A study of acoustic transmission of transient signal in an inhomogeous medium with the help of a wavelet transform. Application to an air-water plane interface.
Résumé
The analysis of acoustic propagation in an inhomopgeneous fluid medium, generated by an impulsive point source (fluid-fluid or fluid-solid interface) has been discussed innumerable times[1-6]. Most of these works use the Cagniard-de Hoop method which consists essentially in an application of a Fourier transform in the space variables along the plane interface and a Laplace transform in the time variable. The resolution of the propagation equation is very easy in the transform domain, but requires elaborate tools for the return to the original space-time domain. An exact analytic solution, hard to interpret physically, can be found only in certain cases. More recently, it has been shown that one can use also a Fourier transform in the time variable (so-called impulse method [7]. The soltion is easier to interpret physically, however the problem then becomes to find an explicit causal solution. Our aim here is the analysis and solution of an acoustic propagation problem in which we preserve at evry scale the time and frequency characteristics of different waves of the transmiited acoustic field (Saracco et al 1989). A recent time-and-scale method adapted to the study of rapid transitions is the wavelet transform. This method can furthermore decompose an arbitrary signal into a sum of elementary contributions, each well localized both in time and in the frequency domain.