Advertisement

Bulletin of Earthquake Engineering

, Volume 14, Issue 10, pp 2629–2642 | Cite as

A partially non-ergodic ground-motion prediction equation for Europe and the Middle East

  • Nicolas M. Kuehn
  • Frank Scherbaum
Original Research Paper

Abstract

A partially non-ergodic ground-motion prediction equation is estimated for Europe and the Middle East. Therefore, a hierarchical model is presented that accounts for regional differences. For this purpose, the scaling of ground-motion intensity measures is assumed to be similar, but not identical in different regions. This is achieved by assuming a hierarchical model, where some coefficients are treated as random variables which are sampled from an underlying global distribution. The coefficients are estimated by Bayesian inference. This allows one to estimate the epistemic uncertainty in the coefficients, and consequently in model predictions, in a rigorous way. The model is estimated based on peak ground acceleration data from nine different European/Middle Eastern regions. There are large differences in the amount of earthquakes and records in the different regions. However, due to the hierarchical nature of the model, regions with only few data points borrow strength from other regions with more data. This makes it possible to estimate a separate set of coefficients for all regions. Different regionalized models are compared, for which different coefficients are assumed to be regionally dependent. Results show that regionalizing the coefficients for magnitude and distance scaling leads to better performance of the models. The models for all regions are physically sound, even if only very few earthquakes comprise one region.

Keywords

Ground-motion prediction equation Non-ergodic PSHA Hierarchical model 

Notes

Acknowledgments

We would like to thank Norm Abrahamson, Christine Goulet and Justin Hollenback for discussions on the topic of regionally vaying GMPEs. We would also like to thank the reviewers Sinan Akkar and John Douglas for their comments, which helped to improve the manuscript. Support from the Pacific Earthquake Engineering Research Center is gratefully acknowledged.

Supplementary material

10518_2016_9911_MOESM1_ESM.xls (23 kb)
Supplementary material 1 (XLS 23 kb)
10518_2016_9911_MOESM2_ESM.stan (4 kb)
Supplementary material 2 (STAN 5 kb)

References

  1. Abrahamson NA, Silva WJ, Kamai R (2014) Summary of the ASK14 ground motion relation for active crustal regions. Earthq Spectra 30(3):1025–1055. doi: 10.1193/070913EQS198M CrossRefGoogle Scholar
  2. Akaike H (1973) Information theory and an extension of the maximum likelihood principle. In: Petrov BN, Csaki F (eds) Proceedings of the second international symposium on information theory. Akademiai Kiado, Budapest, pp 267–281. Reprinted in: Kotz S (ed) (1992) Breakthroughs in statistics. Springer, New York, pp 610–624Google Scholar
  3. Akkar S, Bommer JJ (2010) Empirical equations for the prediction of PGA, PGV, and spectral accelerations in Europe, the Mediterranean Region, and the Middle East. Seismol Res Lett 81(2):195–206. doi: 10.1785/gssrl.81.2.195 CrossRefGoogle Scholar
  4. Akkar S, Cagnan Z (2010) A local ground-motion predictive model for Turkey, and its comparison with other regional and global ground-motion models. Bull Seismol Soc Am 100(6):2978–2995. doi: 10.1785/0120090367 CrossRefGoogle Scholar
  5. Akkar S, Sandikkaya MA, Bommer JJ (2014a) Empirical ground-motion models for point- and extended-source crustal earthquake scenarios in Europe and the Middle East. Bull Earthq Eng 12(1):359–387. doi: 10.1007/s10518-013-9461-4 CrossRefGoogle Scholar
  6. Akkar S, Sandikkaya MA, Şenyurt M, Azari Sisi A, Ay BÖ, Traversa P, Douglas J, Cotton F, Luzi L, Hernandez B, Godey S (2014b) Reference database for seismic ground-motion in Europe (resource). Bull Earthq Eng 12(1):311–339. doi: 10.1007/s10518-013-9506-8 CrossRefGoogle Scholar
  7. Al-Atik L, Abrahamson N, Bommer JJ, Scherbaum F, Cotton F, Kuehn N (2010) The variability of ground-motion prediction models and its components. Seismol Res Lett 81(5):794–801. doi: 10.1785/gssrl.81.5.794 CrossRefGoogle Scholar
  8. Ambraseys NN, Douglas J, Sarma SK, Smit PM (2005) Equations for the estimation of strong ground motions from shallow crustal earthquakes using data from Europe and the Middle East: horizontal peak ground acceleration and spectral acceleration. Bull Earthq Eng 3(1):1–53. doi: 10.1007/s10518-005-0183-0 CrossRefGoogle Scholar
  9. Anderson JG, Brune JN (1999) Probabilistic seismic hazard analysis without the ergodic assumption. Seismol Res Lett 70(1):19–28CrossRefGoogle Scholar
  10. Atkinson GM, Morrison M (2009) Observations on regional variability in ground-motion amplitudes for small-to-moderate earthquakes in North America. Bull Seismol Soc Am 99(4):2393–2409. doi: 10.1785/0120080223 CrossRefGoogle Scholar
  11. Bindi D, Pacor F, Luzi L, Puglia R, Massa M, Ameri G, Paolucci R (2011) Ground motion prediction equations derived from the Italian strong motion database. Bull Earthq Eng 9(6):1899–1920. doi: 10.1007/s10518-011-9313-z CrossRefGoogle Scholar
  12. Bindi D, Massa M, Luzi L, Ameri G, Pacor F, Puglia R, Augliera P (2014) Pan-European ground-motion prediction equations for the average horizontal component of PGA, PGV, and 5 %-damped PSA at spectral periods up to 3.0 s using the RESORCE dataset. Bull Earthq Eng 12(1):391–430. doi: 10.1007/s10518-013-9525-5
  13. Bommer JJ, Abrahamson NA (2006) Why do modern probabilisitc seismic hazard analyses often lead to increased hazard estimates? Bull Seismol Soc Am 96(6):1967–1977CrossRefGoogle Scholar
  14. Boore DM, Stewart JP, Seyhan E, Atkinson GM (2014) NGA-West2 equations for predicting PGA, PGV, and 5% damped PSA for shallow crustal earthquakes. Earthq Spectra 30(3):1057–1085. doi: 10.1193/070113EQS184M CrossRefGoogle Scholar
  15. Bora SS, Scherbaum F, Kuehn N, Stafford P (2014) Fourier spectral- and duration models for the generation of response spectra adjustable to different source-, propagation-, and site conditions. Bull Earthq Eng 12(1):467–493. doi: 10.1007/s10518-013-9482-z CrossRefGoogle Scholar
  16. Bozorgnia Y, Abrahamson NA, Atik LA, Ancheta TD, Atkinson GM, Baker JW, Baltay A, Boore DM, Campbell KW, Chiou BSJ, Darragh R, Day S, Donahue J, Graves RW, Gregor N, Hanks T, Idriss IM, Kamai R, Kishida T, Kottke A, Mahin SA, Rezaeian S, Rowshandel B, Seyhan E, Shahi S, Shantz T, Silva W, Spudich P, Stewart JP, Watson-Lamprey J, Wooddell K, Youngs R (2014) NGA-West2 Research Project. Earthq Spectra 30(3):973–987. doi: 10.1193/072113EQS209M CrossRefGoogle Scholar
  17. Bragato PL, Slejko D (2005) Empirical ground-motion attenuation relations for the eastern Alps in the magnitude range 2.5–6.3. Bull Seismol Soc Am 95(1):252–276. doi: 10.1785/0120030231 CrossRefGoogle Scholar
  18. Campbell KW, Bozorgnia Y (2014) NGA-West2 ground motion model for the average horizontal components of PGA, PGV, and 5% damped linear acceleration response spectra. Earthq Spectra 30(3):1087–1115. doi: 10.1193/062913EQS175M CrossRefGoogle Scholar
  19. Chiou BSJ, Youngs RR (2014) Update of the Chiou and Youngs NGA model for the average horizontal component of peak ground motion and response spectra. Earthq Spectra 30(3):1117–1153. doi: 10.1193/072813EQS219M CrossRefGoogle Scholar
  20. Chiou B, Youngs R, Abrahamson N, Addo K (2010) Ground-motion attenuation model for small-to-moderate shallow crustal earthquakes in California and its implications on regionalization of ground-motion prediction models. Earthq Spectra 26(4):907. doi: 10.1193/1.3479930 CrossRefGoogle Scholar
  21. Danciu L, Tselentis GA (2007) Engineering ground-motion parameters attenuation relationships for Greece. Bull Seismol Soc Am 97(1):162–183. doi: 10.1785/0120040087 CrossRefGoogle Scholar
  22. Delavaud E, Cotton F, Akkar S, Scherbaum F, Danciu L, Beauval C, Drouet S, Douglas J, Basili R, Sandikkaya MA, Segou M, Faccioli E, Theodoulidis N (2012) Toward a ground-motion logic tree for probabilistic seismic hazard assessment in Europe. J Seismol 16(3):451–473.  10.1007/s10950-012-9281-z
  23. Derras B, Bard PY, Cotton F (2014) Towards fully data driven ground-motion prediction models for Europe. Bull Earthq Eng 12(1):495–516. doi: 10.1007/s10518-013-9481-0 CrossRefGoogle Scholar
  24. Douglas J (2007) On the regional dependence of earthquake response spectra. ISET J Earthq Technol 44(1):71–99Google Scholar
  25. Douglas J, Akkar S, Ameri G, Bard PY, Bindi D, Bommer JJ, Bora SS, Cotton F, Derras B, Hermkes M, Kuehn NM, Luzi L, Massa M, Pacor F, Riggelsen C, Sandikkaya MA, Scherbaum F, Stafford PJ, Traversa P (2014) Comparisons among the five ground-motion models developed using RESORCE for the prediction of response spectral accelerations due to earthquakes in Europe and the Middle East. Bull Earthq Eng 12(1):341–358. doi: 10.1007/s10518-013-9522-8 CrossRefGoogle Scholar
  26. Gelman A (2006) Prior distributions for variance parameters in hierarchical models. Bayesian Anal 3:515–533Google Scholar
  27. Gelman A, Hill J (2006) Data analysis using regression and multilevel/hierarchical models. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  28. Gelman A, Rubin D (1992) Inference from iterative simulation using multiple sequences. Stat Sci 7:457–511CrossRefGoogle Scholar
  29. Gelman A, Hwang J, Vehtari A (2013) Understanding predictive information criteria for Bayesian models. Stat Comput 24(6):997–1016. doi: 10.1007/s11222-013-9416-2 CrossRefGoogle Scholar
  30. Gianniotis N, Kuehn N, Scherbaum F (2014) Manifold aligned ground motion prediction equations for regional datasets. Comput Geosci 69:72–77. doi: 10.1016/j.cageo.2014.04.014 CrossRefGoogle Scholar
  31. Hermkes M, Kuehn NM, Riggelsen C (2014) Simultaneous quantification of epistemic and aleatory uncertainty in GMPEs using Gaussian process regression. Bull Earthq Eng 12(1):449–466. doi: 10.1007/s10518-013-9507-7 CrossRefGoogle Scholar
  32. Kuehn NM, Abrahamson NA (2015) Non-ergodic seismic hazard: using Bayesian updating for site-specific and path-specific effects for ground-motion models. In: CSNI workshop on “testing PSHA results and benefit of bayesian techniques for seismic hazard assessment”, pp 84–98Google Scholar
  33. Kuehn NM, Scherbaum F (2015) Ground-motion prediction model building: a multilevel approach. Bull Earthq Eng 13(9):2481–2491. doi: 10.1007/s10518-015-9732-3 CrossRefGoogle Scholar
  34. Sammon JW (1969) A nonlinear mapping for data structure analysis. IEEE Trans Comput 5:401–409CrossRefGoogle Scholar
  35. Scherbaum F, Kuehn NM, Ohrnberger M, Koehler A (2010) Exploring the proximity of ground-motion models using high-dimensional visualization techniques. Earthq Spectra 26(4):1117–1138. doi: 10.1193/1.3478697 CrossRefGoogle Scholar
  36. Spiegelhalter D, Rice K (2009) Bayesian statistics. Scholarpedia 4(8):5230.  10.4249/scholarpedia.5230 (Revision #91036)
  37. Stafford PJ (2014) Crossed and nested mixed-effects approaches for enhanced model development and removal of the ergodic assumption in empirical ground-motion models. Bull Seismol Soc Am 104(2):702–719. doi: 10.1785/0120130145 CrossRefGoogle Scholar
  38. Stan Development Team (2015): Stan: A c++ library for probability and sampling, version 2.5.0. URL http://mc-stan.org
  39. Stan Development Team (2015a) Stan modeling language users guide and reference manual, version 2.5.0Google Scholar
  40. Vehtari A, Gelman A (2014) Waic and cross-validation in Stan (May), 1–15. http://www.stat.columbia.edu/gelman/research/unpublished/waic_stan.pdf
  41. Vehtari A, Gelman A, Gabry J (2015) Efficient implementation of leave-one-out cross-validation and WAIC for evaluating fitted Bayesian models. http://arxiv.org/abs/1507.04544
  42. Watanabe S (2010) Asymptotic equivalence of Bayes cross validation and widely applicable information criterion in singular learning theory. J Mach Learn Res 11:3571–3594Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Pacific Earthquake Engineering Research CenterUniversity of California, BerkeleyBerkeleyUSA
  2. 2.Institute of Earth and Environmental SciencesUniversity of PotsdamPotsdamGermany

Personalised recommendations