Stability of Pulse‐Like Earthquake Ruptures

Abstract

AbstractPulse‐like ruptures arise spontaneously in many elastodynamic rupture simulations and seem to be the dominant rupture mode along crustal faults. Pulse‐like ruptures propagating under steady state conditions can be efficiently analyzed theoretically, but it remains unclear how they can arise and how they evolve if perturbed. Using thermal pressurization as a representative constitutive law, we conduct elastodynamic simulations of pulse‐like ruptures and determine the spatiotemporal evolution of slip, slip rate, and pulse width perturbations induced by infinitesimal perturbations in background stress. These simulations indicate that steady state pulses driven by thermal pressurization are unstable. If the initial stress perturbation is negative, ruptures stop; conversely, if the perturbation is positive, ruptures grow and transition to either self‐similar pulses (at low background stress) or expanding cracks (at elevated background stress). Based on a dynamic dislocation model, we develop an elastodynamic equation of motion for slip pulses and demonstrate that steady state slip pulses are unstable if their accrued slip b is a decreasing function of the uniform background stress τb. This condition is satisfied by slip pulses driven by thermal pressurization. The equation of motion also predicts quantitatively the growth rate of perturbations and provides a generic tool to analyze the propagation of slip pulses. The unstable character of steady state slip pulses implies that this rupture mode is a key one determining the minimum stress conditions for sustainable ruptures along faults, that is, their “strength.” Furthermore, slip pulse instabilities can produce a remarkable complexity of rupture dynamics, even under uniform background stress conditions and material properties.