A rheologically layered three‐dimensional model of the San Andreas Fault in central and southern California
Authors: Williams Charles A. , Richardson Randall M. 
Published: February 2008

Three‐dimensional kinematic finite element models of the San Andreas fault in central and southern California have been used to estimate the effects of rheological parameters and fault slip distribution on the horizontal and vertical deformation in the vicinity of the fault. The models include the effects of vertically layered power law viscoelastic rheology, and isostatic forces are considered in calculations of vertical uplift. Several different rheological layering schemes are used, using laboratory results on rock rheology to define the properties of the various layers. The depth to which the fault remains locked between earthquakes (D) is held constant at 20 km for the entire locked portion of the fault between Cholame and the Salton Sea. Between Hollister and Cholame the entire fault is assumed to slip at a rate consistent with a relative plate velocity of 35 mm/yr along a direction striking N41°W. Steady aseismic slip corresponding to plate velocity is imposed below the fault locking depth to a depth H on the locked section of the fault. The depth to which aseismic slip occurs (H) is assigned a value of either 20 km or 40 km, resulting in two versions of each rheological model. Variations in the model parameters are found to produce distinctive deformation patterns, providing a means for differentiating between models. Specifically, lower effective viscosities near the surface result in increased strain rates and uplift rates at all times during the earthquake cycle. Lower effective viscosities also produce subsidence near the creeping portion of the fault. Models that do not include aseismic slip below the fault locking depth (H = 20 km) display greater time dependence in both horizontal and vertical deformation than those including aseismic slip below the locking depth (H = 40 km). These differences are due, in part, to the time‐invariant nature of the imposed slip condition. The differences are more pronounced as the effective viscosity close to the surface is increased. The vertical uplift rate is particularly sensitive to the depth of aseismic slip (H) at the two bends in the fault, especially for models with high effective viscosities below the surface. For models in which the effective viscosity near the surface is relatively low, measurements of total uplift at the two bends in the fault could provide sufficient resolution to distinguish between models with and without aseismic slip over time periods of 10 to 20 years or more with current abilities to measure vertical uplift. Among our San Andreas fault models, the one most consistent with current strain rate data includes aseismic slip between 20 and 40 km (H = 40 km) and uses assumed rheological properties from the surface to 100 km depth consistent with laboratory results for wet rock samples. The rheological parameters for this model are based on laboratory results for the following rock types wet granite in the upper crust (0 to 20 km), wet diabase in the lower crust (20 to 40 km), wet dunite in the upper mantle (40 to 100 km), and dry olivine below 100 km. These modeling results are preliminary, however, and several additional factors should be considered prior to constructing a comprehensive model. Furthermore, it should be emphasized that the present models represent a small subset of possible rheological models, and numerous other models may provide similar or better fits to the data. The field of possible models will continue to narrow with further knowledge of the variations in Earth composition and temperature with depth, with more information on rock rheology, and with further observations of the earthquake cycle.