Constant dimensionality of fault roughness from the scale of micro‐fractures to the scale of continents

Abstract

Abstract Many faults and fractures in various natural and man‐made materials share a remarkable common fractal property in their morphology. We report on the roughness of faults in rocks by analyzing the out‐of‐plane fluctuations of slip surfaces. They display a statistical power‐law relationship with a nearly constant fractal exponent from millimeter scale micro‐fractures in fault zones to coastlines measuring thousands of kilometers that have recorded continental breakup. A possible origin of this striking fractal relationship over 11 orders of magnitude of length scales is that all faulting processes in rocks share common characteristics that play a crucial role in the shaping of fault surfaces, such as the effects of elastic long‐range stress interactions and stress screening by mechanical heterogeneities during quasi‐static fracture growth.