Advertisement

Natural Hazards

, Volume 78, Issue 3, pp 1917–1930 | Cite as

Effect of alternative distributions of ground motion variability on results of probabilistic seismic hazard analysis

  • V. A. Pavlenko
Original Paper

Abstract

Probabilistic seismic hazard analysis (PSHA) is a regularly applied practice that precedes the construction of important engineering structures. The Cornell–McGuire procedure is the most frequently applied method of PSHA. This paper examines the fundamental assumption of the Cornell–McGuire procedure for PSHA, namely the log-normal distribution of the residuals of the ground motion parameters. Although the assumption of log-normality is standard, it has not been rigorously tested. Moreover, the application of the unbounded log-normal distribution for the calculation of the hazard curves results in nonzero probabilities of the exceedance of physically unrealistic amplitudes of ground motion parameters. In this study, the distribution of the residuals of the logarithm of peak ground acceleration is investigated, using the database of the strong-motion seismograph networks of Japan and the ground motion prediction equation of Zhao and co-authors. The distribution of residuals is modelled by a number of probability distributions, and the one parametric law that approximates the distribution most precisely is chosen by the statistical criteria. The results of the analysis show that the most accurate approximation is achieved with the generalized extreme value distribution for a central part of a distribution and the generalized Pareto distribution for its upper tail. The effect of replacing a log-normal distribution in the main equation of the Cornell–McGuire method is demonstrated by the calculation of hazard curves for a simple hypothetical example. These hazard curves differ significantly from one another, especially at low annual exceedance probabilities.

Keywords

Ground motion variability Probabilistic seismic hazard analysis Hazard curve Ground motion prediction equation Peak ground acceleration 

Notes

Acknowledgments

I would like to express my appreciation to Professor Andrzej Kijko for formulating the problem, guidance during this study, the review of this paper, and the valuable comments that helped to significantly improve its quality. I would like to thank two anonymous reviewers for their valuable comments and suggestions that allowed to make this paper even better. I am grateful to the K-NET and KiK-net strong-motion seismograph networks of Japan for seismic ground motion records (available online at http://www.kyoshin.bosai.go.jp).

References

  1. Abrahamson N (2000) State of the practice of seismic hazard evaluation. In: Proceedings of GeoEng 2000, international conference on geotechnical & geological engineering, Melbourne, Australia, vol 1, pp 659–685Google Scholar
  2. Akaike H (1974) A new look at the statistical model identification. IEEE Trans Autom Control 19(6):716–723CrossRefGoogle Scholar
  3. Anderson J, Brune J (1999) Probabilistic seismic hazard analysis without the ergodic assumption. Seismol Res Lett 70(1):19–28CrossRefGoogle Scholar
  4. Arroyo D, Ordaz M, Rueda R (2014) On the selection of ground-motion prediction equations for probabilistic seismic-hazard analysis. Bull Seismol Soc Am 104(4):1860–1875CrossRefGoogle Scholar
  5. Atkinson G, Boore D (2003) Empirical ground-motion relations for subduction-zone earthquakes and their application to Cascadia and other regions. Bull Seismol Soc America 93(4):1703–1729CrossRefGoogle Scholar
  6. Baker J (2008) An introduction to probabilistic seismic hazard analysis (PSHA) version 1.3. Available at http://web.stanford.edu/~bakerjw/Publications/Baker_(2008)_Intro_to_PSHA_v1_3.pdf
  7. Beirlant J, Goedebeur Y, Teugels T, Segerus J, De Waal D, Ferro C (2004) Statistics of extremes: theory and applications. Wiley, ChichesterCrossRefGoogle Scholar
  8. Bender B (1984) Incorporating acceleration variability into seismic hazard analysis. Bull Seismol Soc Am 74(4):1451–1462Google Scholar
  9. Bol’shev L, Smirnov N (1965) Tables of mathematical statistics. Fizmatigiz, MoscowGoogle Scholar
  10. Bommer J, Abrahamson N (2006) Why do modern probabilistic seismic-hazard analyses often lead to increased hazard estimates? Bull Seismol Soc Am 96(6):1967–1977CrossRefGoogle Scholar
  11. Bommer J, Abrahamson N, Strasser FO, Pecker A, Bard P, Bungum H, Cotton F, Fäh D, Sabetta F, Scherbaum F, Studer J (2004) The challenge of defining upper bounds on earthquake ground motions. Seismol Res Lett 75(1):82–95CrossRefGoogle Scholar
  12. Boore D, Joyner W (1982) The empirical prediction of ground motion. Bull Seismol Soc Am 72(6):S43–S60Google Scholar
  13. Campbell K (1981) Near source attenuation of peak horizontal acceleration. Bull Seismol Soc Am 71(6):2039–2070Google Scholar
  14. Cornell C (1968) Engineering seismic risk analysis. Bull Seismol Soc Am 58(5):1583–1606Google Scholar
  15. Cornell C (1971) Probabilistic analysis of damage to structures under seismic loads. In: Howells D, Haigh I, Taylor C (eds) Dynamic waves in civil engineering. Society for earthquake and civil engineering. Wiley, New York, pp 473–488Google Scholar
  16. Corradini M (2003) June 27 letter from Michael L. Corradini, Chairman, US Nuclear Waste Technical Review Board, to Margaret S. Y. Chu, Director, Office of Civilian Radioactive Waste Management, on the Boards reactions to presentations at the February 2003 joint meeting of the Panel on the Natural System and the Panel on the Engineered SystemGoogle Scholar
  17. Douglas J (2011) Ground-motion prediction equations 1964–2010. Final Rept. RP-59356-FR, Bureau de Recherches Géologiques et Minières (BRGM), Orléans, France, 444 pp. Available at http://peer.berkeley.edu/globalgmpe/wp-content/uploads/2011/03/douglas2011_RP-59356-FR.pdf
  18. Dupuis D, Flemming J (2006) Modelling peak accelerations from earthquakes. Earthq Eng Struct Dyn 35:969–987CrossRefGoogle Scholar
  19. Embrechts P, Klüppelberg C, Mikosch T (1997) Modelling extremal events for insurance and finance. Springer, BerlinCrossRefGoogle Scholar
  20. Hill B (1975) A simple and general approach to inference about the tail of a distribution. Ann Stat 3(5):1163–1174CrossRefGoogle Scholar
  21. Joyner W, Boore D (1981) Peak horizontal acceleration and velocity from strong-motion records including records from the 1979 Imperial Valley, California, earthquake. Bull Seismol Soc Am 71(6):2011–2038Google Scholar
  22. Kanno T, Narita A, Morikawa N, Fujiwara H, Fukushima Y (2006) A new attenuation relation for strong ground motion in Japan based on recorded data. Bull Seismol Soc Am 96(3):879–897CrossRefGoogle Scholar
  23. Kijko A (2008) Data driven probabilistic seismic hazard assessment procedure for regions with uncertain seismogenic zones. NATO Science Series: IV: Earth and Environmental Sciences 81:237–251CrossRefGoogle Scholar
  24. Kossobokov V, Nekrasova A (2011) Global seismic hazard assessment program (GSHAP) maps are misleading. Probl Eng Seismol 38(1):65–76 (in Russian)Google Scholar
  25. Kossobokov V, Nekrasova A (2012) Global seismic hazard assessment program maps are erroneous. Seism Instrum 48(2):162–170CrossRefGoogle Scholar
  26. Lemeshko B, Lemeshko S (2009) Distribution models for nonparametric tests for fit in verifying complicated hypotheses and maximum-likelihood estimators. Part 1. Meas Tech 52(6):555–565Google Scholar
  27. Massey F (1951) The Kolmogorov–Smirnov test for goodness of fit. J Am Stat Assoc 46(253):68–78CrossRefGoogle Scholar
  28. McGuire R (1976) Fortran program for seismic risk analysis. US Geological Survey, open-File Report, pp 76–67Google Scholar
  29. McGuire R (1978) FRISK: computer program for seismic risk analysis using faults as earthquake sources. US Geological Survey, open-File Report, pp 78–1007Google Scholar
  30. McGuire R (2008) Review. Probabilistic seismic hazard analysis: early history. Earthq Eng Struct Dyn 37:329–338CrossRefGoogle Scholar
  31. Pickands J (1975) Statistical inference using extreme order statistics. Ann Stat 3(1):119–131CrossRefGoogle Scholar
  32. Pictet O, Dacorogna M, Muller U (1998) Hill, bootstrap and jackknife estimators for heavy tails. In: Feldman RE, Taqqu MS, Adler RJ (eds) A practical guide to heavy tails, statistical techniques and applications. Birkhäuser, Boston, pp 283–310Google Scholar
  33. Pisarenko V, Rodkin M (2010) Heavy tailed distributions in disaster analysis. Springer, HeidelbergCrossRefGoogle Scholar
  34. Raschke M (2013) Statistical modeling of ground motion relations for seismic hazard analysis. J Seismol 17:1157–1182CrossRefGoogle Scholar
  35. Scherbaum F, Delavaud E, Riggelsen C (2009) Model selection in seismic hazard analysis: an information-theoretic perspective. Bull Seismol Soc Am 99(6):3234–3247CrossRefGoogle Scholar
  36. Shumilina L, Gusev A, Pavlov V (2000) An improved technique for determination of seismic hazard. J Earthq Predict Res 8:104–110Google Scholar
  37. Stamatakos J (2004) Review by the office of nuclear material safety and safeguards of the US Department of Energy’s responses to key technical issue agreements SDS.2.01 and SDS.2.02 for a potential Geologic Repository at Yucca Mountain, Nevada, Project No: WM-011. Center for Nuclear Waste Regulatory Analyses, San Antonio, Texas, prepared for US Nuclear Regulatory Commission Contract NRC-02-02-012, available at http://pbadupws.nrc.gov/docs/ML0428/ML042870242.pdf
  38. Strasser F, Bommer J, Abrahamson N (2004) The need for upper bounds on seismic ground motion. In: Proceedings of 13th world conference on earthquake engineering, Vancouver, B.C., Canada, paper No. 3361Google Scholar
  39. Wang Z (2011) Seismic hazard assessment: issues and alternatives. Pure Appl Geophys 168(1–2):11–25CrossRefGoogle Scholar
  40. Wyss M, Nekrasova A, Kossobokov V (2012) Errors in expected human losses due to incorrect seismic hazard estimates. Nat Hazards 62(3):927–935CrossRefGoogle Scholar
  41. Zhao J, Zhang J, Asano A, Ohno Y, Oouchi T, Takahashi T, Ogawa H, Irikura K, Thio H, Somerville P, Fukushima Y, Fukushima Y (2006) Attenuation relations of strong ground motion in Japan using site classification based on predominant period. Bull Seismol Soc Am 96(3):898–913CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.University of PretoriaPretoriaSouth Africa

Personalised recommendations