The difficulties of solving this inverse problems are well known: ambiguity and instability of the solution, uncertainty in choosing of regularization parameter, etc. Actually, the situation is complicated even more by the fact that the sound field observed at the receiving array contains, not only the signal but also the noise. This noise is the sum of both internal noises and the ambient noise. In some other cases the relation between the source and the field may not be deterministic.

In this work we have abandoned the deterministic approach and selected the statistical approach. In this method, the likelihood ratio of the probability measures of the field under the condition of presence and absence of the signal is obtained. Obviously, this ratio will depend on the velocity, attenuation, and the density of the medium. The maximum likelihood estimates can be assumed as estimates of these fields. A set of maximization criteria thus provide a set of equations from which the wave velocity, attenuation, and medium density can be estimated.

We will present tin this work the details of the method and the application to certain problems of nondestructive estimation of acoustical properties.