Fractal relations for the diameter and trace length of disc‐shaped fractures

Abstract

Analytic relations are developed between the fractal parameters of a random, isotropic population of disc‐shaped fractures and the parameters of the corresponding population of fracture traces expressed in outcrop. These relations indicate that a fractal distribution of fracture diameters translates to a fractal distribution of trace lengths and that the parameters for diameter may be uniquely determined from the parameters for trace length. Probabilistic results demonstrate the accuracy of the analytic relations and identify nonideal behaviors at the limits of the computed trace length data. It is expected that these relations will be useful in the three‐dimensional characterization of fracture systems in rock from in situ trace length data.