Application of Fractures Mathematical Models in Exploration Seismology Problems Modeling

Abstract

This chapter is about description of developed mathematical models of fractures, which can be used for numerical solution of exploration seismology problems with use of grid-characteristic method on unstructured triangular (in 2D-case) and tetrahedral (in 3D-case) meshes. The base of developed models is the concept of infinitely thin fracture, which aperture does not influence on wave processes in fracture area. These fractures are represented by boundaries and contact boundaries with different conditions on contact and boundary surfaces. Such approach significantly reduces the consumption of computer resources by the absence of the mesh definition inside of fracture necessity. On the other side, it lets state the fractures discretely in integration domain, therefore one can observe qualitative new effects, such as diffractive waves forming and multi-phase wave front due to multiple reflections between surfaces of neighbor fractures, which are not available to observe by use of effective models of fractures actively used in computational seismic.