Geodetic observations at many active plate margins reveal relatively steady aseismic motion during the time between major earthquakes. We model the aseismic motion by the relative motion between several blocks that suffer frictional resistance in the upper crust. Frictional drag is represented by uniform dislocation on a fault surface. We assume that friction occurs only on the upper ''brittle zone'' of each block boundary and that frictionless sliding occurs below this zone. Using a Bayesian inversion procedure, we invert geodetic data to determine the parameters of the block and dislocation model. Parameters to be estimated include the two horizontal components of velocity for each block and the dislocation rate, dip angle, slip angle, and width of each rectangular fault patch.

For Hollister we assume five blocks and nine rectangular fault patches. Rates of length change on 92 lines observed by trilateration make up the data. Triangulation, leveling, very long baseline interferometry, satellite ranging, and global positioning system data can also be easily included in our model. Our inversion procedure uses prior estimates of all block and fault parameters based on geological and seismological data. The block parameters are estimated from geological observations of fault displacement rates, while the widths of the fault patches are estimated from earthquake hypocentral depths. We choose prior estimates of the dislocation rate to match observed creep rates. The estimated block motion is well resolved by the geodetic data and agrees well with the geological estimates. This suggests that the block motion is steady on time scales from 10 years to 1 m.y. The net motion across the San Andreas-Calaveras fault system is 38¿3 mm/yr oriented S38¿E.

Thus some additional displacement, possibly offshore, is needed to match the rate of 56 mm/yr predicted by plate tectonic models. The depth of the transition from frictional to free sliding varies considerably, from 0.4 km on the southern Calaveras to 11 km on the central San Andreas fault. Two segments of the San Andreas, north of 36¿50' and south of 36¿40', have the greatest potential for moderate to large earthquakes.