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


Corresponding author: F. Renard, ISTerre, University of Grenoble I and CNRS, BP 53, 38041 Grenoble, France. (


[1] 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.