Critical evaluation of state evolution laws in rate and state friction: Fitting large velocity steps in simulated fault gouge with time-, slip-, and stress-dependent constitutive laws

The variations in the response of different state evolution laws to large velocity increases can dramatically alter the style of earthquake nucleation in numerical simulations. But most velocity step friction experiments do not drive the sliding surface far enough above steady state to probe this relevant portion of the parameter space. We try to address this by fitting 1-3 orders of magnitude velocity step data on simulated gouge using the most widely used state evolution laws. We consider the Dieterich (Aging) and Ruina (Slip) formulations along with a stress-dependent state evolution law recently proposed by Nagata et al. (2012). Our inversions confirm the results from smaller velocity step tests that the Aging law cannot explain the observed response and that the Slip law produces much better fits to the data. The stress-dependent Nagata law can produce fits identical to, and sometimes slightly better than, those produced by the Slip law using a sufficiently large value of an additional free parameter c that controls the stress dependence of state evolution. A Monte Carlo search of the parameter space confirms analytical results that velocity step data that are well represented by the Slip law can only impose a lower bound on acceptable values of c and that this lower bound increases with the size of the velocity step being fit. We find that our 1-3 orders of magnitude velocity steps on synthetic gouge impose this lower bound on c to be 10-100, significantly larger than the value of 2 obtained by Nagata et al. (2012) based on experiments on initially bare rock surfaces with generally smaller departures from steady state.