Skip to main content
SpringerLink
Log in

Bayesian Estimation of the Maximum Magnitude mmax Based on the Extreme Value Distribution for Probabilistic Seismic Hazard Analyses

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

Abstract

This work proposes a new approach, based on Bayesian updating and extreme value statistics to determine the maximum magnitudes for truncated magnitude-frequency distributions such as the Gutenberg Richter model in the framework of Probabilistic Seismic Hazard Analyses. Only the maximum observed magnitude and the associated completeness period are required so that the approach is easy to implement and there is no need to determine and use the completeness periods for smaller events. The choice of maximum magnitudes can have a major impact on hazard curves when long return periods as required for safety analysis of nuclear power plants are considered. Here, not only a singular value but a probability distribution accounting for prior information, data and uncertainty is provided. Moreover, uncertainties related to magnitude frequency distributions, including the uncertainty related to the maximum observed magnitude are discussed and accounted for. The accuracy of the approach is validated based on simulated catalogues with various parameter values. Then the approach is applied to French data for a specific region characterized by high-seismic activity in order to determine the maximum magnitude distribution and to compare the results to other approaches.

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
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  • Akkar, S., Sandıkkaya, M. A., Şenyurt, M., Azari, S. A., Ay, B. Ö., Traversa, P., et al. (2014). Reference database for seismic ground-motion in Europe (RESORCE). Bulletin of Earthquake Engineering. https://doi.org/10.1007/s10518-013-9506-8

    Article  Google Scholar 

  • Ameri, G. (2014) Integration of sigma improvement for PSHA and sensibility studies (intermediate results). Report SIGMA-2014-D4–138, Sections 4 5 and Annexe 4.

  • Ameri, G., Baumont, D., Gomes, C., Dortz, Le., Goff, Le., & Martin, S. (2015). On the choice of maximum earthquake magnitude for seismic hazard assessment in metropolitan France—insight from the Bayesian approach. Paris: Colloque AFPS.

    Google Scholar 

  • Anderson, J. G. (1979). Estimating the seismicity from geological structure for seismic risk studies. Bulletin of the Seismological Society of America, 69, 135–158.

    Google Scholar 

  • Beirlant, J., Goegebeur, Y., Segers, J., & Teugels, J. (2004). Statistics of extremes: theory and applications. Probability and statistics. Hoboken: Wiley.

    Book  Google Scholar 

  • Bommer, J. J., & Crowley, H. (2017). The purpose and definition of the minimum magnitude limit in PSHA calculations. Seismological Research Letters, 88(4), 1097–1106.

    Article  Google Scholar 

  • Bommer, J. J., Coppersmith, K. J., Coppersmith, R. T., et al. (2015). A SSHAC level 3 probabilistic seismic hazard analysis for a new-build nuclear site in South Africa. Earthquake Spectra, 31(2), 661–698. https://doi.org/10.1193/060913EQS145M

    Article  Google Scholar 

  • Burton, M. (1985). Seismic risk of circum-pacific earthquakes: II. Extreme values using Gumbel’s third distribution and the relationship with strain energy release. Pure and Applied Geophysics, 123(6), 849–869. ((Birkhäuser Verlag, Basel)).

    Article  Google Scholar 

  • Campbell, K. W. (1982). Bayesian analysis of extreme earthquake occurrences. Part I. Probabilistic hazard model. Bulletin of the Seismological Society of America, 72(5), 1689–1705.

    Google Scholar 

  • Campbell, K. W. (1983). Bayesian analysis of extreme earthquake occurrences. Part II. Application to the San Jacinto fault zone of Southern California. Bulletin of the Seismological Society of America, 73(4), 1099–1115.

    Google Scholar 

  • Coles, S. (2001). An introduction to statistical modeling of extreme values. Berlin: Springer-Verlag. ((ISBN 1-85233-459-2)).

    Book  Google Scholar 

  • Cornell, C. A. (1968). Engineering seismic risk analysis. Bulletin of the Seismological Society of America, 58(5), 1583–1606.

    Google Scholar 

  • Cornell, C.A. (1994). Statistical analysis of maximum magnitudes. In: The Earthquakes of Stable Continental Regions, Vol. 1. Assessment of Large Earthquake Potential, Electric Power Research Institute, Palo Alto, 5.1–5.27.

  • Drouet, S., Ameri, G., Le Dortz, K., et al. (2020). A probabilistic seismic hazard map for the metropolitan France. Bulletin of Earthquake Engineering, 18, 1865–1898. https://doi.org/10.1007/s10518-020-00790-7EDF(2017).HID-ProbabilisticseismichazardmapsfortheFrenchmetropolitanterritory.ReportGTR/EDF/0217-1573_rev1

    Article  Google Scholar 

  • Epstein, B., & Lomnitz, C. (1966). A model for the occurrence of large earthquakes. Nature, 211, 954–956.

    Article  Google Scholar 

  • Grünthal, G., Stromeyer, D., Bosse, C., Cotton, F., & Bindi, D. (2018). The probabilistic seismic hazard assessment of Germany–-version 2016, considering the range of epistemic uncertainties and aleatory variability. Bulletin of Earthquake Engineering, 16, 4339–4395.

    Article  Google Scholar 

  • Gutenberg, B., & Richter, C. F. (1944). Frequency of earthquakes in California. Bulletin of the Seismological Society of America, 34(4), 185–188.

    Google Scholar 

  • Holschneider, M., Zöller, G., & Hainzl, S. (2011). Estimation of the maximum possible magnitude in the framework of a doubly truncated Gutenberg-Richter model. Bulletin of the Seismological Society of America, 101(4), 1649–1659.

    Article  Google Scholar 

  • Holschneider, M., Zöller, G., Clements, R., & Schorlemmer, D. (2014). Can we test for the maximum possible earthquake magnitude? Journal of Geophysical Research: Solid Earth, 119, 2019–2028. https://doi.org/10.1002/2013JB010319

    Article  Google Scholar 

  • Jaynes, E. T. (2007). Probability theory: the logic of science (5 print. ed.). Cambridge: Cambridge Univ Press. ((978-0-521-59271-0)).

    Google Scholar 

  • Johnston. (1994). The stable continental region earthquake database. In: The Earthquakes of Stable Continental Regions, Vol. 1. Assessment of Large Earthquake Potential, Electric Power Research Institute, Palo Alto, 3.1–3. 75.

  • Kagan, Y. Y., & Jackson, D. D. (2000). Probabilistic forecasting of earthquakes. Geophysical Journal International, 143, 438–453.

    Article  Google Scholar 

  • Kijko, A. (2004). Estimation of the maximum earthquake magnitude, mmax. Pure and Applied Geophysic. https://doi.org/10.1007/s00024-004-2531-4

    Article  Google Scholar 

  • Kijko, A., & Singh, M. (2011). Statistical tools for maximum possible earthquake magnitude estimation. Acta Geophysica, 59, 674.

    Article  Google Scholar 

  • Kijko. (2012). On Bayesian procedure for maximum earthquake magnitude estimation. Research in Geophysics 2 (1).

  • Knopoff, L., & Kagan, Y. (1977). Analysis of the theory of extremes as applied to earthquake problems. Journal of Geophysical Research, 82(36), 5647–5657.

    Article  Google Scholar 

  • Koravos, G., Main, I. G., Tsapanos, T. M., & Musson, R. W. (2003). Maximum earthquake magnitudes in the Aegean area constrained by tectonic moment release. Geophysical Journal International, 152, 94–112.

    Article  Google Scholar 

  • Lomnitz-Adler, L. (1979). A modified form of the Gutenberg-Richter magnitude-frequency relation. Bulletin of the Seismological Society of America, 96(4), 1209–1214.

    Google Scholar 

  • Main, I. G., & Burton, P. W. (1984). Information theory and the earthquake frequency-magnitude distribution. Bulletin of the Seismological Society of America, 74, 1409–1426.

    Google Scholar 

  • Manchuel, K., Traversa, P., Baumont, D., Cara, M., Nayman, E., & Durouchoux, C. (2017). The French seismic CATalogue (FCAT-17). Bulletin of the Seismological Society of America. https://doi.org/10.1007/s10518-017-0236-1

    Article  Google Scholar 

  • Martin, C., Ameri, G., Baumont, D., Carbon, D., Senfaute, G., Thiry, J. M., et al. (2017). Probabilistic seismic hazard assessment for South-Eastern France. Bulletin of Earthquake Engineering, 16(6), 2477–2511. https://doi.org/10.1007/s10518-017-0249-9

    Article  Google Scholar 

  • Nordquist, J. N. (1945). Theory of largest value applied to earthquake magnitudes. Transactions American Geophysical Union, 26(29), 29–31.

    Article  Google Scholar 

  • Ordaz, M., & Faccioli, E. (2018). Modelling correlation between Gutenberg-Richter parameters a and b in PSHA. Bulletin of Earthquake Engineering, 16, 1829–1846. https://doi.org/10.1007/s10518-017-0274-8

    Article  Google Scholar 

  • Pisarenko, V. F., & Sornette, D. (2003). Characterization of frequency of extreme earthquake events by the generalized Pareto distribution. Pure and Applied Geophysics, 160, 2343–2364.

    Article  Google Scholar 

  • Pisarenko, V. F., Lyubushin, A. A., Lysenko, V. B., & Golubeva, T. B. (1996). Statistical estimation of seismic hazard parameters: Maximum possible magnitude and related parameters. Bulletin of the Seismological Society of America, 86(3), 691–700.

    Google Scholar 

  • Pisarenko, V. F., Sornette, A., Sornette, D., & Rodkin, M. V. (2008). New approach to the characterization of mmax and the tail of the distribution of earthquake magnitudes. Theory. Pure and Applied Geophysics, 165, 847–888.

    Article  Google Scholar 

  • Pisarenko, V. F., Sornette, A., Sornette, D., & Rodkin, M. V. (2014). Characterization of the tail of the distribution of earthquake magnitudes by combining the GEV and GPD descriptions of extreme value theory. Pure and Applied Geophysics, 171, 1599–1624.

    Article  Google Scholar 

  • Raschke, M. (2012). Inference for the truncated exponential distribution. Stochastic Environmental Research and Risk Assessment, 26(1), 127–138.

    Article  Google Scholar 

  • Raschke, M. (2016). Comment on Pisarenko et al. “Characterization of the tail of the distribution of earthquake magnitudes by combining the GEV and GPD descriptions of extreme value theory.” Pure and Applied Geophysics, 173(2), 701–707.

    Article  Google Scholar 

  • Rong Y., Bird P., Jackson D.D. (2017). Earthquake potential and magnitude limits in Southern Europe. Proceedings of WCEE, Santiago, Chile.

  • Salamat, M., Zöller, G., & Amini, M. (2019). Prediction of the maximum expected earthquake magnitude in Iran: From a Catalog with varying magnitude of completeness and uncertain magnitudes. Pure and Applied Geophysics, 176, 3425–3438. https://doi.org/10.1007/s00024-019-02141-3

    Article  Google Scholar 

  • Stevens, V. L., & Avouac, J.-P. (2017). Determination of mmax from background seismicity and moment conservation. Bulletin of the Seismological Society of America, 107(6), 2578–2596.

    Article  Google Scholar 

  • Stucchi, et al. (2012). The SHARE European earthquake catalogue (SHEEC) 1000–1899. Journal of Seismology. https://doi.org/10.1007/s10950-012-9335-2

    Article  Google Scholar 

  • USNRC (2012). Central and eastern united states seismic source characterization for nuclear facilities. Technical Report. EPRI, Palo Alto, CA, U.S. DOE, and U.S. NRC.

  • Vanneste, K., Vleminckx, B., Stein, S., & Camelbeeck, T. (2016). Could mmax be the same for all stable continental regions? Seismological Research Letters, 87(5), 1214–1223.

    Article  Google Scholar 

  • Wheeler, R. L. (2016). Maximum magnitude (mmax) in the central and eastern United States for the 2014 U.S. geological survey Hazard Model. Bulletin of the Seismological Society of America, 106(5), 2154–2167. https://doi.org/10.1785/0120160048

    Article  Google Scholar 

  • Wheeler (2009). Methods for mmax estimation east of the Rocky Mountains. USGS report prepared for US Geological Survey  Open-File Report 2009–1018.

  • Wiemer, S., Danciu, L., Edwards, B., Marti, M., Fäh, D., Hiemer, S., Wössner, J., Cauzzi, C., Kästli, P., Kremer, K. (2016). Seismic hazard model 2015 for Switzerland (SUIhaz2015). Swiss Seismological Service (SED) at ETH Zurich, DOI 10.12686/a2.

  • Woessner, et al. (2015). The 2013 European Seismic hazard model: Key components and results. Bull EarthqEng, 13(12), 3553–3596.

    Article  Google Scholar 

  • Zöller, H. (2016). The earthquake history in a fault zone tells us almost nothing about mmax. Seismological Research Letters, 87(1), 132–137.

    Article  Google Scholar 

  • Zöller, G., & Hainzl, S. (2007). Recurrence time distributions of large earthquakes in a stochastic model for coupled fault systems: The role of fault interaction. Bulletin of the Seismological Society of America, 97(5), 1679–1687.

    Article  Google Scholar 

  • Zöller, G., Holschneider, M., & Hainzl, S. (2013). The maximum earthquake magnitude in a time horizon: Theory and case studies. Bulletin of the Seismological Society of America, 103(2A), 860–875.

    Article  Google Scholar 

Download references

Acknowledgements

This work has been funded by SIGMA-2 project. The authors want to thank Ian Main and the second anonymous reviewer for their careful revisions and detailed feedback that helped us to improve the quality of the paper.

Author information

Authors and Affiliations

  1. EDF R&D Lab Paris Saclay, Palaiseau, France

    Irmela Zentner

  2. SEISTER, Aubagne, France

    Gabriele Ameri

  3. EDF DIPNN Technical Direction, Lyon, France

    Emmanuel Viallet

Authors
  1. Irmela Zentner
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gabriele Ameri
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Emmanuel Viallet
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Irmela Zentner.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zentner, I., Ameri, G. & Viallet, E. Bayesian Estimation of the Maximum Magnitude mmax Based on the Extreme Value Distribution for Probabilistic Seismic Hazard Analyses. Pure Appl. Geophys. 177, 5643–5660 (2020). https://doi.org/10.1007/s00024-020-02612-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00024-020-02612-y

Keywords

Search

Navigation