Scale Transitions in Fracture and Active Fault Networks

Detailed box counting analysis was conducted of (1) fractures observed in exposures of the Devonian Shale in the central Appalachians Valley and Ridge Province of West Virginia, (2) several fracture patterns presented in the literature, and (3) active faults mapped throughout the main island (Honshu) of Japan. Box curves reveal, with few exceptions, that most naturally occurring fracture patterns are characterized by nonfractal behavior. In many cases, two linear regions separated by an abrupt transition are observed in the logN/logr box curves. The small-scale (larger r) features generally have higher fractal dimension than do the larger scale features in the pattern. Transitions from one region to another are usually abrupt. These transitions are not associated with sampling problems or other data limitations. In some cases three or more linear regions may appear. Box counting analysis of model fracture patterns indicate that transitions are related to the dominant spacing of individual sets or to the dominant fragment size in the network. This study provides detailed documentation of scale invariant features in natural fracture and active fault patterns. Although the relationship of the geometrical properties of a pattern to the location of transitions is understood in terms of the models, to understand the physical mechanisms responsible for these transitions deserves further study.