Abstract : The purpose of this thesis is principally the problem of the transmission of spherical waves through a plane interface separating two fluid media. The source is located in the medium of the lowest celerity. Under some conditions, this simple and physical model presents a particular interest due to the existence of a "surface wave", the so-called lateral or inhomogeneous wave.
First, we have verified, in the case of a point monochromatic source, with the help of asymptotic methods, the existence of this contribution. For an air-water plane interface, we have experimentally separated the lateral contribution from the geometric contribution, and point out their behavior and properties. Particular interferences zones appear in the total refracted field in a good accordance with the theoretical and numerical study. The lateral contribution presenting a "dispersive" behavior, shows the necessity to use a time-scale method in the case of transient sources.
The Green's function can be decomposed in a natural three contributions analoguous to the contributions of harmonic regime.
The wavelet transform allows us to calculate precisely these different contributions and to study their frequency behavior. The new obtnained results is to point out at particular scales, some transient and rapid phenomena (echoes), that allows a new discussion of this kind of problem. An experimentation coupled to a time-scale analysis (complex continuous wavelet transform) confirmed these observations.
By analogy of the simple reconstitution formula of the inverse wavelet transform, we have obtained, for great radial distance values, a formula for reconstruction of the time-dependent source-signal (inverse problem), from the measure of the transmitted pressure (playing the role of "pseudo-wavelet coefficients") over depths.
At last, we have applied this transformation to a problem of acoustic backscattering by spherical elastic shells (fluid/solid interface) and showed that it is possible to obtain some physical characteristics of the target.