Stress transfer and strain rate variations during the seismic cycle

The balance of forces implies stress transfers during the seismic cycle between the elastobrittle upper crust and the viscoelastic lower crust. This could induce observable time variations of crustal straining in the interseismic period. We simulate these variations using a one-dimensional system of springs, sliders, and dashpot loaded by a constant force. The seismogenic zone and the zone of afterslip below are modeled from rate-and-state friction. The ductile deeper fault zone is modeled from a viscous slider with Newtonian viscosity nu. The force per unit length, F, must exceed a critical value F-c to overcome friction resistance of the fault system. This simple system produces periodic earthquakes. The recurrence period, T-cycle, and the duration of the postseismic relaxation phase, which is driven dominantly by afterslip, then both scale linearly with n. Between two earthquakes, interseismic strain buildup across the whole system is nonstationary with the convergence rates V-i, just after each earthquake, being systematically higher than the value V-f at the end of the interseismic period. We show that V-i/V-f is an exponential function of alpha = T-cycle/T-M proportional to Deltatau/(F - F-c) proportional to Deltatau/(nuV(0)), where Deltatau is the coseismic stress drop and V-0 is the long-term fault slip rate. It follows that departure from stationary strain buildup is higher if the contribution of viscous forces to the force balance is small compared to the coseismic stress drop ( due to a low viscosity or low convergence rate, for example). This simple model is meant to show that the far-field deformation rate in the interseismic period, which can be determined from geodetic measurements, might not necessarily be uniform and equal to the long-term geologic rate.