3D elastic scattering theorems for point-generated dyadic fields

The problem of scattering of elastic spherical waves by a rigid body, cavity or a penetrable obstacle in 3D linear elasticity is considered. For two point sources, dyadic far-field pattern generators are defined, which are used for the formulation of a general scattering theorem. The main reciprocity principle and mixed scattering relations are also established. We provide the necessary energy considerations, presenting relative energy functionals and expressions for the differential and the scattering cross section due to point -source dyadic incidence. Finally, an application of the general scattering theorem for appropriate locations of the point source leads to an optical theorem.