Theory of resonant scattering from spherical cavities in elastic and viscoelastic media

Plane incident p‐waves which propagate through continuous (possibly absorptive) media are scattered by a fluid‐filled spherical cavity contained in it. Using an approach familiar in nuclear scattering theory but novel to acoustics and elastodynamics, it is possible to express the scattering amplitudes (or the partial waves contained in them) for the scattered p‐and s‐waves in a form which clearly exhibits their dependence on two interacting contributions, one being the broad background of an ideally soft cavity, and the other the superimposed narrow spikes due to resonances excited in the cavity fluid. The cavity appears as a perfectly soft obstacle to the incident waves at all frequencies except in the near vicinity of the cavity eigenfrequencies where there is wave penetration into the filler fluid. When this happens, the interference of this wave with the ’’potential scattering’’ of the background is seen to cause the fluctuating character of the amplitudes (or cross section). We have numerically compu...