SFA, Inc., Gateway Building East, 6188 Oxon Hill Rd., Suite 809, Oxon Hill, MD 20745 and Naval Research Laboratory, Washington, DC 20375
This is a counterpart of the companion paper above, with the additional complexity that is introduced by the spherical focusing. It is based on the previous ray formulation for a thin elastic spherical shell [J. M. Ho and L. B. Felsen, J. Acoust. Soc. Am. 88, 2389--2414 (1990)], again augmented by the Fresnel integral to accommodate the transition region. The shell guided wave field is focused near the backscatter direction, or the polar axis, according to the zeroth-order Bessel function, which may be approximated by Debby asymptotics when away from the focusing regime, thus leading to the regular region where the two counter-circumnavigating surface waves are distinguishable from one another. The excellent agreement between the ray field and the reference solution (normal modes), as achieved in the spherical as well as the cylindrical case, supports that the ray-acoustic technique is effective for evaluation of sound scattering and radiation from submerged elastic shells in the mid- and high-frequency ranges. The successful numerical implementation also helps understand, and extract, wave objects dominant on the structure, which can then be generalized to describe more practical geometries with increased confidence.