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Updated: Mar 15, 2026

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Self-similar aftershock rates.

Jörn Davidsen1,2, Marco Baiesi3,4

  • 1Complexity Science Group, Department of Physics and Astronomy, University of Calgary, Calgary, Alberta, Canada T2N 1N4.

Physical Review. E
|September 15, 2016
PubMed
Summary

Researchers developed a new model for aftershock rates that aligns with self-similar behavior, resolving a paradox in seismicity. This unified description of earthquake aftershocks and foreshocks improves seismic hazard assessment and forecasting.

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Area of Science:

  • Geophysics
  • Complex Systems Science
  • Statistical Physics

Background:

  • Crackling noise systems exhibit intermittent, avalanche-like relaxation with power-law distributed event sizes, suggesting self-similarity.
  • Observed aftershock rates in systems like seismicity often contradict theoretical expectations of self-similar behavior.
  • A paradox exists between the self-similar nature of earthquake sizes and the non-self-similar decay of aftershock rates.

Purpose of the Study:

  • To propose a generalized description of aftershock rates that is self-similar.
  • To reconcile the observed aftershock rate behavior with the overall self-similar characteristics of crackling noise systems.
  • To provide a unified framework for understanding earthquake aftershocks and foreshocks.

Main Methods:

  • Developed a theoretical model for generalized aftershock rates.
  • Applied the model to high-resolution earthquake data from Southern California.
  • Compared theoretical predictions with empirical earthquake data.

Main Results:

  • The proposed generalized description of aftershock rates is self-similar.
  • The model demonstrates excellent agreement with Southern California earthquake data.
  • Evidence supports a unified description of aftershocks and foreshocks.

Conclusions:

  • The new model resolves the paradox between earthquake size distribution and aftershock rate behavior.
  • This unified framework offers potential for improved time-dependent seismic hazard assessment.
  • The findings may enhance earthquake forecasting capabilities.