Fractal and multifractal measures of natural and synthetic fracture networks

Abstract

We have analyzed the fractal and multifractal nature of a series of 17 natural fracture trace maps, representing a wide variety of scales, geological settings, and lithologies, as well as a number of typical synthetic fracture networks in which fracture locations, orientations, and lengths are drawn from various probability distribution functions. Recent studies have shown that multifractal methods can be used to investigate fracture networks at greater depth, since the fractal dimension represents only part of the scaling spectrum characterizing each network. We find that the real and synthetic fracture maps display fractal and multifractal properties. Moreover, the properties of the synthetic networks are very similar to those of the real networks, with nontrivial fractal dimensions and multifractal spectra. We suggest that different fracturing mechanisms can lead to two or more distinct subranges over which a fractal dimension can be defined, while the heterogeneity of the rock, and the nature of the fracturing mechanisms, lead to multifractal properties. We also find that the fractal dimension of a synthetic fracture network is relatively insensitive to parameters such as fracture length and orientation but can be controlled by appropriate choice of the relative fracture density.