Mid-frequency enhancement of the impulse response of a thin spherical shell: Ray approximation and a related frequency-domain analysis.

Abstract

A ray approximation was previously applied to the mid-frequency enhancement of the backscattering that occurs for ka close to the shell radius to thickness ratio a/h for thin shells [L. Zhang etal., J. Acoust. Soc. Am. 90, 2341(A) (1991) and L. G. Zhang etal., J. Acoust. Soc. Am. 91, 1862–1874 (1992) ]. The enhancement is primarily associated with the earliest guided ray contribution (that circumnavigates only the backside of the shell) of the slightly subsonic guided wave denoted by l=a0− by some authors. This ray contributes a large wave packet to the impulse response that is approximated in the present work. It is shown that the form function contribution ‖fm=0,l‖ is well approximated by a Gaussian centered on the ka where the damping βl≊1/π Np/rad. The resulting time-domain wave packet has an approximate Gaussian envelope and carrier frequency associated with that spectrum. The envelope amplitude is affected by the ka dependence of the phase velocity cl. This ray analysis, although incomplete, also gives insight into the background-subtracted steady-state form function. [Work supported by ONR.]