A 3-D Semi-analytic Viscoelastic Model of the San Andreas Fault System: A 1000-year Perspective of the Earthquake Cycle

Combining historical earthquake data, coastal tide gauge measurements, and continuous vertical and horizontal geodetic velocities, we simulate one thousand years of the earthquake cycle for the entire San Andreas Fault System. We employ a model based on a new semi-analytic solution that provides the displacement and stress caused by time-dependent dislocations embedded in an elastic layer overlying a Maxwell viscoelastic half-space. The problem is solved analytically in both the vertical dimension and the time dimension, while the solution in the two horizontal dimensions is developed in the Fourier transform domain to exploit the computational advantages offered by the convolution theorem. Hundreds of dislocations imbedded in a 2048 x 2048 km sized grid are used to represent the San Andreas Fault System from the Gulf of California to the Mendocino Triple Junction. Major historical earthquakes (from 1812-present, M_w > 6.0) are used in conjunction with published recurrence intervals to produce the time-dependent velocity and stress tensor spanning the past 1000 years. The model simulates interseismic stress accumulation on the upper locked portion of subfaults and adjacent crust, repeated earthquakes on prescribed fault segments, and the viscoelastic response of the asthenosphere following major ruptures. Continuous geodetic observations (σ < 1.5 mm/yr) from the Scripps Orbit and Permanent Array Center (SOPAC) and USGS networks are used to constrain model parameters of elastic plate thickness (H), half-space viscosity ({η ), Poisson's ratio ({ν ), and apparent locking depth. We identify best fitting models with rms < 2.5 mm/yr for H > 60 km, {η = 1-5 x10¹⁹ Pa s, {ν = 0.35-0.45, and locking depths that are approximately 1/4 less deep than those required to fit an equivalent elastic half-space model. Using these model parameters, we calculate present-day Coulomb stress and observe large amounts of stress focused along the Carrizo and Mojave regions of the San Andreas, as expected from the absence of major earthquakes along these fault segments over the past 150 years. These results, along with corresponding time-dependent deformation results, have been assembled to form animations of the San Andreas Fault System that capture temporal variations in the plate-boundary velocity vector and stress tensor spanning the past 1000 years of the earthquake cycle.