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


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.


Ground-motion prediction equation Non-ergodic PSHA Hierarchical model 



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)


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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

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