Abstract
The Sommerfeld–Watson transformation (SWT) was recently applied to the acoustic backscattering from elastic spheres in water having ka≫1 [K. L. Williams and P. L. Marston, J. Acoust. Soc. Am. 78, 1093–1102 (1985)]. Expressions for the scattering due to each class of elastic surface wave (e.g., the Rayleigh wave) were interpreted in terms of contributions from repeated circumnavigations. In the present paper, these expressions are summed in closed form as in the analysis of Fabry–Perot resonators. The form function is synthesized by adding this sum to the specular reflection. The procedure is confirmed by comparison with the exact form function f for a tungsten carbide sphere in the range 10≤ka≤80. In this case, the interference of the specular and Rayleigh contributions produces the underlying structure in ‖f(ka)‖, while the whispering gallery wave resonances produce a finer superposed structure. Phase shifts and coupling coefficients are identified which affect the signatures in ‖f(ka)‖ of the Rayleigh wave resonances.
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