1 Introduction

The local near-surface geology plays an important role in ground motion since it may amplify seismic waves from incoming earthquakes (Borcherdt 1970; Borcherdt and Gibbs 1976; Borcherdt and Glassmoyer 1992; Boore 2004; Towhata 2008). Shear wave velocity (VS), unlike P-wave velocity, is directly related to the shear modulus of the soil skeleton (Foti et al. 2014; Shearer and Orcutt 1987). Therefore, VS of subsurface soil is considered to be the key factor for an accurate evaluation of the site response (Stokoe et al. 1994; Tokimatsu 1997; Wald and Mori 2000) and is widely used for site characterization (Borcherdt 1994; Xia et al. 1999; Derras et al. 2017; Hollender et al. 2018). The average shear-wave velocity in the uppermost 30 m (VS30) was initially introduced to provide uniform definitions of site classes (Borcherdt 1992, 1994; Dobry et al. 2000), and to estimate site response: National Earthquake Hazard Reduction Program (NEHRP) building code provisions (BSSC 1994) or Eurocode 8 provision (CEN 2004).

Several studies described a consistent correlation between VS30 and site response (Borcherdt 1994; Hartzell et al. 2001; Rošer and Gocar 2010; Rastogi et al. 2011; Boore et al. 2011; Sairam et al. 2011, 2019) and as Borcherdt (2012) noted, correlations of VS30 with strong-motion spectral amplification measurements, empirical amplifications inferred from ground motion prediction equations, and average shear-wave velocity at other depths have established VS30 as a robust single parameter for characterizing site response.

Some studies questioned the ability of VS30 to solely capture the complexity of site effects (Steidl 2000; Di Giacomo et al. 2005; Wald and Mori 2000; Lee and Trifunac 2010, Farrugia et al. 2021). Ghanbari et al. (2018) warned practitioners against solely relying on the VS30 in ground motion response studies because of possibly oversimplifying the subsurface profile. Anbazhagan et al. (2011) discussed in detail the correlation between amplification and shear wave velocities with the conclusion that site response amplification is much more than empirical values for same shear wave velocity. Anbazhagan et al. (2018) noted that a direct correlation of the site response and VS30 for shallow bedrock sites may result in an overestimation of soil average velocity values and an underestimation of site effects and suggested preferably determining amplification (one of the site responses effects) by using average shear wave velocity up to bedrock (VSbedrock). This parameter characterizes a substantial part of the environment responsible for amplification. However, as noted by Foti et al. (2018) and referred to by Garofalo et al. (2016), while the average velocities within the first tens of metres are rather well determined by surface wave methods, the determination of VSbedrock has greater uncertainties. Gallipoli and Mucciarelli (2009) performed a microzonation study in Italy and noticed that VS10 could predict site classification with the same efficiency as VS30 and thus can be a substitute for it.

Some studies proposed improving the evaluation process by using VS30 in combination with other parameters such as fundamental resonance frequency of the site f0 (Luzi et al. 2011), depth at which the shear wave velocity profile exceeds 800 m/s H800 (Derras et al. 2017) or S-wave impedance (Shingaki et al. 2018). Paolucci et al. (2021) proposed H800 and VS,H (average Vs to a depth of H, where H is conditional on H800) as a new proxy in the draft Part 1 of Eurocode 8.

However, one of the strongest dismissals of VS30 as an amplification proxy came from Castellaro et al. (2008), who reanalysed the empirical bases of the correlation between VS30 and amplification from Borcherdt (1994) and claimed that seismic amplification is too complex to be related only to the VS30. Nevertheless, Borcherdt (2012) replied that Castellaro et al. (2008) used incorrect assumptions leading to a misapplication of the regression model. One of the most serious concerns raised by Castellaro et al. (2008) is the large scatter of empirical data used by Borcherdt (1994) to derive the regression models. Since one of the reasons for such scatter could be the data quality, we decided to carry out a study on a dataset recorded by an instrumentally homogeneous and spatially dense seismic network. Earthquake recordings from the West Bohemia Seismic Network (WEBNET) were correlated with VS30 estimated at the seismic station locations by the multichannel analysis of surface waves (MASW). For a more comprehensive analysis of the VS30 site proxy suitability we used two additional parameters characterizing the near-surface geology: (i) H800 determined by surface wave analysis using MASW and (ii) bedrock densities estimated by Blížkovský et al. (1981).

2 Site description

The West Bohemia/Vogtland region (Fig. 1) on the Czech–German border was selected for the analysis. It forms the western section of the Bohemian Massif and is located in the transition zone between three distinct Variscan structural units: the Teplá-Barrandian in the centre of the region, the Moldanubian in the south-east and the Saxothuringian in the north-west (Babuška et al. 2007; Fischer et al. 2014). The area is intersected by two main neotectonic structures: the Eger rift, a 300 km long and 50 km wide ENE–WSW trending zone (Dèzes et al. 2004; Blecha et al. 2009, 2018; Fischer et al. 2014), and by the Mariánské Lázně fault striking NNW–SSE with a length of 100 km (Prodehl et al. 1995; Bankwitz 2003). In terms of seismicity, the West Bohemia/Vogtland region is characterized by the frequent occurrence of weak earthquake swarm events, mostly of magnitudes ML ≤ 3.5 (Fischer et al. 2010, 2014). The predominant part of the present seismic activity in the region is roughly defined by the area between 49.9° to 51.0°N and 12.0° to 12.8°E and is characteristically spatially and temporarily clustered (Fischer and Bachura 2014). The prevailing lithologies of bedrock are Proterozoic and early Paleozoic metasedimentary rocks with low and medium grades of metamorphosis (Czech Geological Survey 2004).

Fig. 1
figure 1

Generalized regional tectonic map of Central Europe (after Dèzes et al. 2004) with a detailed section showing a digital elevation model map of the West Bohemia/Vogtland region. WEBNET seismic stations are marked with triangles and a code designation. Major cities are marked with black circles. BF: Black Forest, EG: Eger (Ohře) Graben, FP: Franconian Platform, HG: Hessian grabens, LRG: Lower Rhine (Roer Valley) Graben, OW: Odenwald, URG: Upper Rhine Graben, VG: Vosges

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The main reason for choosing this region for VS30 verification is the presence of the West Bohemia Seismic Network (WEBNET) which provides high quality earthquake catalogues. This is given by an instrumentally homogeneous and spatially dense seismic network primarily designed to monitor weak events of local seismicity (Institute of Geophysics AS CR 1991; Horálek et al. 2000; Fischer et al. 2010, 2014; Fischer and Bachura 2014).

The construction of the WEBNET began after the significant earthquake swarm in 1985/1986 (Horálek and Vavryčuk 1987; Horálek et al. 2000). The network currently covers over 900 km2 and currently consists of 25 temporary and permanent stations and ensures an appropriate spatial and azimuthal coverage of the focal area, especially with respect to the main, active Nový Kostel zone (Fischer et al. 2010). WEBNET stations are equipped with broadband, three-component, weak motion seismometers, mostly Guralp CMG-3ESPC. The basic station parameters were described by Fischer et al. (2010), the updated information and earthquake catalogues are available from the website of the Geophysical Institute of the CAS (https://www.ig.cas.cz/en/observatories/local-seismic-network-webnet). Seventeen representative and accessible WEBNET stations were chosen for this study, as depicted on the map in Fig. 1.

The use of data from a well-established seismic network offers a significant advantage: individual stations are well calibrated, ensuring reliable amplitude values. However, a drawback of such networks arises from the preference for locating stations on hard bedrock to achieve optimal sensor-ground coupling. Consequently, it is anticipated that very low VS30 values may not be present in the datasets.

3 Data analysis

3.1 Surface waves analysis and VS30 determination

In order to obtain shear wave velocity (VS) models and estimate VS30 for 17 WEBNET station sites, a Multichannel analysis of surface waves (MASW) was performed. The method was introduced by Park et al. (1998, 1999) as a tool for elastic property of near-surface materials investigation. The complete MASW process consists of (i) multichannel surface-wave data acquisition, (ii) dispersion analysis and (iii) inversion analysis leading to the VS model (Fig. 2).

Fig. 2
figure 2

Example of the surface wave analysis for the KOC station: a multichannel shot gather record (source position 81 m); b Rayleigh wave dispersion image with picked dispersion curve (black circles); c final (bold black) and initial (black dashed line) VS models with estimated RMSE

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Due to its simplicity, MASW has found wide applications such as bedrock mapping (Miller et al. 1999; Park 2016), marine environments investigation (Kaufmann et al. 2005), landslides (Strelec et al. 2017), karst investigation (Debeglia et al. 2006) and in particular site characterization and VS30 estimation (Hollender et al. 2018; Olafsdottir et al. 2019, Gaytan et al. 2020). Incorporating basic MASW analysis into standard refraction surveys can reduce solution ambiguity and enhance knowledge without incurring additional costs (Mazanec and Valenta 2023).

Although the analysis of Comina et al. (2011) confirmed the robustness of surface wave testing for estimating VS30 and the uncertainty in the VS30 measurements using MASW was quantified at only 5–6% (Moss 2008), standard MASW approach suffers from several shortcomings. Dal Moro (2014, 2023) warned that subjective interpretation of the vertical component of Rayleigh wave phase velocity spectrum may lead to mode misidentification, especially when analysing only fundamental mode. Dal Moro also highlighted the risk of non-uniqueness of the solution obtained from the inversion of only one observable. A possible remedy for the above shortcomings could be joint analysis of actively acquired MASW data with passively acquired ambient vibration data using one of the robust methods (Aki 1957; Asten et al. 2006; Cho et al. 2013) or incorporation of Love wave or group velocity (Safani et al. 2005; Dal Moro and Mazanec 2024) into the analysis.

However, if the acquisition of ambient noise is not possible and/or only vertical geophones are available, standard MASW may yield reliable results, if only the analysis is performed cautiously and the limitations (such as near/far-field effects, complex multimodal dispersion spectra, penetration depth and resolution limits given by the acquisition geometry, etc.) are considered and obeyed. With the addition of a few shots within the profile, a P-wave velocity refraction tomography cross-section can be obtained as an addition for the MASW (Mazanec and Valenta 2023).

In the WEBNET stations sites data acquisition was carried out using a 24-channel linear receiver array with 4.5 Hz vertical geophones. Receiver spacing varied from 3 to 5 m according to local spatial and morphology conditions. To achieve a high signal/noise ratio (Foti et al. 2018), eight vertically stacked sledgehammer (10 kg) impacts on the metal plate were performed at two shot points with different offsets (usually 2.5 and 10 m) at both ends of each profile. In addition, for seismic refraction tomography, shot gathers were acquired from five shot points within the seismic profiles. The length of the seismic records was 1 or 2 s to record all the generated wave types (Fig. 2).

The common shot gather data from opposite ends of the profile were transformed into the phase velocity-frequency domain using the Phase-Shift method (Park et al. 1998) and a Rayleigh wave dispersion spectrum was generated. Next, the observed dispersion curves were extracted using the fundamental mode picking in the frequency range from 5 to 45 Hz (Figs. 2 and 3). This was usually done for all four source positions and the resulting dispersion curve is their average.

Fig. 3
figure 3

Example of dispersion spectra with picked Rayleigh wave dispersion curves for four WEBNET sites: a LAC; b MAC; c LOUD and d STC

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In the inversion analysis, a starting theoretical VS model was first created, then a theoretical dispersion curve representing the model was obtained. The non-linear least squares method (LSM) iteratively seeks the VS profile with the dispersion curve best matching with the observed dispersion curve in the least squares sense and subsequently modifies the theoretical model in an iterative way. During the inversion process the smoothness of the velocity model was controlled by regularization to reduce the risk of over-parametrization. The root means square error (RMSE) of the final VS model defines the matching error between the two dispersion curves.

To further reduce the ambiguity of dispersion curve inversion, the resulting velocity models were cross-validated using the results of P-wave velocity refraction tomography (retrieved from the same datasets extended by additional shot points inside the profile). Finally, the average shear wave velocity of the upper 30 m was estimated using the following formula (Eq. 1):

$${V}_{S30}=\frac{30}{{\sum }_{i=1}^{N}\frac{{h}_{i}}{{v}_{i}}}$$
(1)

where hi and vi denote the thickness and the shear wave velocity for the i-th formation or layer, in a total of N. H800 values were retrieved from the Vs models as a depth at which the shear wave velocity profile exceeds the value of 800 m/s.

3.2 Comparison between amplification and VS30

To evaluate the site response and understand the link between VS30 and seismic amplification, a comparison was made of the VS30 values determined for WEBNET stations and the amplitudes of two recent earthquakes recorded by the WEBNET (Institute of Geophysics AS CR 1991): (1) Mw 6.4 Petrinja, Croatia and (2) Mw 4.2 SE of Vienna, Austria (Fig. 4).

Fig. 4
figure 4

European map showing the location of the two earthquakes: Mw 4.2 Vienna and Mw 6.4 Petrinja (red stars) in relation to the WEBNET (red square)

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The main reasons for selecting Petrinja and Vienna earthquakes for the study were: (i) the distances from stations to epicentres (~ 300 km and 600 km) are much larger than inter-station distances (less than 30 km) making the differences in distances and azimuths of individual station-epicentre pairs negligible (Figs. 1 and 3); (ii) the peak amplitudes of velocity and acceleration of earthquakes propagating to the Bohemian Massif from SE are considerably higher (up to the order of one magnitude) compared to other directions (Vavryčuk et al. 2004; Málek et al. 2005, 2017) and (iii) from the practical point of view the strong earthquakes with magnitudes exceeding 4.0 are not common within the Bohemian Massif.

On December 29, 2020, a Mw 6.4 earthquake occurred (45.42°N, 16.26°E) west of the town Petrinja in central Croatia (Ganas et al. 2021). The earthquake was located ∼ 600 km from WEBNET with azimuth ∼ 150° (Fig. 4). On April 30, 2021, a moderate Mw 4.2 earthquake was located 5.3 km from Wiener Neustadt (47.76°N, 16.21°E, for simplicity hereinafter referred to as the “Vienna” earthquake) with a distance of ∼ 300 km and azimuth ∼ 133° from WEBNET (Fig. 4). Both earthquakes were recorded by all WEBNET seismic stations and are well defined with a high S/N ratio. Only the Vienna earthquake was not recorded by the VAC station due to temporary technical problems. See the Petrinja and Vienna earthquake seismograms on Fig. 5.

Fig. 5
figure 5

Example of an earthquake recording from the BUBD station, in the left column for the Mw 4.2 Vienna earthquake, and in the right column for the Mw 6.4 Petrinja earthquake: a and b seismograms (three components Z, R and T); c and d acceleration spectra (three components: Z, R and T); e and f acceleration spectra (P, S, and surface wave sections). Please, note that due to the different magnitude and distance of the two earthquakes analysed, the range of amplitudes is different

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The analysis using earthquake records from 17 WEBNET stations consisted of the following steps. First, amplitude spectra of both earthquake records were computed similarly to Borcherdt and Gibbs (1976). Subsequently an acceleration spectrum was obtained (Fig. 5) and acceleration spectrum amplitudes were summed in nine frequency windows: 0 − 10 Hz, 0 − 0.5 Hz, 0.5 − 1 Hz, 0.5 − 2 Hz, 1 − 2 Hz, 1 − 3 Hz, 2 − 4 Hz, 4 − 8 Hz, 5 − 10 Hz. These windows were selected as they are generally considered to be the most representative for the site amplification (Borcherdt 1976; Harmsen 1997; Castellaro et al 2008). Next, for each analysed frequency window separately, the acceleration spectrum amplitudes were summed and represent here the amplification ratio. To be able to compare the correlation results between the different frequency windows, we related the amplification ratio values to the JOC station values (here, amplification ratio = 1) and refer this correlated parameter relative amplification ratio. To understand the effect of different seismic wave types on seismic amplification, four wave type categories were analysed: (i) complete seismogram; (ii) P-waves group; (iii) S-waves group and (iv) surface waves sections. Finally, the relative amplification ratios for four wave type categories (i–iv) were plotted for analyzed frequency windows as a function of estimated VS30. Based on previous studies (Midorikawa 1987; Borcherdt et al. 1991; Borcherdt 1994; Gallipoli and Mucciarelli 2009) and observations within the WEBNET dataset, the dependence between VS30 and seismic amplification was characterized using a simple empirical model:

$$A={A}_{0}+\frac{k}{{V}_{S30}},$$
(2)

where A represents the amplification amplitude, k is the slope of decline, VS30 is the average shear-wave velocity in the uppermost 30 m and A0 represents amplitudes for high VS30. The goodness of fit of the proposed model describes how well it fits a set of observations and is expressed by the regression coefficient R2.

4 Results

4.1 Surface waves analysis and VS30 determination

The surface waves analysis carried out at 17 WEBNET sites using MASW resolved 1D shear-wave velocity profiles (Fig. 2) and parameters H800 and VS30 (Table 1). The RMSE, defining the match of theoretical dispersion curves for VS profiles and the observed dispersion curves, is in the range of 0.3–1.7% (Table 1). In general, VS30 values range from 486 to 1594 m/s with 9 sites exceeding 1000 m/s. The high average shear wave velocity is characteristic for this dataset because the WEBNET stations are purposely situated in sites with shallow bedrock depths to obtain a good S/N ratio. For most sites, the Rayleigh wave phase velocity increases continuously as the frequency decreases, indicating a monotonous increase of the shear-wave velocity with depth (Fig. 3). Nevertheless, there are also sites with the presence of velocity reversals: HOPD, JOC, KVC caused by differential weathering of the bedrock.

Table 1 Site characterization for 17 WEBNET stations: location name, seismic station abbreviation, geographic coordinates, actual seismic station depth, RMSE of the surface waves inversion, VS30*—MASW estimated, VS30**—corrected to the actual depth position of the seismic station, site category according to EC8-1 (CEN 2004), parameter H800, general geology of the bedrock based on the geological map 1: 50 000 (Czech Geological Survey 2004) and bulk density taken from the results of density mapping at a scale of 1:200 000 (Blížkovský et al. 1981)
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Based on the estimated VS30 values, the sites were classified according to the Eurocode 8 (CEN 2004), see Table 1. The dataset contains 11 WEBNET sites classified as a EC8-1 A class, and six sites classified as category B.

The wide range of VS30, despite all the sites being selected in locations with sound bedrock, is a consequence of varying lithologies and is also reflected in the reported densities in Table 1 (based on Blížkovský et al. 1981). Low densities typically correlate with the lowest VS30 values, while the highest VS30 values typically indicate quartz-rich metasediments such as quartzites and quartz-rich phyllites, as well as high-grade metamorphic rocks. Conversely, low VS30 values correspond to less compact metamorphic rocks with lower densities that are more susceptible to weathering. A consistent characteristic among all B class sites is the presence of low VS values in the upper approximately 10 m, reflecting a higher degree of surface rock weathering.

Second parameter derived from surface wave analysis is H800 (Table 1). Values of this parameter are correlated with VS30 as sites with low average shear wave velocity usually show high H800 (sites MAC and NKC reach VS > 800 m/s at depths exceeding 30 m) and vice versa the high VS30 sites reach shear wave velocity 800 m/s near surface or at the surface.

WEBNET seismic stations are installed on concrete pillars in 1–5 m deep vaults (Fischer et al. 2010) to improve the S/N ratio. The actual WEBNET stations’ subsurface depths are listed in Table 1. To compensate for the different subsurface stations’ depths in the correlation analysis the VS30 (Table 1) was corrected by calculating the average shear wave velocity to a depth of 30 m below the actual station position using Eq. 1 and neglecting the layers above the station. This correction has slightly changed the estimated VS30, because shifting the zero-depth value has suppressed the effect of the shallowest layers, that usually have the slowest shear-wave velocities. The average change in the VS30 is 7%. From now on, if VS30 is referred to in connection with the correlation analysis, it means depth-corrected values.

4.2 Amplification and VS30 correlation

For the nine frequency windows examined, the sums of the acceleration spectrum amplitudes (referred as a relative amplification ratio) of two earthquake ground motions (recorded by WEBNET) representing amplification, were plotted as a function of VS30 (Fig. 7). In each frequency window, the comparison was performed for four wave type categories (i–iv), resulting in 36 plots. To characterize the relationship between VS30 and site amplification, a simple model was applied (defined by Eq. 2) to each correlation plot.

Figure 7 shows six correlation plots with the highest regression coefficient R2 (three plots for each of the two earthquakes analysed). Seismic stations are represented by black triangles and marked with station codes. The regression model is represented by the dashed line. For each frequency window and wave type category, the relationship between the two studied variables is different, however, there are trends, which are elaborated on further in the Discussion.

Figure 8 shows the results of the regression analysis for the four wave categories (above denoted as i–iv) analyzed in the nine frequency windows. The range of the regression coefficient R2 is 0.01–0.66 and there is a clear frequency dependence of R2. The lowest correlation coefficients R2 are achieved in low-frequency windows < 1 Hz. With increasing frequency, the R2 increases with the highest values in the range 1–4 Hz. The R2 in this frequency range usually varies between 0.5 and 0.6 depending on the wave type. In terms of regression correlation, across all the wave categories analysed, the highest R2 values were in the 1–3 Hz frequency window. The R2 generally decreases for frequencies > 4 Hz. Statistically evaluated, the category (i) has the most balanced correlation results and category (ii) has the lowest correlation values.

5 Discussion

The presented results of comprehensive analysis (evaluating site effects using VS30, H800, density and lithology) suggest that there could be several approaches to identifying the soil classes. One of the possible way could be the above-mentioned direct link between VS30, densities and lithology. This correlation, however, is severely biased by the fact that it only deals with acidic rocks (and their derivates—quartz rich sediments and metamorphic). If mafic rocks are added to the dataset, the correlation is likely to fail. These high-density rocks are more prone to weathering following the reversed Bowen’s reaction scheme (Bowen 1922) and weathering, together with mechanical disintegration, are obviously the key factors affecting the VS30 (Barton 2006) and thus the amplification. All the B class sites within the analysed dataset are typical with low shear-wave velocities near the surface and a high velocity gradient within the first ten metres indicating that near-surface weathering plays a key role here. Moreover, the difference in density values is low which, together with the mentioned similarity in lithology indicates that mechanical properties of the geological units encountered should be comparable and no special attention should be paid to the variations in bedrock geology. The observed differences in site amplification do not stem from the lithological change solely.

Figure 7 indicates that there is a link between amplification and VS30 in the analysed dataset. For sites with a high average VS (EC8 class A), the amplification is considerably lower than for sites with the lowest (within the dataset) VS30 (EC8 class B). This is consistent with the general assumption that site amplification increases as a function of soil category (Sairam et al. 2019). Three different zones can be observed in Fig. 7: (1) High velocity zone with VS30 above ∼ 1300 m/s-sites HOPD, ZHC and TRC. In this zone the amplification is the lowest in the dataset and attains amplitudes less than about half of the observed dataset maximum (which is in zone 3); (2) Middle velocity zone in which the VS30 range is ∼ 680–1300 m/s and for sites in this zone the amplification does not vary significantly with velocity; (3) Slow velocity zone with VS30 under ∼ 680 m/s (primarily sites LAC, MAC and NKC), in which the lowest average shear-wave velocity is observed and amplification reaches the dataset maximum (usually at least double the High velocity zone).

As shown in Fig. 8, there is a visible frequency dependence of R2, which is supported by the energy distribution visible in the acceleration spectra in Fig. 6, with the dominant highest amplitudes in the 1–4 Hz frequency range. Statistically evaluated 1–4 Hz window is the best suited for tracking the dependence of VS30 and amplification. Such frequency range is in good agreement with previous observations: Borcherdt and Gibbs (1976) reported that amplitude changes in the frequency range 0.25–3.0 Hz are consistently related to the local geological conditions of the recording site. Borcherdt and Gibbs (1976) also indicated that the horizontal and vertical spectral amplification curves are approximately constant as a function of frequency in the interval 0.25–4.0 Hz. Our observations are also consistent with the mid-period site amplification factor Fv, which is defined as the average of the amplitude response over a 0.4–2.0 s (0.5–2.5 Hz) period band and is incorporated in building code provisions (Borcherdt 1994; BSSC 1994; BSSC 2020). In this frequency range, the correlation for Vienna earthquake dataset shows R2 = 0.64 (wave category i). Gallipoli and Mucciarelli (2009) performed the horizontal to vertical spectral ratio (HVSR) at 40 sites in Italy and reported, similarly, that most of their HVSR peaks fell in the range of 0.5–1.5 s (0.6–2 Hz). Harmsen (1997) correlated averaged site-amplification spectra within two frequency bands (0.5–1.5 Hz and 2–6 Hz) with VS30 and concluded that statistically significant correlation is found in both frequency bands.

Fig. 6
figure 6

The shear-wave velocity profiles of 17 WEBNET sites obtained using MASW. The VS30 value for each site and RMSE of the surface waves inversion is shown in Table 1

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Figure 9 reports the joint scatter plot of the amplification as a function of the VS30. For this analysis, the statistically best evaluated frequency window and wave type category based on the regression analysis (Fig. 8) is used: 1–3 Hz for wave category i (all wave types). Figure 9 contains data from both analysed earthquakes, 33 values in total, with a single regression model defined by Eq. 2 (presented with the curve parameters). The regression model is estimated with R2 = 0.59 and shows above described VS30-amplification trend. The analysis also reveals a large scatter in amplification within EC8 category B. For sites with velocities in the range of 600–750 m/s, the amplification varies by up to a factor of two. This may have a complex origin, but a common feature visible in the analysed data (Fig. 6) is the significantly lower Vs in the first ⁓ 5 m of the velocity model for stations with high amplification (LAC and MAC). This slow near-surface layer can have a substantial effect on local amplification but could be easily left undetected by using the standard site proxies. Similar observation was noted by Anbazhagan et al. (2018). Nevertheless, as we suggest by a hyperbolic regression in the Fig. 9, it could be used as general tool to indicate the relation between amplification and VS30 accounting also for this effect by a steep part of the regression. The increase in amplifications for the LAC and MAC stations are addressed by the regression in contrast to standard EC8 or NEHRP classifications (Table 1).

Fig. 7
figure 7

Example of scatter plots showing the amplification as a function of VS30. Seismic stations are represented by black triangles and marked with an abbreviation. The regression model defined by Eq. 2 is represented by a dashed line and estimated with regression coefficient R2. The left column shows four correlation plots for the Petrinja earthquake and right column incudes Vienna earthquake dataset, both in the 1–3 Hz frequency window: a and b all waves; c and d P waves; e and f S waves; g and h Surface waves.

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Fig. 8
figure 8

Bar plot of the regression coefficient R2 for the Petrinja (black bars) and Vienna (white bars) datasets in the nine examined frequency windows and four wave type categories (i–iv): a regression coefficient R2 for i) all wave types; b for ii) P waves; c represents iii) S waves and d bar plot shows iv) surface waves

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Fig. 9
figure 9

Joint scatter plot of amplification as a function of VS30 for both Vienna (black dots) and Petrinja (white dots) datasets. The dashed line represents the model defined by Eq. 2 (here presented with the curve parameters). Goodness of fit is expressed by the regression coefficient R2. Plot represents the correlation in the 1–3 Hz frequency window for all wave types. EC8 A and B classes with the velocity boundary (800 m/s) is marked with blue (B class) and magenta (A class) lines and labels

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Nevertheless, it is understood that the analysed dataset is characterized (and potentially biased) by several specific features:

  1. (a)

    The dataset consists of only 17 sites (33 observations in total for the correlation shown in Fig. 9), although the number of observations in other studies is not substantially different—Gallipoli and Mucciarelli (2009) used 45 sites and the classical work of Borcherdt (1994) used 35 stations (and only one earthquake recording).

  2. (b)

    The estimated average shear waves velocities to a depth of 30 m are relatively high and the correlation lacks low velocity stations with VS30 < 500 m/s. However, most high-quality seismic networks will face the same problem, as this station positioning is essential to create a quality seismic network that reliably detects weak seismic events (Di Giulio et al. 2021). Nevertheless, due to a high quality and instrumentally homogeneous seismic network such as WEBNET (Institute of Geophysics AS CR 1991) differences in the amplification of incoming earthquake signals caused by local conditions, can be observed. The data scatter is thus lower than in the original Borcherdt’s (1994) dataset, which was one of the reasons why Castellaro et al. (2008) criticised the use of VS30 as a site proxy.

Previous research and discussions have shown that local site response is a complex task, often with a nonunique solution (Boore 2004; Castellaro et al. 2008). There is understanding for the objections of several authors about the VS30 and search for new site proxy (Park and Hashash 2005; Castellaro et al. 2008; Gallipoli and Mucciarelli 2009; Lee and Trifunac 2010; Pitilakis et al. 2013; Michel et al. 2014). Derras et al. (2017) tested several site-condition proxies with the intention of finding their optimal combinations for characterizing local conditions. One of their suggestions was to combine VS30 with the H800 parameter. Such suggestion was supported by Paolucci et al. (2021) who proposed H800 and VS,H as a new site categorization criteria for the Eurocode 8. This is in a good agreement with this study’s results, as the four stations with high amplification and lowest VS30 (LAC, MAC, NKC and SNED) have also a very high H800 (> 20 m) and H800 decreases as a function of VS30. However, unlike the proposed regression analysis, none of the parameters H800 or VS30 is able to detect the effect of the near-surface low-velocity layers on amplification shown for LAC and MAC sites.

6 Conclusions

Using high-quality seismic records from WEBNET this study addressed a question of whether VS30 is a suitable proxy for seismic amplification. Using MASW at 17 WEBNET sites shear-wave velocity models were obtained and H800 and VS30 were estimated. Surface waves analysis showed that WEBNET sites are characterized by high shear-wave velocities (Fig. 6 and Table 1) with the VS30 range 486–1594 m/s belonging to the EC8 classes A and B. H800 correlate with VS30 as sites with low average shear wave velocity generally show high H800 and vice versa.

Estimated VS30 and relative amplification ratios (summed acceleration amplitudes representing amplification) of the Mw 6.4 Petrinja and Mw 4.2 Vienna earthquakes (Fig. 5) were correlated in nine frequency windows and in four wave type categories. The analysis (Fig. 7) indicates that there is a clear relation between VS30 and amplification in certain frequency windows (Fig. 8). Three different zones can be observed in Fig. 7: (1) High velocity zone with VS30 above ∼ 1300 m/s. In this zone the amplification is the lowest in the dataset; (2) Middle velocity zone in which the VS30 range is ∼ 680–1200 m/s and for sites in this zone the amplification does not vary significantly with velocity; (3) Slow velocity zone with VS30 under ∼ 680 m/s in which the lowest average shear-wave velocity is observed, and amplification reaches the dataset maximum (stations LAC and MAC). The relative amplification ratios in the High velocity zone are roughly half of those in the Slow velocity zone. Following the discussion on the suitability of VS30 as a proxy for seismic amplification, it can be concluded that for the WEBNET sites with shear-wave velocity lower than ∼ 680 m/s the amplification is significantly higher than for the sites with higher VS30. However, there is a visible amplification values scatter within the EC8 B class that VS30 and most of the standard site proxy could not reveal. In contrast, the results show that there is a certain value of VS30 over which the amplification does not change significantly. According to the results, for sites with a VS30 over ∼ 680 m/s (soft to hard rocks) the site conditions only have a negligible effect on earthquake amplification. This visible pattern is characterized by the regression model defined by Eq. 2. Using the regression model (Eq. 2) the observed relation in nine frequency windows was characterized for four wave type categories. Goodness of fit, presented in Fig. 8, showed, that there is a visible frequency dependence of R2. The best frequency range for observing the above defined dependence is, in general, 1–4 Hz zone with the 1–3 Hz window being rated with the highest R2 within the dataset. It turns out that this dependence can be observed in all four categories of wave types tested, with category i) (all waves) being the best statistically evaluated.

Based on the observations from the WEBNET dataset analysis, the approach demonstrated in Fig. 9 is put forward as a general tool to indicate the relation between amplification and VS30 as it could serve as a fine and sensitive tool for amplification estimation without the need for defining new parameters. In contrast to other methods the regression offers a smooth scale rather than a classification and in addition directly states an amplification ratio for a particular site which is a key factor for all engineering purposes. It is appreciated that the analysed dataset is characterized and potentially biased by several distinctive features, especially the high VS30 range so the robustness of proposed approach needs to be tested on various data.