Stability of Pulse‐Like Earthquake Ruptures

Abstract

Pulse‐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.

Unstable cracks trigger asymptotic rupture modes in bimaterial friction

“…Numerical calculations have predicted that this coupling gives rise [28,29] to both directional effects as well as to interesting modes of rupture called 'slip pulses' in which slip is highly localized at the rupture tip. We note that slip pulses are not solely generated by bimaterial coupling, they have also been numerically observed under strong velocity weakening of friction [30] that can be induced, for example, by poroeleastic [31] or thermal pressurization [32] effects.…”

A minimal model for the onset of slip pulses in frictional rupture

“…Recent studies have demonstrated the inherent instability of slip-pulses for different kinds of friction constitutive laws [22,24,26,34]. These models reported the existence of a steady-state pulse solutions located at the sharp transition between growing pulses, whose spatial extent increases during propagation, and decaying pulses, whose spatial extent progressively shrinks and eventually arrests the pulse.…”

“…The ubiquity of pulse-like rupture observed in frictional systems has motivated the development of theoretical and numerical models to investigate the conditions supporting the emergence of slip pulses. Slip-pulses have been found in systems with a large variety of boundary conditions and domain approximations [19][20][21][22][23][24][25][26] and friction laws including from rate-and-state friction [22,23,26], velocity-weakening friction [19,20], slip-dependent friction [27] and Coulomb friction [25].…”

“…Large aspect ratios may favour the formation of slip pulses [31], and the seismogenic depth can limit the width of earthquake slip pulses [32,33]. Recent studies have also demonstrated the inherent instability of slip-pulses for different friction constitutive laws [22,24,26,34].…”

Velocity-driven frictional sliding: Coarsening and steady-state pulse trains

“…Such instabilities typically result in rapid slip propagation along frictional interfaces, mediated by rupture modes [34][35][36][37][38][39][40][41][42][43][44][45][46]. Spatiotemporal rupture propagation modes can be generally classified into expanding cracklike rupture fronts and compact self-healing slip pulses [35][36][37][38][39][47][48][49][50][51]. In the former, v at an interfacial position behind the propagating mode remains finite as long as propagation persists, while in the latter, v vanishes over a finite time as propagation persists.…”