Fault zones are often surrounded by a damage zone that exhibits lower seismic velocities than the wall-rock, influencing earthquake propagation and arrest. We present a one-dimensional minimal model of frictional rupture, that approximates the elastodynamics of a fault embedded within a low velocity damage zone. This model predicts two families of steady-state rupture solutions: an overdamped regime, describing a crack-like rupture, and an underdamped regime with oscillating slip-rate in the wake of the rupture, which promotes pulse-like dynamics. The minimal model contains two free parameters: pre-stress on the fault, and seismic velocity reduction in the damage zone. The 1D model results are validated by two-dimensional elastodynamics simulations of earthquake rupture. We discuss the applicability of our model results to natural observations, identifying the preferred rupture style as function of structure of the fault zone, and the geological consequences of oscillatory slip in the wake of pulse-like ruptures.

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 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 $\bar \tau_k$ (initial pre-stress on the fault) and $\bar d_c$ (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.