We discuss a finite-difference modeling technique for the simplified case of scalar, two-dimensional wave propagation in a medium containing a large number of small-scale cracks. The cracks are characterized by an explicit (Neumann) boundary condition whereas the embedding medium can be heterogeneous. The boundaries of the cracks are not represented in the finite-difference mesh, but the cracks are incorporated as distributed point sources. This enables the use of grid cells that are considerably larger than the crack sizes. We compare our method to an accurate integral-equation solution for the case of a homogeneous embedding and conclude that the finite-difference technique is accurate and computationally fast.

You do not currently have access to this article.