Numerical evaluation of modal resonances in the echoes of compressional waves scattered from fluid-filled spherical cavities in solids

We extend our previous resonance formalism for the scattering of compressional waves by fluid-filled spherical cavities in sound-absorbing media by analyzing the resonances in the partial-wave amplitudes both as functions of frequency for a given mode number, or as a function of (continuous) mode number n, at a given frequency. In both cases we isolate the resonances by subtracting an appropriate smooth nonresonant background. The frequency analysis leads to a unique identification of the resonances in the summed backscattering amplitudes. This finding can be used to decipher the scattering code contained in the cavity’s echo, since with it we can identify the material composition of the cavity’s filler. The frequency analysis also leads to a study of the resonance-decay phenomenon of ’’ringing’’. The mode-number analysis leads to an interpretation of the scattering process taking place around the cavity in terms of Regge poles representing creeping waves, whose trajectories in the complex n plane and associated dispersion curves for the phase velocities are obtained and displayed. We exhibit the curves for the angular amplitude decay parameter of the waves. We find a condition on the wavelength of the surface waves at each resonance which allows us to physically interpret the resonances as a phase-match reinforcement of the creeping waves with themselves; we verify the results of our resonance theory via the Watson-Sommerfeld method and display numerous plots of the resonances in the scattering amplitudes (some in three dimensions for the modular surfaces) for various combinations of materials in the filler and in the matrix.