Scale transitions in fracture and active fault networks

Detailed box counting analysis was conducted of (1) fractures observed in e xposures of the Devonian Shale in the central Appalachians Valley. and Ridg e province of West Virginia, (2) several fracture patterns presented in the literature, and (3) active faults mapped throughout the main island (Honsh u) of Japan. Box curves reveal, with few exceptions, that most naturally oc curring fracture patterns are characterized by nonfractal behavior In many, cases, two linear regions separated by an abrupt transition are observed i n the logN/logr box curves. The small-scale (larger r) features generally h ave higher fractal dimension than do the larger scale features in the patte rn. Transitions from one region to another are usually abrupt. These transi tions 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 do minant spacing of individual sets or to the dominant fragment size in the n etwork. This study, provides detailed documentation of scale invariant feat ures in natural fracture and active fault patterns. Although the relationsh ip of the geometrical properties of a pattern to the location of transition s is understood in terms of the models, to understand the physical mechanis ms responsible for these transitions deserves further study.