Elastic waves in inhomogeneously oriented anisotropic materials

Ray theory is developed for elastic waves propagating in inhomogeneously oriented anisotropic solids. These are materials of uniform density with moduli which are uniform up to a rotation of the underlying crystalline axes about a common direction, the degree of rotation varying smoothly with position. The ordinary differential equations governing the evolution of a ray have a simple form, and involve the angle of deviation between the slowness and wave velocity directions. The general theory is demonstrated for the case of SH waves in a transversely isotropic medium. The equations required for the description of SH Gaussian beams are derived, including the transport equation and the wavefront curvature equation. The theory is combined with an equivalent complex-source representation to generate an approximation to a time harmonic point source.