The abundance of geodetic and seismic data recording postseismic deformation following the 2004 Parkfield earthquake provides an unprecedented opportunity to resolve frictional properties on the Parkfield section of the San Andreas fault. The Parkfield segment transitions between the locked section to the southeast that last ruptured in the 1857 Fort Tejon earthquake and the creeping section to the northwest. We develop 3D rate- and state-dependent friction models of afterslip following the 2004 earthquake to investigate the frictional behavior of the fault. It is assumed that the coseismic rupture occurred on an area of the fault surrounded by aseismic creep that accelerated after the earthquake. We estimate the distribution of coseismic slip, afterslip, and rate-state frictional parameters by inverting a two-step slip model. In the model we: 1) estimate the coseismic slip distribution from 1 Hz GPS data, and 2) use the corresponding coseismic shear stress change on the fault as input into a numerical afterslip model governed by rate-state friction. We find the rate-state frictional parameter A-B, which is an indicator of frictional stability, is in the range $10^{-4}-10^{-3}$ at 50 MPa normal stress, about an order of magnitude lower than experimental values for granite at conditions well above or below the transition from potentially unstable (negative A-B) to nominally stable (positive A-B) friction. The estimate of A-B values fall within a wide range of experimental values reported for Serpentinite which crops out along the San Andreas fault zone. The critical slip distance, $d_c$, which characterizes the distance over which strength breaks down during a slip event, is in the range 0.01-0.1 m, consistent with seismic estimates and a fault gouge thickness of 1-10 m. The afterslip model reproduces most features observed in the GPS time-series data including high surface velocities in the first few months after the earthquake and lower rates at later times, as well as the cumulative postseismic displacement. The model tends to under-predict the displacement data at later times, suggesting that perhaps the modeled afterslip period ends too quickly or an un-modeled deformation process dominates the signal at later times.

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