Spatially variable fault friction derived from dynamic modeling of aseismic afterslip due to the 2004 Parkfield earthquake

We investigate fault friction from dynamic modeling of fault slip prior to and following the M_w 6.0 earthquake which ruptured the Parkfield segment of the San Andreas Fault in 2004. The dynamic modeling assumes a purely rate-strengthening friction law, with a logarithmic dependency on sliding rate: μ=μ *+a-blnvv*. The initial state of stress is explicitly taken into account, and afterslip is triggered by the stress change induced by the earthquake source model given a priori. We consider different initial stress states and two coseismic models, and invert for the other model parameters using a nonlinear inversion scheme. The model parameters include the reference friction μ_*, the friction rate dependency characterized by the quantity a-b, assumed to be either uniform or depth dependent. The model parameters are determined from fitting the transient postseismic geodetic signal measured at continuous GPS stations. Our study provides a view of frictional properties at the kilometers scale over the 0-15 km depth illuminated by the coseismic stress change induced by the Parkfield earthquake. The reference friction is estimated to be between 0.1 and 0.5. With independent a priori constraints on the amplitude of differential stress, the range of possible values narrows down to 0.1-0.17. The friction rate coefficient a-b is estimated to be ∼ 10^{- 3} - 10^{- 2} with a hint that it increases upward from about 1-3 × 10^-3 at 3-7 km depth to about 4-7 × 10^-3 at 0-1 km depth. It is remarkable that our results are consistent with frictional properties measured on rock samples recovered from the fault zone thanks to the San Andreas Fault Observatory at Depth experiment.