This online resource summarizes all empirical ground-motion prediction equations (GMPEs), to estimate earthquake peak ground acceleration (PGA) and elastic response spectral ordinates, published between 1964 and 2018 (inclusive). This resource replaces: the Imperial College London reports of Douglas (2001b), Douglas (2002) and Douglas (2004a), which provide a summary of all GMPEs from 1964 until the end of 2003; the BRGM report of Douglas (2006), which summarizes all GMPEs from 2004 to 2006 (plus some earlier models); the report of Douglas (2008), concerning GMPEs published in 2007 and 2008 (plus some earlier models); and the report of Douglas (2011), which superseded all these reports and covered the period up to 2010. It is planned to continually update this website when new GMPEs are published or errors/omissions are discovered. In addition, this resource lists published GMPEs derived from simulations, although details are not given since the focus here is on empirical models. Studies that only present graphs are only listed, as are those nonparametric formulations that provide predictions for different combinations of distance and magnitude because these are more difficult to use for seismic hazard analysis than those which give a single formula. Equations for single earthquakes or for earthquakes of approximately the same size are excluded due to their limited usefulness. Those relations based on conversions from macroseismic intensity are only listed.

This website summarizes, in total, the characteristics of 452 empirical GMPEs for the prediction of PGA and 292 empirical models for the prediction of elastic response spectral ordinates. In addition, 78 simulation-based models to estimate PGA and elastic response spectral ordinates are listed but no details are given. 49 complete stochastic models, 40 GMPEs derived in other ways, 28 non-parametric models and 13 backbone (Atkinson et al., 2014a) models are also listed. Finally, the table provided by Douglas (2012) is expanded and updated to include the general characteristics of empirical GMPEs for the prediction of: Arias intensity (30 models), cumulative absolute velocity (6 models), Fourier spectral amplitudes (16 models), maximum absolute unit elastic input energy (6 models), inelastic response spectral ordinates (5 models), Japanese Meterological Agency seismic intensity (4 models), macroseismic intensity (48 models, commonly called intensity prediction equations), mean period (5 models), peak ground velocity (130 models), peak ground displacement (34 models), relative significant duration (16 models) and vertical-to-horizontal response spectral ratio (9 models). This report will be updated roughly once every six months.

It should be noted that the size of this resource means that it may contain some errors or omissions. The boundaries between empirical, simulation-based and non-parametric ground-motion models are not always clear so I may classify a study differently than expected. No discussion of the merits, ranges of applicability or limitations of any of the relationships is included herein except those mentioned by the authors or inherent in the data used. This compendium is not a critical review of the models.

This compilation was made when I was employed at: Imperial College London, University of Iceland, BRGM and University of Strathclyde. I thank: my current and former employers for their support, many people for references, suggestions and encouragement while producing this resource, and the developers of LATEXand associated packages, without whom this report would never have been written.

If required, you can cite this resource in the following way:

Douglas, J. (2018), Ground motion prediction equations 1964–2018, http://www.gmpe.org.uk. |