Fully three-dimensional exact and ray asymptotic formulation of the characteristic wave fields on a spherical shell surface

Abstract

Fully three-dimensional Green’s functions are important for synthesizing the acoustic scattering response from submerged spherical shells due to excitation not only by actual radiating sources without special symmetries but also by induced sources on the shell which can characterize the effects of truncations or loadings of the empty undisturbed shell prototype. As in a previous two-dimensional (2-D) study of scattering due to axisymmetric (azimuthally independent) source configurations [J. M. Ho and L. B. Felsen, J. Acoust. Soc. Am. 88, 2389–2414 (1990)], the goal is the derivation of self-consistent hybrid ray-mode asymptotic algorithms from appropriate rigorous alternative spectral representations; hybrid ray-mode algorithms have been shown to be well matched to the wave phenomena which generate the scattered acoustic fields in the fluid in the mid- and high-frequency range ka≳5, where k is the wave number in the fluid and ‘‘a’’ is the mean radius of the shell, and also under pulsed excitation. The presentation here deals with the rigorous spectral foundation, asymptotics, and ray-acoustic interpretation of the rich variety of generic 3-D wave phenomena encountered on the shell surface, which must be understood in order to treat the general case of arbitrary source and observer locations in a follow-up paper.