Crack Models of Repeating Earthquakes Predict Observed Moment‐Recurrence Scaling. Issue 1 (2nd January 2019) - Cattania, C.
Abstract: Small repeating earthquakes are thought to represent rupture of isolated asperities loaded by surrounding creep. The observed scaling between recurrence interval and seismic moment, T r ∼ M 1/6, contrasts with expectation assuming constant stress drop and no aseismic slip ( T r ∼ M 1/3 ). Here we demonstrate that simple crack models of velocity‐weakening asperities in a velocity‐strengthening fault predict the M 1/6 scaling; however, the mechanism depends on asperity radius, R . For small asperities ( R ∞ < R < 2 R ∞, where R ∞ is the nucleation radius) numerical simulations with rate‐state friction show interseismic creep penetrating inward from the edge, and earthquakes nucleate in the center and rupture the entire asperity. Creep penetration accounts for ∼25% of the slip budget, the nucleation phase takes up a larger fraction of slip. Stress drop increases with increasing R ; the lack of self‐similarity being due to the finite nucleation dimension. For 2 R ∞ < R ≲ 6 R ∞ simulations exhibit simple cycles with ruptures nucleating from the edge. Asperities with R ≳ 6 R ∞ exhibit complex cycles of partial and full ruptures. Here T r is explained by an energy criterion: full rupture requires that the energy release rate everywhere on the asperity at least equals the fracture energy, leading to the scaling T r ∼ M 1/6 . Remarkably, in spite of the variability in behavior with source dimension, the scaling of T r with stress drop Δ τ, nucleation length and creep rate v pl is the same across all regimes: T r ∼ R ∞ Δ τ 5 / 6 M 0 1 / 6 / v pl . This supports the use of repeating earthquakes as creepmeters and provides a physical interpretation for the scaling observed in nature. Plain Language Summary: While most earthquake sequences have complex temporal patterns, some small earthquakes are quite predictable: they repeat periodically. The time between consecutive events (recurrence interval) grows with earthquake size: as intuitive, it takes longer to accumulate the mechanical energy for large earthquakes. However, the scaling between the recurrence interval and earthquake energy (seismic moment) is not what simple physical considerations predict. It is often assumed that faults are locked between events and seismic slip must therefore keep up with long‐term plate motion. This leads to the scaling: T r ∼ M 0 1 / 3, but the observed scaling is T r ∼ M 0 1 / 6 . In fact, faults are not fully locked between earthquakes: they can slip slowly, or release part of the energy in smaller quakes between the larger ones. Here we use numerical simulations, and ideas from fracture mechanics, to understand what controls the time between repeating quakes. The main results are (1) analytical expressions of the recurrence interval as a function of earthquake size, predicting the observed scaling; (2) explanation of the differences between the cycle of small and large earthquakes (fraction of slow slip, direction of rupture propagation, and the occurrence of smaller quakes between large ones) and the quantities determining these transitions. Key Points: We derive analytical expressions for recurrence interval and stress drop of events on circular asperities in creeping faults The theory produces the observed scaling between recurrence interval and seismic moment of repeating earthquakes We predict and quantify a break in self‐similarity and decrease in stress drops close to the nucleation dimension