Reconstruction of the reflection coefficient and interface in homogeneous medium by means of Gaussian jets

This paper is devoted to the inverse problem of reconstruction of a shape of interface separating two homogeneous media in acoustic approximation from from the knowledge of the scattered field data. It is assumed that the infinitely smooth surface representing the interface is illuminated by an incident Gaussian jet described as a high-frequency non-stationary localized asymptotic solution (wave package). The parameters of the medium above the interface are known. Measuring the intensity of the reflected Gaussian jet along a horizontal line placed at some height above the interface gives the inverse data to solve the problem of reconstruction of a shape of interface as well as determination of velocity of wave propagation and density below the interface. In the paper we describe a corresponding algorithm of solving the inverse problem and demonstrate a few examples of its numerical testing.