Quantitative Ray Methods for Scattering of Sound by Spherical Shells

The application of ray methods to the scattering of high-frequency plane waves from evacuated elastic spherical shells is investigated. The investigation of ray methods for spherical shells is a precursor to the application of such methods to shells having more complicated shapes. Ray models are developed to synthesize the form function f(Theta, ka) where k is the wavenumber of the incident wave and Theta is the scattering angle. The forward scattering amplitude, f(Theta = 0), is related to the extinction cross section, sigma sub e by the optical theorem. If the absorption by the scatterer is negligible, the sigma sub e is equal to the total scattering cross section sigma sub t. A ray synthesis partition f(Theta = 0) into a component for ordinary forward diffraction about the shell, f sub FD, and contributions from surface guided elastic waves. For high-frequency scattering, the relevant surface guided elastic waves are leaky Lamb waves. A similar ray synthesis of the backscattering amplitude f(Theta = pi) contains a specular reflection component, f sub sp(Theta = pi), and leaky Lamb wave contributions. A generalization of the geometrical theory of diffraction is employed to synthesize f sub l(Theta = 0, ka) and f sub l (Theta = pi, ka) for the lth leaky Lamb wave contribution. The syntheses for forward and backwards scattering correctly describe the leaky Lamb wave contributions and are expressible in a Fabry-Perot resonator form. While the ray description of backscattering ordinarily accurately reproduces exact computations and experiments with tone burst, certain anomalies are discussed.