HR: 14:10h
AN: S13E-03    [Abstracts]
TI: Self-Similar Earthquake Nucleation on Rate-and-State Faults
AU: * Rubin, A M
EM: arubin@princeton.edu
AF: Department of Geosciences, Princeton University, Princeton, NJ 08540 United States
AU: Ampuero, J
EM: jampuero@princeton.edu
AF: Department of Geosciences, Princeton University, Princeton, NJ 08540 United States
AB: We obtain self-similar solutions (two-dimensional and quasi-static) for the acceleration to instability of a fixed-length patch on a fault obeying rate-and-state friction. The solution is applicable in the limit $V\theta/D_c$$\gg$$1$, so that the evolution of the state variable is well-approximated by $\dot{\theta}$=$V\theta/D_c$. For simulations on an infinite fault with $a/b$$<$$\sim$0.5, the nucleation zone spontaneously evolves to the size and velocity distribution of the self-similar solution for which the stress intensity factor $K$=0, for which the nucleation length $L_\nu$=$1.3774G^*D_c/b\sigma$, independent of $a$, where $G^*$ is the elastic stiffness. For $a/b$$<$$0.3781$, $V\theta$ increases with time and the large $V\theta/D_c$ solution remains applicable until elastodynamics comes into play. For larger $a/b$, $V\theta$ at the crack center diminishes to a quasi-constant value modestly larger than 1, and the nucleation zone ultimately appears similar to an expanding slip-weakening crack with constant slip-weakening rate but time-varying peak and residual stresses. The nucleation length in these cases (defined as the minimum of the time-dependent size of the nucleation zone) generally increases with $a/b$ but is very sensitive to the boundary and initial conditions. For sufficiently large values of $V\theta/D_c$ upon localization, the nucleation zone can undergo velocity increases of many orders of magnitude before the self-similar solution becomes inapplicable; this is why this solution dominates the simulations of Dieterich [1992] even for $a/b$\sim$0.9. For $a/b$$<$0.3781, smaller nucleation zones are capable of reaching instability; these correspond to self-similar solutions with $[\dot{V\theta}]$\ge$0 and $K$$>$0, so they could be applicable to faults shorter than $L_\nu$. The smallest viable nucleation zone $L_{min}$ increases in size with increasing $a/b$ and equals $L_\nu$ at $a/b$=0.3781. For $a$=0, which in the limit $V\theta/D_c$\gg$1 corresponds to slip-weakening behavior, $L_{min}$ equals the universal nucleation length of $0.579G^*D_c/b\sigma$ found for slip-weakening behavior by Uenishi and Rice [2003] (the slip-weakening rate is $b\sigma/D_c$). The family of self-similar solutions can thus be viewed as linking the observation of Dieterich [1992] that $L_\nu$ scales as $b^{-1}$ (the $K$=0 solution), with the expectation from stability analyses that $L_{min}$ scales as $(b-a)^{-1}$ (the $K$$>$0 solutions for which $[\dot{V\theta}]$=0).
DE: 7209 Earthquake dynamics and mechanics
SC: Seismology [S]
MN: 2004 AGU Fall Meeting