On solution of an inverse non-stationary scattering problem in a two-dimentional homogeneous layered medium by means of $\tau-p$ Radon transform

We consider a two-dimensional non-stationary inverse scattering problem in a layered homogeneous acoustic medium. Data is the scattered wavefield from a surface point source, registered on the boundary of the half-plane. We prove the uniqueness of recovering of an acoustic impedance and a velocity in a medium from the scattering data. An algorithm for solving of the inverse two-dimensional scattering problem as a one-dimensional problem with parameter, based on $\tau-p$ Radon transform is constructed. Also, some results of numerical modeling of the direct scattering problem and solving a pair of inverse scattering problems in a layered homogeneous acoustic medium are presented. The proposed algorithm is applicable to data processing in geophysical prospecting as in surface seismics and vertical seismic profiling.