Exact elastodynamic Green functions for simple types of anisotropy derived from higher-order ray theory

Using higher-order ray theory, we derived exact elastodynamic Green functions for three simple types of homogeneous anisotropy. The first type displays an orthorhombic symmetry, the other two types display transverse isotropy. In all cases, the slowness surfaces of waves are either ellipsoids, spheroids or spheres. All three Green functions are expressed by a ray series with a finite number of terms. The Green functions can be written in explicit and elementary form similar to the Stokes solution for isotropy. In two Green functions, the higher-order ray approximations form a near-singularity term, which is significant near a kiss singularity. In the third Green function, the higher-order ray approximations also form a near-field term, which is significant near the point source. No effect connected with the line singularity was observed.