Inverse problem of predicting an inhomogeneous medium via vertical seismic profiling data (Q1975800)

The paper is devoted to consideration of mathematical models for the vertical seismic profiling of horizontally homogeneous media. The questions of the uniqueness of the determination of the acoustic impedance of a medium are studied on the basis of the measurement of oscillations at a certain point when the source is situated both on the daytime surface and at a deeper level. It is shown that, in some classes of such sources, the reconstruction of a medium is unique. A method for solving the problem under consideration is proposed. This method is based on the solution of an integral equation of special form. The results of the numerical modeling are discussed.