Non-universal scaling of fracture length and opening displacement

Abstract

THE deformation of the Earth's brittle crust is dominated by the formation and growth of faults in response to tectonic loading. The scaling properties of such systems provide clues to the underlying mechanisms of fault propagation. For example, if fault growth were a self-similar process, described by a scaling law that applies in all locations¹, this might imply a universal faulting mechanism governed by either constant fracture toughness or constant yield stress. Universal scaling laws have been proposed^1–4, but their general applicability remains the subject of some debate⁵. In the natural environment, strict scale invariance can apply only between well-defined bounds⁶, and it is known that the Earth's crust has many distinct length scales—ranging from the grain size of rocks and the thickness of sedimentary layers up to the finite width of the seismogenic crust—each of which may vary from place to place. Here we report the scaling properties of two populations of tensile fractures in the Krafla fissure swarm of northeast Iceland (spanning nearly four orders of magnitude in length and five in displacement), which clearly show that the presence of such length scales dramatically alters the scaling behaviour. Despite the geological homogeneity of the region studied, our data cannot be described by a single scaling law.