Skip to main content
SpringerLink
Log in

A review of stochastic earthquake ground motion prediction equations for stable regions

  • Published:
International Journal of Advances in Engineering Sciences and Applied Mathematics Aims and scope Submit manuscript

Abstract

Ground motion prediction equations (GMPEs), which give estimates of ground motion parameters for any given earthquake scenario expressed in terms of magnitude, distance and site class, have been an essential element in probabilistic seismic hazard assessment for development of seismic hazard maps. Traditionally, most designers of built infrastructure do not become involved directly with their use although seismic hazard maps are being used in the design of structures. In pursuing site-specific seismic design of a civil engineering structure, it is necessary of engineers to make direct use of GMPEs to construct the conditional mean spectra, as this forms part of the advanced design process. This article is written for engineers who have interests in going for site-specific seismic design in a stable (low-to-moderate seismicity) tectonic environment including countries like Australia, most part of India, Malaysia and Western Europe. The development of stochastic GMPEs in a stable region involves seismological modelling and stochastic simulations (leading to the development of stochastic GMPEs) which have been evolving for almost half a century. This article aims at presenting the state-of-art review for this specialised field of technology. The targeted readers are engineers who have no prior knowledge in engineering seismology. Summarising decades long of research and development in one article serves the purpose of facilitating the uptake of GMPEs and site-specific seismic design by engineering practitioners. Thus, many seismological phenomena are explained in engineering terms. This review article should also be beneficial to researchers who are engaged into investigation into the seismic performance of structures.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. Cornell, C.A.: Engineering seismic risk analysis. Bull. Seismol. Soc. Am. 58(5), 1583–1606 (1968)

    Article  Google Scholar 

  2. McGuire, R. K. (1976). FORTRAN computer program for seismic risk analysis. Open File Report 76–67. United States Geological Survey Organisation.

  3. McGuire, R. K. (2004). Seismic hazard and risk analysis. Earthquake engineering research institute.

  4. Kijko, A., Graham, G.: Parametric-historic procedure for probabilistic seismic hazard analysis. Part II: assessment of seismic hazard at specified site. Pure Appl. Geophys. 154(1), 1–22 (1999)

    Article  Google Scholar 

  5. Tsang, H.H., Chandler, A.M.: Site-specific probabilistic seismic-hazard assessment: direct amplitude-based approach. Bull. Seismol. Soc. Am. 96(2), 392–403 (2006)

    Article  Google Scholar 

  6. Standards Australia (2018), AS1170. 4-2007 (R2018)- Structural design actions, Part 4: earthquake actions in Australia (incorporating amendments), Standards Australia, Sydney, NSW.

  7. ASCE. (2013). Minimum design loads for buildings and other structures (ASCE/SEI 7-10). American Society of Civil Engineers.

  8. Frankel, A, Mueller, C., Barnhard, T., Perkins, D., Leyendecker, E.V., Dickman, N, Hanson, S. and Hopper, M. (1996) National seismic hazard maps; documentation, Open-file report 96–532, United States Geological Survey.

  9. Baker, J.W.: Conditional mean spectrum: tool for ground-motion selection. J. Struct. Eng. 137(3), 322–331 (2011)

    Article  Google Scholar 

  10. Baker, J.W., Cornell, C.: Spectral shape, epsilon and record selection. Earthq. Eng. Struct. Dynam. 35(9), 1077–1095 (2006)

    Article  Google Scholar 

  11. Hu, Y., Lam, N.T.K., Menegon, S.J., Wilson, J.L.: The selection and scaling of ground motion accelerograms for use in stable continental regions. J. Earthq. Eng. (2021). https://doi.org/10.1080/13632469.2021.1913456

    Article  Google Scholar 

  12. Brune, J.N.: Tectonic stress and the spectra of seismic shear waves from earthquakes. J. Geophys. Res. 75(26), 4997–5009 (1970)

    Article  Google Scholar 

  13. Atkinson, G.M., Boore, D.M.: Ground-motion relations for eastern North America. Bull. Seismol. Soc. Am. 85(1), 17–30 (1995)

    Article  Google Scholar 

  14. Atkinson, G.M., Boore, D.M.: Evaluation of models for earthquake source spectra in Eastern North America. Bull. Seismol. Soc. Am. 88(4), 917–934 (1998)

    Article  Google Scholar 

  15. Boore, D.M.: Stochastic simulation of high-frequency ground motions based on seismological models of the radiated spectra. Bull. Seismol. Soc. Am. 73(6A), 1865–1894 (1983)

    Google Scholar 

  16. Hanks, T.C., McGuire, R.K.: The character of high-frequency strong ground motion. Bull. Seismol. Soc. Am. 71(6), 2071–2095 (1981)

    Article  Google Scholar 

  17. Atkinson, G.M., Boore, D.M.: Earthquake ground-motion prediction equations for eastern North America. Bull. Seismol. Soc. Am. 96(6), 2181–2205 (2006)

    Article  Google Scholar 

  18. Lam, N., Wilson, J., Chandler, A., Hutchinson, G.: Response spectral relationships for rock sites derived from the component attenuation model. Earthq. Eng. Struct. Dynam. 29(10), 1457–1489 (2000)

    Article  Google Scholar 

  19. Tang, Y., Lam, N., Tsang, H.-H., Lumantarna, E.: An adaptive ground motion prediction equation for use in low-to-moderate seismicity regions. J. Earthq. Eng. 26(5), 2567–2598 (2020)

    Article  Google Scholar 

  20. Geoscience Australia (2022), accessed 22 June 2022, <https://www.ga.gov.au>

  21. Hoult, R., Allen, T., Borleis, E., Peck, W., Amirsardari, A.: Source and attenuation properties of the 2012 Moe, southeastern Australia, earthquake sequence. Seismol. Res. Lett. 92(2A), 1112–1128 (2021)

    Article  Google Scholar 

  22. Hoult, R., Pascale, A., Jones, A. & Allen, T.(2021b) The Mw 5.9 Woods point earthquake: a preliminary investigation of the ground motion observations, Proceedings of the Australian Earthquake Engineering Society Virtual Conference, 25–26 November.

  23. Douglas, J. (2022) Ground motion prediction equations 1964–2021. The Compendium PDF can be accessed via weblink: http://www.gmpe.org.uk

  24. Boore, D.M., Di Alessandro, C., Abrahamson, N.A.: A generalization of the double-corner-frequency source spectral model and its use in the SCEC BBP validation exercise. Bull. Seismol. Soc. Am. 104(5), 2387–2398 (2014)

    Article  Google Scholar 

  25. Chiou, B., Youngs, R.R.: 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 (2014)

    Article  Google Scholar 

  26. Gaull, B., Michael-Leiba, M., Rynn, J.: Probabilistic earthquake risk maps of Australia. Aust. J. Earth Sci. 37(2), 169–187 (1990)

    Article  Google Scholar 

  27. Chandler, A.M., Lam, N.T.K.: Intensity attenuation relationship for the south china region and comparison with the component attenuation model. J. Asian Earth Sci. 20, 775–790 (2002)

    Article  Google Scholar 

  28. Newmark, N.M., Rosenblueth, E.: Fundamentals of earthquake engineering. Prentice Hall, New Jersey, USA (1971)

    Google Scholar 

  29. Standards Australia (2007), AS1170. 4-2007 Structural design actions, part 4: earthquake actions in Australia, Standards Australia, Sydney, NSW.

  30. Lam, N.T.K., Sinadinovski, C., Koo, R., Wilson, J.L.: Peak ground velocity modelling of Australian intraplate earthquakes. J. Seismol. Earthq. Eng. 5, 11–21 (2003)

    Google Scholar 

  31. Yaghmaei-Sabegh, S., Tsang, H.H., Lam, N.T.K.: Conversion between peak ground motion parameters and modified mercalli intensity values. J. Earthq. Eng. 15, 1138–1155 (2011)

    Article  Google Scholar 

  32. Atkinson, G.M., Kaka, S.I.: Relationship between felt intensity and instrumental ground motion in the Central United States and California. Bull. Seismol. Soc. Am. 97, 497–510 (2007)

    Article  Google Scholar 

  33. Lam, N.T.K., Wilson, J.L., Hutchinson, G.L.: Generation of synthetic earthquake accelerograms using seismological modelling: a review. J. Earthq. Eng. 4(3), 321–354 (2000)

    Article  Google Scholar 

  34. Atkinson, G.M.: Ground-motion prediction equations for eastern North America from a referenced empirical approach: Implications for epistemic uncertainty. Bull. Seismol. Soc. Am. 98(3), 1304–1318 (2008)

    Article  Google Scholar 

  35. Boore, D.M. (2015) Point-source stochastic-method simulations of ground motions for the PEER NGA-East project. Chapter 2 in PEER Rept. No. 2015/04. Pacific Earthquake Engineering Research Center, University of California, Berkeley, California.

  36. Atkinson, G.M.: Earthquake source spectra in Eastern North America. Bull. Seismol. Soc. Am. 83(6), 1778–1798 (1993)

    Google Scholar 

  37. Atkinson, G.M., Silva, W.: Stochastic modeling of California ground motions. Bull. Seismol. Soc. Am. 90(2), 255–274 (2000)

    Article  Google Scholar 

  38. Boore, D.M., Atkinson, G.M.: Source spectra for the 1988 Saguenay, Quebec earthquakes. Bull. Seismol. Soc. Am. 82(2), 683–719 (1992)

    Google Scholar 

  39. Boore, D.M., Alessandro, C., Abrahamson, N.A.: A generalisation of the double - corner - frequency source spectral model and its use in the SCEC BBP validation exercise. Bull. Seismol. Soc. Am. 104(5), 2387–2398 (2014)

    Article  Google Scholar 

  40. Boore, D.M.: Short note: determining generic velocity and density models for crustal amplification, with an update of the Boore & Joyner (1997) Generic site amplification for Vs (Z) = 760 m/s. Bull. Seismol. Soc. Am. 106(1), 316–320 (2016)

    Article  Google Scholar 

  41. Yenier, E., Atkinson, G.M.: Equivalent point-source modelling of moderate-to-large magnitude earthquakes and associated ground-motion saturation effects. Bull. Seismol. Soc. Am. 104(3), 1458–1478 (2014)

    Article  Google Scholar 

  42. Mahani, A.B., Atkinson, G.M.: Evaluation of the functional forms for the attenuation of small-to-moderate earthquake response spectral amplitudes in North America. Bull. Seismol. Soc. Am. 102(6), 2714–2726 (2012)

    Article  Google Scholar 

  43. Boore, D.M.: Comparing stochastic point-source and finite-source modelling ground motion simulations: SIMSM and EXSIM. Bull. Seismol. Soc. Am. 99(6), 3202–3216 (2009)

    Article  Google Scholar 

  44. Motazeian, D., Atkinson, G.M.: Stochastic finite-fault modelling based on a dynamic corner frequency. Bull. Seismol. Soc. Am. 95(3), 995–1010 (2005)

    Article  Google Scholar 

  45. Atkinson, G.M., Mereu, R.F.: The shape of ground motion attenuation curves in southeastern Canada. Bull. Seismol. Soc. Am. 82(5), 2014–2031 (1992)

    Article  Google Scholar 

  46. Wilkie, J., Gibson, G.: Estimation of seismic quality factor Q for Victoria, Australia. AGSO J. Geol. Geophys. 15(4), 511–517 (1995)

    Google Scholar 

  47. Abercrombie, R.: Near-surface attenuation and site effects from comparison and surface and deep borehole recordings. Bull. Seismol. Soc. Am. 87(3), 731–744 (1997)

    Google Scholar 

  48. Boore, D.M., Joyner, W.B.: Site amplifications for generic rock sites. Bull. Seismol. Soc. Am. 87(2), 327–341 (1997)

    Article  Google Scholar 

  49. Boore, D.M.: The uses and limitations of the square-root-impedance method for computing site amplification. Bull. Seismol. Soc. Am. 103(4), 2356–2368 (2013)

    Article  Google Scholar 

  50. Chandler, A.M., Lam, N.T.K., Tsang, H.H.: Near-surface attenuation modelling based on rock shear-wave velocity profile. Soil Dyn. Earthq. Eng. 26, 1004–1014 (2006)

    Article  Google Scholar 

  51. Drouet, S., Cotton, F., Guéguen, P.: VS30, κ, regional attenuation and MW from accelerograms: application to magnitude 3–5 French earthquakes. Geophys. J. Int. 182(2), 880–898 (2010)

    Article  Google Scholar 

  52. Edwards, B., Fäh, D., Giardini, D.: Attenuation of seismic shear wave energy in Switzerland. Geophys. J. Int. 185(2), 967–984 (2011)

    Article  Google Scholar 

  53. Silva, W., N. N. Gregor, and R. B. Darragh (2002) Development of regional hard rock attenuation relations for Central and Eastern North America, Report to Pacific Engineering and Analysis. El Cerrito, CA, USA

  54. Van, H.C., Drouet, S., Cotton, F.: Analysis of the origins of (Kappa) to compute hard rock to rock adjustment factors for GMPEs. Bull. Seismol. Soc. Am. 101(6), 2926–2941 (2011)

    Article  Google Scholar 

  55. Chandler, A.M., Lam, N.T.K., Tsang, H.H.: Shear wave velocity modelling in crustal rock for seismic hazard analysis. Soil Dyn. Earthq. Eng. 25(2), 167–185 (2005)

    Article  Google Scholar 

  56. Tang, Y., Lam, N., Tsang, H.-H., Lumantarna, E.: Use of macroseismic intensity data to validate a regionally adjustable ground motion prediction model. Geosciences 9(10), 422–444 (2019)

    Article  Google Scholar 

  57. Brocher, T.M.: Empirical relations between elastic wavespeeds and density in the earth’s crust. Bull. Seismol. Soc. Am. 95(6), 2081–2092 (2005)

    Article  Google Scholar 

  58. Allen, T., Griffin, J.D., Leonard, M., Clark, D.J., Ghasemi, H.: The 2018 national seismic hazard assessment of Australia: quantifying hazard changes and model uncertainties. Earthq. Spectra 36(S1), 5–43 (2020)

    Article  Google Scholar 

  59. Tang, Y., Lam, N., Tsang, H.H.: A computational tool for ground-motion simulations incorporating regional crustal conditions. Seismol. Res. Lett. 92(2A), 1129–1140 (2021)

    Article  Google Scholar 

  60. Pezeshk, S., Zandieh, A., Tavakoli, B.: Hybrid empirical ground-motion prediction equations for eastern North America using NGA models and updated seismological parameters. Bull. Seismol. Soc. Am. 101(4), 1859–1870 (2011)

    Article  Google Scholar 

  61. Shahjouei, A., & Pezeshk, S. (2015). Hybrid empirical ground‐motion model for central and eastern North America using hybrid broadband simulations and NGAWest2 GMPEs. NGA-East: Median Ground-Motion Models for the Central and Eastern North America Region, PEER Report Number 2015, 4.

  62. Campbell, K.W.: Prediction of strong ground motion using the hybrid empirical method and its use in the development of ground-motion (attenuation) relations in eastern North America. Bull. Seismol. Soc. Am. 93(3), 1012–1033 (2003)

    Article  Google Scholar 

  63. Atkinson, G.M., Boore, D.M.: Modifications to existing ground-motion prediction equations in light of new data. Bull. Seismol. Soc. Am. 101, 1121–1135 (2011)

    Article  Google Scholar 

  64. Atkinson, G.M., Motazedian, D.: Ground-motion amplitudes for earthquakes in Puerto Rico. Bull. Seismol. Soc. Am. 103(3), 1846–1859 (2013)

    Article  Google Scholar 

  65. Hassani, B., Atkinson, G.M.: Referenced empirical ground-motion model for Eastern North America. Seismol. Res. Lett. 86(2A), 477–491 (2015)

    Google Scholar 

  66. Allen, T.: Stochastic ground-motion prediction equations for southeastern Australian earthquakes using updated source and attenuation parameters. Geosci. Aust. Rec. 69, 55 (2012)

    Google Scholar 

  67. Somerville, P., Graves, R., Collins, N., Song, S. G., Ni, S., & Cummins, P. (2009). Source and ground motion models for Australian earthquakes. Proceedings of the Annual Technical Conference of the Australian Earthquake Engineering Society.

  68. Ameri, G., Drouet, S., Traversa, T., Bindi, D., Cotton, F.: Towards an empirical ground motion prediction equation for France: accounting for regional differences in the source stress parameter. Bull. Earthq. Eng. 15, 4681–4717 (2017)

    Article  Google Scholar 

  69. Edwards, B., Fäh, D.: A stochastic ground-motion model for Switzerland. Bull. Seismol. Soc. Am. 103(1), 78–98 (2013)

    Article  Google Scholar 

  70. Morasca, P., Malagnini, L., Akinci, A., Spallarossa, D., Herrmann, R.B.: Ground-motion scaling in the Western Alps. J. Seismol. 10(3), 315–333 (2006)

    Article  Google Scholar 

  71. Lam, N.T.K., Wilson, J.L., Chandler, A.M.: Seismic displacement response spectrum estimate from the frame analogy soil amplification model. Eng. Struct. 23, 1437–1452 (2001)

    Article  Google Scholar 

  72. Tsang, H.H., Chandler, A.M., Lam, N.T.K.: Estimating non-linear site response by single period approximation. Earthq. Eng. Struct. Dynam. 35(9), 1053–1076 (2006)

    Article  Google Scholar 

  73. Tsang, H.H., Chandler, A.M., Lam, N.T.K.: Simple models for estimating site period shift and damping in soil. Earthq. Eng. Struct. Dynam. 35(5), 1925–1947 (2006)

    Article  Google Scholar 

  74. Tsang, H.H., Sheikh, M.N., Lam, N.T.K.: Modelling shear rigidity of stratified bedrock in site response analysis. Soil Dyn. Earthq. Eng. 34, 89–98 (2012)

    Article  Google Scholar 

  75. Tsang, H.H., Wilson, J.L., Lam, N.T.K., Su, R.K.L.: A design spectrum model for flexible soil sites in regions of low-to-moderate seismicity. Soil Dyn. Earthq. Eng. 92, 36–45 (2017)

    Article  Google Scholar 

  76. Al Atik, L., Abrahamson, N., Bommer, J., Scherbaum, F., Cotton, F., Kuehn, K.: The variability of ground-motion prediction models and its components. Seismol. Res. Lett. 81(5), 794–801 (2010)

    Article  Google Scholar 

  77. Al Atik, L. (2015) NGA-East: ground-motion standard deviation models for Central and Eastern North America, PEER Rept. No. 2015/07, Pacific Earthquake Engineering Research Center, University of California, Berkeley, California.

  78. Lam, N.T.K., Chandler, A.M.: Peak displacement demand in stable continental regions. Earthq. Eng. Struct. Dynam. 34, 1047–1072 (2005)

    Article  Google Scholar 

  79. Chandler, A.M., Lam, N.T.K., Tsang, H.H.: Regional and local factors in attenuation modelling: Hong Kong case study. J. Asian Earth Sci. 27, 892–906 (2006)

    Article  Google Scholar 

  80. Yenier, E., Atkinson, G.M.: Regionally adjustable generic ground-motion prediction equation based on equivalent point-source simulations: Application to central and eastern North America. Bull. Seismol. Soc. Am. 105(4), 1989–2009 (2015)

    Article  Google Scholar 

  81. Hassani, B., Atkinson, G.M.: Adjustable generic ground-motion prediction equation based on equivalent point-source simulations: accounting for kappa effects. Bull. Seismol. Soc. Am. 108(2), 913–928 (2018)

    Article  Google Scholar 

  82. Hoult, R. (2022) Personal communication with the author.

  83. Goulet,C.A., Kishida,T., Ancheta,T.D., Cramer,C.H., Darragh,R.B., Silva,W.J., Hashash, Y.M.A., Harmon, J., Stewart, J.P. & Wooddell, K.E.(2014). PEER NGA-East database, Pacific Earthquake, Engineering Research Center PEER Report 2014/17.

Download references

Acknowledgements

The data used in Fig. 3 were provided by Dr Ryan Hoult at the Universite Catholigque de Louvain, at Brussel, Belgium. His generosity in the sharing of data is gratefully acknowledged. Feedbacks from AProf Hing Ho Tsang at Swinburne University of Technology, Australia, and Yiwei Hu at The University of Melbourne during the course of preparation of the manuscript are also gratefully acknowledged.

Author information

Authors and Affiliations

  1. Structures and Buildings, Infrastructure Engineering, The University of Melbourne, Melbourne, Australia

    Nelson Lam

Authors
  1. Nelson Lam
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nelson Lam.

Ethics declarations

Conflict of interest

The author declares that there is no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lam, N. A review of stochastic earthquake ground motion prediction equations for stable regions. Int J Adv Eng Sci Appl Math 15, 1–14 (2023). https://doi.org/10.1007/s12572-022-00325-0

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12572-022-00325-0

Keywords

Search

Navigation