Including Non-Stationary Magnitude–Frequency Distributions in Probabilistic Seismic Hazard Analysis
- 66 Downloads
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.
KeywordsNon-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: https://doi.org/10.4095/299419. We thank Clayton Deutsch for discussion on the Monte Carlo simulation method. We also thank anonymous reviewers for their careful reading and suggestions.
- Aki, K. (1965). Maximum likelihood estimate of b in the formula logN= a-bM and its confidence limits. Bull. Earthq. Res. Inst, 43, 237–239.Google Scholar
- Baker, J. W. (2008). An introduction to probabilistic seismic hazard analysis (PSHA). Version, 1(3), 2017. https://web.stanford.edu/~bakerjw/Publications/Baker_(2008)_Intro_to_PSHA_v1_3.pdf. Accessed Dec.
- Baker, J. W. (2013). Probabilistic Seismic Hazard Analysis. White Paper Version 2.0.1. https://web.stanford.edu/~bakerjw/Publications/Baker_(2013)_Intro_to_PSHA_v2.pdf. Accessed Dec 2017.
- B.C Oil and Gas Commission (2012). Investigation of observed seismicity in the Horn River Basin, technical report. www.bcogc.ca/node/8046/download?documentID=1270. Accessed Dec 2017.
- Bourne, S. J., Oates, S. J., van Elk, J., & Doornhof, D. (2014). A seismological model for earthquake induced by fluid extraction from a subsurface reservoir. Journal of Geophysical Research: Solid Earth, 119, 8991–9015.Google Scholar
- Cornell, C. (1968). Engineering seismic risk analysis. Bulletin of the Seismological Society of America, 58, 1583–1606.Google Scholar
- Gardner, J. K., & Knopoff, L. (1974). Is the sequence of earthquakes in Southern California, with aftershocks removed, Poissonian? Bulletin of the Seismological Society of America, 64(5), 1363–1367.Google Scholar
- Gutenberg, R., & Richter, C. F. (1944). Frequency of earthquakes in California. Bulletin of the Seismological Society of America, 34, 185–188.Google Scholar
- Halchuk, S., Allen, T. I., Adams, J., & Rogers G. C. (2014). Fifth generation seismic hazard model input files as proposed to produce values for the 2015 National Building Code of Canada. Geol. Surv. Canada, Open-File Report. 7576, https://doi.org/10.4095/293907.
- Musson, R. M. W. (2000). The use of Monte Carlo simulations for seismic hazard assessment in UK. Annali di Geofisica, 43, 1–9.Google Scholar
- Petersen, M. D., Mueller, C. S., Moschetti, M. P., Hoover, S. M., Llenos, A. L., Ellsworth, W. L., et al. (2016). 2016 One-year seismic hazard forecast for the Central and Eastern United States from induced and natural earthquakes. U.S: Geological Survey, Open-File Report. https://doi.org/10.3133/ofr20161035.
- Roche, V., Grob, M., Eyre, T., & van der Baan, M. (2015). Statistical characteristics of Microseismic events and in-situ stress in the Horn Basin. Geoconvention 2015: New Horizons.Google Scholar
- Scholz, C. H. (1982). Scaling laws for large earthquakes: Consequences for physical models. Bulletin of the Seismological Society of America, 72, 1–14.Google Scholar
- Shi, Y., & Bolt, B. A. (1982). The standard error of the magnitude-frequency \(b\)-value. Bulletin of the Seismological Society of America, 72, 1677–1687.Google Scholar
- Sigman, K. (2013). Non-stationary Poisson processes and Compound (batch) Poisson processes. Columbia Edu., 2018, http://www.columbia.edu/~ks20/4404-Sigman/4404-Notes-NSP.pdf. Last accessed Feb.