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A class of problems arising in seismic exploration are investigated, namely, seismic signal propagation in multilayered geological rock and near surface disturbance propagation in massive rock with heterogeneities, such as empty or filled fractures and cavities. Numerical solutions are obtained for wave propagation in such highly heterogeneous media, including those taking into account the plastic properties of the rock, which can be manifested near a seismic gap or a wellbore. All types of explosion generated elastic and elastoplastic waves and waves reflected from fractures and the bound aries of the integration domain are analyzed. The identification of waves in seismograms recorded with near surface receivers is addressed. The grid characteristic method is used on triangular, parallelepi pedal, and tetrahedral meshes with boundary conditions set on the rock-fracture interface and on free surfaces in explicit form. The numerical method proposed is suitable for the study of the interaction between seismic waves and heterogeneous inclusions, since it ensures the most correct design of com putational algorithms on the boundaries of the integration domain and at media interfaces. A parallel software code implemented with the help of OpenMP and MPI was used to execute computations on parallelepipedal and tetrahedral grids.

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