Spherical wave functions and dyadic Green’s functions for homogeneous elastic anisotropic media

A spherical-wave-function theory of bounded homogeneous elastic anisotropic media is developed. The anisotropic elastodynamic wave equations are solved exactly by using the method of plane-wave angular spectrum expansions. The series, integral representations, and addition theorems of the spherical wave functions of the first, second, third, and fourth kind for homogeneous elastic anisotropic media (HEAM) are presented. Weyl's method for the scalar Green's functions in isotropic media is generalized to the study of the dyadic Green's functions in HEAM. The series representations of Green's functions are of the form of separated variables. These representations are well suited to imposing a boundary condition when dealing with waves in spherically layered HEAM.