The development of the proposed SZC GMM followed what is commonly referred as the “traditional” or “multi-GMPE” approach. The selection of the suite of GMPEs considered in the GMM followed a rigorous and systematic approach where candidate models were identified using the comprehensive compendium of published GMPEs by Douglas (2018). The preliminary exclusion criteria were predominantly based on recommendations from Cotton et al. (2006) and Bommer et al. (2010), with consideration also given to selection criteria used in previous project for nuclear facilities (e.g. Renault 2014). From this preliminary selection, 11 GMPEs were retained for further assessment. These GMPEs were assessed by comparing ground-motion predictions from each of the individual GMPEs for various earthquake scenarios in terms of distance and magnitude scaling and in terms of response spectra. Also, Sammon’s maps were produced for selected IMs considering the magnitude and distance ranges of interest to the PSHA; this allowed identifying clusters of GMPEs in ground-motion space.
The assessment process was complemented by comparing predictions to various observations of ground shaking from a project-specific database that included ground-motion records from the UK, northern France, Belgium and western Germany. Comparisons against ground-shaking observations, although important and necessary, provided only limited, qualitative, guidance for the selection of the most appropriate GMPEs for a site-specific PSHA in the UK. This was mainly because of the small number of records available, which are limited to those from events with magnitudes generally below M 5.3 recorded at considerably (> 100 km) source-to-site distances. Also, due to limitations of the instrumental data (e.g. a lack of detailed site information for most strong-motion stations), quantitative methods to assess the match between predictions from the GMPEs and observations, such as those proposed by Scherbaum et al. (2004, 2009), were not applied.
The final step of the GMPE selection process consisted of an expert assessment of the preliminary selected GMPEs by the GMM team based on the comparisons previously described. The aim of this assessment was to reduce the number of candidate GMPEs to a more manageable figure, whilst ensuring that the range of selected GMPEs was sufficient to account for the considerable epistemic uncertainty associated with ground-motion prediction in the UK. Other factors, such as whether the GMPEs could be adjusted for site-specific conditions or would allow scaling to correct for stress drop variation were also taken into consideration, along with other technical and project-specific issues.
As result of this process, the following suite of GMPEs were selected for the proposed GMM:
Bindi et al. (2014a; b) [BETAL14] – model using RJB and VS30
Cauzzi et al. (2015) [CETAL15] – considering the period dependent reference VS30 option
Chiou and Youngs (2014) [CY14]
Rietbrock and Edwards (2019) [RE19] – 5 MPa stress-drop model
Yenier and Atkinson (2015) [YA15] – model for central and eastern North America (CENA)
The compatibility of the ground-motion predictions from the selected suite of GMPEs was reviewed as the GMPEs may use different definitions of the predicted ground motion parameters and explanatory variables. The only compatibility issue identified was the consideration of alternative faulting mechanisms or “style of faulting”. BETAL14, CETAL15 and CY14 all include a style-of-faulting term in their functional from; also, the criterion used to define style-of-faulting is consistent across these three models. However, RE19 and YA15 do not provide an explicit style-of-faulting.
To address the style-of-faulting compatibility issue, reverse to strike-slip and normal to strike-slip adjustment factors (FRV/SS and FN/SS, respectively) were developed. Predictions from the YA15 model were adjusted using these adjustment factors, following the approach recommended by Bommer et al. (2003), in conjunction with the faulting composition observed in the NGA East flatfile (i.e. 68% reverse, 2% normal and 30% strike-slip). Predictions from the RE19 model were left unadjusted as any adjustments required were estimated to be small (< 1%). Therefore, any improvements in the predictions are likely to be offset by the introduction of additional epistemic uncertainty in the development of the adjustment factors.
All selected GMPEs are generic (i.e. non-site specific) models based on data from regions other than the UK, with exception of RE19 which used UK data. Therefore, the GMPEs required adjustments to consider the site-specific conditions at the reference velocity horizon, which for this study was defined at 82 m depth, with a VS30 of 1,139 m/s. These adjustments were performed via the application of host-to-target adjustments (HTTAs) designed to account for differences in the shear-wave velocity profile, VS, and the factor characterising the high-frequency attenuation, kappa. HTTAs are also commonly known as VS-kappa adjustments.
The calculation of the HTTAs requires four inputs to be defined, the average VS profiles of the host (VS,host) and target (VS,target) locations, which allow the amplification due to VS impedance to be computed; and the average kappa in the host (kappahost) and target (kappatarget) locations, which allow for modelling differences in the high-frequency attenuation.
The VS,host profiles were assessed based on the information provided by the model developers for the stochastic models (RE19 and YA15). For the three empirical models (BETAL14, CETAL15 and CY14) the generic VS profiles of Cotton et al. (2006) for a VS30 value of 1,000 m/s were used.
The kappahost values were assessed using the inverse random vibration theory technique (Al Atik et al. 2014) and considering a single pair of magnitude and distance (M 5.5 and 24 km) that are representative of the earthquake scenario controlling the hazard in the high-frequency range. The kappahost values assessed for the five selected GMPEs were: BETAL14, 0.0405 s; CETAL15, 0.0281 s; CY14, 0.0332 s; RE19, 0.0222 s; and YA15, 0.0209 s. These values are comparable to other estimates published for the same or similar GMPEs, where available (Zandieh et al. 2016).
The VS,target profile was developed based on the Poggi et al. (2011) VS profile with a VS of 1,100 m/s (VS30 of 1,139 m/s) at 82 m depth and 3,410 m/s at 4 km depth, which provided the best fit to site-specific data at the reference velocity horizon and the generic UK model (Turbitt 1985) and other regional deep VS profiles (Davis et al. 2012; Ottemöller et al. 2009) at around 4 km.
The best estimate kappatarget value for the site was thoroughly investigated for the project site using a combination of approaches including site-specific estimates from an “analogous” site (~ 70 km from the project site) with very similar geological conditions at the reference velocity horizon, estimates from other UK data/sites and estimates based on the VS30-kappa correlations from global data. Based on these various estimates of kappa, the following logic-tree branches were used to construct the HTTAs: lower target kappa of 0.01 s; middle target kappa of 0.02 s; and higher target kappa of 0.03 s.
The approach of Al Atik et al. (2014) was extended to account for differences in VS profiles as followed by Bommer et al. (2015) and Rodriguez-Marek et al. (2014), and then was implemented for the estimation and application of the final HTTAs. The final HTTAs were developed for the three target kappa values stated above and all five GMPEs, leading to a suite of 15 adjustment factors.
Specifications for the SZC PSHA required the GMM should provide ground-motion for periods up to 10 s. To account for unrealistic behaviour observed in the predicted spectral displacements (SD) above TD (i.e., the period at which the displacement spectrum becomes constant) and to extrapolate to periods above the longest period for which the GMPEs provide coefficients, the GMM team developed an approach to adjust long-period ground predictions for all GMPEs. This approach consisted of capping the SD for long periods at TD, where TD was calculated using the equation below assuming a stress drop, ∆σ, of 80 bars (8 MPa):
In the case where TD was longer than the longest period for which the GMPE provides coefficients, a linear extrapolation was performed in the PSA domain considering a log-log scale for periods below TD and capped at TD, in the SD domain, for longer periods. TD from the Equation 1 was constrained to be always above 1.0 s, where the predictions from the GMPEs are expected to be reliable and no adjustment is required.
The median ground-motion logic tree is presented in Figure 1. This captures the uncertainty in the selection of the most appropriate GMPE for the purposes of seismic hazard assessment at the SZC site as well as on the kappatarget. The weights assigned to the GMPEs were based on the assessments of the GMPE’s merits and weaknesses and reflect the level of confidence in each particular GMPE to provide an appropriate prediction of the ground-motion amplitudes expected at the SZC site. Weights assigned to each kappatarget branch reflect the GMM team’s expectations, based on the assessment discussed above, that the “true” kappa value at the SZC site is more likely to be somewhere between 0.01 s and 0.02 s (and closer to the latter) than above 0.02 s.