The article describes the method of calculating the wave field of reflected waves of a certain type of re-reflection from localized target objects. A special feature of the method is the combination of the wave field continuation operator calculated by means of layer-by-layer recalculation based on the Kirchhoff integral and the finite-difference operator of reflected waves. Parameterization of the wave field continuation operator type is determined on the basis of the frame effective depth-velocity model. The research is carried out by Seismotech, Ltd under the grant support of "Skolkovo" Foundation.

Seismic deghosting algorithms involve wavefield extrapolation. The operator of such a transformation is integral, and when applied to discrete seismic data, its approximation is used, which corresponds to a method of numerical integration. The paper examines the limits of applicability of the approximation by the method of cells and the method of rectangles. It is shown that when processing 3D seismograms recorded using traditional survey geometries, correct ghost prediction is possible only after interpolation. When processing 2D seismic gathers, it is possible to predict and remove ghost waves for deep and shallow streamers. The streamer shape can be arbitrary. The results of the study and the conclusions made are valid not only for ghost prediction operators, but also for all seismic exploration tasks that involve wavefield extrapolation.

The physical modelling of elastic waves reflected from the boundary between the water and the model of low-velocity azimuthally anisotropic medium was carried out. The model of anisotropic medium was made using 3D printer. The results of experiments showed that the reflection coefficients are practically independent from the azimuth at the angles of incidence less than 25°. At larger angles of incidence, the azimuthal dependence of the reflection coefficients is observed, which is most pronounced at azimuths from 45° to 75°. The results of measurements in the layering direction are in good agreement with the theoretical reflection coefficients for the boundary of isotropic media.

We solve the problem of constructing the mathematical model of a vibroseis signal distorted by harmonics. Basis function decomposition is used for the approximation. The basis decomposition coefficients are frequency-dependent, i. e. filters are applied instead of multipliers. The resulting model will be the starting point for further research aimed at developing processing algorithms for the suppression of harmonic distortion, or for utilizing the harmonics to extend the frequency range of the signal.