The study of dynamical processes in problems of mesofracture layers exploration seismology by methods of mathematical and physical simulation

The article is devoted to the study of the propagation of elastic waves in a fractured seismic medium by methods of mathematical modeling. The results obtained during it are compared with the results of physical modeling on similar models. For mathematical modeling, the grid-characteristic method with hybrid schemes of 1-3 orders with approximation on structural rectangular grids is used. The ability to specify inhomogeneities (fractures) of various complex shapes and spatial orientations has been implemented. The description of the developed mathematical models of fractures, which can be used for the numerical solution of exploration seismology problems, is given. The developed models are based on the concept of an infinitely thin fracture, the size of the opening of which does not affect the wave processes in the fracture area. In this model, fractures are represented by boundaries and contact boundaries with different conditions on their surfaces. This approach significantly reduces the need for computational resources by eliminating the need to define a mesh inside the fracture. On the other hand, it allows you to specify in detail the shape of fractures in the integration domain, therefore, using the considered approach, one can observe qualitatively new effects, such as the formation of diffracted waves and a multiphase wavefront due to multiple reflections between the surfaces, which are inaccessible for observation when using effective fracture models actively used in computational seismic. The obtained results of mathematical modeling were verified by physical modeling methods, and a good agreement was obtained.