Introduction

ESEE Report 01-1 ‘A comprehensive worldwide summary of strong-motion attenuation relationships for peak ground acceleration and spectral ordinates (1969 to 2000)’ (Douglas, 2001b) was completed and released in January 2001. A report detailing errata of this report and additional studies was released in October 2002 (Douglas, 2002). These two reports were used by Douglas (2003) as a basis for a review of previous ground-motion prediction equations (GMPEs). Following the release of these two reports, some further minor errors were found in the text and tables of the original two reports, and additional studies were found in the literature that were not included in ESEE 01-1 or the follow-on report. Also some new studies were published. Rather than produce another report listing errata and additions it was decided to produce a new report that included details on all the studies listed in the first two reports (with the corrections made) and also information on the additional studies. This report was published as a research report of Imperial College London at the beginning of 2004 (Douglas, 2004a). At the end of 2006 a BRGM report was published (Douglas, 2006) detailing studies published in 2004–2006 plus a few earlier models that had been missed in previous reports. Finally, at the end of 2008 another BRGM report was published (Douglas, 2008) containing summaries of GMPEs from 2007 and 2008 and some additional earlier models that had been recently uncovered.

Because of the large number of new GMPEs published in 2009 and 2010 and the discovery of some additional earlier studies and various errors in the previous reports, it was decided to publish a new comprehensive report to replace the previous reports (Douglas, 2001b, 2002, 2004a, 2006, 2008) containing all previous reports plus additional material rather than publish yet another addendum to the 2004 report. It was also decided that, for completeness and due to the lack of another comprehensive and public source for this information, to include a list of GMPEs developed using other methods than regression of strong-motion data, e.g. simulation-based models (e.g. Douglas and Aochi, 2008). However, due to the complexity of briefly summarizing these models it was decided not to provide details but only references. This report was published as Douglas (2011).

In order to make the compendium easier to use and to update in the future it was decided to port the entire report to html using the LATEXTEX 4ht package as well as add models from 2011 to summer 2018 and some older GMPEs that were recently found. Finally, GMPEs for intensity measures other than PGA and elastic response spectral ordinates are listed but details are not given (although some of these correspond to models for PGA and elastic spectral ordinates and hence they are summarized elsewhere in this compendium).

This report summarizes, in total, the characteristics of 450 empirical GMPEs for the prediction of peak
ground acceleration (PGA) and 290 models for the prediction of elastic response spectral ordinates as well
as 30 models for the prediction of Arias intensity, 6 models for cumulative absolute velocity, 16 models
for Fourier spectral amplitudes, 6 models for maximum absolute unit elastic input energy, 5 models for
inelastic response spectral ordinates, 4 models for Japanese Meterological Agency seismic intensity, 46
models^{1}
(intensity prediction equations) for macroseismic intensity, 5 models for mean period, 129 for peak ground velocity, 31
for peak ground displacement, 16 for relative significant duration and 9 models for vertical-to-horizontal response
spectral ratio. With this many GMPEs available it is important to have criteria available for the selection of appropriate
models for seismic hazard assessment in a given region — Cotton et al. (2006) and, more recently, Bommer
et al. (2010) suggest selection requirements for the choice of models. For the selection of GMPEs routinely applicable to
state-of-the-art hazard analyses of ground motions from shallow crustal earthquakes Bommer et al. (2010) summarize
their criteria thus.

- 1.
- Model is derived for an inappropriate tectonic environment (such as subduction-zone earthquakes or volcanic regions).
- 2.
- Model not published in a Thomson Reuters ISI-listed peer-reviewed journal (although an exception can be made for an update to a model that did meet this criterion).
- 3.
- The dataset used to derive the model is not presented in an accessible format; the minimum requirement would be a table listing the earthquakes and their characteristics, together with the number of records from each event.
- 4.
- The model has been superseded by a more recent publication.
- 5.
- The model does not provide spectral predictions for an adequate range of response periods, chosen here to be from 0 to 2s.
- 6.
- The functional form lacks either non-linear magnitude dependence or magnitude-dependent decay with distance.
- 7.
- The coefficients of the model were not determined with a method that accounts for inter-event and intra-event components of variability; in other words, models must be derived using one- or two-stage maximum likelihood approaches or the random effects approach.
- 8.
- Model uses inappropriate definitions for explanatory variables, such as M
_{L}or r_{epi}, or models site effects without consideration of V_{s,30}. - 9.
- The range of applicability of the model is too small to be useful for the extrapolations generally required
in PSHA: M
_{min}> 5, M_{max}< 7, R_{max}< 80km. - 10.
- Model constrained with insufficiently large dataset: fewer than 10 earthquakes per unit of magnitude or fewer than 100 records per 100km of distance.

Similar criteria could be developed for other types of earthquakes (e.g. subduction). For example, the reader is referred to Stewart et al. (2015) for a discussion of the selection of GMPEs for hazard assessments for the three principal tectonic regimes. Application of such criteria would lead to a much reduced set of models. The aim of this report, however, is not to apply these, or any other, criteria but simply to summarize all models that have been published. Bommer et al. (2010) also note that: ‘[i]f one accepts the general approach presented in this paper, then it becomes inappropriate to develop and publish GMPEs that would subsequently be excluded from use in PSHA [probabilistic seismic hazard analysis] on the basis of not satisfying one or more of the requirements embodied in the criteria.’

Predictions of median ground motions from GMPEs show great dispersion (Douglas, 2010a,b, 2012) demonstrating the large epistemic uncertainties involved in the estimation of earthquake shaking. This uncertainty should be accounted for within seismic hazard assessments by, for example, logic trees (e.g. Bommer and Scherbaum, 2008).

^{1}Only those models using magnitude rather than epicentral intensity are listed.