A Newton–Marchenko equation and generalized optical theorem for elastodynamics

Abstract

Two new results are derived for the scattering theory of waves in nondissipative elastic media. These results are (1) a Newton–Marchenko equation, and (2) a generalized optical theorem. The Newton–Marchenko equation is an integral equation for the wavefield in terms of scattering amplitude data. It is supposed that it may play an important role in the development of exact inverse scattering methods for elastodynamics. The generalized optical theorem provides explicit relations between the scattering amplitudes, and is expected to be useful in the analysis of both the forward and inverse scattering problem. The results are presented within the context of a localized, possibly anisotropic, inhomogeneity contained in an otherwise uniform isotropic elastic medium of infinite extent in R3.