Identification du signal source dans un problème de transmission
Résumé
We are interested in a particular inverse problem of transient waves propagation. From the measure of transmitted pressure in the lowest velocity media, we want to identify the source signal emitted in the first medium. We show how we can reconstruct the time dependence of the transient source signal by analogy of the simple reconstruction formula of the inverse wavelet transform, due to the presence of "surface" or "lateral" contribution. We show that this reconstruction involves an integration over depths (dilation paramaters) of the transmitted pressure (wavelet coefficient) along a vertical line (antenna) with a specific analyzing wavelet. Numerical results are presented and compared to experimental results in the case of transient source signal in the air, and hydrophones (vertical antenna) in water.