Earthquake nucleation on model faults with rate- and state-dependent friction: Effects of inertia

Laboratory studies suggest that earthquake nucleation involves a transition from quasi-static slip when inertial effects are negligible to inertia-driven, dynamic motion. This transition occurs via quasi-dynamic motion, during which the effects of inertia become increasingly important. The characteristics of this transition, which depend on frictional properties of the fault, determine the observability of earthquake nucleation by seismic, geodetic, or other means. By investigating the role of inertia during nucleation, we obtain a quantitative definition of the limiting velocity Vin, which marks the end of quasi-dynamic motion and the onset of instability. For reasonable friction parameters and fault widths, we obtain estimates of Vin for crustal faults. To study the roles of inertia, stiffness, and friction parameters on preseismic motion, we simulate triggered instabilities in a one-dimensional model of a homogeneous fault, with rate and state variable friction. In most of our simulations, triggering is achieved by applying a stress perturbation to an initially creeping fault under steady state friction. We also investigate triggering on faults which are initially locked and overstressed compared to their nominal frictional strength, due to time-dependent healing. We study the amount, Up, and duration, Tp, of preseismic slip as a function of system mass m and other model parameters. For crustal faults, we interpret the relevant mass as a product of density and fault width and find that wider fault zones result in smaller Up and larger Tp. Both Up and Tp are proportional to the system stiffness K, the characteristic slip distance Dc, and the friction constitutive parameter a and inversely proportional to the size of the triggering event. We find greater Up and Tp for constitutive laws which allow strengthening at zero velocity, compared to laws that require slip or a combination of slip and aging for state evolution. In contrast to quasi-static modeling, our simulations suggest a minimum stress perturbation criterion for instability, which may be interpreted in terms of a strain threshold for triggered seismicity.