Propagation of elastic energy in a general anisotropic medium

Abstract

Propagation of plane harmonic waves is studied in anisotropic elastic medium. Anisotropy is of general type, i.e., no symmetry enforced and no rotation of elastic tensor. The propagation is not restricted to a fixed plane but along a general direction in three-dimensional space. A new procedure is presented to study the reflection in anisotropic media. Phase direction of incident wave is calculated from its ray direction. For this incident phase direction, the Snell's law is used to calculate the phase direction of each of the homogeneous reflected waves, This identifies a critical angle of incidence for the reflected wave such that, for incidence beyond this angle, this reflected wave becomes inhomogeneous. Group (energy) velocities and ray directions of the homogeneous quasi-waves reflected at the free surface are calculated analytically and without using energy flux. An energy matrix is defined to explain the energy share of different reflected waves and interaction energy. The incidence of the quasi-waves is considered along a given (arbitrary) ray direction. The numerical results compute the group velocities and ray directions of reflected waves for the numerical model of Dolomite crystalline rock. The partition of incident energy among the homogeneous reflected waves is also calculated. The energies reflected as different homogeneous waves vary with the ray direction of the incident wave. These variations are plotted and discussed for the numerical model.