• earthquake cycle;
  • slip rates

[1] We introduce new forward and inverse methods for inferring long-term fault slip rates, interseismic fault creep rates, and distribution of locked and creeping patches on faults using geodetic and geologic data. The forward model consists of fault-bounded blocks in an elastic crust overlying a Maxwell viscoelastic mantle. Interseismic elastic distortion of the blocks is modeled due to periodic locking and unlocking of faults throughout the earthquake cycle. Patches on the fault are assumed to be either locked during the interseismic period or creeping at constant shear stress. We utilize a Bayesian, probabilistic inversion method to infer the posterior probability distribution of long-term interseismic fault slip rates, distribution of locked and creeping patches, and relative weighting of multiple data sets. We illustrate the method with an inversion of a synthetic data set. We apply the method to estimate fault slip rates and the distribution of interseismic creep on faults in the San Francisco Bay Area, CA, using GPS-derived velocities and geologic measurements of fault slip rates. We show that the inferred fault slip rates and areas of the locked regions of faults are sensitive to the assumed viscosity of the upper mantle and the timing of past earthquakes and can be significantly different from values inferred from elastic models that do not include viscous flow. Considering models with different viscosities, inferred fault slip rates on major Bay Area faults can differ by factors of 1.5–4.0 and the inferred moment accumulation rate can differ by factors of 2–13.