GTD synthesis of resonance amplitudes in the backscattering from an elastic spherical shell

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An elastic generalization of the geometrical theory of diffraction [P. L. Marston, J. Acoust. Soc. Am. 83, 25–37 (1988)] was used to describe the backscattering of short tone bursts from an elastic spherical shell in water [S. G. Kargl and P. L. Marston, J. Acoust. Soc. Am. 85, 1014–1028 (1989)]. In the present research, steady‐state backscattering amplitudes are synthesized. The GTD model contains explicit terms for the specular reflection and individual Lamb surface wave contributions in a Fabry‐Perot form. Numerical calculations compare the exact partial‐wave series result with the GTD synthesis for the frequency range 7 < kA < 100. These computations correspond to a stainless steel shell with an inner‐to‐outer radius ratio b/a = 0.838. An important feature of the GTD model is that only two parameters are needed to fully describe the individual Lamb wave resonance amplitudes. These parameters are the ratio of the Lamb wave phase velocity to the velocity of sound in water (c1/c) and the radiation damping β1. These should depend on local properties of the shell‐water system. This simple parametrization of the direct scattering problem should facilitate novel approaches to the inverse problem. Identification of a scatterer may be achieved through an examination of the Lamb wave resonances via a numerical fitting of these parameters. [Work supported by ONR.]