Acoustic wave propagation in heterogeneous two-dimensional fractured porous media

This paper addresses an important fundamental question: the differences between wave propagation in fractured porous media with a uniform matrix (constant bulk modulus) and those in which the matrix is heterogeneous with its bulk modulus distributed spatially. The analysis of extensive experimental data [Phys. Rev. E 71, 046301 (2005)] indicated that such distributions are self-affine and induce correlations at all the relevant length scales. The comparison is important from a practical view point because in many of the traditional models of fractured rock, particularly those that are used to study wave propagation or fit some data, the matrix is assumed to be uniform. Using extensive numerical simulation of propagation of acoustic waves, we present strong evidence indicating that the waves' amplitude in a fractured porous medium with a heterogeneous matrix decays exponentially with the distance from the source. This is in sharp contrast with a fractured porous medium with a uniform matrix in which not only the waves' amplitude decays with the distance as a stretched exponential function, but the exponent that characterizes the function is also dependent upon the fracture density. The localization length depends on the correlations in the spatial distribution of the bulk modulus, as well as the fracture density. The mean speed of the waves varies linearly with the fractures' mean orientation.