We have formulated the resonance scattering theory (RST) for the general case of acoustic reflection from (and transmission through) a stack of arbitrarily many elastic fiat plates. The multilayered system separates two, possibly dissimilar, outer fluids. An incident plane harmonic wave impinges on the structure at an arbitrary angle of incidence from one of the outer fluids, and is subsequently reflected and transmitted. The simple form of the RST formulation permits a clear interpretation of the scattering process taking place in the structure. According to the RST, these resonances and the scattered waves they cause are described by a series of simple poles which yield meromorphic expressions for the transmission and reflection coefficients. The reflection coefficient is numerically computed and graphically displayed for several n-layered configurations, n <4. In these figures the generally good agreement of the RST with the classical approach of Thomson [ J. Appl. Phys. 21, 89 (1950) ] and Haskell [Bull. Seismol. Soc. Am. 43, 17 (1953) ] is demonstrated. We show how the multilayered formulation can be put in the same simple resonance form we have previously developed for single and double layered configurations, and we recover many of our earlier results for these simpler layered configurations. The methodology lends itself to the solution of some aspects of the inverse scattering problem for the entire structure.

We construct the prediction of the resonance scattering theory (RST) for the reflection of sound waves by a bilaminar rubber configuration separating two dissimilar semi-infinite acoustic media. The layers are further assumed to contain distributions of spherical air-filled perforations, of various concentrations in each layer, whose behavior is governed by a simple, static, "effective parameter" model. We compare the direct scattering prediction of the RST to that of the exact solution in order to show the usefulness of the RST to yield clear physical interpretations of complex phenomena. The casting of the direct scattering solution in "RST-form" also provides a systematic method to solve the inverse scattering problem for the composition of the bilaminar rubber configuration. The "response surface" and response curves of the returned echoes are shown to contain certain modulation effects, described in the text, that actually characterize the material composition of each of the layers making up the coating model. The process disentangles which resonance feature present in the reflection coefficient is caused by which one of the interacting layers. In particular, we can separate and identify the impedances and the respective thickness-to-speed ratios (transit times) of each of the layers, and if additionally, either the thicknesses or the speeds are known, then, the process determines the other one and also the layer densities all from the resonances in the remotely sensed acoustic reflections.

The echoes reflected by a stratified ocean bottom that is insonified by acoustic plane waves emerging from a distant source are studied. The various strata in the bottom are modeled as elastic layers bonded together and allowing longitudinal (acoustic) and transverse (shear) waves to penetrate and be propagated through, and reflected from, the overall configuration. There can be as many layers as one wishes, all of arbitrary compositions. The bottom layer is a half-space of infinite thickness upon which all other layers rest. The top layer is the fluid layer that simulates the ocean and contains the source. The reflections versus frequency at fixed angles of incidence, or versus angle of incidence at fixed frequencies are studied. Numerous resonances are present in these returns and emerge in the analysis. This investigation has the eventual, ultimate, goal of determining details about the bottom composition and stratification, from the remotely sensed reflections. Of particular interest is a five-layer ease in which the consolidation and rigidity of the sediments in the various layers increases as one penetrates deeper into the bottom.

The prediction of the Resonance Scattering Theory (RST) for the reflection coefficient from a set of two contiguous plane dielectric layers separating two semi-infinite dissimilar nonconducting media, is constructed and compared to the exact classical model solution. The comparison serves to: (a) show the excellence, accuracy, and simplicity of the RST prediction, and (b) to underline the usefulness of the RST to produce clear physical interpretations of generally complex phenomena. In addition, the analysis serves to provide a systematic method for detecting the presence of a dielectric layer under another one covering it (possibly the situation caused by an oil spill in ice-covered Arctic regions), by certain modulation effects present in the ‘‘response surface’’ of the returned echoes, which we describe in the text. This method not only serves to detect, but also to characterize/identify, the material composition of the low or hidden layer in the bilaminar configuration. The process disentangles which resonance feature present in the radar reflection coefficient is caused by which of the two interacting layers. This, therefore, solves the inverse scattering problem for the composition and thickness not only of the top visible (ice) layer, but also of the substance (oil) hidden under that upper layer, via the radar resonances of the reflected echoes.

Each of the perforated rubber layers constituting the multilayered composites used to absorb underwater sound waves can be (ideally) modeled as a fluid layer having density ρi and sound speed Ci. The volume concentration of the gas-filled perforations controls the (effective) values of ρi and Ci in each of the layers. We consider a plane two-layer coating having a (possibly different) fluid on each side, and we study its reflection coefficient R(f, θ) as a function of frequency f and incidence angle θ, as plane sound waves are reflected by it. Resonances are evident in R(f, θ) both as functions of f and θ, and we display many of these in three-dimensional graphs that are as informative as esthetically pleasing to view. We then show how these resonances in R can be analyzed in the light of the resonance scattering theory (RST) in order to generate simple (and approximate) but quite accurate reflection predictions, which we then use to extract information about the material composition of the bilaminar composite. The method determines which of the reflection features is caused by which of the two interacting layers.