Numerical Modeling of Seismic Responses from Fractured Reservoirs by the Grid-characteristic Method

Novel Approach to Modeling the Seismic Waves in the Areas with Complex Fractured Geological Structures

“…We consider a model of ideal isotropic linear elastic material. The grid-characteristic method (GCM) uses the characteristic properties of the systems of hyperbolic equations, describing the elastic wave propagation [16]. The mathematical principles of the GCM approach are described in detail in [22].…”

“…where indexes i and j vary from 0 to 1 in order to simplify the final formulas, and n 0 = n. It is shown in [16] that, the solution of Equation 1, vector q, along the x and y directions can be written as follows:…”

“…In order to obtain a unique solution of the system of hyperbolic Equation (1), one should use the corresponding boundary conditions on the surface of the modeling domain, which, in general terms, can be written as follows [16]:…”

“…This drawback can be overcome by using non-structural grids for modeling the fractured media. Examples of such approaches can be found in [5][6][7] where the finite-volume methods [14,15] and a grid-characteristic method [16] are used. Unstructured meshes are suitable for calculating the wave propagation in a physical region of complex shape, but they require large additional memory for storing information about the relationships of the mesh's cells.…”

“…The method is also built on unstructured meshes. In [19], three methods were compared: The discontinuous Galerkin method [20,21], the grid-characteristic method on unstructured meshes [16], and the grid-characteristic method on structural grids [22][23][24]. In the work [19], it is shown that the method based on the structural grids has better performance in comparison to the unstructured meshes, in addition to a simpler implementation and operation with the grids.…”