Resonance theory of elastic waves ultrasonically scattered from an elastic sphere

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Abstract
The interaction of elastic waves incident on an elastic spherical inhomogeneity is studied in detail, particularly in the resonance scattering regime. Incident and scattered compression and shear waves in lossless elastic media separate into three modes: a p mode for the compression wave, and s and t modes for the shear wave. A description of how the acoustic energy redistributes among these modes during the scattering process is contained in the scattering matrix that we separate here into background and resonance portions for the two extreme cases of a nearly soft and a nearly rigid elastic sphere. This produces farfield scattering amplitudes which are a superposition of a background contribution felt to contain reflected and Franz-type circumferential waves and a resonance contribution that seems to contain refracted, Rayleigh, and whispering gallery waves. Limiting cases (a fluid sphere in an elastic medium, an elastic sphere in a liquid medium, and a fluid sphere in a fluid medium) are extracted from these results to show agreement with previous work. Plots show the background and resonance portions of the scattered amplitudes and their connections with the poles of the scattering amplitude in the complex frequency plane. The methodology of the resonance scattering theory (RST) is summarized with a very general yet basic example of importance in acoustic/ultrasonics and elastodynamics/NDE, which contains all earlier situations.

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