Earthquake stress drop and laboratory-inferred interseismic strength recovery

We determine the scaling relationships between earthquake stress drop and recurrence interval t_r that are implied by laboratory-measured fault strength. We assume that repeating earthquakes can be simulated by stick-slip sliding using a spring and slider block model. Simulations with static/kinetic strength, time-dependent strength, and rate- and state-variable-dependent strength indicate that the relationship between loading velocity and recurrence interval can be adequately described by the power law V_L∝t_rⁿ where n≈−1. Deviations from n=−1 arise from second order effects on strength, with n>−1 corresponding to apparent time-dependent strengthening and n<−1 corresponding to weakening. Simulations with rate and state-variable equations show that dynamic shear stress drop Δτ_d scales with recurrence as dΔτ_d/dlnt_r≤σ_e(b-a), where σ_e is the effective normal stress, μ=τ/σ_e, and (a-b)=dμ_ss/dlnV is the steady-state slip rate dependence of strength. In addition, accounting for seismic energy radiation, we suggest that the static shear stress drop Δτ_s scales as dΔτ_s/dlnt_r≤σ_e(1 +ζ)(b-a), where ζ is the fractional overshoot. The variation of Δτ_s with lnt_r for earthquake stress drops is somewhat larger than implied by room temperature laboratory values of ζ and b-a. However, the uncertainty associated with the seismic data is large and the discrepancy between the seismic observations and the rate of strengthening predicted by room temperature experiments is less than an order of magnitude.