An approach to computing the dispersion of wavespeed for the most general 3D anisotropic media

Abstract

In this paper,we develop a method to calculate the dispersion of seismic wave speed (phase velocity and group velocity) for a general anisotropic medium, which is defined by twenty-one elastic moduli. The solution includes,as special cases, the isotropic and transversely isotropic problems. We apply the plane-wave analysis to the general 3D anisotropic medium and obtain explicit expressions for three eigenvalues (phase velocities) and their corresponding group velocities, which are the propagation speeds of the wavefronts and the energy fluxes (ray-paths) of one qP wave and two qS waves. Basing on the solutions,we show that the phase and group-velocity vectors generally have different directions and they depend on twenty-one elastic moduli and the direction cosines of the incident wave. As examples of using the eigenvalue solutions, we numerically calculate the phase velocities and the group velocities for an isotopic medium, a VTI-medium and a qTI-medium. Two real models (clay shale and phenolic) were used for moduli selection. These results clearly show that the wave speeds vary with the azimuthal angle and the vertical angle of the incident wave, as well as the elastic moduli. This means that the solutions may be applied to investigation of kinematic features of real samples of rocks and the sensitivity of the wavespeed to each elastic modulus. We also show the application of the eigenvalue solutions to the 2D/3D ray tracing in the most general anisotropic media.