Application of Spectral Methods to Inverse Dynamic Problem of Seismicity of a Stratified Medium

Under study is the wave propagation process in the half-space y₃ = 0 with the Cartesian coordinates y₁, y₂, and y₃ which is filled with an elastic medium. The parameters of the medium are discontinuous and depend only on the coordinate y₃. The wave process is induced by an external perturbation source that generates a plane wave moving from the domain y₃ > h > 0. It is proved that the direct dynamic problem is uniquely solvable in the corresponding function space, and a special presentation is found for the solution. The problem of determination of the acoustic impedance of the medium from the wave field measurements on the surface is investigated by the spectral methods of the theory of differential equations.