Bulletin of Earthquake Engineering

, Volume 17, Issue 3, pp 1099–1115 | Cite as

Uncertainty in intraevent spatial correlation of elastic pseudo-acceleration spectral ordinates

  • Pablo HeresiEmail author
  • Eduardo Miranda
Original Research


The probabilistic nature of seismic ground motion intensity measures such as peak ground acceleration and spectral acceleration ordinates has been extensively studied during the last decades. However, their spatial correlation is mostly considered without any event-to-event variability, using a mean estimate from a number of seismic events. The present study quantitatively evaluates the event-to-event uncertainty of intraevent spatial correlations, using 39 well-recorded earthquakes. Results indicate a high event-to-event variability in the correlation model parameters, which if taken explicitly into account, would improve regional hazard and risk analyses. Event magnitude was found to be a statistically significant predictor variable of the model parameter, however it explains less than 20% of the total event-to-event variability. Moreover, clustering of site conditions, tectonic region, and fault mechanism are not statistically significant as predictor variables of the spatial correlation model parameter. Finally, this paper proposes a simple Monte Carlo approach for considering the high event-to-event variability of spatial correlation models, taking advantage of the Markov dependence of residuals for reducing the number of correlated variables to be simulated. This approach can be used with different intraevent spatial correlation models, as long as proper estimates of the dispersion of their parameters are considered.


Spatial correlation Uncertainty Ground motion intensity measure Regional risk assessment 



The authors would like to acknowledge CONICYT—Becas Chile, the Nancy Grant Chamberlain Fellowship, the Charles H. Leavell Fellowship, the Shah Graduate Student Fellowship, and the John A. Blume Fellowship for their financial support to the first author for conducting his doctoral studies under the supervision of the second author. Records used in this investigation were obtained from the PEER NGA-West2 ground motion database. The authors are grateful to the various government agencies responsible for the installation and maintenance of seismic instrumentation and for making their data publicly available, and to PEER for collecting, processing, and distributing these records. The authors would also like to thank the two anonymous reviewers, whose comments helped improve the quality of this paper.


  1. Abrahamson NA (1988) Statistical properties of peak ground accelerations recorded by the SMART 1 array. Bull Seismol Soc Am 78:26–41Google Scholar
  2. Abrahamson NA, Silva WJ (2007) Abrahamson & Silva NGA ground motion relations for the geometric mean horizontal component of peak and spectral ground motion parameters. PEER Report Draft v2, Pacific Earthquake Engineering Research Center, Berkeley, CAGoogle Scholar
  3. Abrahamson NA, Silva WJ, Kamai R (2013) Update of the AS08 ground-motion prediction equations based on the NGA-West2 data set. PEER Report 2013-04, Pacific Earthquake Engineering Research Center, Berkeley, CAGoogle Scholar
  4. Ancheta TD, Darragh RB, Stewart JP, Seyhan E, Silva WJ, Chiou BS-J, Wooddell KE, Graves RW, Kottke AR, Boore DM, Kishida T, Donahue JL (2014) NGA-West2 database. Earthq Spectra 30:989–1005CrossRefGoogle Scholar
  5. Au SK, Beck JL (2003) Subset simulation and its application to seismic risk based on dynamic analysis. J Eng Mech 129:901–917CrossRefGoogle Scholar
  6. Baker JW, Cornell CA (2006) Correlation of response spectral values for multicomponent ground motions. Bull Seismol Soc Am 96:215–227CrossRefGoogle Scholar
  7. Baker JW, Jayaram N (2008) Correlation of spectral acceleration values from NGA ground motion models. Earthq Spectra 24:299–317CrossRefGoogle Scholar
  8. Blom G (1958) Statistical estimates and transformed beta-variables. Wiley, New YorkGoogle Scholar
  9. Boore DM, Gibbs JF, Joyner WB, Tinsley JC, Ponti DJ (2003) Estimated ground motion from the 1994 Northridge, California, earthquake at the site of interstate 10 and La Cienega Boulevard bridge collapse, West Los Angeles, California. Bull Seismol Soc Am 93:2737–2751CrossRefGoogle Scholar
  10. 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 30:1057–1085CrossRefGoogle Scholar
  11. Bozorgnia Y, Abrahamson NA, Al Atik L, 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 30:973–987CrossRefGoogle Scholar
  12. Cunnane C (1978) Unbiased plotting positions—A review. J Hydrol 37:205–222CrossRefGoogle Scholar
  13. Goda K (2011) Interevent variability of spatial correlation of peak ground motions and response spectra. Bull Seismol Soc Am 101:2522–2531CrossRefGoogle Scholar
  14. Goda K, Atkinson GM (2009) Probabilistic characterization of spatially correlated response spectra for earthquakes in Japan. Bull Seismol Soc Am 99:3003–3020CrossRefGoogle Scholar
  15. Goda K, Atkinson GM (2010) Intraevent spatial correlation of ground-motion parameters using SK-net data. Bull Seismol Soc Am 100:3055–3067CrossRefGoogle Scholar
  16. Goda K, Hong HP (2008) Spatial correlation of peak ground motions and response spectra. Bull Seismol Soc Am 98:354–365CrossRefGoogle Scholar
  17. Goovaerts P (1997) Geostatistics for natural resources evaluation. Oxford University Press, New York, p 483Google Scholar
  18. Hong HP, Zhang Y, Goda K (2009) Effect of spatial correlation on estimated ground-motion prediction equations. Bull Seismol Soc Am 99:928–934CrossRefGoogle Scholar
  19. Inoue T, Cornell CA (1990) Seismic hazard analysis of multi-degree-of-freedom structures. Reliability of marine structures. Report RMS-8, Stanford, CAGoogle Scholar
  20. Jayaram N, Baker JW (2008) Statistical tests of the joint distribution of spectral acceleration values. Bull Seismol Soc Am 98:2231–2243CrossRefGoogle Scholar
  21. Jayaram N, Baker JW (2009) Correlation model for spatially distributed ground-motion intensities. Earthq Eng Struct Dyn 38:1687–1708CrossRefGoogle Scholar
  22. Kawakami H, Mogi H (2003) Analyzing spatial intraevent variability of peak ground accelerations as a function of separation distance. Bull Seismol Soc Am 93:1079–1090CrossRefGoogle Scholar
  23. Lee R, Kiremidjian AS (2007) Uncertainty and correlation for loss assessment of spatially distributed systems. Earthq Spectra 23:753–770CrossRefGoogle Scholar
  24. Loth C, Baker JW (2013) A spatial cross-correlation model of spectral accelerations at multiple periods. Earthq Eng Struct Dyn 42:397–417CrossRefGoogle Scholar
  25. Massey FJ (1951) The Kolmogorov-Smirnov test for goodness of fit. J Am Stat Assoc 46:68–78CrossRefGoogle Scholar
  26. Park J, Bazzurro P, Baker JW (2007) Modeling spatial correlation of ground motion intensity measures for regional seismic hazard and portfolio loss estimation. In: 10th international conference applications of statistics and probability in civil engineering. July 31-August 3, 2007, Tokyo, JapanGoogle Scholar
  27. Rubinstein RY (1981) Simulation and the Monte-Carlo method. Wiley, New YorkCrossRefGoogle Scholar
  28. Sokolov V, Wenzel F (2011) Influence of ground-motion correlation on probabilistic assessments of seismic hazard and loss: sensitivity analysis. Bull Earthq Eng 9:1339–1360CrossRefGoogle Scholar
  29. Sokolov V, Wenzel F (2013a) Further analysis of the influence of site conditions and earthquake magnitude on ground-motion within-earthquake correlation: analysis of PGA and PGV data from the K-NET and the KiK-net (Japan) networks. Bull Earthq Eng 11:1909–1926CrossRefGoogle Scholar
  30. Sokolov V, Wenzel F (2013b) Spatial correlation of ground motions in estimating seismic hazards to civil infrastructure. In: Tesfamariam S, Goda K (eds) Handbook of seismic risk analysis and management of civil infrastructure systems. Woodhead Publishing Limited, Cambridge, pp 57–78CrossRefGoogle Scholar
  31. Sokolov V, Wenzel F, Wen KL, Jean WY (2012) On the influence of site conditions and earthquake magnitude on ground-motion within-earthquake correlation: analysis of PGA data from TSMIP (Taiwan) network. Bull Earthq Eng 10:1401–1429CrossRefGoogle Scholar
  32. Wang M, Takada T (2005) Macrospatial correlation model of seismic ground motions. Earthq Spectra 21:1137–1156CrossRefGoogle Scholar
  33. Wesson RL, Perkins DM (2001) Spatial correlation of probabilistic earthquake ground motion and loss. Bull Seismol Soc Am 91:1498–1515CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.John A. Blume Earthquake Engineering Center, Department of Civil and Environmental EngineeringStanford UniversityStanfordUSA

Personalised recommendations