Abstract
A Bayesian ground-motion model is presented that directly estimates the coefficients of the model and the correlation between different ground-motion parameters of interest. The model is developed as a multi-level model with levels for earthquake, station and record terms. This separation allows to estimate residuals for each level and thus the estimation of the associated aleatory variability. In particular, the usually estimated within-event variability is split into a between-station and between-record variability. In addition, the covariance structure between different ground-motion parameters of interest is estimated for each level, i.e. directly the between-event, between-station and between-record correlation coefficients are available. All parameters of the model are estimated via Bayesian inference, which allows to assess their epistemic uncertainty in a principled way. The model is developed using a recently compiled European strong-motion database. The target variables are peak ground velocity, peak ground acceleration and spectral acceleration at eight oscillator periods. The model performs well with respect to its residuals, and is similar to other ground-motion models using the same underlying database. The correlation coefficients are similar to those estimated for other parts of the world, with nearby periods having a high correlation. The between-station, between-event and between-record correlations follow generally a similar trend.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
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
Akkar S, Sandıkkaya MA, Bommer JJ (2014) 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
Akkar S, Sandıkkaya MA, Şenyurt M, Sisi AA, Ay BÖ, Traversa P, Douglas J, Cotton F, Luzi L, Hernandez B, Godey S (2014) Reference database for seismic ground-motion in Europe (RESORCE). Bull Earthq Eng 12(1):311–339
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
Arroyo D, Ordaz M (2010) Multivariate Bayesian regression analysis applied to ground-motion prediction equations, part 1: theory and synthetic example. Bull Seismol Soc Am 100(4):1551–1567
Arroyo D, Ordaz M (2010) Multivariate bayesian regression analysis applied to ground-motion prediction equations, part 2: numerical example with actual data. Bull Seismol Soc Am 100(4):1568–1577
Atkinson GM (2006) Single-station sigma. Bull Seismol Soc Am 96(2):446–455
Baker JW, Cornell CA (2006) Correlation of response spectral values for multicomponent ground motions. Bull Seismol Soc Am 96(1):215–227
Baker JW, Jayaram N (2008) Correlation of spectral acceleration values from NGA ground motion models. Earthq Spectra 24(1):299–317
Baker JW (2011) Conditional mean spectrum: tool for ground-motion selection. J Struct Eng 137(3):322–331
Baker JW, Cornell CA (2006) Spectral shape, epsilon and record selection. Earthq Eng Struct Dyn 35(9):1077–1095
Bazzurro P, Cornell CA (2002) Vector-valued probabilistic seismic hazard analysis (VPSHA). In Proceedings of the 7th US national conference on earthquake engineering
Bommer JJ, Abrahamson NA (2006) Why do modern probabilistic seismic-hazard analyses often lead to increased hazard estimates? Bull Seismol Soc Am 96(6):1967–1977
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
Bradley BA (2011) Empirical correlation of PGA, spectral accelerations and spectrum intensities from active shallow crustal earthquakes. Earthq Eng Struct Dyn 40(15):1707–1721
Bradley BA (2012) Empirical correlations between peak ground velocity and spectrum-based intensity measures. Earthq Spectra 28(1):17–35
Chen L, Faccioli E (2013) Single-station standard deviation analysis of 2010–2012 strong-motion data from the Canterbury region, New Zealand. Bull Earthq Eng 11(5):1617–1632
Cimellaro GP (2013) Correlation in spectral accelerations for earthquakes in Europe. Earthq Eng Struct Dyn 42(4):623–633
Douglas J (2003) Ground motion estimation equations 1964–2003. Technical Report 01, BRGM
Douglas J (2006) Errata of and additions to ground motion estimation equations 1964–2003. Technical Report December, BRGM
Douglas J (2008) Further errata of and additions to ground motion estimation equations 1964–2003. Technical Report December, BRGM
Douglas J, Akkar S, Ameri G, Bard P-Y, Bindi D, Bommer JJ, Bora SS, Cotton F, Derras B, Hermkes M, Kuehn NM, Luzi L, Massa M, Pacor F, Riggelsen C, Sandıkkaya 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
Gelman A, Hill J (2006) Data analysis using regression and multilevel/hierarchical models. Cambridge University Press, Cambridge
Gelman A, Rubin DB (1992) Inference from iterative simulation using multiple sequences. Stat Sci 7:457–511
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
Rodriguez-Marek A, Montalva GA, Cotton F, Bonilla F (2011) Analysis of single-station standard deviation using the KiK-net data. Bull Seismol Soc Am 101(3):1242–1258
Spiegelhalter D, Rice K (2009) Bayesian statistics. Scholarpedia 4(8):5230 (revision #91036)
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
Stan Development Team (2014) Stan: a c++ library for probability and sampling, version 2.2
Toro GR (2006) The effects of ground-motion uncertainty on seismic hazard results: examples and approximate results. In: SSA Annual Meeting
Acknowledgments
We would like to thank Carsten Riggelsen for fruitful discussions about the modeling procedure. We would also like to thank two reviewers for their comments on the manuscript.
Author information
Authors and Affiliations
Corresponding author
Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Kuehn, N.M., Scherbaum, F. Ground-motion prediction model building: a multilevel approach. Bull Earthquake Eng 13, 2481–2491 (2015). https://doi.org/10.1007/s10518-015-9732-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10518-015-9732-3