Periodic crustal deformation associated with repeated strike-slip earthquakes is computed for the following model: A depth L (≤H) extending downward from the Earth's surface at a transform boundary between uniform elastic lithospheric plates of thickness H is locked between earthquakes. It slips an amount consistent with remote plate velocity Vpl after each lapse of earthquake cycle time Tcy. Lower portions of the fault zone at the boundary slip continuously so as to maintain constant resistive shear stress. The plates are coupled at their base to a Maxwellian viscoelastic asthenosphere through which steady deep-seated mantle motions, campatible with plate velocity, are transmitted to the surface plates. The coupling is described approximately through a generalized Elsasser model. We argue that the model gives a more realistic physical description of tectonic loading, including the time dependence of deep slip and crustal stress buildup throughout the earthquake cycle, than do simpler kinematic models in which loading is represented as imposed uniform dislocation slip on the fault below the locked zone.

Parameters of the model are chosen to fit seismic and geologic constraints and the apparent time dependence of surface strain rates along presently locked traces of the 1857 and 1906 San Andreas ruptures. We fix Vpl=35 mm/yr, Tcy=160 years, and L=9--11 km based on earthquake nucleation depths. The geodetic data are then found to be described reasonably, within the context of a model that is locally uniform along strike and symmetric about a single San Andreas fault strand, by lithosphere thickness H=20--30 km and Elsasser relaxation time tr=10--16 years. We therefore suggest that the asthenosphere appropriate to describe crustal deformation on the earthquake cycle time scale lies in the lower crust and perhaps crust-mantle transition zone and has an effective viscosity between about 2¿1018 and 1019 Pa s, depending on the thickness assigned to the asthenospheric layer. Predictions based on the chosen set of parameters are also consistent with data on variations of contemporary surface strain and displacement rates as a function of distance from the 1857 and 1906 rupture traces, although the fit is degraded by asymmetry relative to the fault and by slip on adjacent fault strands. ¿ American Geophysical Union 1987