Wave propagation in disordered fractured porous media

Extensive computer simulations have been carried out to study propagation of acoustic waves in a two-dimensional disordered fractured porous medium, as a prelude to studying elastic wave propagation in such media. The fracture network is represented by randomly distributed channels of finite width and length, the contrast in the properties of the porous matrix and the fractures is taken into account, and the propagation of the waves is studied over broad ranges of the fracture number density rho and width b. The most significant result of the study is that, at short distances from the wave source, the waves' amplitude, as well as their energy, decays exponentially with the distance from the source, which is similar to the classical problem of electron localization in disordered solids, whereas the amplitude decays as a stretched exponential function of the distance x that corresponds to sublocalization, exp(-x(alpha)) with alpha < 1. Moreover, the exponent alpha depends on both rho and b. This is analogous to electron localization in percolation systems at the percolation threshold. Similar results are obtained for the decay of the waves' amplitude with the porosity of the fracture network. Moreover, the amplitude decays faster with distance from the source x in a fractured porous medium than in one without fractures. The mean speed of wave propagation decreases linearly with the fractures' number density.