Dynamic Emergence of Plate Motions and Great Megathrust Earthquakes Across Length and Time Scales

The slow motion of tectonic plates over thousands of kilometers is intermittently interrupted by great earthquakes with sudden slips localized near convergent plate boundaries. We developed a subduction model that self-consistently integrates buoyancy forces, diffusion and dislocation creep, and inter-plate friction. From the nonlinear dynamics emerge long-term plate motions that achieve velocities of $\approx 5$ cm/year, effective viscosities of $\approx 10^{19}$ Pa$\cdot$s below plates, and sudden slips up to $\approx 10$ m repeating every several hundred years. Along-strike resistance arising from long-wavelength variation of coseismic slip is naturally incorporated with a rupture length scale, $\stackrel{\sim }{L}$. Computations with $\stackrel{\sim }{L}\sim 10^3$ km generate events with $M_w\approx 9$. When $\stackrel{\sim }{L}$ decreases, there is a commensurate decrease in the effective moment of rupture events. Predicted long-term plate velocities, mantle viscosities, cycles of stress loading and release, and rupture event size and magnitude all show good agreement with observations.