Including Non-Stationary Magnitude–Frequency Distributions in Probabilistic Seismic Hazard Analysis

  • Mauricio Reyes CanalesEmail author
  • Mirko van der Baan


We describe a first principles methodology to evaluate statistically the hazard related to non-stationary seismic sources like induced seismicity. We use time-dependent Gutenberg–Richter parameters, leading to a time-varying rate of earthquakes. We derive analytic expressions for occurrence rates which are verified using Monte Carlo simulations. We show two examples: (1) a synthetic case with two seismic sources (background and induced seismicity); and (2) a recent case of induced seismicity, the Horn River Basin, Northeast British Columbia, Canada. In both cases, the statistics from the Monte Carlo simulations agree with the analytical quantities. The results show that induced seismicity affects seismic hazard rates but that the exact change greatly depends on both the duration and intensity of the non-stationary sequence as well as the chosen evaluation period. The developed methodology is easily extended to handle spatial source distributions as well as ground motion analysis in order to generate a complete methodology for non-stationary probabilistic seismic hazard analysis.


Non-stationary seismicity time-dependent Gutenberg–Richter parameters Monte-Carlo simulations induced seismicity Horn River Basin Canada 



The author would like to thank the sponsors of the Microseismic Industry Consortium for financial support, and Honn Kao for providing an updated event catalog for the Horn River area. The event catalog used in this study is available at: We thank Clayton Deutsch for discussion on the Monte Carlo simulation method. We also thank anonymous reviewers for their careful reading and suggestions.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of AlbertaEdmontonCanada

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