Modelling the wave phenomena in acoustic and elastic media with sharp variations of physical properties using the grid‐characteristic method

Abstract

This paper introduces a novel method of modelling acoustic and elastic wave propagation in inhomogeneous media with sharp variations of physical properties based on the recently developed grid‐characteristic method which considers different types of waves generated in inhomogeneous linear‐elastic media (e.g., longitudinal, transverse, Stoneley, Rayleigh, scattered PP‐, SS‐waves, and converted PS‐ and SP‐waves). In the framework of this method, the problem of solving acoustic or elastic wave equations is reduced to the interpolation of the solutions, determined at earlier time, thus avoiding a direct solution of the large systems of linear equations required by the FD or FE methods. We apply the grid‐characteristic method to compare wave phenomena computed using the acoustic and elastic wave equations in geological medium containing a hydrocarbon reservoir or a fracture zone. The results of this study demonstrate that the developed algorithm can be used as an effective technique for modelling wave phenomena in the models containing hydrocarbon reservoir and/or the fracture zones, which are important targets of seismic exploration.

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

“…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]. It is based on representing the equations of motion of the linear elastic medium in the following form:…”

“…A fracture can be modeled as a linear slip and contact conditions imposed independently for every fracture which allows us to avoid constructing the computational grid within the fracture itself. The double-coastal model described in [22] is used as a model of a fracture. It is a special case of the Schoenberg model [1] for a model of a fracture with zero openness.…”

“…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.…”

Calculation of Seismic Resistance of Various Structures Using the Grid-Characteristic Method

“…To obtain numerically solution the systems of equations (1), (2) and (3), (4), the gridcharacteristic method was used, which was described in detail in works [17,18]. The Rusanov scheme was used [19].…”

Editorial for Special Issue “Geophysics for Mineral Exploration”

“…Khokhlov and Stognii [8] introduced a novel approach to modeling the propagation of seismic waves in a medium containing subvertical fractured inhomogeneities, typical for mineralization zones. It was based on the use of the grid-characteristic method [10], which could model the seismic responses from subvertical fractured inhomogeneities on a structural rectangular grid. This approach significantly simplified the construction of the numerical model and the use of the algorithms.…”