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
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, , 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.