Crack Models of Repeating Earthquakes Predict Observed Moment‐Recurrence Scaling

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 < 2R ∞ , 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 2R ∞ < R ≲ 6R ∞ simulations exhibit simple cycles with ruptures nucleating from the edge. Asperities with R ≳ 6R ∞ 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 , nucleation length and creep rate v pl is the same across all regimes:This supports the use of repeating earthquakes as creepmeters and provides a physical interpretation for the scaling observed in nature. Plain Language SummaryWhile 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 1∕3 0 , but the observed scaling is T r ∼ M 1∕6 0 . 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.1∕6 0 for small repeaters on the San Andreas fa...

Scaling and Variability of Interacting Repeating Earthquake Sequences Controlled by Asperity Density

“…When ρ < ρ * , asperities are either far from each other or separated by strong velocity strengthening barriers, so that they could be considered as isolated. The behavior of asperities is then similar to what is analyzed by T. Chen & Lapusta (, ) and Cattania and Segall (); some amount of aseismic slip occurs on the velocity weakening patches during interseismic periods, due to the penetration of a slow slip front from the edges of the patches. When ρ > ρ * , it is shown in Figure S6 and S8, that the seismic activity is highly clustered in time around a mainshock that ruptures the entire fault.…”

“…If the stress drop is constant and if no slip is accumulated on the asperity during interseismic periods, T r increases as . However, considering a moment dependent stress drop, or a small amount of aseismic creep, or partial ruptures during interseismic periods of the asperity, the scaling is usually recovered (Cattania & Segall, ; Beeler et al, ; T. Chen & Lapusta, , ; Sammis & Rice, ). This success has motivated the use of repeating earthquake sequences to monitor aseismic creep on deep faults (Bürgmann et al, ; Chen et al, ; Gardonio et al, , ; Igarashi et al, ; Nadeau & McEvilly, ; Schmidt et al, ; Templeton et al, ; Uchida & Matsuzawa, ; Uchida et al, , , ).…”

“…This is in particular the case of the transient variations in T r associated with accelerated creep following the Loma‐Prieta earthquake (Schaff et al, ), or the changes in T r and M 0 observed for repeating earthquake sequences on the San Andreas fault following moderate size earthquakes (K. H. Chen et al, , ; Lengliné & Marsan, ). Even though some of the variability could be attributed to partial ruptures of the main asperity (Cattania & Segall, ; T. Chen & Lapusta, ), seismological observations suggest more complex models. Asperities are in particular far from being isolated on faults, and a precise analysis of source parameters often suggest a set of overlapping sources of slightly different sizes rather than a single asperity (Dublanchet et al, ; Ellsworth & Bulut, ; Godano et al, ).…”

Complex Earthquake Sequences On Simple Faults

“…When it reaches a critical distance L n , nucleation occurs. During creep propagation, the fracture energy term is typically negligible (Cattania & Segall, ), so equation can be written as K L ( l )≈ K Δ τ ( l ). The SIFs are and (Tada et al, ), where for antiplane and for plane strain deformation ( μ is the shear modulus and ν the Poisson ratio); Δ τ is the stress increase behind the creep front, which is equal and opposite to the stress drop in the previous event (section S3).…”

The Long Recurrence Intervals of Small Repeating Earthquakes May Be Due to the Slow Slip Rates of Small Fault Strands

“…The correct physical model for repeaters remains unclear, and a range of models have been proposed. Repeating earthquakes could have long recurrence intervals because some of the slip on repeating earthquake patches accumulates aseismically or via partial ruptures in postseismic, interseismic, or preseismic periods (Beeler et al, ; Chen & Lapusta, , ; Cattania & Segall, ). Alternatively, repeating earthquakes could have long recurrence intervals because they occur within regions of low slip rate or low stressing rate.…”