The theory of resonance scattering in acoustics, nondestructive testing, and geophysics

Abstract

This paper summarizes recent progress concerning modal and surface‐wave resonances in scattering and reflection of acoustic waves from elastic (or viscoelastic) objects, and of elastic waves from cavities or solid inclusions. Experiments and normal‐mode calculations have revealed a large, often confusing variety of resonance phenomena in both acoustic and elastic‐wave scattering. In collaboration with L. Flax, L. R. Dragonette, G. C. Gaunaurd, and others, we have developed a systematic theory based on the Breit‐Wigner formalism of nuclear resonance scattering, in which the observed resonances can be explained physically, and interpreted in terms of the modal eigenvibrations of the elastic targets. or the contents of the cavity, respectively. Modal scattering amplitudes consist of a nonresonant background with superimposed, and interfering, resonance contributions. The latter can be isolated by subtracting the background, both in the “rigid” and the “soft” limits and in the general intermediate case. The same resonances may be viewed differently, with the mode index being considered a complex variable. This permits interpreting the scattering amplitude in terms of surface waves (“creeping waves”) corresponding to the Regge Poles of Nuclear Physics. We unify the two viewpoints, demonstrating that the resonances of the modal target eigenvibrations correspond to “phase‐matching” of the creeping waves, which occurs when the target's circumference measures an even (for cylinders) or odd (for spheres) integer number of half‐wave lengths. [Supported by ONR Code 421.]