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On the far field amplitude for elastic waves

Alves, Carlos J. S.; Ha-Duong, T

Modern mathematical methods in diffraction theory and its applications in engineering (Editor: Meister, E.). Methoden Verfahren Math. Phys. Peter Lang., 42 (1997), 49-67

It is known that the solution of an elastic scattering problem behaves asymptotically like a sum of a spherical P wave and a spherical S wave. This result, as its acoustic counterpart, can be generally proved by way of some integral representation formula, which contains rather complicated terms in the elastic case. We adopt here a different viewpoint, considering the scattered wave as a solution of the inhomogeneous Navier’s equation with a distribution data, and obtain both simpler proofs for these results and more precise properties of the far field amplitudes, in particular a characterization theorem for elastic far fields and a density result.