These assessments have become exceedingly complex, but unfortunately remain quite uncertain, in part because site-specific recurrence statistics for infrequent large earthquakes are unknown. Recent advances in large-scale simulations of earthquakes in fault systems make it possible to accurately model earthquake rupture processes and stress interactions in high resolution representations of fault systems for large numbers of earthquakes (typically 10⁵ to 10⁶ events, M5.0 to M8.0). The simulations incorporate clustering processes including foreshocks and aftershocks. Possible applications of simulators in assessments of earthquake probabilities include the generation of site-specific empirical density distributions of earthquake recurrence times, characterization of stress interactions and possible clock-resets for use with conditional probability estimates, and probabilistic evaluation of the effects of segment-to-segment ruptures and fault branching.
 
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Current simulators utilize faults with temporally constant failure stresses and/or rate- and state-friction but usually do not include poroelastic effects, viscoelasticity, or dynamic triggering effects. Earthquakes may include multiple faults but we do not have sufficiently detailed structural models of fault intersections, which limits our ability to model fault-to-fault jumps. Despite failing to include all of the known physical processes or accurate fault structures, it may be possible to validate simulators based on their ability to replicate known properties of earthquakes and seismicity catalogs. Unfortunately, many of these key properties are poorly constrained. Recently improved understanding of uncertainties in finite fault slip inversions suggests that we may not accurately understand the behavior of individual events. Some properties of earthquake catalogs are controversial, such as the degree of characteristic behavior and whether or not earthquakes are semi-periodic, and thus their use in validation methods would be similarly controversial. Another problem is that Gutenberg-Richter and modified-Omori behavior may be produced by so many different models that they can not be used to differentiate between them. That the simple and intuitively appealing idea of slip-predictability has failed observational tests demonstrates the complexity of the seismogenic process and thus we should be cautious about using simulators to extrapolate our current physical understanding into earthquake hazards assessments. In fairness to the physics-based simulation methods, many of these issues also plague current statistical approaches.
 
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