Local geological features can have a strong impact on earthquake ground shaking, especially at sites with mainly loose sediments, which have been observed to amplify the recorded ground motion. Knowing the soil and sediment composition of a site is therefore necessary for computing the possible earthquake site amplification for seismic hazard and risk assessments. For a single site and site-specific analysis, several site parameters for characterizing shallow site conditions (e.g. fundamental frequency f0, shear wave velocity profile, horizontal-to-vertical spectral ratio (HVSR), depth to bedrock) can be obtained from seismic and geotechnical investigations and used to predict local site amplification e.g.. For larger areas and regional site-amplification analysis, however, the site conditions must be derived from empirical relations between relevant proxies available through regional or global maps e.g.. Currently, the common practice for characterizing site amplification in seismic hazard and risk assessment is using the average shear wave velocity of the upper 30 m of the soil column (VS30). For a single site the velocity profile and VS30 can be measured directly, but for larger areas and regions, however, VS30 must be inferred from other parameters. A much-used method to calculate VS30 uses slope from digital elevation models (DEMs), following . This method is based on the hypothesis that steep (high) slopes generally have less sediment and therefore higher shear-wave velocity (VS), while flat (low) slopes are more likely to be basins filled with sediment and thus with lower VS. used measured VS30 to derive a relation between VS30 and slope for active and stable tectonic regions separately and provided a global map of predicted VS30 values. However, inferring VS30 based on slope has several limitations. As already stated by , the assumption of correlation between VS30 and slope breaks down for continental glaciated terrains and nominally flat volcanic plateaus. In addition, have shown that other geological conditions, in particular narrow sedimentary basins and small topographic heterogeneity, have a poor correlation with the VS30 model based on slope.

Since the model, several VS30 maps based on new methods and other geological proxies in addition to slope have been made, both on local and national level e.g.. However, as also argued by , the main purpose of VS30 is as a proxy to predict site amplification, and when inferring VS30 from other parameters, it thus becomes a proxy of a proxy. In fact, site amplification predicted by VS30 based on slope shows little improvement to the site-amplification models based directly on slope . Furthermore, it is important to keep in mind that inferred VS30 should not be used interchangeably with measured VS30 values without properly accounting for the additional uncertainty related to the VS30 calculations . The variability of ground motion predictions can have great impact on the resulting probabilistic seismic hazard and risk assessments. Properly accounting for and separating between aleatory uncertainty, coming from natural randomness, and epistemic uncertainty, due to lack of knowledge, is therefore important. It has long been acknowledged that the site variability is a significant contributor to ground motion variability e.g.. In particularly, using inferred site proxies in place of measured site parameters results in an increase in uncertainty. To account for this increase in uncertainty, derived separate site-amplification models for measured and inferred proxies and compared their impact on the final hazard and risk calculation. It was found that, although the median amplification predicted using inferred VS30 was notably lower than the median predicted amplification using measured VS30, the resulting seismic hazard and risk curves from the different approaches were within the same range. This emphasizes how seismic hazard is controlled not only by the median amplification but also by the uncertainty. Indeed this increase in uncertainty, related to inferred proxies, compensates for the change in predicted median amplification in a probabilistic hazard and risk context.

In this study, we follow the approach of , to test the suitability of new site proxies as predictors for site amplification and investigate the effect on epistemic uncertainty when using different regional and globally available site proxies. We skip the step of deriving a site proxy ourselves and look beyond the field of engineering seismology for already available large-scale models of soil and sediment conditions that would allow for inference of soil amplification across a wide region. One such model is the geomorphological model for sedimentary thickness. As the thickness of soil and sediments down to bedrock is an important factor for modelling amplification of earthquake ground shaking, the thickness of porous weathered material above unweathered bedrock is necessary for land surface modelling of, for example, the water and carbon cycle . therefore developed a global dataset of soil, intact regolith and sedimentary deposit thicknesses intended as input for hydrology and ecosystem models. The model is based on a combination of data including slope, lithology and stratigraphy, and water table depth, all of which correlate with geotechnical soil conditions known to yield seismic amplification. Because it is based on more robust geomorphological theories than traditional inferred site proxies, like VS30 based on slope or geology, we acknowledge the potential value of the model and other similar large-scale models of soil thickness derived from other fields than our own, as possible input in site-amplification modelling in large-scale seismic hazard and risk modelling.

To test the whether the geomorphological model can provide extra information and is suitable for ground-shaking prediction, we derive a simple site-amplification prediction model using site-to-site residuals (δS2Ss) from the European Engineering Strong-Motion (ESM) dataset . The site-to-site residuals (δS2Ss) are derived from a simple ground motion model (GMM) following the method of . We compare the ability of the geomorphological model to predict site amplification to site-amplification models based on the traditional site proxies, VS30 derived from slope from , and slope alone, as well as a combination of slope and geological era. To better investigate the differences in the site-amplification prediction maps derived from the different proxies, we focus on eastern Türkiye and Syria, where the recent February 2023 Kahramanmaraş earthquake sequence occurred .

The site response at sites where ground motion records are available is often derived as the standard spectral ratio (SSR) between a site and a nearby rock reference, or, in the rare cases it is available, a borehole reference at the same site. However, a nearby rock reference or borehole stations are not always available for ground motion recording stations. Instead, when a station has recorded several earthquakes, the repeatable site response can be separated from the source and path effect of the ground motion, using methods like generalized inversion technique GIT, e.g., empirical spectral modelling technique or empirical ground motion modelling e.g.. In this study we use the latter method to remove the source and path effect from the ground motions using a simple GMM. To derive the GMM we use robust mixed-effects regression rlmm,, where statistical outliers are down-weighted and hierarchical data are dealt with by distinguishing between fixed effects as explanatory variables and random effects as grouping factors . A GMM is typically composed of three main explanatory variables describing the source, path and site effects of the ground motion. In its most basic form, magnitude and distance are used to describe the source and path, while VS30 is usually used to characterize the site effects. Here, however, only the source and path effects are used as fixed effects, while the site is included as a random effect: 1ln⁡(μ)=fR,gRJB+fR,aRJB+fMMW+δBe+δS2Ss+δWSe,s2fR,gRJB=c1ln⁡RJB2+hD2Rref2+hD23fR,aRJB=c3100RJB2+hD2-Rref2+hD24fMMW=b1MW-Mh+b2MW-Mh2ifMW≤Mhb3MW-MhifMh<MW, where ln⁡(μ) is the median ground motion prediction and fR,g(RJB), fR,a(RJB) and fM(MW) are the fixed effects capturing the scaling of the ground motion with geometric spreading, anelastic attenuation and magnitude for Joyner–Boore distance RJB, hypocentral depth hD and magnitude MW. The reference values, Rref=30 km, Mh=5.7 and hD=4, 8 and 12 km, are frequency-independent and defined by . Following the notation of , the between-event random effect δBe and site-to-site random effect δS2Ss represent the systematic deviation of recorded ground motions from the GMM median predictions related to an event e and a site s, respectively, and δWSe,s is the “remaining” record-to-record variability . If a site-proxy-dependent site term were included in the fixed effect, δS2Ss would represent the systematic deviation of the observed amplification at site s from the median amplification predicted by the model using the site proxy . However, because no site-proxy-dependent site term is included in the GMM derived here, δS2Ss captures all the site-specific response and thus can be used as an empirical site-amplification function describing the local amplification, or deamplification, of each station with respect to the median of all sites . δS2Ss is comparable to site amplification from GIT, as shown by recent studies . The δS2Ss is assumed to follow a frequency-dependent normal distribution with standard deviation, ϕs2s: 5δS2Ss=N0,ϕs2s. In this study the GMM and corresponding δS2Ss are derived in the Fourier amplitude spectra (FAS) from the ESM dataset . While most GMMs are derived for response spectral amplitudes (SAs), representing the damped response of an elastic single-degree-of-freedom oscillator, we here derive the GMM and δS2Ss in FAS to better capture the physical effects that can be masked in the response spectra, in particularly at high frequencies .

To derive the GMM we use the same data selection criteria and similar functional form as . The GMM of is a regionally adaptable model in FAS for shallow crustal earthquakes in Europe and Mediterranean regions. The regionalization in these models is represented by including an earthquake locality-to-locality variability term and an attenuation region-to-region variability term to the random effects. In the GMM derived for this study, these terms are not included and only event and site are used as random effects. This is done to minimize the possibility that regional differences in site effects propagate into the region-to-region random effect.

Unlike traditional site-amplification factors, δS2Ss is not relative to a reference rock condition but to δS2Ss=0, which is the centre of the distribution, median, of all the stations. The final δS2Ss dataset contains site terms in the frequency range f=0.460–9.903 Hz for 1680 stations in Europe and the Middle East, as shown on the map in Fig.  at f=0.529, 1.062 and 9.903 Hz. Although the site amplification shows a high variability and is mainly dominated by very local effects, some regional effects can be observed. For example for Italy, the amplification is mainly high (above the median, red) in the Po Plain and low (below the median, blue) in the Alps.

We evaluate the ability of the different proxies to predict site amplification by deriving a site-amplification model for each proxy using linear regression to capture the relation between the empirical amplification δS2Ss(f) and the proxies: 6Ys(f,Proxy)=aln⁡xProxy+b, where Ys(f,Proxy) is the predicted site amplification for a site s at frequency f using a proxy xProxy, and a and b are the coefficients derived from the linear regression.

A log-normal distribution is generally assumed for VS30 and depth to bedrock e.g., and the relation between site amplification and measured VS30 is often derived as log-linear e.g.. Indeed, Fig.  shows the linear regression between the empirical amplification δS2Ss(f) at frequencies f=0.529 and 1.062 Hz, with measured VS30. The coefficient of determination r2 shows that the correlation between δS2Ss(f) and ln⁡(VS30) is higher than between δS2Ss(f) and VS30 on linear scale. We therefore, and following common practice, also assume a log-linear relation between the site amplification and the inferred site proxies.

As shown by the distribution of the inferred proxies (Fig. ), the log-normal assumption is not fully fulfilled for inferred VS30 and especially geomorphological sediment thickness. This is because the proxies are limited to a certain range during their calculation process. In the case of geomorphological sediment thickness, set the maximum value to 50 m, effectively meaning the thickness of the sediment layer is 50 m or more. Likewise, the inferred VS30 is limited to a maximum value of 900 m s-1.

When dealing with such uneven distribution caused by censoring the data, so-called “censored data”, tobit regression is a possibility. The tobit model is developed to estimate linear relationships when the dependent variable is censored and uses the likelihood function to deal with the uneven distribution . However, as can be seen in Fig.  (red line), the tobit regression strongly overestimates the slope of the relation between the site proxies and site amplification, which is also demonstrated by the non-parametric fit (dashed yellow lines, Fig. ) and the low coefficient of determination r2 for the tobit regression (red line Fig. ) compared to the other regression models, as shown in Fig. . The slope from the tobit regression is especially overestimated at high frequencies, where a weak relation between the empirical site amplification and site proxies is expected due to the impact of small-scale heterogeneities at the site where even the location or housing of the strong-motion station can affect the amplification and the coarse spatial resolution (30 arcsec) of the site-amplification model. Interestingly, at very low frequencies (below 0.5 Hz), the coefficients of determination r2 for the regressions based on geomorphological sediment thickness are slightly reduced. This behaviour is not observed for r2 based on the regressions with inferred VS30 and might be caused by the geomorphological sediment thickness being limited to 50 m depth.

Another alternative approach to deal with the censored data is to exclude the end values when running the regression. However, this step only excludes a high number of sites while not having a strong impact on the regression line (Fig. , green, purple, orange and yellow line). Instead, we only omit sites with geomorphological sediment thickness = 0 m, which is the value that causes the highest unevenness in the distribution, as well as sites with missing values for any of the proxies, leaving us with 1508 sites for the regression. To evaluate the dependency of the regression on the selection of sites, we run a 10-fold cross-validation test, which is a method to separate the data used for the regression (training set) and the data used to validate the regression (validation set) when dealing with small datasets . Because our dataset consists of 1508 sites, we choose to separate the data into 10 parts in order to have a sufficiently large validation set (about 150 sites). In the 10-fold cross-validation test, the dataset is thus split into 10 equal parts and the model is derived on 10–1 parts and tested on the remaining 1 part of the dataset. This is done 10 times, and for each run a different subset of the data is used for validation. The distributions of the site proxies for each of the 10 cross-validation iterations are shown in Fig. .

Because the object of this study is not to find the best possible relation between each proxy and empirical site amplification, but rather to compare the ability of the proxies to predict site amplifications, we choose linear regression for simplicity. We do, however, acknowledge that site amplification is a complex phenomenon that the linear assumption cannot fully capture. Furthermore, because the models are based on the proxies’ relation with δS2Ss, the resulting amplification predictions are, as δS2Ss, relative to the median prediction of the associated GMM used to obtain the δS2Ss (Eqs. –).

We derive site-amplification models from linear regression between δS2Ss for the frequency range f=0.460–9.903 Hz and the site proxies, VS30 from slope, slope alone, geomorphological sediment thickness and geological era combined with slope. The selected sites and the regression lines are shown for f=0.529 Hz and f=1.062 Hz in Fig.  for inferred VS30, slope and geomorphological sediment thickness. Although the δS2Ss shows a high scatter with the site proxies, a general trend of higher amplification for low VS30, low slope and high sediment thickness and low amplification for vice versa can be identified. For the regression over geological era and slope combined, we apply multiple linear regression, meaning with multiple independent variables where the categorical predictor, geological era, is transformed to dummy variables for each era and the regression then derives a constant coefficient for slope with a different intercept for each geological era (Fig. ). The variation in prediction coefficients due to the alteration of the training set in the cross-validation process, shown as dotted red lines in Figs.  and , is small for all the proxies except inferred VS30 and geological era. This indicates that the site-amplification models based on inferred VS30 and geological era and slope combined are more dependent on the data selection than the other proxies, causing a higher final uncertainty. The coefficients of determination for the linear regressions shown in Figs.  and  and for the entire frequency range are shown in Fig. .

After deriving an amplification model based on each proxy, we compare the predicted amplification δS2Ss(f,Proxy) with the empirical amplification δS2Ss(f) at a site s and frequency f. We measure the ability of each proxy to capture the site amplification using the reduction in site-to-site variability ϕs2s as an indicator of the efficiency of each proxy in predicting the amplification . We compute the corrected site term for each proxy-specific predicted amplification δS2Ss,cor.(f,Proxy): 7δS2Ss,cor.(f,Proxy)=δS2S(f)-δS2Ss(f,Proxy)8δS2Ss,cor(f,Proxy)=N0,ϕs2scor.(f,Proxy), where δS2Ss,cor.(f,Proxy) represents the remaining site amplification that is not captured by the proxy-based amplification prediction δS2Ss(f,Proxy), and ϕs2scor.(f,Proxy) is the site-to-site variability of δS2Ss,cor.(f,Proxy). δS2Ss,cor.(f,Proxy) with the four site proxies is shown for f=0.529, 1.062 and 9.903 Hz in Fig. . If the site-amplification model were able to perfectly predict and capture the full range of the site amplification at a specific site, ϕs2scor.(f,Proxy) would be reduced to zero. However, such an ideal case is not realistic and conventional site-amplification models can only aim to reduce ϕs2scor.(f,Proxy) as much as possible. Hence, the greater the reduction in variability, meaning a lower ϕs2scor.(f,Proxy), the better the ability of the proxy to capture the site amplification. Still, it is important to keep in mind that this measure and the correlation between δS2Ss(f) and the site proxies are purely statistical and do not give any insight into what is causing the amplification and its variability.

As described in Sect. , the site-amplification models and corresponding reduction in ϕs2s were derived and calculated 10 times following the 10-fold cross-validation technique. This means we are dealing with two sources of variability: the site-to-site variability ϕs2s and the variability related to running the regression on different subsets of the data in the 10-fold cross-correlation, here called ϵcc. ϕs2s is a combination of the natural, random and irreducible (aleatory) variability of site response and the epistemic uncertainty related to the site proxies not being able to fully capture the site properties controlling the site amplification. ϵcc is fully epistemic as it is related to the difference between the site-amplification models derived using different datasets. Figure  shows the mean ϕs2s for all stations (black lines) and ϕs2scor.(Proxy) for each proxy (coloured lines) from the 10 cross-validation iterations derived on the training sets (Fig. a) and the validation sets (Fig. b). The ϕs2s for each cross-validation iteration is shown in Fig. . In Fig. , the shaded areas around the means are the variance ϵcc related to the cross-validation process. ϵcc is, as expected, higher for the validation set (Fig. b), which for each iteration corresponds to only 10 % of the dataset, than for the training set (90 % of the data, Fig. a). Nonetheless, the general pattern is similar for both sets, where the highest reduction in site-to-site variability is caused by the site-amplification model based on geological era and slope. Inferred VS30, slope and geomorphological sediment thickness show similar reductions in variability for both the training and validation sets, with around a 1 % difference for the training set. For the validation set the reduction caused by inferred VS30, slope and geomorphological sediment thickness are within the same standard deviation ϵcc and are not clearly distinguishable (Fig. b). For both the training and validation set, none of the site-amplification models are distinguishable for frequencies above 3 Hz, which might be caused by the low resolution (30 arcsec and 1:1500000) of all the proxies considered in this study. This poor correlation between site amplification and topography- and geology-based proxies at high frequencies (f>3.0 Hz) has also been observed by other studies , also when higher-resolution indirect proxies were used , indicating that inferred site proxies mainly capture the average and deep properties of the subsurface and not the finer local nuances of a site.

The results shown in Fig. , indicate that the site-amplification model based on geological era and slope combined is better at capturing site amplification relative to the other proxies used in this study. These results are consistent with the findings of , who also derived site-amplification models based on several inferred proxies for Japan. However, when applying the same model to Europe, found that the reduction from geological era and slope was not significantly lower than for inferred VS30 or slope alone. They speculate that this could be an artefact of the mixed-effects regression used to derive the model, where geological era and slope were included as a random effect, meaning the coefficient for slope changes with each geological era, which is different for the multiple linear regression applied in this study where the slope coefficient stays the same for each geological era. In addition, our study uses δS2Ss(f) from FAS, which is likely to affect the site-to-site variability.

Nevertheless, the case that geological era and slope combined give the highest reduction to the site-to-site variability shows the importance of including geology in site-amplification modelling. Furthermore, the new proxy geomorphological sedimentary thickness shows a similar or even slightly higher reduction in site-to-site variability as the traditional proxies inferred VS30 and slope, indicating the potential of geomorphological sedimentary thickness as an alternative site proxy for seismic hazard assessments for large areas or areas without measured site parameters.

To further evaluate the ability of the site proxies to predict site amplification, we compare the predicted site amplification with empirical site amplification for the entire frequency range (f=0.460–9.903 Hz). The object of this study is to test regionally or globally available site proxies as predictors for regional site amplification over a large area. It is therefore not necessarily meaningful to compare our site-amplification predictions to empirical site amplification at a single site. Instead, we compare the predicted amplification to empirical amplification grouped according to the Eurocode 8 classes EC8 provided in the ESM database. Based on the station distribution with VS30 (Fig. ) and the number of stations per class (Fig. a), we only use the stiffer classes, A, B and C, for the comparison. Selecting corresponding ranges of site properties for predicting the site amplification for each EC8 class using other proxies than inferred VS30 requires some attention. The correlation between measured VS30 and slope in Fig. b shows that slope generally increases with increasing VS30. Although the relation has a high variability, especially for high VS30, we select high slope (0.1–0.3 m m-1) for A, 0.05–0.1 m m-1 for B and 0.01–0.03 m m-1 for C. Because the relation between geomorphological sediment thickness and measured VS30 has a high variability over the entire range (Fig. c), we use the newly proposed Eurocode 8 draft with very shallow geomorphological sediment thickness at (<5 m) for A, shallow (5–30 m) and intermediate (30–50 m) for B and intermediate for C. When selecting corresponding geological eras, we use Holocene and Pleistocene for C (Fig. b, yellow and pink scatter points), the remaining geological eras (leaving out Cenozoic) Cretaceous, Jurassic–Triassic, Precambrian and Paleozoic for B (Fig. c, brown, green, blue and purple scatter points), and Cretaceous and Jurassic–Triassic for A (Fig. c, brown and green scatter points). The selected ranges of site properties are given in Table .

Figure  shows the mean of the empirical site amplification (solid black line) with the standard deviation (shaded black area) of the sites in each of the EC8 classes A, B and C. The variability of the empirical site amplification even within each class is very high, and the predicted site amplifications using any of the proxies are within the standard deviation of the three classes. For A, slope and geomorphological sediment thickness are continuously in the upper range of the empirical site-amplification standard deviation, while the predictions based on inferred VS30 and geological era with slope slightly underpredict relative to the mean empirical site amplification for low frequencies and overpredict for higher frequencies. For class B, inferred VS30 and slope are in the lower range of the empirical site-amplification standard deviation but generally follow the shape of the mean empirical site amplification, while the prediction based on shallow (5–30 m) and especially intermediate (30–50 m) geomorphological sediment thickness overpredicts with respect to the mean empirical amplification, The site-amplification models based on geological era and slope underpredict relative to the mean empirical site amplification, especially for low frequencies, but get closer to the mean empirical amplification at higher frequencies. For the softer soil class C, the different proxies have similar predictions and are close to the mean of the empirical amplification. At low frequencies, in particular the model predictions based on geomorphological sediment thickness and inferred VS30 are close to the mean empirical amplification. However, the differences between the predictions and empirical amplification could also be due to a poor correspondence between the selected ranges of inferred proxy values and the measured VS30, particularly for geological era.

Finally, we use the proxy-based site-amplification models to predict the site amplification for the whole of Europe, as shown in Fig.  for f=1.062 Hz. The amplification maps at f=0.529 Hz and f=9.903 Hz are shown in Figs.  and . The site-amplification maps show the amplification (red) and deamplification (blue) relative to the median site amplification (white) predicted by the associated GMM defined in Eqs. ()–(). This is different from conventional amplification maps used in probabilistic seismic hazard analysis, where the site amplification is relative to a rock reference. In this study, we keep the amplification relative to the median to avoid biasing the result with poorly constrained rock properties. Furthermore, the δS2Ss used to develop the models is obtained from strong-motion stations mainly located in southern Europe and the Mediterranean region (Fig. ); some regional bias is therefore likely to be present in the amplification predictions. The maps all show similar features, for example, high amplification in the soft-sediment basins of the Po Plain in northern Italy, the Danubian Plain of eastern Romania and the Great Hungarian Plain and strong deamplification in the Alps, the Carpathian Mountains and western Norway. However, clear differences are also evident in the different site-amplification maps, for example around the Rhine Valley, in the Baltic and eastern Türkiye. These differences show not only that the proxies are capturing different aspects of the site effects, but also that there is a need for characterizing the epistemic uncertainty related to the site-amplification predictions.

To test whether the geomorphological model for sediment thickness derived by can be used as an alternative site proxy, we have derived site-amplification models based on the geomorphological sediment thickness, as well as traditional site proxies like inferred VS30, slope, and geological era and slope combined. Although the predicted site-amplification maps based on the different proxies show similar trends, there are also notable differences, indicating that the proxies capture different aspects of the site effects. Using only one proxy, for example, inferred VS30, which is often the standard procedure, is therefore not sufficient to fully capture the range of possible amplifications. The differences in the site-amplification predictions based on the different proxies thus contribute to the characterization of the epistemic uncertainty. In a probabilistic seismic hazard and risk context, this uncertainty needs to be included and properly accounted for. In this study, we calculate the site amplification for Europe and the Middle East but focus particularly on eastern Türkiye and Syria. As a measure of how well the site proxies capture the empirical site amplification, we used the reduction in site-to-site variability. The results show that the site-amplification predictions based on geological era and slope combined cause the highest reduction, while the prediction based on geomorphological sediment thickness causes a similar, but slightly larger, reduction in site-to-site variability than the traditional site proxies, inferred VS30 and slope. This result shows the value of including geology and geomorphology in prediction models for site amplification. Furthermore, the geological map used in this study is only available for Europe, while geomorphological sediment thickness is available globally and easily accessible. However, although the geomorphological sediment thickness has potential, further investigations and tests are needed before establishing it as an alternative to the much-used inferred VS30 model from , in particular in areas where inferred VS30 and slope are known to have a weak correlation with site amplification. Moreover, the correlation between the empirical site amplification and the site proxies all weakens above 3 Hz, which shows the need for models with higher resolution or including more local and shallow information. Our results therefore show the potential of not only the geomorphological sediment thickness model but also of other models for soil and sediment thickness from geomorphology and similar fields outside seismology and earthquake engineering. The outputs of this study have been made available (see the “Code and data availability” section below); however, it is important to state that the site-amplification models and maps developed in this study can only be interpreted as referenced to the associated GMM median prediction and should be considered as exploratory as they were developed for the purpose of testing the different site proxies and show the epistemic uncertainty related to using different proxies. Additionally, using inferred site proxies should only be done for regional seismic hazard studies of larger areas or when more detailed site parameters are missing.