How Do Earthquakes Stop? Insights From a Minimal Model of Frictional Rupture

The question "what arrests an earthquake rupture?" sits at the heart of any potential prediction of earthquake magnitude. Here, we use a one-dimensional, thin-elastic-strip, minimal model, to illuminate the basic physical parameters that may 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 (tau) over bar (kappa) (initial dimensionless stress parameter on the fault) and (G) over bar (c) (dimensionless fracture energy), 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, H, 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 derive 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. It provides additional predictions such as generic stable pulse-like rupture solutions, stress drop independence of the rupture size, the existence of back-propagating fronts, and predicts that asymmetric slip profiles arise under certain pre-stress conditions. These diverse features occur also in natural earthquakes, and the fact that they can all be predicted by a single minimal framework is encouraging and pave the way for future developments of this model. Plain Language Summary Untangling the dynamics that governs the propagation and arrest of earthquakes is still challenging, mainly because of the few constraints available on the fault zone geometry, the constitutive properties of fault materials, as well as fault rheology during the rupture event. The present study aims at formulating a model containing a minimal number of parameters to describe the dynamics of large earthquakes. 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). We demonstrate how the proposed model can be used to simulate the propagation and arrest of large earthquakes, which are controlled by local variations of shear stress and material properties on the fault. With this simple and generic description, the proposed model could be readily extended to account for additional processes controlling the dynamics of large earthquakes.