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Smith, BR, Sandwell DT.  2006.  A model of the earthquake cycle along the San Andreas Fault System for the past 1000 years. Journal of Geophysical Research-Solid Earth. 111   10.1029/2005jb003703   AbstractWebsite

[1] We simulate 1000 years of the earthquake cycle along the San Andreas Fault System by convolving best estimates of interseismic and coseismic slip with the Green's function for a point dislocation in an elastic plate overlying a viscoelastic half-space. Interseismic slip rate is based on long-term geological estimates while fault locking depths are derived from horizontal GPS measurements. Coseismic and postseismic deformation is modeled using 70 earthquake ruptures, compiled from both historical data and paleoseismic data. This time-dependent velocity model is compared with 290 present-day geodetic velocity vectors to place bounds on elastic plate thickness and viscosity of the underlying substrate. Best fit models (RMS residual of 2.46 mm/yr) require an elastic plate thickness greater than 60 km and a substrate viscosity between 2 x 10(18) and 5 x 10(19) Pa s. These results highlight the need for vertical velocity measurements developed over long time spans (> 20 years). Our numerical models are also used to investigate the 1000-year evolution of Coulomb stress. Stress is largely independent of assumed rheology, but is very sensitive to the slip history on each fault segment. As expected, present-day Coulomb stress is high along the entire southern San Andreas because there have been no major earthquakes over the past 150 - 300 years. Animations S1 and S2 of the time evolution of vector displacement and Coulomb stress are available as auxiliary material.

Smith, B, Sandwell D.  2004.  A three-dimensional semianalytic viscoelastic model for time-dependent analyses of the earthquake cycle. Journal of Geophysical Research-Solid Earth. 109   10.1029/2004jb003185   AbstractWebsite

[ 1] Exploring the earthquake cycle for large, complex tectonic boundaries that deform over thousands of years requires the development of sophisticated and efficient models. In this paper we introduce a semianalytic three-dimensional (3-D) linear viscoelastic Maxwell model that is developed in the Fourier domain to exploit the computational advantages of the convolution theorem. A new aspect of this model is an analytic solution for the surface loading of an elastic plate overlying a viscoelastic half-space. When fully implemented, the model simulates ( 1) interseismic stress accumulation on the upper locked portion of faults, ( 2) repeated earthquakes on prescribed fault segments, and ( 3) the viscoelastic response of the asthenosphere beneath the plate following episodic ruptures. We verify both the analytic solution and computer code through a variety of 2-D and 3-D tests and examples. On the basis of the methodology presented here, it is now possible to explore thousands of years of the earthquake cycle along geometrically complex 3-D fault systems.