FRACTAL AND MULTIFRACTAL MEASURES OF NATURAL AND SYNTHETIC FRACTURE NETWORKS

We have analyzed the fractal and multifractal nature of a series of 17 natural fracture trace maps, representing a wide variety of scales, g eological settings, and lithologies, as well as a number of typical sy nthetic fracture networks in which fracture locations, orientations, a nd lengths are drawn from various probability distribution functions. Recent studies have shown that multifractal methods can be used to inv estigate fracture networks at greater depth, since the fractal dimensi on represents only part of the scaling spectrum characterizing each ne twork. We find that the real and synthetic fracture maps display fract al and multifractal properties. Moreover, the properties of the synthe tic networks are very similar to those of the real networks, with nont rivial fractal dimensions and multifractal spectra. We suggest that di fferent fracturing mechanisms can lead to two or more distinct subrang es over which a fractal dimension can be defined, while the heterogene ity 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 suc h as fracture length and orientation but can be controlled by appropri ate choice of the relative fracture density.