Advertisement

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

  • Mauricio Reyes CanalesEmail author
  • Mirko van der Baan
Article
  • 66 Downloads

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.

Keywords

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

Notes

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.

References

  1. 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
  2. Anagnos, T., & Kiremidjian, A. (1988). A review of earthquake occurrence models for seismic hazard analysis. Probabilistic Engineering Mechanics, 3, 3–11.CrossRefGoogle Scholar
  3. 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.CrossRefGoogle Scholar
  4. 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.CrossRefGoogle Scholar
  5. 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.CrossRefGoogle Scholar
  6. 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.
  7. 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.
  8. 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.
  9. 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
  10. 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.CrossRefGoogle Scholar
  11. 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.CrossRefGoogle Scholar
  12. Brodsky, E. E., & Lajoie, L. J. (2013). Anthropogenic seismicity rates and operational parameters at the Salton Sea geothermal field. Science, 341, 543–546.CrossRefGoogle Scholar
  13. Cornell, C. (1968). Engineering seismic risk analysis. Bulletin of the Seismological Society of America, 58, 1583–1606.Google Scholar
  14. 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.CrossRefGoogle Scholar
  15. Ellsworth, W. (2013). Injection induced earthquakes. Science, 341, 142–145.CrossRefGoogle Scholar
  16. 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.CrossRefGoogle Scholar
  17. 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.CrossRefGoogle Scholar
  18. 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
  19. 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.CrossRefGoogle Scholar
  20. Gutenberg, R., & Richter, C. F. (1944). Frequency of earthquakes in California. Bulletin of the Seismological Society of America, 34, 185–188.Google Scholar
  21. 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.
  22. 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.CrossRefGoogle Scholar
  23. 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.CrossRefGoogle Scholar
  24. Langenbruch, C., Dinske, C., & Shapiro, S. A. (2011). Inter event times of fluid induced earthquakes suggest their Poisson nature. Geophysical Research Letters, 38, L21302.CrossRefGoogle Scholar
  25. 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.CrossRefGoogle Scholar
  26. Marzocchi, W., & Taroni, M. (2014). Some thoughts on declustering in probabilistic seismic hazard analysis. Bulletin of the Seismological Society of America, 104, 1838–1845.CrossRefGoogle Scholar
  27. 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
  28. Ogata, Y., & Zhuang, H. C. (2006). Space-time ETAS models and an improved extension. Tectonophysics, 413, 13–23.CrossRefGoogle Scholar
  29. 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.
  30. 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.CrossRefGoogle Scholar
  31. Reasenberg, P. (1985). Second-order moment of central California seismicity, 1969–82. Journal of Geophysical Research: Solid Earth, 90, 5479–5495.CrossRefGoogle Scholar
  32. 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
  33. 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
  34. 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.CrossRefGoogle Scholar
  35. 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
  36. 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.
  37. 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.
  38. 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.CrossRefGoogle Scholar
  39. 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.CrossRefGoogle Scholar
  40. Wyss, M. (1979). Estimating maximum expectable magnitude of earthquakes from fault dimensions. Geology, 7, 336–340.CrossRefGoogle Scholar
  41. 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.
  42. 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.

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of AlbertaEdmontonCanada

Personalised recommendations