The present article addresses classical elastic and/or acoustic wave-scattering problems for situations in which the pertinent targets are penetrable. In contrast to impenetrable scatterers, penetrable bodies admit interior fields coupled to the external fields through suitable (sets of) boundary conditions. When the wavelength of the incident radiation is either very long or very short, the scattered echoes returned to an interrogating active sensor can be described in a relatively simple way. This is not the case in the resonance region of the scattering cross section of any penetrable body. This region is sandwiched in between the long-wavelength (Rayleigh) region and the short-wavelength (geometrical) spectral regime. For penetrable (viz, acoustic, elastic, viscoelastic) structures, the resonance region becomes very broad, and results within it are quite difficult to describe analytically, to compute numerically, or to confirm experimentally. Resonance scattering (by definition) implies that the situation at hand occurs within that most troublesome of spectral regimes. We describe a technique particularly useful to simplify and interpret predictions and measurements in the resonance region. This technique exploits the presence of certain “features” clearly observable in the echoes returned by the targets that scatter them. It is by means of these (resonance) features that, for example, different submerged structures can be remotely distinguished from one another. The natural resonances of the structure, not in vacuum, but accounting for its fluid-loaded condition, are communicated to its returned echo in a unique fashion that unambiguously characterizes it as a “fingerprint.” It is always these echoes that we investigate for their “resonance” contents, either in the frequency or time domains. The resonance technique described here, often called the resonance scattering technique (RST), is a linear approximation that makes the understanding of resonance signatures from scatterers not only easier, but possible at all. Results obtainable from strictly classical approaches are so cluttered with information that it is difficult to use them. One simply “cannot see the forest for the trees.” The applications of the RST to various separable and nonseparable configurations are shown. Validating experiments are described, and a bibliography emphasizing the recent target-identification and target-camouflaging aspects of the technique is provided.

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