Rubin and Ampuero: Slip Pulses during Earthquake Nucleation

For a wide range of conditions, earthquake nucleation zones 6 on rate-and state-dependent faults that obey either of the popular state evo-7 lution laws expand as they accelerate. Under the " slip " evolution law, which 8 experiments show to be the more relevant law for nucleation, this expansion 9 takes the form of a unidirectional slip pulse. In numerical simulations these 10 pulses often tend to approach, with varying degrees of robustness, one of a 11 few styles of self-similar behavior. Here we obtain an approximate self-similar 12 solution that accurately describes slip pulses growing into regions initially 13 sliding at steady state. In this solution the length scale over which slip speeds 14 are significant continually decreases, being inversely proportional to the log-15 arithm of the maximum slip speed V max , while the total slip remains con-16 stant. This slip is close to D c (1−a/b) −1 , where D c is the characteristic slip 17 scale for state evolution and a and b are the parameters that determine the 18 sensitivity of the frictional strength to changes in slip rate and state. The 19 pulse has a " distance to instability " as well as a " time to instability " , with 20 the remaining propagation distance being proportional to (1−a/b) −2 [ln(V max θ bg /D c)] −1 , 21 where θ bg is the background state into which the pulse propagates. This so-22 lution provides a reasonable estimate of the total slip for pulses growing into 23 regions that depart modestly from steady state.