RST analysis of monostatic and bistatic acoustic echoes from an elastic sphere

Abstract

We readdress the basic problem of the scattering of acoustic waves by an elastic sphere, now under the dissecting knife of the Resonance Scattering Theory (RST), with the purpose of illustrating the power of the method, and the versatile options and information it offers. These options include ease of understanding, novel physical interpretation of the phenomenon, and striking calculational simplicity. The principal findings presented here include: (a) the actual modal resonances, quantitatively separated from the corresponding modal backgrounds in the frequency (the ‘‘acoustic spectrogram’’—already a target-identification tool) domain, and in the combined frequency and mode-order domain (the ‘‘response surface’’). (b) The bistatic plots of the scattering cross section, to illustrate the point that if the cross section is redetermined at certain selected observation angles, the resonance contributions from each individual mode can actually be isolated from those of all other modes. (c) A study of the nulls or dips present in the partial waves (i.e., modes), and in the summed cross section. We show the cause and physical meanings of these dips analytically and computationally, in both instances. (d) A derivation of the analytic conditions predicting the nulls and also the influence of the elastic resonance (SEM) poles in the scattered echoes. These conditions, which emerge from our scattering approach, are shown to be in agreement with early results of Love [A Treatise on the Mathematical Theory of Elasticty (Dover, New York, 1944)], obtained on a purely vibrational basis. A tungsten carbide sphere is used in all the examples, since this is a favorite target for experimental calibrations. Our future work will underline the intimate connection between his direct approach, and that (leading to the solution) of the inverse scattering problem for sonar target identification.