalized method was proposed to achieve this goal in 3D tilted transverse isotropic media, which involves solving a nonlinear equation of two unknowns, the inclination and azimuthal angles of the slowness direction, and is computationally demanding. To overcome the difficulty, the equation was recast by projecting it onto the local coordinates that align with the axis of symmetry of the medium. Under the local coordinate system, the nonlinear equation reduces to an equation of one unknown, the inclination angle, with the azimuthal angle obtained from the given ray direction. Hence, the nonlinear equation can be solved efficiently and its solutions can be used to calculate the phase and group velocities. As an application, the proposed method was used to compute traveltimes in 3D vertical transverse isotropic (VTI) media. The calculated group velocities are incorporated into the fast sweeping method to solve the original anisotropic Eikonal equation directly on uniform meshes. The feasibility of the proposed group velocity calculation method is evaluated in three 3D homogeneous anisotropic models, and the application on traveltime computation is tested on a 3D homogeneous VTI model and the British Petroleum anisotropic VTI model.