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Earthquake clustering has proven the most useful tool to forecast changes in seismicity rates in the short and medium term (hours to months), and efforts are currently being made to extend the scope of such models to operational earthquake forecasting. The overarching goal of the research presented in this thesis is to improve physics-based earthquake forecasts, with a focus on aftershock sequences. Physical models of triggered seismicity are based on the redistribution of stresses in the crust, coupled with the rate-and-state constitutive law proposed by Dieterich to calculate changes in seismicity rate. This type of models are known as Coulomb- rate and-state (CRS) models. In spite of the success of the Coulomb hypothesis, CRS models typically performed poorly in comparison to statistical ones, and they have been underepresented in the operational forecasting context. In this thesis, I address some of these issues, and in particular these questions: (1) How can we realistically model the uncertainties and heterogeneity of the mainshock stress field? (2) What is the effect of time dependent stresses in the postseismic phase on seismicity? I focus on two case studies from different tectonic settings: the Mw 9.0 Tohoku megathrust and the Mw 6.0 Parkfield strike slip earthquake. I study aleatoric uncertainties using a Monte Carlo method. I find that the existence of multiple receiver faults is the most important source of intrinsic stress heterogeneity, and CRS models perform better when this variability is taken into account. Epistemic uncertainties inherited from the slip models also have a significant impact on the forecast, and I find that an ensemble model based on several slip distributions outperforms most individual models. I address the role of postseismic stresses due to aseismic slip on the mainshock fault (afterslip) and to the redistribution of stresses by previous aftershocks (secondary triggering). I find that modeling secondary triggering improves model performance. The effect of afterslip is less clear, and difficult to assess for near-fault aftershocks due to the large uncertainties of the afterslip models. Off-fault events, on the other hand, are less sensitive to the details of the slip distribution: I find that following the Tohoku earthquake, afterslip promotes seismicity in the Fukushima region. To evaluate the performance of the improved CRS models in a pseudo-operational context, I submitted them for independent testing to a collaborative experiment carried out by CSEP for the 2010-2012 Canterbury sequence. Preliminary results indicate that physical models generally perform well compared to statistical ones, suggesting that CRS models may have a role to play in the future of operational forecasting. To facilitate efforts in this direction, and to enable future studies of earthquake triggering by time dependent processes, I have made the code open source. In the final part of this thesis I summarize the capabilities of the program and outline technical aspects regarding performance and parallelization strategies.
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 approximate to M-1/6, contrasts with expectation assuming constant stress drop and no aseismic slip (T-r approximate to 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 ( , 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 approximate to 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 less than or similar to 6Rsimulations exhibit simple cycles with ruptures nucleating from the edge. Asperities with R6R 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 approximate to M-1/6. Remarkably, in spite of the variability in behavior with source dimension, the scaling of T-r with stress drop , nucleation length and creep rate v(pl) is the same across all regimes: Tr approximate to vpl. 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: Tr approximate to M01/3, but the observed scaling is . 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.