Earthquake stress drop and laboratory‐inferred interseismic strength recovery

Abstract

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 r n 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 d Δτ d / d ln t r ≤σ e ( b‐a ), where σ e is the effective normal stress, μ=τ/σ e , and ( a‐b )= d μ ss / d ln V 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 d Δτ s / d ln t r ≤σ e (1 +ζ)( b‐a ), where ζ is the fractional overshoot. The variation of Δτ s with ln t 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.