Wave velocities in a pre-stressed anisotropic elastic medium

Modified Christoffel equations are derived for three-dimensional wave propagation in a general anisotropic medium under initial stress. The three roots of a cubic equation define the phase velocities of three quasi-waves in the medium. Analytical expressions are used to calculate the directional derivatives of phase velocities. These derivatives are, further, used to calculate the group velocities and ray directions of the three quasi-waves in a pre-stressed anisotropic medium. Effect of initial stress on wave propagation is observed through the deviations in phase velocity, group velocity and ray direction for each of the quasi-waves. The variations of these deviations with the phase direction are plotted for a numerical model of general anisotropic medium with triclinic/ monoclinic/orthorhombic symmetry