From ambient vibration data analysis to 1D ground-motion prediction of the Mj 5.9 and the Mj 6.5 Kumamoto earthquakes in the Kumamoto alluvial plain, Japan

Abstract

We present horizontal ground motion predictions at a soft site in the Kumamoto alluvial plain for the Mj 5.9 and Mj 6.5 Kumamoto earthquakes of April 2016, in the framework of an international blind prediction exercise. Such predictions were obtained by leveraging all available information which included: (i) analysis of earthquake ground motions; (ii) processing of ambient vibration data (AMV); and (iii) 1D ground response analysis. Spectral analysis of earthquake ground-motion data were used to obtain empirical estimates of the prediction site amplification function, with evidence of an amplification peak at about 1.2 Hz. Horizontal-to-vertical spectral ratio analysis of AMV confirmed this resonance frequency and pointed out also a low-frequency resonance around 0.3 Hz at the prediction site. AMV were then processed by cross-correlation, modified spatial autocorrelation and high-resolution beamforming methods to retrieve the 1D shear-wave velocity (Vs) structure at the prediction site by joint inversion of surface-wave dispersion and ellipticity curves. The use of low frequency dispersion curve and ellipticity data allowed to retrieve a reference Vs profile down to few thousand meters depth which was then used to perform 1D equivalent-linear simulations of the M 5.9 event, and both equivalent-linear and nonlinear simulations of the M 6.5 event at the target site. Adopting quantitative goodness-of-fit metrics based on time–frequency representation of the signals, we obtained fair-to-good agreement between 1D predictions and observations for the Mj 6.5 earthquake and a poor agreement for the Mj 5.9 earthquake. In terms of acceleration response spectra, while ground-motion overpredictions were obtained for the Mj 5.9 event, simulated ground motions for the Mj 6.5 earthquake severely underestimate the observations, especially those obtained by the nonlinear approach.

Graphical Abstract

Introduction

The assessment of our capability of predicting earthquake ground motion is of paramount importance for performance-based design and retrofitting of existing building stock. Moreover, earthquake risk mitigation strategies also rely on the capability of earth scientists and earthquake engineers to predict the ground motion at a site of interest (Chaljub et al 2015). Such importance have stimulated the research on this field, with particular emphasis on the determination of the earthquake source characteristics (Galvez et al 2014), the development of methods for the reconstruction of realistic 3D subsurface structures (Di Michele et al 2022) and the implementation of efficient and accurate computational methods for ground motion estimation (Bielak et al 2010), including the nonlinear behavior of shallow geologic materials (Esmaeilzadeh et al 2019, to name a few).

A relatively long tradition of ground motion prediction assessment has been established in the framework of IASPEI/IAEE international symposia on the Effects of Surface Geology (ESG) on Seismic Motion; in these conferences, such as Odawara, Japan (1992), Yokohama, Japan (1998) and Grenoble, France (2006), several blind prediction exercises were devoted to test geophysical methods for retrieving realistic models of the subsurface and verify the accuracy of computational methods in reproducing real earthquake ground motion in complex settings (Chaljub et al. 2010).

Following this tradition, the more recent ESG6, held in Kyoto, Japan, in 2021, promoted a similar international blind prediction exercise with the aim of evaluating the capability of expert researchers to retrieve a realistic 1D shear-wave velocity (Vs) structure from seismic surveys performed at a prediction site in the Kumamoto plain (Step 1; Matsushima et al., submitted to Earth Planets and Space; Chimoto et al. 2023). This target site recorded seismic events of the 2016 Kumamoto sequence, and the blind exercise (Tsuno et al., submitted to Earth Planets and Space) further investigated the accuracy in reproducing weak- (Step 2) and strong- (Step 3) ground motions belonging to the sequence by both empirically based and numerical methods.

It is well known that ground motion amplification at a site is controlled by seismic wave propagation, particularly close to the surface, therefore the knowledge of the Vs subsurface structure is an essential element for ground response analysis (Kramer 1996; Boore 2004). Vs structure at a site can be obtained by both invasive and non-invasive methods; while the former were usually considered more reliable due to their processing simplicity, the latter have gained increasing popularity due to their cost-effectiveness (Bard et al. 2010; Garofalo et al. 2016a). In fact, invasive methods, such as down-hole or cross-hole tests, imply moderate-cost operations and logistic difficulties due to the need of borehole drillings. Whereas passive non-invasive methods, which are based on surface-wave propagation analysis (Foti et al. 2014), require as easy and low-cost field operations as deploying standard seismic instrumentation on the surface in a predetermined 2D geometry (Maranò et al. 2014). Moreover, non-invasive approaches allow to investigate, even if with lower accuracy, the deeper part of soil columns. However, these advantages are countered by complex and time-consuming processing and inversion of the acquired data.

More in detail, several processing methods were proposed to retrieve Rayleigh and Love-wave dispersion curve (DC) from ambient vibrations (Aki 1957; Capon 1969; Tokimatsu 1997; Bettig et al. 2001; Ohori et al. 2002; Shapiro and Campillo 2004; Okada 2006; Maranò et al. 2017; Wathelet et al. 2018; Vassallo et al. 2019). Several approaches were proposed as well for the inversion of DC data to obtain the Vs profile at the investigated site (Herrmann 1987; Yamanaka and Ishida 1996; Wathelet 2008). This last step of analysis is characterized by high non-linearity and non-uniqueness of the solution (Foti et al. 2009; Renalier et al. 2010; Boaga et al. 2011; Di Giulio et al. 2012; Gosselin et al. 2022) which affects the output of a ground response analysis (GRA). The significant expertise required by passive surface wave methods promoted the development of projects and international initiatives devoted to the advancement of the current state-of-practice (Bard et al. 2010; Garofalo et al. 2016a, 2016b).

A general limitation on the use of passive surface-wave methods is their formal applicability to 1D site conditions, namely subsurface structures which can be approximated to a stack of homogeneous isotropic horizontal viscoelastic layers overlying an elastic half-space. An approach for the practical verification of such conditions could be performing horizontal-to-vertical spectral ratio (H/V) analysis (Nogoshi and Igarashi 1971; Nakamura 1989; SESAME 2005) of the data acquired by a 2D array of seismic sensors. In case of homogeneous results in terms of H/V curves across the 2D array, the 1D condition may be reasonably assumed for the investigated site. In addition, H/V data represent also a valuable support for Vs profile retrieval due to their relation with Rayleigh-wave ellipticity data (Fäh et al. 2003, 2009; Hobiger et al. 2009), which can be used as a joint-inversion target along with DC data (Hobiger et al. 2013; Marcucci et al. 2019). Under the 1D site approximation, the analysis of seismic wave propagation can be reduced to that of vertically propagating horizontally polarized shear-wave (SH) through horizontal soil layering from a transmitting half-space boundary at the bottom of the 1D soil column (Kramer 1996). This assumption is at the foundation of 1D GRA, which allows for the prediction of surface ground motion based on the availability of a representative bedrock ground motion input, realistic Vs vertical profile at the site, a mass density profile and a description of the soil constitutive model. In particular, recent studies focused on the comparison between linear, equivalent-linear (EQL) and nonlinear (NL) soil behavior with observations (see Kaklamanos and Bradley 2018 for a comprehensive review).

Regarding the relation between input ground motion level and soil constitutive model, it was found that the commonly adopted EQL fails in reproducing observations if the maximum shear strain induced by the input earthquake excitation in the soil exceeds some threshold level, estimated to be in the range 0.2–0.3% (Kim and Hashash 2013; Yee et al. 2013). Therefore, NL ground simulations are recommended in case of strong ground motions (Stewart et al. 2014).

Studies also addressed the issue of the applicability of 1D GRA given that it cannot take into account complex 2D and 3D subsurface structures which severely affects seismic wave propagation in valleys and basins (Aki and Larner 1970; Bard and Bouchon 1985). Experimental validation of the 1D assumption is indeed a difficult task which can be tackled by different approaches (Pilz and Cotton 2019). This could explain the large variability of the percentage of sites in a given sample for which the 1D assumption holds, ranging from 16% (Thompson et al. 2012) to 69% (Tao and Rathje 2020), that was estimated by several studies based on different comparison criteria between 1D GRA results and ground motion observations.

In this paper, we describe and discuss the ground motion predictions obtained for two events of the Kumamoto seismic sequence which occurred in southwest Japan in 2016 and culminated with the April 15th Mj 7.3 mainshock. In particular, we focused on the largest aftershock (Mj 5.9, Step 2) of the Kumamoto earthquake sequence and the April 14th, 2016 foreshock (Mj 6.5, Step 3) at the prediction site (KUMA) by: i) the estimation of the 1D Vs structure at the prediction site by processing of ambient vibration (AMV) data recorded by 2D seismic arrays; and ii) numerical simulation of earthquake strong- and weak-motions by 1D ground response analysis (GRA).

The aim is to quantitatively compare the recordings of the two Kumamoto earthquakes (Mj 5.9 and Mj 6.5) with the predictions obtained by current state-of-practice in earthquake engineering, which include building a large depth 1D Vs model from advanced processing of AMV data acquired by several 2D arrays of different aperture (Step 1; Matsushima et al., submitted to Earth Planets and Space; Chimoto et al. 2023), and performing 1D GRA adopting EQL and NL constitutive models (Steps 2 and 3; Tsuno et al., submitted to Earth Planets and Space). The paper is organized as follows: after a brief description of the available data (Matsushima et al., submitted to Earth Planets and Space), we describe the H/V analysis of AMV data carried out to evaluate the feasibility of the 1D assumption for the site and obtain information on Rayleigh-wave ellipticity. Then, we describe the results of the processing methods adopted for the wide frequency band DC data retrieval, which include Modified Spatial Autocorrelation (MSPAC, Bettig et al. 2001), cross-correlation (Shapiro and Campillo 2004) and high-resolution Rayleigh-wave three-component beam forming (RTBF, Wathelet et al. 2018). Subsequently, the procedures for the joint-inversion of DC and ellipticity data are described and the results in terms of Vs profile are illustrated (Step 1; Chimoto et al. 2023). Finally, we depict the 1D GRA predictions obtained for Steps 2 and 3 (Mj 5.9 and 6.5, respectively) and compare these with the observed ground motions at the KUMA site.

Geological setting and available data

The prediction site, KUMA, is located in the N sector of the Kumamoto plain in the Kumamoto prefecture, Japan (Fig. 1a). In its easternmost sector facing the Ariake bay, this plain has a width of roughly 9000 m in the NS direction and it is filled by alluvial deposits of the Shirakawa and Midorikawa rivers and by volcano-clastic deposits from the Aso volcano (Tsuno et al. 2017). Previous 2D geophysical surveys (MEXT, 2016) inferred that the alluvial and volcano-clastic layered units have a total thickness of roughly 500 m, while a deep seismic discontinuity is present down to a maximum depth of roughly 1500 m in the N part of the basin. The northern margin of the basin is limited by a south dipping fault which separates the layered sedimentary units from the andesite rocks of Mt. Kinbo outcropping northward. In the Mt. Kinbo area a reference recording site, SEVO, is located (Fig. 1a). Information about the deep P-wave velocity (Vp), Vs and density vertical structures in the area is also available from the Japan Integrated Velocity Structure Model (JIVSM, Koketsu et al. 2012) and the Japan Seismic Hazard Information System (J-SHIS ver.2, NIED). Both models show discontinuities in all parameter vertical profiles at depths between 400 and 600 m, which well correlate with the estimated thickness of the alluvial and volcano-clastic filling of the Kumamoto plain (Fig. 2 c,d). In particular, the J-SHIS model shows a sharp increase in Vp and Vs at about 450 m depth, where Vp varies from 2600 m/s to 5000 m/s and Vs from 1200 m/s to 2600 m/s (dotted lines in Fig. 2,c). Only the JIVSM model highlights a large Vs and Vp discontinuity at about 1450 m depth, roughly corresponding with the estimated basin maximum depth (MEXT, 2016), where Vp varies from 4200 m/s to 5600 m/s and Vs from 2400 to 3200 m/s (solid lines in Fig. 2,c).

Fig. 1

Map showing the location of the prediction KUMA and reference SEVO sites (a) and 2D arrays geometry (b). Panel a: distribution of earthquakes belonging to the Kumamoto sequence for which recordings at the sites are available (red circles). The epicenter of the Mj 5.9 (Step 2) aftershock and the Mj 6.5 (Step 3) and Mj 7.3 mainshocks are shown as yellow stars. Panel b: deployment geometry for the KUM-LL, KUM-M and KUM-SM arrays around the prediction site KUMA (Kumamoto plain). KUM-SS1 and KUM-S arrays have similar geometry but are not visible at the scale of the image due to their lower aperture (side lengths of the larger triangular geometry of about 20 m for KUM-S and 2 m for KUM-SS1)

Fig. 2

a Shallow Vp and Vs models obtained from PS logging (OYO 2020) and from passive geophysical measurements (Chimoto et al. 2016). The horizontal dotted lines show the subdivision between the main shallow geological units from geotechnical investigation (OYO 2020). b Shallow density model by Chimoto et al. (2016). c Vp, Vs and density (d) vertical structures from the Japan Integrated Velocity Structure Model (JIVSM, Koketsu et al. 2012) and the Japan Seismic Hazard Information System by (J-SHIS ver.2, NIED)

The prediction site KUMA and the reference site SEVO (Matsushima et al., submitted to Earth Planets and Space), were equipped with a strong-motion sensor and a seismic sensor, respectively. These stations recorded several ground motions of the 2016 Kumamoto seismic sequence (Table 1), including the 14th April 2016 Mj 6.5 foreshock and the April 15th Mj 7.3 mainshock. The foreshock was caused by right-lateral strike-slip faulting along the Hinagu fault while the mainshock started from a Northern slip patch of this same fault and transferred to the Futagawa fault to the NE (Fig. 1a), where also a significant normal slip component was observed (Asano and Iwata 2016). Among those waveforms, we focused on the Mj 6.5 foreshock (Step 3) and the largest aftershock (Mj 5.9, Step 2) of the sequence (Fig. 1a and Table 1). We neglected the Mj 7.3 mainshock ground-motions because the recording is incomplete due to a system malfunctioning at the KUMA site instrument.

Table 1 List of earthquakes for which recordings are available at the prediction KUMA and reference SEVO sites

For the passive analysis, the AMV data consist of 3-component recordings acquired by seismic sensors (fundamental period equal to 10 s) connected to high-resolution data loggers (24-bit dynamic range) and deployed in 2-D array configuration around KUMA site. The 5 arrays (KUM-SS1, KUM-S, KUM-SM, KUM-M and KUM-LL) considered in the blind prediction have nested triangular geometry (Fig.  1b) with increasing aperture (larger side of the triangle ranging from about 2 m to 960 m), therefore allowing for surface wave dispersion retrieval in a wide range of frequencies. Each array is made of 7 sensors with a central station. The recording length is 45 min for KUM-SS1, 1 h for KUM-S and 2 h for the remaining arrays; recording sampling frequency is 200 Hz for all signals. Given the short aperture of the smallest array which severely limits its investigated frequency bandwidth, recordings from the SS1 array were only used for single-station analysis. Due to a system malfunction in the NS component of the central sensor (station 1) in common with all arrays, data acquired by this sensor were discarded from the processing method which required all three-component (3C) recordings at each sensor for DC retrieval (three-component Rayleigh Beam Forming—RTBF, see “Vs-profile retrieval from AMV data” Section for further details). But data from the central station were included in the remaining analyses which focus only on the vertical component of motion.

The description of the finer structure of the basin infilling and the geotechnical parameters of the investigated soils at the KUMA site were obtained by passive geophysical measurements (Chimoto et al. 2016) and geotechnical investigations, including borehole stratigraphic log, Vp and Vs profiles from PS logging and laboratory testing (Fig. 2a; OYO 2020). Laboratory tests, including cyclic triaxial testing, were carried out on 5 samples (T1–T5) collected at different depths (from 4 to 23 m) to estimate physical and nonlinear properties of the soils which we included in our 1D modeling. The shallower 30 m are mainly composed of sands, below which an 8-m-thick gravel layer is found. At the bottom of the borehole, around 40 m depth, the stratigraphic log reports the presence of tuff breccia (Fig. 2a). The shallower velocity profile shows Vs values lower than 200 m/s down to 20 m depth (solid red line in Fig. 2a). Such values are in agreement with the estimated Vs from passive geophysical measurements (dotted red line in Fig. 2a; Chimoto et al. 2016). Then the Vs values gradually increase to 420 m/s in correspondence of the tuff deposits.

Data analysis

Empirical amplification function at KUMA by earthquake data analysis

The earthquake ground motions (Table 1) recorded at the predictions site KUMA, located on soft and deep alluvial deposits, and at the reference site SEVO, located on andesite rock of Mt. Kinbo, were processed by means of spectral analysis to obtain empirical estimates of the KUMA site amplification functions. To this aim, we employed the well known horizontal-to-vertical spectral ratio (EHV, Field and Jacob 1995) and standard spectral ratio (SSR; Borcherdt 1994) methods, both of which are considered to provide robust estimates of the investigated site amplification function. SSR method relies on the identification of a reference recording site (Steidl et al. 1996), usually located on rock or firm soil, for which site effects could be considered negligible. Under the conditions of (i) close site-to-reference distance (Rref) with respect to the site epicentral distance (Rd, such that Rref <  < Rd/5) and ii) sufficient signal-to-noise ratio of the recordings obtained at both stations (SNR > 3), the SSR estimates can be obtained by calculating the ratio between Fourier amplitude spectra (FAS) of soft site and reference station as:

$$SSR = \frac{{FAS_{site} }}{{FAS_{reference} }}.$$

Since a reference site is not always available, the EHV method has been proposed which consist in the ratio between the FAS of the horizontal earthquake ground motion and the FAS of vertical component at the same site:

$$EHV = \frac{{FAS_{horizontal} }}{{FAS_{vertical} }}.$$

EHV method assumes that the vertical component of ground motions is not affected by site effects; however, it has been proved that this hypothesis is often not verified in real data (Felicetta et al. 2021) and, therefore, the EHV could be considered as a lower boundary of the site amplification level with respect to the SSR method. In any case, both SSR and EHV can provide consistent and robust estimates of the investigated site fundamental resonance frequency (Pilz et al. 2009).

Calculation of SSR and EHV includes common processing steps, like removal of the DC component and detrending before tapering and conversion to the frequency domain. The earthquake velocity records acquired at SEVO station were differentiated to obtain acceleration records before computation of FAS. Horizontal FAS were calculated for each station as geometric average of NS and EW components of ground motions. Then, the average SSR and EHV estimates from all earthquake records were calculated assuming lognormal distribution of FAS amplitudes.

The SSR empirical amplification function at KUMA, and EHVs calculated for both prediction KUMA and reference SEVO stations using the signals originated by the 12 earthquakes with Mj < 5 listed in Table 1 are reported in Fig. 3. The EHV function calculated at the reference SEVO site shows maximum value around 0.4 Hz, with amplitude around value 3.5, a secondary maximum around 1.2 Hz and average amplitude below 2.5 for frequencies larger than 1 Hz (Fig. 3, top panel). This result suggests that this site is likely affected by a low-frequency amplification (< 1 Hz) and could be considered a good reference in the higher frequency band. The EHV calculated at KUMA evidenced a clear amplification peak around 1.2 Hz, with average amplitude around 6 and a secondary maximum around 2 Hz (Fig. 3, middle panel). The SSR function at KUMA presented maxima at 1.2 and 7 Hz, with similar average amplitude around 8, and at 2.5 Hz, with slightly lower amplitude. The comparison between the two site amplification function estimation methods allowed us to identify the site fundamental resonance frequency at Kuma, which is around 1.2 Hz. A dubitative peak is also suggested in the low frequency part (around 0.4–0.5 Hz) but not well resolved by the SSR analysis.

Fig. 3

Empirical amplification functions at KUMA and SEVO sites. Average EHV functions calculated at SEVO reference site (top panel) and KUMA prediction site (middle panel). SSR function calculated at KUMA (bottom panel)

H/V spectral ratios of AMV and Rayleigh-wave ellipticity retrieval

AMV data were analyzed by computing the H/V spectral ratios to evaluate the degree of homogeneity in the subsurface conditions below each array. We used the Geopsy code (Wathelet et al. 2020) using a running time-window of 120 s, and a logarithmic spectral smoothing algorithm (Konno and Ohmachi 1998) with the default value of 40 for the bandwidth coefficient b. The H/V curves of all the arrays (KUM-SS1, KUM-S, KUM-SM, KUM-M and KUM-LL) consistently show two resonance peaks at about 0.3 and 1.1 Hz with amplitude as large as 4 and 8, respectively (Fig. 4). For the arrays with the largest aperture (KUM-SM, KUM-M and KUM-LL), the second resonance peak slightly increases in frequency up to 1.3 Hz. The systematic lower amplitude of the H/V curve calculated for station 01 is clearly visible from the comparison of the average H/V curves for the 3 lower aperture arrays and is due to the system malfunction of the NS component. Neglecting this outlier, the average H/V curves are similar and suggest homogenous subsurface conditions for the arrays. As expected, the average curves show larger dispersion (Fig. 4e) for the KUM-LL array, which spans a much wider area in which the homogenous assumption may not strictly hold. However, also for KUM-LL data the two frequency peaks in the H/V ratios are clearly observed. To evaluate the polarization of the estimated frequency peaks, we have also calculated the H/V ratios as a function of rotated horizontal components in the horizontal plane (see Additional file 1). We do not show the results here for the sake of brevity but we did not observe any clear directional dependence of the H/V peaks amplitude along a particular direction, therefore we related the two H/V peaks to the presence of seismic velocity contrasts along the depth profile. Although different peaks in the H/V curves can be also related to the presence of Rayleigh-wave higher modes (Arai and Tokimatsu 2004), given the objective difficulties of proper mode addressing, we based our further analysis on the simplified assumption that the observed H/V peaks are both related to the contribution of the fundamental mode Rayleigh wave.

Fig. 4

H/V curves at the five arrays with increasing aperture: KUM_SS1 (a), KUM_S (b), KUM_SM (c), KUM_M (d) and KUM_LL (e). The average H/V curves at the seven stations (solid curves, in left panels), their mean curve with standard deviation (solid and dashed lines in middle panels), and array geometry (open circles in right panels) are also shown. The comparison between the average H/V curve (solid line) and the average fundamental Rayleigh wave ellipticity curve (dashed line) obtained by Raydec analysis (Hobiger et al. 2009) for station #7 of the KUM_S array is also shown (f)

H/V curve is considered as a proxy for the Rayleigh wave ellipticity (Fäh et al. 2003), but the similarity of actual H/V and ellipticity is controlled by the relative proportion of Rayleigh waves and other seismic phases in the AMV wavefield (Molnar et al. 2022). To extract the Rayleigh wave ellipticity curve to be used in surface wave inversion and evaluate the relative contribution of surface waves and body waves in the H/V composition, the random decrement technique (Raydec; Hobiger et al. 2009) was applied to one station of KUM-S array. This method aims at suppressing the occurrence of seismic phases other than Rayleigh waves by stacking the narrow-band filtered time windows of the signals starting at positive zero-crossing of the vertical component of motion, and projecting the corresponding horizontals into the direction which maximizes the correlation to the vertical with the theoretical 90° phase shift of the Rayleigh wave. Since the method applies to the 3-components of motion, station 1 was discarded due to the malfunction and sensor 7 was selected for the analysis. The Raydec ellipticity curve (Fig. 4f) has a shape similar to the H/V curve calculated for the same station. The two curves have close amplitude above 2 Hz and show a main peak at 1.1 Hz but Raydec ellipticity has a lower amplitude with respect to the corresponding H/V curve (maximum amplitude difference of 2.2 at 1.1 Hz). The Raydec curve stays below the H/V in the frequency range 0.4–2 Hz. The amplitude difference between the curves is almost constant (0.5) in the frequency range 0.4 Hz up to the first trough at 0.6 Hz. Finally, Raydec ellipticity shows a lower frequency peak than H/V (below 0.3 Hz). This result suggests that whereas a significant uncertainty affects the low frequency resonance, the higher frequency resonance is well retrieved from both methods. In addition, the Rayleigh wave predominance in the ambient vibration wavefield seems confirmed for the higher frequency range (above 2 Hz) where the curves are closer, whereas the relative contribution of the other different phases increases and varies with frequency in the lower range.

Vs-profile retrieval from AMV data

To retrieve the surface-wave DC from AMV data, we employed different techniques and datasets. In particular, the vertical components of AMV recorded at all sensors of the arrays with the largest aperture (KUM-SM, KUM-M and KUM-LL) were analyzed by the cross-correlation (CC) and the Modified Spatial Autocorrelation (MSPAC; Bettig et al. 2001; Wathelet et al. 2005) methods to derive the fundamental-mode Rayleigh-wave DC. 3C AMV data recorded at all sensors composing the largest arrays, excepting for those recorded at the malfunctioning central sensor (station 1) in common with all arrays, were used to retrieve both the fundamental mode Rayleigh- and Love-wave DCs by the high-resolution Rayleigh Beam Forming (RTBF) technique. The CC analysis was implemented by ad hoc software (Vassallo et. al. 2019; Di Giulio et al. 2020) whereas MSPAC and RTBF analyses were performed by using the Geopsy software suite (Wathelet et al. 2020). In the following, for the sake of brevity and readability, we focused on the comparison of the results from each method and their combination to derive the inversion target DCs rather than on the processing details. Interested readers are referred to the supplementary materials for an exhaustive description of the processing steps adopted in each technique (see Additional file 2).

DC data obtained from the different methods show a very good agreement (Fig. 5), and allow to select a final Rayleigh curve in a wide frequency band (from 0.71 to 20 Hz). DCs and their uncertainties (please see Additional file 2) derived from different methods were combined, i.e., resampled and averaged in the slowness domain, producing a final uncertainty at a given frequency (shown as error bar in Fig. 5).

Fig. 5

Rayleigh-wave DC estimated using Cross-correlation (a), MSPAC (b) and RTBF analysis (c). The DCs are overlaid in d

The Rayleigh-wave DCs obtained by the three methods are within their experimental uncertainty in the frequency range 1.5–8 Hz. The most significant discrepancy in the DCs is observed in the lowest frequencies part (below 1 Hz) where RTBF analysis gives higher phase-velocities with respect to MSPAC analysis (Fig. 5d). We decided to select DC data for the lowest frequencies based on the MSPAC curve, because the spatial autocorrelation method in principle can provide a better resolution (Ohori et al. 2002) assuming the plane-wave stationarity and an isotropic AMV wavefield. Table 2 summarizes how the target DC was built: the target Rayleigh DC was selected combining the MSPAC results below 1 Hz (using data from KUM_LL to KUM_S arrays), the CC results above 8 Hz and averaging the DCs obtained from the three methods in the range 1.5–8 Hz. Only the RTBF analysis exploited the AMV horizontal data providing the Love-wave DC in the range 0.74–3.5 Hz.

Table 2 Frequency range limits of DCs from array analysis

Rayleigh and Love dispersion curves were jointly inverted for deriving an S-wave velocity profile through an improved neighborhood algorithm as developed in Geopsy (Wathelet 2008). Since the results of the geotechnical and geophysical investigation (OYO 2020) were not yet released to the participants of the blind prediction step 1 at the time of the inversion, the model parameter space (Table 3) was mainly based on the information available from the JIVSM and J-SHIS models for Vs and densities and on the Chimoto et al. (2016) model for Vs and densities in the very shallow part of the profile (Fig. 2); in particular, we tested different model parameterization during the inversion and the better fitting results were obtained using seven uniform layers overlying the half-space (Table 3 and Fig. 6). S-wave velocities were allowed to vary in a range of ± 50% with respect to the values in the reference models. A linear increase of S-wave velocity with depth was allowed for the uppermost layer (maximum thickness of 25 m; see Table 3). Both density and P-wave velocity were linked to Vs profile, Vp with the condition of the Poisson’s ratio to be within the range 0.2–0.5.

Table 3 Model parameterization used in the inversion

Fig. 6

From left to right: Vp and Vs models derived from the joint inversion of Rayleigh (R), Love (L) DC (fundamental mode), and with the absolute Rayleigh-wave ellipticity. The experimental curves are plotted in black, whereas the models are plotted in a color scale proportional to the misfit obtained during the inversion. The best model (i.e., minimum misfit) is shown in red color

Although the inversion software allows for taking into account the ellipticity sign (i.e., prograde or retrograde Rayleigh-wave particle motion), we used the absolute value of the fundamental mode Rayleigh-wave ellipticity derived by Raydec analysis (Fig. 4f) as an additional inversion constraint because of its clear depiction of both ellipticity peaks at about 0.3 Hz and 1.1 Hz. In fact, in addition to the Raydec method, the RTBF method allows for the extraction of Rayleigh wave ellipticity as well; to this aim we performed some tests and found that the two methods provide consistent results for frequencies above 0.6 Hz, whereas the Raydec method outperforms RTBF in the low frequency range where the ellipticity peak around 0.3 Hz was observed (please refer to Figure D of Additional file 2).

During the inversion, we fixed an equal weight to all input data (dispersion and ellipticity curves). We tried to fit the two ellipticity peaks at about 0.3 Hz and 1 Hz and the main trough at about 3 Hz of the fundamental mode Rayleigh-wave ellipticity curve. Overall, we obtained a good fit between our results and the observations (Fig. 6). The results are shown for a misfit value lower than 0.4, where misfit is calculated as (Wathelet et al. 2008):

$$misfit=\sqrt{\sum_{i}\frac{{(x{d}_{i}-x{c}_{i})}^{2}}{{\sigma }_{i}^{2}{n}_{f}},}$$

with xd_i and xc_i representing the observed and the calculated data sample at frequency i, σ is the data standard deviation and n_f is the number of frequency samples.

The best fit model (misfit = 0.36) shows shallow velocities ranging from 150 to 250 m/s in the top 20 m. Vs increases up to 400 m/s down to 80 m depth, where a first Vs discontinuity is found and the velocity increases at about 1000 m/s. The Vs profile shows this last value down to roughly 400 m depth, where a second Vs sudden increase to 1700 m/s is observed. The main seismic impedance contrast is estimated at a large depth around 1500 m, where the seismic bedrock Vs is estimated to be larger than 3700 m/s. It is worth noting that the bedrock depth estimate is mainly controlled by the low-frequency peak in the ellipticity curve.

1D ground motion simulations

We simulated the weak motions (Mj 5.9, step 2) observed at the prediction site KUMA by the STRATA code, which allows performing 1D total stress ground response analysis in the frequency domain (Kottke and Rathje 2008). This code takes into account nonlinearity of subsurface materials through the equivalent-linear (EQL) approach (Schnabel et al. 1972), an iterative procedure for which the assigned properties of the viscoelastic subsurface layers, namely normalized shear modulus (G/G₀) and material damping ratio (D), are iteratively adjusted to be consistent with the effective level of shear strain (γ %) induced by the input motion. The EQL implementation requires that for each viscoelastic layer of the 1D model the values of thickness, unit weight, shear-wave velocity (Vs) and normalized shear modulus reduction and damping curves as a function of γ are specified. For the shallower layers, nonlinear modulus reduction and damping curves (Table 4) were drawn from laboratory tests (Fig. 7) and from the literature (Rollins et al. 1998), taking into account the information included in the OYO report (OYO 2020), which was made available at this stage of the blind prediction exercise. In particular, this report includes both the results of cyclic triaxial laboratory testing performed on the specimens and the hyperbolic model fitting of the G/G0-γ and D-γ curves for each sample as proposed by Hardin and Drnevich (1972). In our modeling, we decided to use the experimental data (colored symbol in Fig. 7) except for the damping estimation at shear strain levels larger than 0.1%, where we used the hyperbolic model.

Table 4 1D EQL model parameters; the codes T1, T2, T3 and T4 refer to shear modulus reduction and damping curves estimated by laboratory testing (OYO 2020) and shown in Fig. 7

Fig. 7

Nonlinear modulus reduction (G/G₀ vs shear strain-ɣ) and damping (D vs shear strain-ɣ) curves obtained from cyclic triaxial testing of soil samples collected at the KUMA site. The symbols represent the experimental data while the solid lines represent the Hardin and Drnevich (1972) hyperbolic model fitting of the experimental data (H–D model). T1 sample was collected at depths between 4 and 5 m, T2 between 7.7 and 8.7 m, T3 between 13 and 14 m and T4 between 20 and 21 m (redrawn from OYO, 2020)

Although the software allows taking into account for the variability of the input model parameters (thickness, velocity and nonlinear properties) by a Monte Carlo approach, which generates a distribution of output, we decided to proceed in the simulation without including model parameter variations to simplify the comparison between ground motion predictions and observations, particularly in terms acceleration time series. We leveraged the code automatic sub-layer discretization to allow for seismic energy transmission at frequencies up to 25 Hz, and maximum iteration number was set equal to 20.

In addition to EQL 1D simulations by STRATA, we also performed a 1D total stress ground response analysis by the Deepsoil software (Hashash et al. 2020) to predict horizontal strong ground motions (Mj 6.5, step 3). This code allows performing fully nonlinear (NL) ground response analysis in the time-domain by integrating the equation of motion in small time steps. This approach fully accounts for nonlinear behavior of subsurface materials through cyclic nonlinear stress–strain models. As a constitutive model for the shallower layers (Table 5), we used an extended version of the modified Kondner–Zelasko constitutive model (MKZ) developed by Matasović and Vucetic (1993). The modulus reduction and damping pressure-dependent hyperbolic model fitting procedure (MRDF; Hashash et al.2020) was used to fit nonlinear normalized shear modulus reduction and damping curves associated with each model layer. This procedure includes a frequency-independent damping as proposed by Phillips and Hashash (2009). In this case, we divided each layer model into sub-layers with thickness h_s to allow for seismic energy transmission up to the maximum frequency ${f}_{max}$= 30 Hz by the following formula:

$$h_{s} = Vs/4 f_{max} ,$$

where $Vs$ is the layer shear-wave velocity.

Table 5 1D NL model parameters

For both EQL and NL 1D simulations, input accelerations were the horizontal ground motion (NS and EW components) recordings acquired at the reference site SEVO for the Mj 5.9 and Mj 6.5 earthquakes. These signals were baseline corrected (processed by de-trending, zero padding and high-pass filtering with 0.1 Hz corner frequency), converted to acceleration time-histories and applied at the half-space level implementing an elastic base boundary condition, therefore considering the input as outcropping motions. The adopted Vs model was that obtained from AMV data analysis as described in subsection “Vs-profile retrieval from AMV data” Section.

For the nonlinear model of the Mj 6.5 foreshock (step 3), the Vs subsurface model was adapted to the layer discretization needed to correctly perform the nonlinear analysis, namely by fulfilling the following condition: sub-layer thickness h <  = Vs/(4 *f_max), where f_max is the maximum frequency of analysis which was set equal to 30 Hz. The 1D nonlinear model is summarized in Table 5, including layer discretization (n# of sub-layers and thickness of each sub-layer). Model was built similarly to what was described for the EQL case. Table 5 also includes target modulus reduction and damping curves for the fitting of the MRDF pressure-dependent hyperbolic model. Similarly to the EQL case, we assumed linear viscoelastic stress–strain behavior with constant damping ratio of 1% for the deeper layers (i.e., at depth larger than about 80 m).

Results

Shear-wave velocity structure at the prediction site

AMV data collected at the KUMA prediction site are characterized by a significant contribution of surface waves, and the use of arrays with increasing aperture allowed to derive surface-waves dispersion curve data in a wide frequency range (from 0.7 to 20 Hz). Moreover the geometry composed of two nested triangles using seven seismic stations proved very convenient since it allowed for good azimuthal coverage of surface-wave propagation fronts with a limited number of stations. We have adopted different techniques of analysis obtaining very consistent results in terms of fundamental mode Rayleigh-wave dispersion data (Fig. 5d). Further, the Raydec and RTBF analyses allowed to extract Rayleigh-wave ellipticity and the fundamental mode Love-wave dispersion curves, respectively.

The best fit model derived from the joint inversion of DC and ellipticity data shows a good agreement between experimental and theoretical curves, except in the frequency band 4–6 Hz where the theoretical Rayleigh DC is not able to follow the inflection of the experimental DC (Fig. 6). The ESG6 Committee has provided its “consensus” model for the target site based on literature data. We compared this “consensus” model with our results in Fig. 8, finding a satisfactory agreement between the two models.

Fig. 8

Comparison between our best model (in red) derived from the joint inversion and the “consensus” ESG6 model (in black). The comparison is shown in terms of Vp, Vs, density and SH transfer functions computed by the reflectivity method (Kennett and Kerry, 1979) implemented in the Geopsy software suite (Wathelet et al. 2020). In the SH modeling, P-wave and S-wave quality factors Qp and Qs were set equal to 1/10 of Vp and Vs values, respectively

It is worth mentioning that even if we adopted the simplified assumption of both ellipticity peaks related to the Rayleigh wave fundamental mode, the fair agreement in the Vs structure obtained by our joint inversion of DC and ellipticity data and that provided by the ESG6 committee, suggests that this assumption may hold true in our case.

The first 400 m of the Vp and Vs profiles are very similar, and also the deep seismic contrast around a depth of 1500 m is found in both models. The main difference between the two is in the depth of the intermediate seismic velocity contrast, which is found at a depth of about 400 m in our model versus 600 m in the “consensus” model. On average, our model shows lower Vs values than the “consensus” one between 400 and 1500 m, and some large discrepancies are also observed in the density values. The density was fixed during our inversion (Table 3) because of its low influence on dispersion curves, and we did not consider the “consensus’’ density profile that was released by ESG6 committee only after the inversion blind exercise (at the end of step1). The comparison between the two models is also performed in terms of SH transfer functions (Fig. 8) computed by the reflectivity method (Kennett and Kerry 1979). Both functions point out that the main ground motion amplification should be observed in the 1–2 Hz frequency range, with SH transfer functions showing some differences in the amplification level, mainly in the lower frequency range (i.e., < 1 Hz) and between 1.5 and 2 Hz.

1D simulation results

The 1D simulations predicted significant horizontal ground motion amplification at the KUMA site with respect to SEVO, where the seismic input was recorded, for both weak- and strong-motion input. For the M 5.9 earthquake (step2), the predicted time series by the EQL approach shows PGA of about 0.036 g for the EW component and of about 0.049 g for the NS component (Table 6 and Fig. 9c, d). Such prediction is in very good agreement with the observation for the EW ground motion recorded at the KUMA site (0.034 g; Fig. 9a, c), whereas peak ground motion for the NS component is largely overestimated by 45% (Fig. 9b, d).

Table 6 Values of peak ground acceleration (PGA) from observations at KUMA (obs), Strata EQL model (strata) and fully nonlinear model (deepsoil)

Fig. 9

Mj 5.9 ground motion observations versus 1D EQL predictions for EW and NS ground-motion components (left and right panel, respectively). a, b, c, d, e, f Acceleration time series, for observations (red), 1D EQL predictions at KUMA (blue) and input ground motion recorded at SEVO reference site (black). g, h Fourier amplitude spectra for input ground motion (black), observations (red) and predictions at KUMA (blue). i, l 5%-damped acceleration response spectra for input ground motion (black), observations (red) and 1D EQL predictions at KUMA (blue)

The comparison of Fourier amplitude spectra (FAS) shows that the 1D EQL predictions have larger amplitude than the observations for low frequencies (below 1 Hz), whereas FAS is rather well predicted for the EW component of motion in the range 1–3 Hz (Fig. 9g, h). This is particularly evident from the examination of the FAS calculated for the NS component of the ground motion in the frequency band 1–2 Hz (Fig. 9h). It is worth noting that in this frequency band, the NS input ground motion component has FAS 3 times larger than the EW input component, so large that the NS input FAS is comparable to that observed at KUMA (Fig. 9h), thus explaining the differential response predicted at the surface due to the two input motions.

This frequency- (or period T)dependent ground motion overestimation of the recordings by the 1D EQL predictions is pointed out by the comparison between observed and predicted 5% damped elastic acceleration response spectra (Fig. 9i, l). At KUMA, peaks of the recorded acceleration spectral ordinates (Sa) are observed in the period band between 0.1 and 0.4 s; the larger amplitudes were recorded for the NS ground motion component, with values around 0.13 g (Fig. 9l). In terms of Sa, the predictions largely overestimate the observed EW response spectra for periods above 0.3 s, where the 1D EQL simulations show amplitudes up to 2.3 times larger than the observations (about 0.07 g, Fig. 9i) and the observed NS response spectra in the period band 0.4–2 s, where the predictions are up to 5 times larger than the observations (about 0.125 g, Fig. 9l).

To obtain a more quantitative evaluation of the goodness-of-fit (GoF) between predicted and recorded motions, we used the categories proposed by Kristeková et al. (2009), which are based on time–frequency (TF) representation of the waveforms to be compared and related misfit metrics. In particular, two indices are used to quantify the agreement between signals based on their envelope quantitative comparison (EG), and the phase GoF (PG). In more detail, for two signals where one is the reference, it is possible to calculate the envelope and phase differences between the TF representations of the two signals normalized by the maximum TF of the reference; then, the obtained misfits are transformed such as to assume values in a finite range which allows for the quantitative evaluation of the agreement between the two signals (Kristeková et al. 2009). Therefore, EG can be interpreted as a single integral value of the overall GoF between the envelopes of the analyzed signals and analogously PG for the phase GoF (Kristeková et al. 2006); these finite values of envelope GoF can also be represented as a function of time (TEG) and frequency (FEG) and similarly for the phase GoF as a function of time (TPG) and frequency (FPG). According to the original formulation of Kristeková et al. (2009), EG and PG, along with the other above described GoF parameters, are allowed to vary in the range 0–10, where 10 means perfect agreement between observed and predicted ground-motion, values below 4 indicate a poor fit, values in the range 4–6 stand for a fair fit, values between 6 and 8 represent a good fit and over 8 are for an excellent fit.

To calculate the GoF, the predicted and recorded ground-motions were bandpass filtered between 0.1 and 20 Hz using a fourth-order non-causal Butterworth filter before computation of their continuous wavelet transform (Daubechies 1992), and the calculation of GoF metrics was obtained through the obspy python package (Beyreuther et al. 2010).

For the Mj 5.9 predictions, the EG values are about 3.5 and 2.5 for the EW and NS horizontal components (Fig. 10), indicating a rather poor amplitude GoF with the observations, whereas the phase GoF is fair for the EW component (PG of about 4.8) and the NS component (PG of about 4). EG as a function of frequency (FEG, insets in Fig. 10) shows that the envelope disagreement between the signals is mainly between 1–2 Hz while PG as a function of frequency (FPG, insets in Fig. 10) shows that the phase disagreement is distributed on a wider frequency band, especially for the NS component.

Fig. 10

Comparison between 1D EQL predictions and recorded ground motions at KUMA for the Mj 5.9 earthquake and GoF evaluation following Kristeková et al. (2009). TF representation of the envelope (TFEG) agreement between 1D EQL predictions and recorded ground motions with the evaluation of envelope GoF along time (TEG) and frequency (FEG) axes (upper panels). TF representation of the phase (TFPG) agreement between 1D EQL predictions and recorded ground motions with the evaluation of phase GoF along time (TPG) and frequency (FPG) axes (lower panels). Overall integral GoF metrics for the envelope (EG) and phase (PG) agreement are reported in the black box with values in the range 0–10, where 10 means perfect agreement. Left panels show TFEG and TFPG for the EW component of predicted (black line in middle panel) and recorded (red line in middle panel) ground motions; right panels show the same quantities for the NS components

For the Mj 6.5 Kumamoto foreshock, we compared horizontal strong ground motion predictions obtained using the EQL and NL approaches with the observations. The observed peak acceleration value is about 0.40 and 0.45 g for the EW and NS components (Table 6 and Fig. 11a, b). The input ground motions recorded at SEVO show similar waveforms and PGA values, about 0.12 g for the EW component and 0.10 for the NS (Fig. 11g, h). The output PGA for the EQL simulations is about 0.32 g for both horizontal components (Fig. 11c, d), whereas the PGA is about 0.18 g for the EW component and 0.15 g for the NS component in the case of the NL predictions (Table 6 and Fig. 11e, f). The visual inspection of acceleration time series reveals a fairly good strong seismic phases alignment between predictions and observations; however, the same inspection highlights the strong low-pass filtering effect of 1D site modeling, particularly for the EQL ground-motion predictions (Fig. 11c, d). In fact, the comparison between FAS obtained by EQL and NL predictions and FAS observations at KUMA show that both 1D modeling approaches underpredict the recorded motions (Fig. 11i, l). The underprediction is larger for the NS than the EW component and for frequencies higher than about 5 Hz.

Fig. 11

Mj 6.5 ground motion observations versus 1D EQL and NL predictions for EW and NS components (left and right panel, respectively). a, b, c, d, e, f, g, h Acceleration time series for EW and NS components. Red, blue, green and black colors refer to observations, EQL and NL ground motions at KUMA, input ground motion recorded at SEVO reference site, respectively. i, l FAS for input motion (black), observations (red), EQL (blue) and NL predictions at KUMA (green). m, n 5%-damped acceleration response spectra for input motion (black), observations (red), 1D EQL (blue) and NL predictions at KUMA (green)

In terms of Sa, the recorded EW 5%-damped elastic response spectra show three main maxima: around 0.15 s, with amplitude of about 0.9 g, around 0.4 s, with amplitude of about 0.7 g and a broad peak centered around 1.0 s, with amplitude of about 0.75 g (Fig. 11m). For this component, the EQL prediction shows a fairly good agreement for the periods higher than 0.8 s. In fact, the 1D EQL simulated response spectra shows a similar broad peak centered around 1 s with amplitude which is only slightly underestimated (of about 7%) with respect to the observed. The main disagreement of Sa value is in the lower periods (T < 0.8 s), for which the observed Sa is up to 125% larger than the prediction (Fig. 11m). The NL simulation for the EW ground motion component severely underpredicts the observed response spectra in the period range 0.1–2.5 s, with amplitudes lower than 110% at 1.0 s and 125% at 0.15 s (Fig. 11m). Similar considerations hold for the predicted NS elastic response spectra; the shape of predicted and observed response spectra are similar but both EQL and NL predictions systematically underpredict the observed Sa in all periods bands, with larger discrepancies for the NL prediction (Sa amplitudes 2.5 times lower than observations at 0.8 s) (Fig. 11n). As a general consideration, the EQL predictions in terms of maximum Sa are 75% larger than the NL ones and thus show lower disagreement with the observed data (Fig. 11m, n).

We have calculated envelope (EG) and phase (PG) GoF between predicted and recorded horizontal motions also for the Mj 6.5 earthquake (Fig. 12) through the time–frequency misfit analysis of Kristeková et al. (2009). For this earthquake, we obtained larger GoF parameters with respect to the Mj 5.9 event. Amplitude GoF between predictions and recorded ground motion is fair (Fig. 12), with higher EG values (EG of about 5.9 for the EW and 5.7 for the NS components) for the 1D EQL motions with respect to the 1D NL (EG lower than 5.5). Phase GoF is good for both EQL and NL models; the higher values of PG are obtained for the NS component predictions (PG of about 6.8 and 6.7 for the EQL and NL simulations) with respect to the EW (PG of about 6.0 and 6.4 for the EQL and NL simulations).

Fig. 12

Comparison between 1D predictions and recorded ground motions at KUMA for the Mj 6.5 earthquake and GoF evaluation following Kristeková et al. (2009). TF representation of the envelope (TFEG) agreement between 1D EQL predictions and recorded ground motions with the evaluation of envelope GoF along time (TEG) and frequency (FEG) axes (a and b upper panels). TF representation of the phase (TFPG) agreement between 1D EQL predictions and recorded ground motions with the evaluation of phase GoF along time (TPG) and frequency (FPG) axes (a and b lower panels). Overall integral GoF metrics for the envelope (EG) and phase (PG) agreement are reported in the black box with values in the range 0–10, where 10 means perfect agreement. Left panels show TFEG and TFPG for the EW component of predicted (black line in middle panel) and recorded (red line in middle panel) ground motions; right panels show the same quantities for the NS components. c and d Show the same quantities and information as in a and b but for the 1D NL approach

For the Kumamoto foreshock, we also calculated the maximum shear strain (γ_max) vertical profile obtained by EQL and NL simulations; for both approaches, the peak strain is reached at the same depth around 37 m, where the implemented Vs model jumps from about 250 m/s–400 m/s (corresponding to the bottom part of layer #7 in Tables 4 and 5). The differences in terms of strain profile between the two approaches are shown in Fig. 13; for the EW component, the peak shear-strain calculated with the EQL approach (about 0.2%) is about double that of the NL one (Fig. 13 left panel). For the NS component the differences are lower, the peak strain is about 0.16% for the NL case whereas it is 0.22% for the EQL case.

Fig. 13

1D EQL and NL peak shear strain profile predictions for the Mj 6.5 Kumamoto earthquake considering the EW ground motion component (left panel) and NS component (right panel) of the input motions

In terms of site transfer function, it is remarkable to note that there is a substantial agreement between the estimates of the main site amplification frequency, around 1.2 Hz, obtained by empirical methods, namely the SSR and EHV, applied to weak ground motions (Mj < 5) and the theoretical site transfer function (TTF), which is calculated as spectral ratio between FAS input ground motion and FAS surface EQL prediction at KUMA (Fig. 14). In particular, the denominator of the TTF is also calculated using weak input motions recorded at SEVO for earthquakes with Mj < 5 (Table 1); for such input motions the calculated TTFs overlap and the soil nonlinear behavior is negligible (the maximum shear strain is equal to 0.015% in our EQL prediction and is reached for the NS component at a depth of about 37 m). The agreement between all three curves is satisfactory in the range 1–2 Hz. Beyond this frequency, the EHV shows lower amplitudes with respect to the SSR, which is considered a more robust estimator of the site amplification function. The agreement between TTF and the average SSR extends to higher frequency up to 4 Hz, where the TTF remains within the uncertainty range of the SSR curve. At higher frequencies, the SSR shows substantially higher amplitudes (up to 2.5 times larger at 7.5 Hz) than both EHV and TTF up to 9 Hz (Fig. 14). Above 10 Hz, the average empirical transfer functions and TTF fall within the average ± 1σ bounds of the expected value and reduce with increasing frequency. It is worth noting that the empirical amplification functions did not pointed out any clear low frequency peak around 0.3 Hz as shown in the H/V curve based on AMV data, likely because of the different sensitivity of the instrumentation used to record earthquake signals at the KUMA site (accelerometer) and AMV (short period sensors) and likely due to the short time-windows used to analyze the earthquake data.

Fig. 14

Comparison between empirical transfer functions calculated at KUMA (red and blue curves with their relative uncertainties) and theoretical transfer function calculated by 1D EQL modeling for the same site (black curve). Empirical transfer functions were calculated for the events in Table 1 with Mj < 5.9

Discussion and conclusions

We analyzed AMV data collected in the Kumamoto alluvial plain (Chimoto et al. 2023) to retrieve a large depth Vs model for the KUMA site and used this model, in combination with available geotechnical information for the site (Matsushima et al., submitted to Earth Planets and Space), to evaluate the agreement between horizontal ground-motion predictions obtained for the Mj 5.9 aftershock (Step 2) and for the Mj 6.5 foreshock (Step 3) of the Kumamoto sequence and the recorded ground-motions at KUMA (Tsuno et al., submitted to Earth Planets and Space). We calculated predicted weak- and strong-ground motions by 1D GRA implementing an EQL model for the Mj 5.9 earthquake and both EQL and NL models for the Mj 6.5 earthquake.

The comparison between Vs structure obtained by AMV-based site characterization methods and by independent information proved the reliability of passive surface-wave testing to derive large depth Vs estimation. The adoption of different techniques of analysis (MSPAC, CC, and RTBF) allowed us to verify the consistency of DC data estimation between methods and to derive a fundamental mode Rayleigh-wave dispersion curve in a large frequency band (Fig. 5). The dispersion curve is very consistent with the one produced by other teams involved in the blind exercise (Chimoto et al. 2023), confirming that the estimation of the surface-wave dispersion curve can be easily computed from the codes nowadays available in the research community. The extraction of Rayleigh-wave ellipticity (Hobiger et al. 2009), as well the estimation of a Love-wave dispersion curve using a three-component array data analysis (Fäh et al. 2008), provided additional constraints to proceed with a joint inversion. We are satisfied with the Vs profile extracted from the joint surface-wave inversion; our group of best Vs fitting models (Fig. 6) for the Kumamoto target site is in reasonably good agreement with the “consensus” Vs profile distributed by the ESG6 committee (Fig. 8). Particularly interesting is that the joint inversion of Rayleigh-, Love-waves DC and Rayleigh-wave ellipticity curve, which is characterized by two clear frequency peaks (centered around 0.3 and 1.1 Hz), provided useful information to constrain the presence of the significant seismic impedance contrasts, including the deep interface at about 1.5 km (Fig. 8). Such convenient integration of AMV-based advanced analysis techniques provided being very effective (Hobiger et al. 2021) and we believe that should be more frequently adopted in the engineering practice, however this would still need additional initiatives for the transfer of knowledge between the research community and practitioners (Bard et al. 2010; Garofalo et al. 2016a, 2016b).

Despite the retrieval of large depth velocity information and the availability of detailed geotechnical information at the site, rather difficult to have in the current state-of-practice, our simulations of the recorded motions (Tsuno et al., submitted to Earth Planets and Space) provided results which are rather controversial regarding the prediction capability of simplified 1D EQL and NL GRA for both events.

For the Mj 5.9 event, we obtained a reasonable agreement between 1D EQL and recorded ground motions in terms of PGA, in particular for the EW component (Fig. 9 and Table 6). A more in-depth analysis of the GoF by quantitative TF misfit criteria (Kristeková et al.2009) reveals a poor to fair agreement in terms of amplitude envelopes, and a fair agreement in terms of phase alignment (Fig. 10). In particular, for the predicted NS component of ground motion, excessive harmonic components around 1.2 Hz in a short time-window around the strong phase arrivals are produced by 1D EQL simulations with respect to the recorded motion (Fig. 10, right-top panel).

In terms of Sa (Fig. 9i, l), we observed a large overestimation of both observed horizontal motions, on average around 70% for the EW and 95% for the NS component, with larger residuals at intermediate periods (0.5 s < T < 1.0 s), this is likely due to the frequency dependent amplification of the site, which has estimated fundamental resonance frequency in the range 1–2 Hz (Fig. 14). Such result is in disagreement with the findings of Kaklamanos and Bradley (2018), who compared a large dataset of recorded ground motions at the KiK-net vertical array sites and simulated ground motions by 1D GRA. In general, these authors found that 1D GRA produces ground motions which underpredict short periods parameters (Sa (T < 0.5 s)) and that this underprediction is dependent on the predicted maximum shear-strain (γ_max): the lower is γ_max, the larger is the underprediction. In our case, for the Mj 5.9 weak-motion where lower γ_max values are expected with respect to the Mj 6.5 event, we observe that the short periods parameters are overpredicted instead of underpredicted, in particular for the NS ground-motion component.

Response spectral ordinates underprediction was calculated by 1D EQL and NL models of the Mj 6.5 Kumamoto earthquake (Fig. 11). The average underprediction is of about 20% for the EW component and 34% for the NS component of the EQL model, and of about 47% for the EW component and of 66% for the NS component of the NL model. Larger biases are observed in the range 0.5–0.7 s and around 2.2 s for the NS component of the NL model. For the EW component, the EQL model still shows an acceptable agreement with observations (Fig. 11), although with an underprediction mostly for intermediate periods in the range 0.8–1.2 s (Fig. 11, left panel), while for the NS component, the systematic bias extends to higher periods (Fig. 11, right panel).

The TF measure of the GoF between predicted and recorded ground motions for the Mj 6.5 event shows fair agreement in terms of amplitude and good agreement in terms of phase, for both 1D EQL and NL models (Fig. 12). Focusing on the envelope disagreement, both 1D EQL and NL predictions lack low-frequency components, below 2 Hz, in a 10- to 15-s-long time-window starting from the strong phase arrivals with respect to both horizontal component recordings.

We speculate that the long period energy in the recorded signal could be related with the properties of the available input motion or with propagation of basin-edge generated surface waves from the alluvial plain margin to the N (Fig. 1). While the latter hypothesis should be tested against more advanced 2D (Bordoni et al 2023) and 3D modeling of the source and seismic wave propagation in the Kumamoto basin, we argue that the selection of the input motion is a critical choice. In particular, the EHV function at the reference SEVO site (Fig. 3) suggests that this site could be affected by intermediate (between 1 and 2 Hz) and low frequency (below 0.6 Hz) site amplification. Therefore, when using the recorded motion at SEVO as input for 1D ground motion prediction, we may introduce in the 1D simulations more low and intermediate frequency energy than really occurred. Thus, this may cause an overprediction of the observations for the more distant and lower magnitude earthquake (Mj 5.9), and an underprediction for the larger magnitude earthquake (Mj 6.5) due to larger strains induced in the 1D soil column model by the excess of energy. The hypothesis of frequency dependent amplification at SEVO could also explain the different bias obtained by the 1D EQL and NL simulations for the Mj 6.5 event, given that predictions in terms of response spectral ordinates obtained by the two approaches start to deviate for peak shear strains (γ_max) similar to those estimated by our simulations (Fig. 13), that is for γ max in the range 0.1–0.4% as a function of period (Kaklamanos and Bradley 2018); however this hypothesis should be investigated by performing additional 1D simulations using different input motions. Moreover, as the difference between predictions obtained by EQL and NL is consistent across a large period interval for the Mj 6.5 event, we hypothesize that there may be other critical issues regarding the accurate representation of modulus reduction and damping behavior for sand dominated stratigraphic profiles (such as in KUMA). This poses a warning in the use of fully nonlinear models, that require a high degree of knowledge of the dynamic properties of the soils that rarely can be obtained in real situations.