Determination of a wave field in a layered medium from boundary data

We deal with the problem of determining a solution to a perturbed wave equation in the half-plane from the Cauchy data on the space-time boundary. The equation in consideration describes, in particular, a non-stationary wave process in a laterally or vertically inhomogeneous medium. Problems of this type relate to the problem of continuation of a wave field from the boundary, arising in geophysics (ground-penetrating radar).