Skip to main content
SpringerLink
Log in

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

  • Published:
Pure and Applied Geophysics Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  • 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 

  • Anagnos, T., & Kiremidjian, A. (1988). A review of earthquake occurrence models for seismic hazard analysis. Probabilistic Engineering Mechanics, 3, 3–11.

    Article  Google Scholar 

  • Assatourians, K., & Atkinson, G. (2013). EqHaz: An open-source probabilistic seismic hazard code based on the Monte Carlo simulation approach. Seismological Research Letters, 84, 516–524.

    Article  Google Scholar 

  • Atkinson, G., Ghofrani, H., & Assatourians, K. (2015). Impact of induced seismicity on the evaluation of seismic hazard: Some preliminary considerations. Seismological Research Letters, 86, 1009–1021.

    Article  Google Scholar 

  • Atkinson, G., Eaton, D., Ghofrani, H., Walker, D., Cheadle, B., Schultz, R., et al. (2016). Hydraulic fracturing drives induced seismicity in the western Canada sedimentary basin. Seismological Research Letters, 87, 631–647.

    Article  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 

  • Bourne, S. J., Oates, S. J., Bommer, J. J., van Elk, J., & Doornhof, D. (2015). A Monte Carlo method for probabilistic hazard assessment of induced seismicity due to conventional natural gas production. Bulletin of the Seismological Society of America, 105, 1721–1738.

    Article  Google Scholar 

  • Bourne, S. J., Oates, S. J., & van Elk, J. (2018). The exponential rise of induced seismicity with increasing stress levels in the Groningen gas field and its implications for controlling seismic risk. Geophysical Journal International, 213, 1693–1700.

    Article  Google Scholar 

  • Brodsky, E. E., & Lajoie, L. J. (2013). Anthropogenic seismicity rates and operational parameters at the Salton Sea geothermal field. Science, 341, 543–546.

    Article  Google Scholar 

  • Cornell, C. (1968). Engineering seismic risk analysis. Bulletin of the Seismological Society of America, 58, 1583–1606.

    Google Scholar 

  • Convertito, V., Maercklin, N., Sharma, N., & Zollo, A. (2012). From induced seismicity to direct time-dependent seismic hazard. Bulletin of the Seismological Society of America, 102, 2563–2573.

    Article  Google Scholar 

  • Ellsworth, W. (2013). Injection induced earthquakes. Science, 341, 142–145.

    Article  Google Scholar 

  • Farahbod, A., Kao, H., Cassidy, J., & Walker, D. (2015a). How did hydraulic-fracturing operations in the Horn River Basin change seismicity patterns in the northeastern British Columbia, Canada? The Leading Edge, 34, 658–663.

    Article  Google Scholar 

  • Farahbod, A., Kao, H., Cassidy, J., & Walker, D. (2015b). Investigation of regional seismicity before and after hydraulic fracturing in the Horn River Basin, northeast British Columbia. Canadian Journal of Earth Sciences, 52, 112–122.

    Article  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 

  • Ghofrani, H., & Atkinson, G. M. (2016). A preliminary statistical model for hydraulic fracture-induced seismicity in the Western Canada Sedimentary Basin. Geophysical Research Letters, 43, 164–172.

    Article  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.

  • Hornbach, M. J., DeShon, H. R., Ellsworth, W. L., Stump, B. W., Hayward, C., Frohlich, C., et al. (2015). Causal factors for seismicity near Azle, Texas. Nature Communications, 6, 6728.

    Article  Google Scholar 

  • Keranen, K. M., Weingarten, M., Abers, G. A., Bekins, B. A., & Ge, S. (2014). Sharp increase in central Oklahoma seismicity since 2008 induced by massive wastewater injection. Science, 345, 448–451.

    Article  Google Scholar 

  • Langenbruch, C., Dinske, C., & Shapiro, S. A. (2011). Inter event times of fluid induced earthquakes suggest their Poisson nature. Geophysical Research Letters, 38, L21302.

    Article  Google Scholar 

  • Langenbruch, C., & Zoback, M. D. (2016). How will induced seismicity in Oklahoma respond to decreased saltwater injection rates? Science Advance, 2, e1601542. https://doi.org/10.1126/sciadv.1601542.

    Article  Google Scholar 

  • Marzocchi, W., & Taroni, M. (2014). Some thoughts on declustering in probabilistic seismic hazard analysis. Bulletin of the Seismological Society of America, 104, 1838–1845.

    Article  Google Scholar 

  • 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 

  • Ogata, Y., & Zhuang, H. C. (2006). Space-time ETAS models and an improved extension. Tectonophysics, 413, 13–23.

    Article  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.

  • Petersen, M. D., Mueller, C. S., Moschetti, M. P., Hoover, S. M., Shumway, A. M., McNamara, D. E., et al. (2017). 2017 one-year seismic hazard forecast for the central and Eastern United States from induced and natural earthquakes. Seismological Research Letters, 88, 772–783.

    Article  Google Scholar 

  • Reasenberg, P. (1985). Second-order moment of central California seismicity, 1969–82. Journal of Geophysical Research: Solid Earth, 90, 5479–5495.

    Article  Google Scholar 

  • 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.

  • 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 

  • Shapiro, S., Dinske, C., & Langenbruch, C. (2010). Seismogenic index and magnitude probability of earthquakes induced during reservoir fluid stimulations. The Leading Edge, 29, 936–940.

    Article  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.

  • van Stiphout, T., Zhuang, J., & Marsan, D. (2012). Seismicity declustering, Community online resource for statistical seismology. https://doi.org/10.5078/corssa52382934.Available at: http://www.corssa.org. Last accessed Feb 2018.

  • van der Baan, M., & Calixto, F. J. (2017). Human-induced seismicity and large-scale hydrocarbon production in the USA and Canada. Geochemistry, Geophysics, Geosystems, 18, 2467–2485.

    Article  Google Scholar 

  • Wiemer, S., & Wyss, M. (1997). Mapping the frequency-magnitude distribution in asperities: An improved technique to calculate recurrence times? Journal of Geophysical Research, 102, 15115–15128.

    Article  Google Scholar 

  • Wyss, M. (1979). Estimating maximum expectable magnitude of earthquakes from fault dimensions. Geology, 7, 336–340.

    Article  Google Scholar 

  • Zhuang, J., D. Harte, M.J. Werner, S. Hainzl, & S. Zhou. (2012).Basic models of seismicity: temporal models, Community Online Resource for Statistical Seismicity Analysis, https://doi.org/10.5078/corssa-79905851.. http://www.corssa.org. Last accessed Feb 2018.

  • Zhuang, J. & Touati S. (2015). Stochastic simulation of earthquake catalogs, Community Online Resource for Statistical Seismicity Analysis. https://doi.org/10.5078/corssa-43806322. http://www.corssa.org. Last accessed Feb 2018.

Download references

Acknowledgements

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.

Author information

Authors and Affiliations

  1. Department of Physics, University of Alberta, Edmonton, Canada

    Mauricio Reyes Canales & Mirko van der Baan

Authors
  1. Mauricio Reyes Canales
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mirko van der Baan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mauricio Reyes Canales.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Reyes Canales, M., van der Baan, M. Including Non-Stationary Magnitude–Frequency Distributions in Probabilistic Seismic Hazard Analysis. Pure Appl. Geophys. 176, 2299–2319 (2019). https://doi.org/10.1007/s00024-019-02116-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00024-019-02116-4

Keywords

Search

Navigation