Interior and exterior resonances in acoustic scattering by arbitrarily shaped targets

Abstract

The T matrix approach useful to describe classical scattering of acoustic (and other) waves from arbitrarily shaped objects, is here “married” to the resonance scattering theory in order to isolate the (complex) resonance frequencies and widths of fluid-loaded targets of arbitrary geometries. For the case of near-impenetrable (i.e., quasirigid/soft) targets, we split the partial-wave scattering amplitudes into terms corresponding to internal resonances of the elastic object which are caused by creeping waves revolving inside it, plus an apparently nonresonant background amplitude. This background, however, further contains the broad “resonances” caused by external, diffracted (or Franz-type, creeping) waves, together with a geometrically reflected contribution which can be extracted by a saddle point integration. The separation of resonant and background terms is done analytically based on the T matrix method for elastic scatterers of arbitrary geometry. [H. Überall is also at the Physics Department, Catholic University of America; additionally supported by ONR, Code 421.]