Seismic exploration of fractured zones remains a relevant area of applied scientific interests, which poses a challenge for scientists to develop new parallel algorithms for solving these problems. This manuscript discusses various methods for taking into account fracturing and curved boundaries in heterogeneous geological environments in 2D and 3D formulations of direct seismic exploration problems. The first method is the construction of curvilinear structured grids that directly coincide with the interfaces in the problem, i.e. with geological rock boundaries and cracks. In the second and third approaches, to take into account these interfaces of geological rocks, Chimera (overlapping) grids are used, the nodes of which are located geometrically in the same place as the nodes of the Cartesian background grid, and between which grids nodes the interpolation is carried out. The difference between the second and third approaches is in the methods of taking into account fracturing. In the second approach, a rotated Cartesian overlapping mesh is built around each crack. In the third approach, a curvilinear structured mesh is built around each crack, the nodes of which, on one hand, exactly lie on the crack, and on the other hand, along its edges, exactly hit the nodes of the background Cartesian grid. The influence of the presence of cracks and dimensionality is investigated. Various methods of static decomposition and partitioning of meshes between separate processes are considered. The speed up graphs are compared. Calculations were performed on CPU using Open MPI software package library and the grid-characteristic computational method.