Grid-Characteristic Method on Overlapping Curvilinear Meshes for Modeling Elastic Waves Scattering on Geological Fractures

Interest in computational methods for calculating wave scattering from fractured geological clusters is due to their application in processing and interpreting the data obtained during seismic prospecting of hydrocarbon and other mineral deposits. In real calculations, numerical methods on structured, regular (Cartesian) computational grids are used to conserve computational resources though these methods do not correctly model the scattering of elastic waves from fractures that are not co-directed to the coordinate axes. The use of computational methods on other types of grids requires an increase in computational resources, which is unacceptable for the subsequent solution of inverse problems. This article is devoted to a possible solution to this problem. We suggest a novel modification of a computational grid-characteristic method on overlapping curvilinear grids. In the proposed approach, a small overlapping curvilinear grid is placed around a fracture that smoothly merges into the surrounding Cartesian background mesh, which helps to avoid interpolation between the background and overlapping meshes. This work presents the results of testing this method, which showed its high accuracy. The disadvantages of the developed method include the limited types of fractured clusters for which this method can be applied since the overlapping meshes should not intersect. However, clusters of subvertical fractures are usually found in nature; therefore, the developed method is applicable in most cases.