Full wave solutions for the scattering of acoustic waves excited by arbitrary source distributions in irregular layered media

Abstract

Generalized Fourier transforms for the acoustic pressure and velocity are derived for propagation in irregular layered media. They provide a basis for the complete expansion of three-dimensionalacoustic fields excited by arbitrary source distributions. The height above a reference plane of the interface between two semi-infinite media, the adiabatic bulk modulus, the equilibrium density and the viscosity of the media above and below the interface are assumed to vary along one coordinate variable in the reference plane. The equations of continuity and force in conjunction with the associated boundary conditions at the irregular interface are converted into rigorous first-order coupled differential (telegraphists') equations for the forward-and backward-propagating wave amplitudes. The differential scattering coefficients are shown to satisfy the reciprocity relationships. The telegraphists' equations are solved iteratively to derive closed-form solutions for the singly scattered radiation and surface fields excited by acoustic sources at large distances from the irregular interface. The full wave solutions account for specular-point as well as diffuse scattering in a unified self-consistent manner.