FULLY 3-DIMENSIONAL EXACT AND RAY ASYMPTOTIC FORMULATION OF THE CHARACTERISTIC WAVE-FIELDS ON A SPHERICAL-SHELL SURFACE

Fully three-dimensional Green's functions are important for synthesizi ng the acoustic scattering response from submerged spherical shells du e to excitation not only by actual radiating sources without special s ymmetries but also by induced sources on the shell which can character ize the effects of truncations or loadings of the empty undisturbed sh ell prototype. As in a previous two-dimensional (2-D) study of scatter ing due to axisymmetric (azimuthally independent) source configuration s V. M. Ho and L. B. Felsen, J. Acoust. Soc. Am. 88, 2389-2414 (1990)] , the goal is the derivation of self-consistent hybrid my-mode asympto tic algorithms from appropriate rigorous alternative spectral represen tations; hybrid ray-mode algorithms have been shown to be wen matched to the wave phenomena which generate the scattered acoustic fields in the fluid in the mid- and high-frequency range ka greater than or simi lar to 5, where k is the wave number in the fluid and ''a'' is the mea n radius of the shell, and also under pulsed excitation. The presentat ion here deals with the rigorous spectral foundation, asymptotics, and my-acoustic interpretation of the rich variety of generic 3-D wave ph enomena encountered on the shell surface, which must be understood m o rder to treat the general case of arbitrary source and observer locati ons in a follow-up paper.