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(GRETSI, Saint Martin d'Hères, France, 1985)Echoes of acoustic or elastic waves scattered from a target carry within them the resonance features caused by the excitation of the eigenvibrations of the target. By means of a suitable background subtraction it is possible to isolate the target's spectrum of resonances . This spectrum characterizes the target just as an optical spectrum characterizes the chemical element or compound that emits it . Extracting the resonance information from the echo allows the possibility of identifying the target as to its size, shape, and composition . This is illustrated by studying the dependence of the resonance spectra of fluid targets upon changes of target shape, including variations front spheres to prolate spheroids and finitelength cylinders. The resulting "acoustic resonance spectroscopy" (a concept introduced by Derem) generates the same type of level scheme as in optics, and it may thus be used for solving some aspects of the "inverse scattering problem" (i . e., the problem of identification of the nature of the target from the returned echoes) . A study along these lines shows that the eigenfrequencies of fluidfilled cavities in a solid medium (obtained by us in the complex frequency plane) are tied to resonance features in the scattering amplitude which can be analyzed to provide the material parameters (density and sound speed) of the fluid filler : the resonance spacing giving the sound speed, and the resonance widths the fluid densityhence leading to a solution of the inverse scattering problem in this case....

(GRETSI, Saint Martin d'Hères, France, 1985)The eigenfrequencies of a cylindrial obstacle (of finite or infinite length) can be interpreted as the resonances due to phase matching of circumnavigating helical surface waves. For the case of a cylinder of finite length, the pitch angle of the helix can assume a discrete set of values only . Resonant eigenvibrations can be excited by waves incident in an oblique fashion, which generates the helical waves . A refraction effect is found to take place between the incident and the helicalwave directions . We obtain pole diagrams of the scattering amplitude in the complexfrequency plane, by using the Tmatrix approximation for finite cylinders . In addition, pole diagrams for spheroidal scatterers are obtained by the use of the Tmatrix and of spheroidal wave functions . While the poles of symmetric scatterers (spheres or infinite cylinders) are degenerate in the azimuthal quantum number in, the degeneracy for the potes of finite cylinders and of spheroids is lifted . This msplitting is explained by the phase matching of helical waves with various allowed pitch angles . Dispersion curves for the phase and group velocities and attenuations of the helical waves are obtained....

(GRETSI, Saint Martin d'Hères, France, 1985)The classical normalmode series of acoustic scattering from solid elastic cylinders and spheres is reformulated in terms of the Sfunction as developed in nuclear scattering theory . It is then subjected to the Watson transformation, which permits an evaluation of the scattering amplitude at its potes ("Regge potes") and saddle points in the complex modenumber plane. The saddle point contributions are obtained after expanding the amplitude in a Debye series, and correspond to a reflected wave and to transmitted dilatational and shear waves that undergo internai reflections and mode conversions . The theory of these waves was experimentally verified by Quentin et al . The pole residues furnish circumferential (surface, creeping) waves which are of both Franz type (propagating externally), and of elastic type (Rayleigh and Whispering Gallery waves, propagating internally) . The theory of these waves was experimentally verified by Ripoche et al....

(GRETSI, Saint Martin d' Hères, France, 1985)We consider the scattering of elastic dilatational and shear waves from cylindrical and spherical cavities and inclusions in an elastic medium. The normal mode series of the scattering amplitude is reformulated in terms of the Sfunction, and the poles of the Sfunction in the complex frequency plane are identified . The amplitude is rewritten as a "background term" including specular reflections and external surface waves, plus a series of (internai) resonance terms . This formulation is termed the "Resonance Scattering Theory" (RST) . The convection between the resonances and the surface waves is established via expressing the complexfrequency poles of the scattering amplitude by the Regge poles in the complexmode number plane, and the frequency resonances in successive modes are recognized as the Regge recurrences of surfacewave resonances . This permits us to obtain the dispersion curves of phase and group velocities of the (internat) surface waves from the eigenfrequencies of the cavity . We also mention experiments on ultrasonic scattering from cavities and inclusions....

(GRETSI, Saint Martin d'Hères, France, 1985)A microinhomogeneous medium, consisting of randomly distributed cavities or inclusions in a homogeneous elastic matrix, can be represented as a dispersive homogeneous medium with effective material constants (moduli, bulk wave speeds, and absorptions) . For wavelengths long compared to the size of the scatterers, Kuster and Toksôz have developed a method (not including rescattering) which obtains these effective material properties by comparing exact and effective monopole, dipole and quadrupole amplitudes . We extend this approach to the case where the wavelength is comparable to the size of the scatterers (assumed spherical) ; in this case, particle resonances are taken into account and lead to widened resonances in the effective material parameters . The cases of bubbly liquids, of perforated solids, and of solids with solid inclusions (particulate composites) are treated in this fashion . Measurements by Kinra and Anand verify our results. In addition, many previous results for the effective moduli of composites, obtained in the static (i . e., lowfrequency) limit, are recovered as particular cases of our approach....

(GRETSI, Saint Martin d'Hères, France, 1985)Baum's "Singularity Expansion Method" (SEM), formulated for radar scattering, is based on the observation that transient scattered echoes appear to be composed of a sum of decaying sinusoids . Fouriertransforming these expressions into frequency space reveals a manifold of simple poles in the complex frequency plane, identical with those of the Resonance Scattering Theory (RST), and commonly grouped in layers . We have carried out a time dependent analysis of scattering from rigid and elastic spheres and cylinders, with the following results . The use of short pulses (of spatial extent small compared to the scatterer's dimension) corresponds to the echo being a residue sum over a large number of SEM potes, and the residue sum over one given pole layer produces a sequence of echo pulses corresponding to a creeping wave repeatedly circumnavigating the sphere with the appropriate group velocity . The use of finitelength sinusoidal wave trains (long compared to the scatterer's extension) produces a reflected wave train, coherently superimposed by a sequence of overlapping creeping wave trains, which cause initial transients as well as a final transient tait following the echo . These transients only appear if the carrier frequency coincides with an eigenfrequency of the target, and the tait amplitude plotted as a function of frequency then reproduces the spectrum of resonances including their widths, leading to a direct target spectroscopy as accomplished experimentally by Ripoche et al. This tait corresponds to the ringing of a given eigenvibration, which is selectively excited when overlapped by the narrow spectrum of the long incident pulse ....

(GRETSI, Saint Martin d'Hères, France, 1985)of an elastic plate imbedded in a fluid medium, including effects of plate viscosity. The purpose of this formulation is to provide a direct means for determining the material parameters of the plate from the measured acoustic resonances of the Rayleigh and Lamb waves in the plate (i . e., their positions in frequency or angle, their widths and their heigths) which are given in our formalism by explicit analytic expressions that depend on the material parameters. Viscosity is seen to manifest itself in a decrease of the resonance heights (especially for the narrow sheartype resonances) and in a broadening and frequency dependence of their widths, which may be used to determine the frequencydependent loss factor of the plate . This approach then solves the inverse scattering problem for the case of a plate . We also consider the special case of a fluid layer imbedded in another fluid . In addition, a layered ocean floor is modeled by a sediment layer on top of a denser substratum, and overlaid by the water column . It is shown for this case again that resonances in the acoustic reflection coefficient are very prominent and can be used to determine the properties of both sediment layer and substratum ....
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