Frictional response to velocity steps and 1-D fault nucleation under a state evolution law with stressing-rate dependence

A new state evolution law has recently been proposed by Nagata et al. (2012) that includes a dependence upon stressing rate through a laboratory derived proportionality constant c. It has been claimed that this law, while retaining the time-dependent healing of the Dieterich (or Aging) law, can also match the symmetric response of the Ruina (or Slip) law to velocity step tests. We show through analytical approximations and numerical results that the new law transitions between the responses of the traditional Aging and Slip laws in velocity step-up/step-down experiments when the value of c is tuned properly. Particularly, for c=0, the response is pure Aging, while for finite, nonzero c one observes Slip law type behavior for small velocity jumps but Aging law type response for larger jumps. The magnitude of the velocity jump required to see this transition between aging and slip behaviors increases as c increases. In the limit of c≫1 the response becomes purely Slip law type for all geologically plausible velocity jumps. We also present results from detailed analytical and numerical studies of the mechanism of rupture nucleation on 1-D faults under this new state evolution law to demonstrate that the style of nucleation can also be made to switch from Aging-type (expanding cracks) to Slip-type (slip pulses) by adjusting the value of c as indicated by the velocity step results.