How do earthquakes stop? Insights from a minimal model of frictional rupture

Abstract

The question "what arrests an earthquake rupture?" sits at the heart of any potential prediction of earthquake magnitude. Here, we present a one-dimensional, thin-elastic-strip, minimal model, to illuminate the basic physical parameters that control the arrest of large ruptures. The generic formulation of the model allows for wrapping various earthquake arrest scenarios into the variations of two dimensionless variables, valid for both in-plane and antiplane shear loading. Our continuum model is equivalent to the standard Burridge-Knopoff model, with an added characteristic length scale, that corresponds to either the thickness of the damage zone for strike-slip faults or to the thickness of the downward moving plate for subduction settings. We simulate the propagation and arrest of frictional ruptures and present closed-form expressions to predict rupture arrest under different conditions. Our generic model illuminates the different energy budget that mediates crack- and pulse-like rupture propagation and arrest. Despite its simplicity, this minimal model is able to reproduce several salient features of natural earthquakes that are still debated (e.g. various arrest scenarios, stable pulse-like rupture, back-propagating front, asymmetric slip profiles).