Ray synthesis of Lamb wave contributions to the total scattering cross section for an elastic spherical shell

Abstract

The optical theorem relates the extinction cross section σe(ka) to the forward-scattering amplitude f (θ=0,ka). Here, θ denotes the scattering angle, k is the wavenumber of the incident sound, and a is the radius of the scatterer. If the absorption by the scatterer is negligible so that the scatterer is elastic, σe is equal to the total scattering cross section σt. By applying this theorem to the partial wave series for f (0,ka), an expression can be obtained for σt for an elastic spherical shell in water. However, the series representation of σt does not facilitate a direct understanding of the rich structure caused by the shell’s elastic response. In particular, the elastic response is attributable to leaky Lamb waves. A generalization of the geometrical theory of diffraction [P. L. Marston, J. Acoust. Soc. Am. 83, 25–37 (1988)] is employed to synthesize f (0,ka). This simple ray acoustic synthesis contains a component for ordinary diffraction by the shell and distinct contributions for the individual Lamb waves that can be excited on the shell. A comparison of numerical computations for σt utilizing the exact partial wave series and the ray synthesis shows good agreement in the description of the resonance structure. The relevant range of ka for this comparison is 7