 
Summary: Earthquake nucleation on (aging) rate and state
faults
A. M. Rubin and J.P. Ampuero1
Department of Geosciences, Princeton University, Princeton, New Jersey, USA
Received 11 February 2005; revised 3 August 2005; accepted 31 August 2005; published 29 November 2005.
[1] We obtain quasistatic, twodimensional solutions for earthquake nucleation on faults
obeying Dieterich's ``aging'' version of the rate and state friction equations. Two distinct
nucleation regimes are found, separated by roughly a/b $ 0.5, where a and b are the
constitutive parameters relating changes in slip rate V and state q to frictional strength.
When fault healing is unimportant (Vq/Dc ) 1, where Dc is the characteristic slip distance
for the evolution of q), the nucleation zone spontaneously evolves toward a state of
accelerating slip on a patch of fixed half length Ln % 1.3774(m0
Dc/bs), where m0
is the
intrinsic stiffness of the medium and s is the normal stress. This is the fixed length
solution for which the stress intensity factor K = 0. Although this solution does not depend
upon a/b explicitly, only for a/b < 0.3781 does healing remain unimportant as instability is
approached. For a/b ^ 0.5 and a wide range of slow loading conditions, Vq/Dc
ultimately approaches a quasiconstant value near 1, and the nucleation zone takes on the
appearance of an expanding slipweakening crack. A fracture energy balance indicates that
