Finite-difference modelling of two-dimensional elastic wave propagation in cracked media

Abstract

We present a finite-difference modelling technique for 2-D elastic wave propagation in a medium containing a large number of small cracks. The cracks are characterized by an explicit boundary condition. 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 one to use grid cells that are considerably larger than the crack sizes. We compare our method with an accurate integral representation of the solution and conclude that the finite-difference technique is accurate and computationally fast.