Cascading foreshocks, aftershocks and earthquake swarms in a discrete fault network

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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 and from the heterogeneous stress changes due to the coseismic stress transfers. By contrast, the inverse Omori law, which characterizes the accelerating rate of foreshocks, emerges only in the simulations with a dense enough fault system. A high-density complex fault zone favours fault interactions and the emergence of an accelerating sequence of foreshocks. Seismicity catalogues generated with our discrete fault network model can generally be fitted with the ETAS model but with some material differences. In the discrete fault network simulations, fault interactions are weaker in aftershock sequences because they occur in a broader zone of lower fault density and because of the depletion of critically stressed faults. The productivity of the cascading process is, therefore, significantly higher in foreshocks than in aftershocks if fault zone complexity is high. This effect is not captured by the ETAS model of fault interactions. It follows that a foreshock acceleration stronger than expected from ETAS statistics does not necessarily require aseismic slip preceding the mainshock (pre-slip). It can be a manifestation of a cascading process enhanced by the topological properties of the fault network. Similarly, earthquake swarms might not always imply transient loading by aseismic slip, as they can emerge from stress interactions.
Original languageEnglish
Pages (from-to)831-852
Number of pages22
JournalGeophysical Journal International
Issue number1
Early online date8 Jul 2023
Publication statusPublished online - 8 Jul 2023

Bibliographical note

Funding Information:
We thank three anonymous reviewers for their insightful and constructive evaluations. This study was supported by the National Science Foundation (award #1822214) via the IUCR centre Geomechanics and Mitigation of Geohazards.

Publisher Copyright:
© 2023 The Author(s). Published by Oxford University Press on behalf of The Royal Astronomical Society.


  • computational seismology
  • Earthquake hazards
  • Earthquake interaction
  • forecasting
  • and prediction
  • statistical seismology
  • Computational seismology
  • Earthquake interaction, forecasting, and prediction
  • Statistical seismology


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