Foreshocks are not uncommon prior to large earthquakes, but their physical mechanism remains controversial. Two interpretations have been advanced: (1) foreshocks are driven by aseismic nucleation and (2) foreshocks are cascades, with each event triggered by earlier ones. Here, we study seismic cycles on faults with fractal roughness at wavelengths exceeding the nucleation length. We perform 2‐D quasi‐dynamic, elastic simulations of frictionally uniform rate‐state faults. Roughness leads to a range of slip behavior between system‐size ruptures, including widespread creep, localized slow slip, and microseismicity. These processes are explained by spatial variations in normal stress (σ) caused by roughness: regions with low σ tend to creep, while high σ regions remain locked until they break seismically. Foreshocks and mainshocks both initiate from the rupture of locked asperities, but mainshocks preferentially start on stronger asperities. The preseismic phase is characterized by feedback between creep and foreshocks: episodic seismic bursts break groups of nearby asperities, causing creep to accelerate, which in turns loads other asperities leading to further foreshocks. A simple analytical treatment of this mutual stress transfer, confirmed by simulations, predicts slip velocities and seismicity rates increase as 1/t, where t is the time to the mainshock. The model reproduces the observed migration of foreshocks toward the mainshock hypocenter, foreshock locations consistent with static stress changes, and the 1/t acceleration in stacked catalogs. Instead of interpreting foreshocks as either driven by coseismic stress changes or by creep, we propose that earthquake nucleation on rough faults is driven by the feedback between the two.

While power law distributions in seismic moment and interevent times are ubiquitous in regional earthquake catalogs, the statistics of individual faults remains controversial. Continuum fault models without heterogeneity typically produce characteristic earthquakes or a narrow range of sizes, leading to the view that regional statistics originate from interaction of multiple faults. I present theoretical arguments and numerical simulations demonstrating that seismicity on homogeneous planar faults can span several orders of magnitude in rupture dimensions and interevent times, if the fault dimension W is sufficiently large compared to a characteristic length Lcrit, related to the nucleation dimension. Large faults are increasingly less characteristic, with the fraction of system‐size ruptures proportional to (Lcrit/W)1/2. Earthquake statistics for large W/Lcrit is remarkably close to nature, exhibiting Omori decay and power law distributed rupture lengths. Simple crack models are consistent with a Gutenberg‐Richter distribution with b=3/4 and provide a physical basis for these distributions on individual faults.

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...

The 2016–2017 Central Apennines earthquake sequence is a recent example of how damages from subsequent aftershocks can exceed those caused by the initial mainshock. Recent studies reveal that physics‐based aftershock forecasts present comparable skills to their statistical counterparts, but their performance remains a controversial subject. Here we employ physics‐based models that combine the elasto‐static stress transfer with rate‐and‐state friction laws, and short‐term statistical Epidemic Type Aftershock Sequence (ETAS) models to describe the spatiotemporal evolution of the earthquake cascade. We then track the absolute and relative model performance using log‐likelihood statistics for a 1‐year horizon after the 24 August 2016 Mw = 6.0 Amatrice earthquake. We perform a series of pseudoprospective experiments by producing seven classes of Coulomb rate‐state (CRS) forecasts with gradual increase in data input quality and model complexity. Our goal is to investigate the influence of data quality on the predictive power of physics‐based models and to assess the comparative performance of the forecasts in critical time windows, such as the period following the 26 October Visso earthquakes leading to the 30 October Mw = 6.5 Norcia mainshock. We find that (1) the spatiotemporal performance of the basic CRS models is poor and progressively improves as more refined data are used, (2) CRS forecasts are about as informative as ETAS when secondary triggering effects from M3+ earthquakes are included together with spatially variable slip models, spatially heterogeneous receiver faults, and optimized rate‐and‐state parameters. After the Visso earthquakes, the more elaborate CRS model outperforms ETAS highlighting the importance of the static stress transfer for operational earthquake forecasting.