Elastic wave modelling in 3-D fractured media: an explicit approach

Abstract

We present a numerical technique for modelling elastic-wave propagation in 3-D media with discrete distributions of 2-D fractures. The scheme treats the fractures as the non-welded interfaces that satisfy the linear-slip displacement-discontinuity conditions, instead of using the equivalent medium theories. We develop the scheme following a so-called 3-D grid method. The key to derive the scheme is to extend the integral forms of the elastic-momentum equations to include the linear-slip displacement-discontinuity (LS) model. The scheme is implemented under a discretization of tetrahedral grid cells. Arbitrary 2-D non-planar fractures can be explicitly, accurately represented on the numerical mesh. The scheme can flexibly accommodate arbitrary 2-D fractures with fracture behaviour from one extreme of being perfectly welded to an extreme characterized by the stress-free conditions. No stability problem arises. In comparison with the seismic response calculation in the background medium in the absence of the fractures, the additional computational cost and memory requirements for incorporating many fractures are small. We propose a parallel numerical implementation of the scheme that needs smaller data exchanges between the subdomains. We also present the comparisons with an equivalent-medium based modelling scheme in the numerical examples.