Earthquakes come in clusters formed of mostly aftershock sequences, swarms and occasional foreshock sequences. This clustering is thought to result either from stress transfer among faults, a process referred to as cascading, or from transient loading by aseismic slip (pre-slip, afterslip or slow slip events). The ETAS statistical model is often used to quantify the fraction of clustering due to stress transfer and to assess the eventual need for aseismic slip to explain foreshocks or swarms. Another popular model of clustering relies on the earthquake nucleation model derived from experimental rate-and-state friction. According to this model, earthquakes cluster because they are time-advanced by the stress change imparted by the mainshock. This model ignores stress interactions among aftershocks and cannot explain foreshocks or swarms in the absence of transient loading. Here, we analyse foreshock, swarm and aftershock sequences resulting from cascades in a Discrete Fault Network model governed by rate-and-state friction. We show that the model produces realistic swarms, foreshocks and aftershocks. The Omori law, characterizing the temporal decay of aftershocks, emerges in all simulations independently of the assumed initial condition. In our simulations, the Omori law results from the earthquake nucleation process due to rate and state friction andmore »
The spatio-temporal properties of seismicity give us incisive insight into the stress state evolution and fault structures of the crust. Empirical models based on self-exciting point processes continue to provide an important tool for analysing seismicity, given the epistemic uncertainty associated with physical models. In particular, the epidemic-type aftershock sequence (ETAS) model acts as a reference model for studying seismicity catalogues. The traditional ETAS model uses simple parametric definitions for the background rate of triggering-independent seismicity. This reduces the effectiveness of the basic ETAS model in modelling the temporally complex seismicity patterns seen in seismic swarms that are dominated by aseismic tectonic processes such as fluid injection rather than aftershock triggering. In order to robustly capture time-varying seismicity rates, we introduce a deep Gaussian process (GP) formulation for the background rate as an extension to ETAS. GPs are a robust non-parametric model for function spaces with covariance structure. By conditioning the length-scale structure of a GP with another GP, we have a deep-GP: a probabilistic, hierarchical model that automatically tunes its structure to match data constraints. We show how the deep-GP-ETAS model can be efficiently sampled by making use of a Metropolis-within-Gibbs scheme, taking advantage of the branching process more »
- Publication Date:
- NSF-PAR ID:
- 10400984
- Journal Name:
- Geophysical Journal International
- Volume:
- 234
- Issue:
- 1
- Page Range or eLocation-ID:
- p. 427-438
- ISSN:
- 0956-540X
- Publisher:
- Oxford University Press
- Sponsoring Org:
- National Science Foundation
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$$k = 10^{-13} - 10^{-12}$$ $$\hbox {m}{^2}$$
