Equations for single earthquakes (e.g. Bozorgnia et al., 1995) or for earthquakes of approximately the same size (e.g. Seed et al., 1976; Sadigh et al., 1978b) are excluded because they lack a magnitude-scaling term and, hence, are of limited use. Also excluded are those originally developed to yield the magnitude of an earthquake (e.g. Espinosa, 1980), i.e. the regression is performed the other way round, which should not be used for the prediction of ground motion at a site. The model of Kim and Shin (2017) is not included because it is based on the ratio of the magnitude of the mainshock to an aftershock rather than the magnitude directly. The model of Zhao and Gerstenberger (2010) is not summarised since it uses recorded motions to estimate motions at sites without observations, within a rapid-response system. Models such as that by Olszewska (2006) and Golik and Mendecki (2012), who use ’source energy logarithms’ to characterize mining-induced events, have been excluded because such a characterization of event size is rare in standard seismic hazard assessments. Similarly, equations derived using data from nuclear tests, such as those reported by Mickey (1971); Hays (1980), are not included.
Those based on simulated ground motions from stochastic source models (e.g Atkinson and Boore, 1990) and other types of simulations (e.g. Megawati et al., 2005), those derived using the hybrid empirical technique (e.g Campbell, 2003b; Douglas et al., 2006), those relations based on intensity measurements (e.g. Battis, 1981) and backbone models (Atkinson et al., 2014a) are listed in Chapter 6 but no details are given because the focus here is on empirical models derived from ground-motion data. Studies using simulation techniques other than the classic stochastic method and which do not provide a closed-form GMPE (e.g. Medel-Vera and Ji, 2016) are not listed as they are often difficult to use. Studies which provide graphs to give predictions (e.g. Schnabel and Seed, 1973) are only listed and not summarized as are those nonparametric formulations that give predictions for different combinations of distance and magnitude (e.g. Anderson, 1997), both of which are generally more difficult to use for seismic hazard analysis than those which report a single formula. For similar reasons, models derived using neural networks (e.g. Güllü and Erçelebi, 2007) are only listed.
GMPEs for the prediction of PGA are summarized in Chapters 2 and 3 and those for spectral ordinates are summarized in Chapters 4 and 5. Chapter 6 lists other ground-motion models that are not detailed in the previous chapters. The final chapter (Chapter 7) provides the general characteristics of GMPEs for intensity measures other than PGA and elastic spectral ordinates. All the studies that present the same GMPE are mentioned at the top of the section and in the tables of general characteristics (Illustrations 3.1 & 5.1). The information contained within each section, and within tables, is the sum of information contained within each of the publications, i.e. not all the information may be from a single source. Note that GMPEs are ordered in chronological order both in the section titles and the order of the sections. Therefore, a well-known model presented in a journal article may not be listed where expected since it had previously been published in a conference proceedings or technical report. To find a given model it is recommended to examine the table of content carefully or apply a keyword search to the PDF. Some models (e.g. Abrahamson and Silva, 1997) provide GMPEs for spectral accelerations up to high frequencies (e.g. 100Hz) but do not explicitly state that these equations can be used for the prediction of PGA. Therefore, they are only listed in the chapters dealing with GMPEs for the prediction of spectral ordinates (Chapters 4 and 5) and their coefficients are not given. This should be considered when searching for a particular model.
To make it easier to understand the functional form of each GMPE the equations are given with variable names replacing actual coefficients and the derived coefficients and the standard deviation, σ, are given separately (for PGA equations). These coefficients are given only for completeness and if an equation is to be used then the original reference should be consulted. If a coefficient is assumed before the analysis is performed then the number is included directly in the formula.
Obviously all the details from each publication cannot be included in this report because of lack of space but the most important details of the methods and data used are retained. The style is telegraphic and hence phrases such as ‘Note that …’ should be read ‘The authors [of the original model] note that …’. The number of records within each site and source mechanism category are given if this information was reported by the authors of the study. Sometimes these totals were found by counting the numbers in each category using the tables listing the data used and, therefore, they may be inaccurate.
This report contains details of all studies for PGA and response spectra that could be found in the literature (journals, conference proceedings, technical reports and some Ph.D. theses) although some may have been inadvertently missed3. Some of the studies included here have not been seen but are reported in other publications and hence the information given here may not be complete or correct. Since this resource has been written in many distinct periods over almost two decades (2000–2018), the amount of information given for each model varies, as does the style.
In the equations unless otherwise stated, D, d, R, r, X, Δ or similar are distance and M or similar is magnitude and all other independent variables are stated. PGA is peak ground acceleration, PGV is peak ground velocity and PSV is relative pseudo-velocity.
In Tables 3.1, 5.1 and 7.1 the gross characteristics of the data used and equation obtained are only given for the main equation in each study. The reader should refer to the section on a particular publication or the original reference for information on other equations derived in the study.
In earlier reports the name ‘attenuation relation(ships)’ is used for the models reported. The current de facto standard is to refer to such models as ‘ground motion prediction equations’ (GMPEs) and, therefore, this terminology is adopted here. However, as discussed by Boore and Atkinson (2007, Appendix A) there is some debate over the best name for these models (e.g. ‘ground-motion model’ or ‘ground motion estimation equations’) and some people disagree with the use of the word ‘prediction’ in this context.
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 report is not a critical review of the models. The ground-motion models are generally reported in the form given in the original references. 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. Note that the size of this report means that it may contain some errors or omissions — the reader is encouraged to consult the original reference if a model is to be used.
3Generally GMPEs from technical reports and Ph.D. theses are only summarized if they have been cited in journal or conference articles.