This paper presents a novel approach to modeling the propagation of seismic waves in a medium containing subvertical fractured inhomogeneities, typical for mineralization zones. The developed method allows us to perform calculations on a structural computational grid, which avoids the construction of unstructured grids. For the calculations, the grid-characteristic method is used. We also present a comparison of the proposed method with the one described at earlier works and discuss the areas of its practical application. As an example, the numerical results for a cluster of subvertical fractures are given. A new approach for modeling fractures makes it quite easy to incorporate fractured objects into the seismic models and perform calculations without using algorithms on unstructured and curved grids.

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.

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