A Short Note on Modeling Wave Propagation in Media with Multiple Sets of Fractures

Abstract

Wave propagation and scattering in fractured formations have been modeled with finite-difference programs and the use of equivalent anisotropic media description of discrete fractures. This type of fracture description allows a decomposition of the compliance matrix into two parts: one accounts for the background medium and another accounts for the fractures. The compliance for the fractures themselves can be a sum of compliances of various fracture sets with arbitrary orientations. Non-orthorgonality of the fractures, however, complicates the compliance matrix. At the moment, we can model an orthorhombic medium (9 independent elastic constants) with the two orthogonal fracture sets. However, if the fractures are non-orthogonal, this results in more general anisotropy (monoclinic) for which we need to specify 11 independent parameters.. Theoretical formulation shows that the finite difference program can be extended to simulate wave propagation in monoclinic media with little additional computational and storage cost.