Background contributions and coupling coefficients for backscattering by thick shells

Abstract

Approximations for leaky wave coupling coefficients and background scattering contributions are usually derived by assuming the shell response is governed by thin shell theory. Comparisons are described with approximations derived by other methods for a thick spherical shell at frequencies above coincidence. The variation of the phase of the coupling coefficient from numerical evaluation of the Watson transformation residue by Kargl [Ph.D. thesis, Washington State University (1990)] is evident in an analytical approximation. The phase of the background includes inertial and wave-kinematic contributions and is related to research by Gaunaurd and Werby [J. Acoust. Soc. Am. 90, 2536–2550 (1991)]. The inertial contribution to the background phase is derived directly from the reflectivity of a plate in the limit of small phase shift for propagation across the thickness of the shell. The frequency and angle dependence of the phase of the exact reflection coefficient of a plate (having the same thickness as the shell) is also examined.