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Peak ground motions and characteristics of nonlinear site response during the 2018 Mw 6.6 Hokkaido eastern Iburi earthquake
Earth, Planets and Spacevolume 71, Article number: 56 (2019)
Abstract
The observed peak ground accelerations and peak ground velocities (PGVs) of the 2018 Mw 6.6 Hokkaido eastern Iburi earthquake generally followed the median values from ground motion prediction equations with reasonable errors at fault distances ≥ 50 km. However, at smaller distances, the equations significantly underestimated the peak ground motions, and it was eminent for PGVs. A comparison of surfacetoborehole spectral ratios of Swaves during the mainshock and other events revealed that the sites at smaller distances experienced various degrees of nonlinear site response. The two most widely known characteristics of nonlinear site response are the weakening of higherfrequency components and shifting of predominant frequencies to lower ones in comparison with the linear site response. At one of the sites that recorded the largest intensity of 7 in JMA scale of 0–7, the latter nonlinear effect was so dominant that the ground motions around the new predominant frequency got intensified by one order of magnitude in comparison with that during the weakmotions. Two sites, which were closely located, recorded vertical peak ground accelerations exceeding 1 g for the upgoing motions. The recordings showed asymmetric waveforms and amplitudes characteristics of the nonlinear site response in extreme vertical ground motions recorded during a few earthquakes in the past. Few sites having lower vertical peak ground accelerations were also suspected of being experienced nonlinear site response on vertical motions. These findings suggest taking a cautious approach to enumerate the reduction in amplification at higher frequencies using the singlestation horizontaltovertical (HtoV) spectral ratio technique. However, we found that the HtoV technique was still useful to detect nonlinearity. Finally, an ad hoc equation was derived to correct the nonlinear site amplification in predicting horizontal PGVs with respect to one of the most widely used attenuation models in Japan. The results indicated that the effect was much stronger for a larger input motion than that for a proportional change in the Vs30 values.
Introduction
The 2018, Mw 6.6 Hokkaido eastern Iburi earthquake occurred on September 6, 03:08 JST (UTC + 9 h). The Mw value of 6.6 was determined by Fnet NIED (Okada et al. 2004). The Mw values determined by USGS (2018) and GCMT (e.g., Ekström et al. 2012) were 6.6 and 6.7, respectively. The Japan Meteorological Agency (JMA) magnitude (Mj) was 6.7, and the focal depth was 37 km. The epicenter of the earthquake was located on the western foreland area of a collision zone known as Hidaka collision zone (e.g., Kimura 1996). Earthquakes of comparable magnitudes with similar focal depths have repeatedly occurred in the region (e.g., Kita et al. 2014). The 2018 earthquake caused loss of 42 lives, resulted into total collapse of 462 and partial collapse of 1570 residential buildings, and brought significant damage to lifelines (e.g., Cabinet Office Japan 2019; Takahashi and Kimura 2019). The casualties and damages were primarily related to geotechnical failures such as landslides and liquefaction (e.g., Yamagishi and Yamazaki 2018).
The earthquake was followed by many aftershocks, which concentrated primarily on a steeply dipping fault plane. Based on the spatial and temporal distribution of hypocenters of the aftershocks, a fault plane of about 28 km in length and 20 km in width was estimated. The minimum depth to the top of the fault plane was assumed to be about 24 km. The coordinates of the fault plane are provided in Table 1. The horizontal vector peak ground accelerations (PGAs) and peak ground velocities (PGVs) recorded by KNET, KiKnet, and JMA accelerometers are plotted in Fig. 1a, b, respectively, for the mainshock. The epicenters of aftershocks and numerical values of the PGAs and PGVs at small distances from the fault are shown in Fig. 1c for the mainshock. A vertical section of the subsurface velocity model (Koketsu et al. 2012) along an east–west direction passing through the epicenter of the mainshock is drawn in Fig. 1d, which also shows the plots of depths to hypocenters of the aftershocks and the mainshock. Figure 1d shows the epicenter area covered by lowvelocity sedimentary layers above the basement rocks, and the thickness of sediments is larger in the western side of the epicenter. In this paper, mainshock is used to mean the 2018 Mw 6.6 Hokkaido eastern Iburi earthquake.
The recorded maximum PGAs and PGVs for the eastern Iburi earthquake were comparable to those recorded during the 1995, Mw 6.9, Kobe earthquake (e.g., Kitagawa and Hiraishi 2004; Kawase 1996) and 2016, Mw 7.1 Kumamoto earthquake (e.g., Sakai 2016; Suzuki et al. 2017). The maximum horizontal vector PGA of 1429 cm/s^{2} was observed at the KiKnet site IBUH01 (Oiwake) (see Fig. 1c). The JMA instrumental intensity (e.g., JMA 2018a, b; Shabestari and Yamazaki 2001) of 6.7 was calculated at the site IBUH01. This value of 6.7 corresponds to the upper limit of JMA intensity on a discrete scale of 0–7 (JMA 2018b). The maximum horizontal vector PGV was 151 cm/s, which was recorded at two sites: KNET site HKD126 (Mukawa) and KiKnet site IBUH03 (Atsuma). The JMA instrumental intensity of 6.4 and 6.2 was calculated at the HKD126 and IBUH03, respectively; these values correspond to the intensity of 6 Upper in a scale of 0–7. The JMA Atsuma station (47,004 in Fig. 1c) recorded JMA instrumental intensity of approximately 6.5 (which rounds to JMA intensity of 7, the largest in the scale of 0–7). Sawazaki et al. (2006) reported that the KIKnet Atsuma site (IBUH03, see Fig. 1c for site location) experienced a strong nonlinear site response during the 2003 Mw 8.3 Tokachioki earthquake. We found that the nonlinear site response was most probably one of the primary causes of the large JMA intensity at the site IBUH03 during the 2018 Mw 6.6 Hokkaido eastern Iburi earthquake. We discuss in some detail the characteristics of nonlinear site response at IBUH03 in later sections. Figure 1a, b shows that the large PGAs and PGVs were observed mostly in the northwest and southeast directions of the epicenter of the mainshock and also close to the southern coastal areas at small distances (Fig. 1c), where the thickness of sediments is substantial. These observations reflect the amplification of seismic waves by the thick sediments. Moreover, as the rupture initiated nearly midway of its bottom line at a deeper portion of the fault plane and propagated along strikes and up dips, some degrees of rupture propagation effects may also be stipulated at sites close to the fault plane.
The typical characteristics of nonlinear site response are the diminution of highfrequency components of ground motions and shift of predominant frequency to lower one with respect to the linear site response (e.g., Wen et al. 1994; Satoh et al. 1995). These effects have been explained by the increase in damping and degradation of soil rigidity during strongmotions (e.g., Idriss and Seed 1968; Hardin and Drnevich 1972). Also known in the seismological and engineering communities are the atypical accelerograms, which contain large amplitude highfrequency acceleration spikes, as direct evidence of nonlinear site response during strong shakings (e.g., Holzer et al. 1989; Iai et al. 1995; Bonilla et al. 2005). These atypical accelerograms are explained as the effect of nonlinear soil response resulting from the pore water pressure changes in dilatant soils during strong shakings (e.g., Holzer et al. 1989; Iai et al. 1995). More recently, asymmetrical waveforms on vertical component accelerograms exceeding 1 g in upward direction have been described as direct evidence of nonlinear site response (e.g., Aoi et al. 2008). The asymmetric waveforms have been qualitatively explained by trampoline effect (Aoi et al. 2008) and as slap down phases (Yamada et al. 2009). During the 2018, Mw 6.6 Hokkaido eastern Iburi earthquake, we did not identify the atypical spiky accelerograms by visual inspection except a small indication on one of the horizontal components at site HKD125 (recordings not shown in this paper); however, the nonlinear site response associated with the decrease in shear modulus and increase in damping in soils was recognized at several sites, and also the asymmetrical waves on vertical components were identified at two sites. In this paper, we describe the abovementioned nonlinear site responses during the mainshock based on observed recordings and discuss that the nonlinear site response was the most probable reason for the highintensity ground motions at smaller distances.
The surfacetoborehole (StoB) spectral ratio method has been proved to be an effective method to identify nonlinear site response during strongmotions (e.g., Wen et al. 1994; Satoh et al. 1995; Sato et al. 1996; Assimaki et al. 2008; Noguchi and Sasatani 2008; Régnier et al. 2013; Kaklamanos et al. 2015; Noguchi et al. 2016). Wen et al. (2006a) introduced the horizontaltovertical (HtoV) spectral ratio method to detect nonlinear site response; the method also has been widely applied in detection of nonlinear site response during strongmotions, especially when downhole recordings or rock outcrops close to the site of interest are not available (e.g., Noguchi and Sasatani 2008; Wen et al. 2011; Dhakal et al. 2017; Ren et al. 2017).
Below, we first describe the selection and processing of the data used in the present study. Then, we inquire into the general attenuation characteristics of the observed PGAs and PGVs with distance to examine whether the peak motions are compliant with the ground motion prediction equations (GMPEs). Thirdly, we compare the StoB spectral ratios of Swaves for the horizontal components, i.e., horizontaltohorizontal (HtoH) spectral ratios for the mainshock and weakmotions from earthquakes before the mainshock at selected KiKnet sites, and discuss the characteristics of nonlinear site response at the sites. We resume the aforementioned analysis for vertical components, i.e., verticaltovertical (VtoV) spectral ratios at the same sites. Then, we discuss the characteristic vertical component waveforms featuring the direct evidence of nonlinear site response during the mainshock at two KiKnet and KNET sites. After discussing the nonlinear site effects on horizontal and vertical component recordings, we present the HtoV spectral ratios from surface recordings at the KiKnet sites where StoB spectral ratios are analyzed. We compare the results between the StoB and HtoV spectral ratios at the KiKnet sites. We also analyze the HtoV spectral ratios at selected KNET sites. Finally, based on the analyses above and comparisons, we conclude by an ad hoc equation to take account of the nonlinear site amplification into an existing GMPE for PGVs.
Data selection and processing
Strongmotion seismometers of KNET and KiKnet recorded ground motion data of mainshock at more than 475 stations and epicentral distances between about 10 and 900 km. Similarly, strongmotion data recorded by JMA intensity meters at 142 stations that spread for 700 km were made available by JMA. The PGAs and PGVs were calculated from the highpassfiltered strongmotion seismograms with a cutoff frequency of 0.07 Hz. In this paper, the PGAs and PGVs refer to the maximum values of the vector sum (i.e., the square root of the sum of squares) of two horizontal component acceleration and velocity time histories, respectively, over the available time steps. We did not show PGAs and PGVs at large distances in Figs. 1 and 2 because of their small values. Attenuation relation by Si and Midorikawa (1999, 2000) has been the basis for seismic hazard evaluation in Japan (e.g., Fujiwara et al. 2009). They defined peak value in their equation as larger one of the two horizontal components. Therefore, when we compared the peak values with the attenuation relation by Si and Midorikawa (1999, 2000) in Fig. 2, we adhere to their definition. The fault distance to use in their equation was determined from the fault geometry model briefly mentioned in the previous section. The fault geometry model was estimated based on the automatically determined hypocenters provided by JMA (see Availability of data and materials). The geographical coordinates of the four corners of the fault model with depths at the corners are given in Table 1. The aftershocks of Mj ≥ 2 that occurred within 9 days were used. In Fig. 1c, d, 460 aftershocks of Mj between 2.0 and 2.9, 136 aftershocks of Mj between 3 and 3.9, 37 aftershocks of Mj between 4.0 and 4.9, and two aftershocks of Mj equal to 5.4 and 5.5 were plotted.
The sites used for analysis of nonlinear characteristics are portrayed in Fig. 3; the total number of sites is 32. The KiKnet sites consist of a pair of surface and borehole sensors, and recordings from 16 KiKnet sites that recorded horizontal vector PGAs of about 70 cm/s^{2} or larger at the surface and 20 cm/s^{2} or larger at boreholes were analyzed. The KNET sites consist of sensors at the surface only, and recordings from 16 KNET sites that recorded horizontal vector PGAs of 200 cm/s^{2} or larger were analyzed. The Vs30 values (average Swave velocities in the upper 30 m of the soil column) (e.g., BSSC 2003) are often used to define site condition. We obtained the Vs30 values at the KiKnet sites from NIED (see Availability of data and materials). Most of the KNET sites have PSloggings down to 10–20 m. We obtained the Vs30 values at the KNET sites having PSloggings down to 20 m by using the correlation formula between Vs30 and Vs20 derived by Kanno et al. (2006). At sites where Vs20 was not available, we obtained the Vs10 values for information. The PGAs, PGVs, and Vs10 or Vs30 values at the KiKnet and KNET sites are listed in Tables 2 and 3, respectively. The shallow soil Vs values were not available at the JMA sites, and hence, the analysis of nonlinear site response was limited to the KNET and KiKnet sites in this paper.
We selected recordings which contained both the P and Swaves to assist in picking the onset of Swaves. The onset of Swaves was handpicked, and a time window of 10 s was used to compute Fourier spectral amplitudes. As a preliminary analysis, we also computed the Fourier spectral amplitudes from a time window of 15 s and compared them from the time window of 10 s. The two results were essentially identical at frequencies of our interest between 0.5 and 20 Hz. However, to avoid the possible effects of 3D subsurface structure on computed spectra due to a longtime window (e.g., Dhakal and Yamanaka 2012), we limited the Swave time window of 10 s in our analysis. The 10s time window was also optimal to evaluate the signaltonoise ratio considering the stability of the computed spectra as the recordings had preevent noise time windows smaller than 15 s. In the actual calculation, the mean acceleration of the noise time window was subtracted from the whole recordings as a baseline correction. Then, cosine tapering of 1 s was applied just outside of the selected Swave time window of 10 s at both ends, i.e., the 10s time window becomes 12 s with the addition of 1s time window for tapering at each end. Then, 20 s of zeroes was padded, so the length of the time window is 32 s. The Fourier spectral amplitudes were smoothed by applying a Parzen window of 0.4 Hz. The recordings were selected if the Fourier spectral ratios between the Swaves and noise window were greater than three at all frequencies between 0.5 and 20 Hz. The weakmotion recordings were obtained from events that occurred within 300 km of each site between 1996 and the day before the mainshock and were recorded by KNET and KiKnet. The magnitudes of the events ranged mostly between Mj 4.0 and 6.5. In this paper, the weakmotion recordings mean those recordings having horizontal vector PGAs between 5 and 20 cm/s^{2} at the surface. A few recordings had PGAs lower than 5 cm/s^{2} or greater than 20 cm/s^{2} but lower than 30 cm/s^{2} to increase the number of recordings. The number of recordings varied from site to site and ranged between 10 and 130 (see Tables 2, 3). For the mainshock recordings, the beginning of Swave time window for analysis was selected based on the dominant wave packet for Swaves. The Fourier spectral amplitudes for vertical components also were computed from the time windows same as horizontal component Swave time windows for the both weakmotions and mainshock. The smoothing operation was also identically applied. An example of Swave time windows for weak and strongmotions is depicted for site IBUH01 in Fig. 4. The site IBUH01 is the site that recorded the largest PGA during the mainshock as described in the previous section.
Comparison of PGAs and PGVs
Si and Midorikawa (1999) developed attenuation relations for PGAs on soil sites. They proposed a factor of 1.4 to convert the PGAs at rock sites to PGAs at soil sites. However, the objective definition of rock and soil was not available in their paper. They referred to the paper by Joyner and Boore (1981) for the definition of site condition. Joyner and Boore (1981) classified sites into two groups: rock and soil based on geological information. They described in another paper (Boore and Joyner 1997) Vs30 value of 620 m/s for generic rock sites in western North America. In the National Earthquake Hazards Reduction Program (NEHRP) recommendations (BSSC 2003; NEHRP 2019), sites having Vs30 value of 760–1500 m/s and higher than 1500 m/s are classified as rock and hard rock sites, respectively. In line with the literature mentioned above, we considered a site having Vs30 value of 760 m/s or larger as a rock site and a site having Vs30 value otherwise as a soil site. None of the sites at small fault distances have Vs30 values between 620 and 760 m/s in our data set. Therefore, selecting site class definition based on Joyner and Boore (1981) or NEHRP recommendations does not make a difference to our conclusions in this paper. We multiplied the PGAs at rock sites by 1.4 as aforementioned and plotted together with other soil sites in Fig. 2a; the prediction curves in Fig. 2a are for soil site condition. In the figure, the backarc and forearc sites, separated by a volcanic front line, are denoted by triangles and circles, respectively. Red color symbols indicate the sites used in the nonlinear analysis. In the figure, it can be seen that the observed values are generally larger than the median predictions between 20 and about 50 km while the values do not show any visible trend at distances over about 50 km for a reasonable range of scattering. It can also be seen that the observed values at backarc sites are systematically smaller than the values at the forearc sites at distances over about 100 km, which can be recognized in the plots of residuals in Fig. 2c. The mean residuals in base10 logscale are approximately 0.28, 0.01, − 0.10, and − 0.08 for binned data between 20 and 50 km, 50 and 100 km, 100 and 200 km, and 200 and 300 km, respectively. The above results suggest that despite the difference between the forearc and backarc data, the absolute values of the mean residuals at the longer distances are smaller than those at smaller distances.
A comparison of the observed PGVs with the empirical attenuation relation by Si and Midorikawa (1999) is shown in Fig. 2b. Unlike the PGAs, attenuation relation for PGVs was developed for a stiff site condition having Vs30 value of about 600 m/s. They adjusted the observed PGV at a site by a factor that is a function of Vs30 value at the site using the equation in Midorikawa et al. (1994). We followed the same procedure and adjusted the observed PGVs for site amplification effect. The adjusted observed values are plotted in Fig. 2b together with the prediction curves for stiff site condition having Vs30 value of 600 m/s. Similar to the PGAs discussed above, the observed PGVs are generally larger than the median predictions at distances smaller than about 40 km and are similar to the predictions at distances over about 40 km for a reasonable range of scattering. The distribution of residuals between the observed and predicted PGVs is plotted in Fig. 2d as a function of fault distance. The mean residuals in base10 logscale are approximately 0.42, 0.02, 0.06, and 0.04 for binned data between 20 and 50 km, 50 and 100 km, 100 and 200 km, and 200 and 300 km, respectively. The remarkably smaller mean residuals at distances beyond 50 km confirm that the observed PGVs at those distances are similar from the typical crustal earthquakes in Japan. On the other hand, the large positive mean residual at smaller distances point toward some specific causes or combination thereof not sufficiently addressed by the GMPEs.
One notable difference between the plots for PGAs and PGVs is that the PGVs scatter less from the median predictions than the PGAs at longer distances, and the difference between the backarc and forearc sites becomes smaller for PGVs. These results are generally desirable because the relatively longperiod ground motions become less sensitive to very shallow earth structures compared to the shortperiod ground motions. Dhakal et al. (2010) reported that the distinction of forearc and backarc data becomes less obvious at periods larger than about 0.5 s. In summary, the observed PGAs and PGVs were generally described very well by the attenuation relations in Si and Midorikawa (1999) at distances larger than about 50 km. In this paper, we are, therefore, primarily interested in sites of large residuals between the observed and predicted PGVs at smaller distances. We explore the observed characteristics of nonlinear site response at the selected KiKnet and KNET sites mostly from the smaller distances in the next four sections.
StoB spectral ratios of horizontal components
In this study, we obtained StoB spectral ratios of horizontal components (HtoH) in the following way. We calculated the Fourier spectral amplitudes for each horizontal component, smoothed them as explained in the data processing section, obtained the vector sum of two components at each frequency, and calculated the ratios between the surface and borehole spectra at each frequency. Wen et al. (2006b) proposed the following equation (Eq. 1) to express the deviation of HtoV spectral ratios of the strong and weakmotions quantitatively:
where \( s\left( f \right) \) is the HtoV spectral ratios of the strongmotions, \( w\left( f \right) \) is the mean HtoV spectral ratios of the weakmotions, and \( \sigma \left( f \right) \) is the standard deviation of the HtoV spectral ratios of the weakmotions at frequency \( f \). This method gives more than a single value of degree of nonlinearity (DNL) because it is calculated for each frequency. Wen et al. (2006b) suggested averaging the values at multiple frequency bands because the nonlinear effects may be stronger at certain frequencies than the others. In this study, we calculated the DNL value using Eq. 2, which was first employed by Noguchi and Sasatani (2008):
where R_{strong} and R_{weak} represent the spectral ratios for strong and weakmotions, respectively, and ∆f is the frequency interval. The DNL value was obtained from spectral ratios between 0.5 and 20 Hz in Noguchi and Sasatani (2008, 2011). We also used the same frequency range for the computation of DNL values in this paper. One of the advantages of this DNL index is that it gives a single value that facilitates the comparison with other parameters like PGA. Equation 2 may be considered as a variant of Eq. 1 and was used in several previous studies. Interested readers can find further variants of Eq. 2 in Régnier et al. (2013) and Ren et al. (2017).
Another important parameter that has been used to describe the effect of nonlinear site response is the amount of shift of predominant frequencies of site response during strongmotions as mentioned above. In this paper, we make use of both indices, DNL and shift of predominant frequencies, in the discussion of the characteristics of nonlinear site response during the mainshock. In this paper, predominant frequency means the frequency that corresponds to the peak spectral ratio between 0.5 and 20 Hz.
The StoB spectral ratios at 16 KiKnet sites are plotted in Fig. 5 in the order of decreasing horizontal vector PGA from topleft to bottomright panels a to p, respectively. The spectral ratios for the mainshock at the first five sites, panels a to e, namely IBUH01, IBUH02, HDKH01, IBUH03, and HDKH04, corroborated the two most wellknown features of nonlinearity: the reduction in highfrequency components and shift of predominant frequency toward lower one during the strongmotions. The DNL values were between 4.7 (at HDKH01, Fig. 5c) and 11.7 (at IBUH03, Fig. 5d). The predominant frequencies of the sites were reduced by approximately 38% (at IBUH02, Fig. 5b) to 92% (at HDKH04, Fig. 5e). It can be seen that the site IBUH03 (Fig. 5d), which attained the largest DNL, was largely depleted in highfrequency components. We found that the reduction in peak frequency at the site IBUH03 was approximately 73% during the mainshock in comparison with the weakmotions (from 1.9 to ~ 0.5 Hz). This result at the site IBUH03 is commensurate with the reduction in peak frequency by 50% (from 1.2 to 0.6 Hz) reported in Sawazaki et al. (2006) during the 2003 Mw 8.3 Tokachioki earthquake. The smaller value of the peak frequency (~ 0.5 Hz) in this study may be due to the much stronger input motions at the site during the 2018 Mw 6.6 earthquake (surface PGA of ~ 651 cm/s^{2}) compared to that during the 2003 Mw 8.3 Tokachioki earthquake (surface PGA of ~ 376 cm/s^{2}). We note that the peak frequencies of weakmotions are slightly different between this study and Sawazaki et al. (2006); this may be due to the difference in the data set of weakmotions being used in the respective analyses. We obtained the peak frequency from Swave portions of the small events while Sawazaki et al. (2006) obtained the values from coda waves. The next six sites, panels f to k in Fig. 5, namely IKRH02, IBUH05, IBUH06, IBUH07, HDKH06, and IKRH03, mostly showed the reduction in higherfrequency components; the DNL values ranged between 2.5 and 7.2. The spectral ratios at IKRH01 (Fig. 5l), SRCH07 (Fig. 5m), and OSMH02 (Fig. 5n) were very similar between the mainshock and weakmotions, suggesting for a little or no nonlinearity; the DNL values at the sites were between 1.5 and 2.7. The remaining two sites, namely SRCH08 (Fig. 5o) and HDKH05 (Fig. 5p), showed the reduction in higherfrequency components primarily; the DNL values were 5.1 and 3.8, respectively. The observed features of spectral ratios and the DNL values described above confirmed that the threshold DNL value of 2.5 suggested by Noguchi and Sasatani (2011) was generally robust to identify nonlinear site response using the StoB spectral ratios of Swaves. The results discussed above are summarized in Table 2.
It is often presumed that one of the reasons for the smaller variance of PGAs at short distances is due to soil nonlinearity because the nonlinearity averages out the amplifications at soft sites to that at stiff sites at highfrequency components (e.g., Midorikawa and Ohtake 2004). The observed spectral ratios at the site IBUH01 manifested the reduction in the spectral ratios at frequency components higher than about 3 Hz during the mainshock compared with those during the weakmotions (see Fig. 5a). At the same time, an increase in spectral ratios occurred between about 1 and 3 Hz. We compared the surface and borehole NS component recordings at two different passbands (0.5–3 Hz and 3–10 Hz) at the site IBUH01 in Fig. 6a for an event of Mj 4.8, an epicentral distance of 123 km, and focal depth of 49 km. It can be seen that the PGAs are larger for both the borehole and surface recordings in the passband of 3–10 Hz than the values in the passband of 0.5–3 Hz. The StoB ratio of PGAs in the passband of 0.5–3 Hz is approximately three while the ratio is approximately 11 in the passband of 3–10 Hz; the amplification of PGAs in the two passbands is in line with the spectral ratios for weakmotions. The borehole and surface NS component recordings during the mainshock are drawn in Fig. 6b. The borehole recording had the larger PGA in the passband of 3–10 Hz than that in the passband of 0.5–3 Hz; this feature was identical with the weakmotions shown in Fig. 6a. On the contrary, the observed PGA at the surface was much larger in the passband of 0.5–3 Hz than that in the passband of 3–10 Hz. The StoB PGA ratios were approximately 11 and 4 in the 0.5–3 Hz and 3–10 Hz passbands, respectively. The above results were very similar between the borehole and surface recordings for the EW components as well. In regions of high intensity, Midorikawa and Fukuoka (1988) found that the lower frequency motions with a frequency of around 2 Hz had a higher correlation with the JMA intensities. As shown in Fig. 4b, the vertical component recording had PGA larger than 1 g at the site IBUH01. However, we confirmed by calculation of the JMA intensity with and without the vertical component recording that the influence of vertical component recording was negligible on the reported intensity (6.74 vs 6.67). The above analysis confirmed that the large increase in amplification factors due to nonlinearity resulted in the largest JMA intensity at the site IBUH01. It is somewhat difficult to notice from only the spectral ratios that the nonlinear site response resulted in the large intensities at short distances such as at the sites IBUH03 and HKD126 because the sites are located updip and in the direction of rupture propagation (see Fig. 3). Indeed, the sourcetype effect that may be forward rupture directivity was recognized at the two sites. Because the site IBUH03 recorded horizontal components of ground motions both on the surface and at the borehole, we presented somewhat detail comparison of the amplification of the PGVs at different frequency bands for a small event and the mainshock in an Additional file 1. The analysis indicated that the nonlinear site amplification at the top of the large input motions caused one of the largest PGVs during the mainshock beyond the predominant frequency of linear site amplification. Examples of similar phenomena from the near field recordings may be found in Bray and RodriguezMarek (2004) and Garini et al. (2017). These observations suggested that the nonlinearity does a favor by reducing amplitudes of some frequency components but at the cost of increasing the strength of ground motions at other frequencies during strongmotions. We discuss the characteristics of nonlinear site response on the vertical components in the next two sections.
StoB spectral ratios of vertical components
The StoB spectral ratios of vertical components (VtoV) for the mainshock and weakmotions are plotted in Fig. 7 at all sites described in the previous section except at the site IBUH03, where the vertical component borehole sensor did not record the shakings correctly. The sites in Fig. 7 are arranged in the same order as those plotted in Fig. 5. The DNL values were obtained using Eq. 2. Our results described shortly indicated that the DNL value of 3.5 or larger may indicate nonlinear site response on vertical components. The threshold value is very similar to the threshold value of 4 suggested by Noguchi and Sasatani (2011) to identify nonlinear site response on horizontal components using the HtoV spectral ratios.
The site IBUH01 (Fig. 7a) exhibited a remarkable shift of peak spectral ratios and considerable amplifications at frequencies between about 3 and 6 Hz during the mainshock compared with those during the weakmotions. The DNL value was 5.5, and the reduction in peak frequency was approximately 76% (from 17.13 to 4.06 Hz). This site recorded vertical ground acceleration exceeding 1 g at the surface during the mainshock; the waveforms were asymmetric in shape and had different amplitudes for the downgoing and upgoing motions for a small duration (see the next section). The shift of peak frequency and relatively larger DNL value are indicative of a nonlinear site response at the site IBUH01. However, the evaluation of nonlinear site response at the site IBUH01 based on spectral ratios may not be suitable due to the presence of asymmetric waves on the surface recordings (e.g., Aoi et al. 2008), and hence, the results presented above are only for information. Similarly, the site HDKH01 (Fig. 7c) showed a possibility of nonlinear site response during the mainshock. The vertical PGA at the surface was approximately 317 cm/s^{2}. The peak frequency was shifted toward lower one (from about 18–6 Hz) with larger amplification than that in the weakmotions. The DNL value was 3.8. At the site IBUH06 (Fig. 7h), the DNL value was 5, and a systematic decrease in spectral ratios was found at frequencies larger than about 10 Hz. This latter feature was not clear at the other sites. These results may indicate that the vertical component at IBUH06 experienced a small degree of nonlinear site response during the mainshock. Also, the site IBUH07 (Fig. 7i) may have experienced a small degree of nonlinearity as suggested by the small shift of the first peak frequency and the substantial decrease in spectral ratios at about 3–6 Hz. The DNL value for the site was 4.1. In fact, two comparable peaks can be seen in the spectral ratios at the IBUH07 site during the strongmotions at 2.1 and 12.3 Hz approximately. If the peak at higher frequency is neglected considering the range of scattering for weakmotions, a systematic decrease in spectral ratios between about 2 and 10Hz points toward a nonlinear site response. Except for the four sites mentioned above, the other sites did not show clear signatures of nonlinearities in vertical component ground motions; the DNL values at the sites were between 2.2 and 3.3 (see also Table 2).
The peak frequencies between StoB spectral ratios for horizontal components (HtoH) (x axis) and vertical components (VtoV) (y axis) during weakmotions are plotted in Fig. 8a. It can be seen in the figure that the peak frequencies are systematically higher for the VtoV spectral ratios than those for the HtoH spectral ratios except at one site, indicating that the two spectral ratios may represent the results for two different wave types: horizontal components mostly for Swaves and vertical components mostly for Pwaves, at least for higherfrequency components. In the case of mainshock, the latearriving Pwaves might have also contaminated the Swaves in the vertical components and contributed to the higher predominant frequency. The peak frequencies for the VtoV spectral ratios for the mainshock and weakmotions are plotted in Fig. 8b. They are similar at most sites. At two sites, namely IBUH01 and HDKH01 having relatively larger DNL values (the two data points near lower right corners in Fig. 8b), the peak frequencies during strongmotions are smaller than those for the weakmotions. However, a reverse trend for peak frequency can be seen at one site near 2.7 Hz along the horizontal axis; this is at the IBUH07 site due to the reason briefly mentioned in the previous paragraph. The spectral ratios at the site IBUH07 had two comparable peaks at about 2.1 and 12.3 Hz during strongmotions. The peak at 12.3 Hz was slightly larger than the peak at 2.1 Hz (see Fig. 7i). Therefore, the plot for IBUH07 is a purely mathematical one in Fig. 8b.
Here we discuss the possible mechanisms qualitatively for the nonlinear site response on the vertical components. Sato and Kanatani (2006) suggested that the nonlinear site response can occur on the vertical motions (pressure waves) for unsaturated soils because the change of bulk modulus and damping for Pwaves occur in response to strong input motions in addition to the changes in shear modulus and damping for Swaves. Meanwhile, they pointed out that the effect of change of shear modulus and damping for Swaves do not contribute significantly to induce nonlinear site response on the vertical motions for the saturated soil. Between the three sites, namely HDKH01, IBUH06, and IBUH07 which are suspected for nonlinear site response on the vertical components, available PSlogging data suggest that the sites HDKH01 and IBUH06 might be unsaturated in its top layers during the earthquake. At the site HDKH01, the measured P and Swave velocity in the top 4 m of soil is 860 and 120 m/s, respectively; the layer beneath the above layer has a thickness of 4 m and has P and Swave velocity of 1200 and 360 m/s, respectively. The recorded PGAs on the horizontal and vertical components were approximately 663 and 317 cm/s^{2}, respectively, at the HDKH01 site (see Table 2). Indeed, the site experienced a significant nonlinear site response on the horizontal components as discussed in the previous section, which means that the nonlinear site response on the vertical component at the HDKH01 site is likely to be due to the changes in Pwave velocity and damping for the Pwaves in addition to the corresponding changes for Swaves. At the site IBUH06, the top 5 m of soil has P and Swave velocity of 460 and 200 m/s, respectively; the second layer having a thickness of 5 m has P and Swave velocity of 850 and 340 m/s, respectively. The recorded PGAs on the horizontal and vertical components were approximately 260 and 203 cm/s^{2}, respectively, at the IBUH06 site (see Table 2). The site also experienced nonlinear site response on the horizontal components (Fig. 5h). The smaller Pwave velocity and relatively large PGA on the vertical component suggest that the changes in both the P and Swave velocities and corresponding damping in response to strong input motions might have induced nonlinear site response on the vertical motions at the site IBUH06. At the site IBUH07, the Pwave velocity in the top 5 m and next 8 m of soil is 1600 m/s; the Swave velocities in the layers are 400 and 200 m/s, respectively (velocity inversion is noted). The recorded PGAs on the horizontal and vertical components were approximately 222 and 82 cm/s^{2}, respectively (see Table 2). The PSlogging velocity model and PGAs suggest that the change in Pwave velocity and damping for it may not be significant at the site, and the site might have experienced nonlinear site response on the vertical motions due to the changes in Swave velocity and damping for Swave. We defer the quantitative evaluation of nonlinear site response at the sites to future study.
Direct evidence of nonlinear site response on vertical components
In this section, we present the direct evidence that we think of nonlinear site response on vertical component waveforms at two sites (IBUH01 and HKD127) during the mainshock. See Fig. 3 for site location. The surface and borehole vertical component recordings at the sites are plotted in Fig. 9. The surface acceleration waveforms at both the IBUH01 and HKD127 showed some characteristic pulses barely reported in strongmotions: the larger amplitude of upgoing acceleration pulses (often exceeding 1 g) than that for downgoing ones (often lower than 1 g) and duration of upgoing acceleration pulses smaller than that of the downgoing ones. The borehole recordings at the site IBUH01 did not show the features above. The largest peak ground accelerations of upgoing and downgoing pulses at IBUH01 were approximately 1060 and − 745 cm/s^{2}, respectively, at the surface, while the corresponding values at a depth of 101 m were approximately 75 and − 84 cm/s^{2}, respectively. Similarly, the largest PGAs of upgoing and downgoing pulses at HKD127 were approximately 1590 and − 880 cm/s^{2}, respectively. The ratio of the sums of duration for upgoing and downgoing pulses for a time window of 4 s plotted in Fig. 9b is 1.15 at IBUH01 and 1.07 at HKD127. The ratios become approximately 1.3 and 1.6 at the former and latter sites when the ratios are computed from the pertinent pulses only. These observations were similar to those observed during the 2008 Mw 6.8 IwateMiyagi crustal earthquake, Japan (Aoi et al. 2008). The asymmetric pulses were pertinent for longer durations at IWTH25 during the IwateMiyagi earthquake than those during the present earthquake. Yamada et al. (2009) summarized the characteristics of asymmetric waveforms in amplitude and duration on vertical component ground motions that had been recorded prior to the largest known vertical acceleration (Aoi et al. 2008), including the features at the site IWTH25 during the IwateMiyagi crustal earthquake.
The mechanisms, threshold motions, site geology, etc. to induce large amplitude asymmetric vertical ground motions are not well understood. Interested readers can find an intuitive explanation for asymmetric waves in extreme vertical component accelerations in Aoi et al. (2008), who explained the phenomena by trampoline effect. Some other explanations on mechanisms for the asymmetric waves can be found in Yamada et al. (2009), who explained the asymmetric waves as slap down phases. Tobita et al. (2010), based on numerical analysis, concluded that the asymmetrical waveforms might be related to the different behaviors of soils in compression and tension.
The StoB spectral ratios of vertical components at IBUH01 for the mainshock, weakmotions, and an aftershock that occurred about 3 h later close to the mainshock hypocenter are plotted in Fig. 10 for the site IBUH01. The aftershock recordings at the surface had a horizontal vector PGA of approximately 124 cm/s^{2} and vertical PGA of approximately 51 cm/s^{2}. In Fig. 10, it can be seen that the peak frequency of spectral ratios from the aftershock is more similar to that from the weakmotions than that from the mainshock recordings. The asymmetrical waveforms also were not present on the aftershock recordings. Thus, it is likely that the characteristic asymmetric waves for the downgoing and upgoing accelerations, which were recorded during the mainshock only, were due to the nonlinear soil response at the sites during the mainshock.
Here we explain the shallow soil velocity profiles briefly at the two sites mentioned above. The P and Swave velocity profiles based on PSloggings are shown in Fig. 11. The velocity model based on PSlogging is available down to the depth of 10 m at the HKD127 site, while the model reaches to a depth of 101 m at the site IBUH01. Since the two sites are closely located, the deeper subsurface model beneath the sites may be considered similar. Based on the PSlogging data, the average Swave velocities in the upper 10 m of the soil column beneath the sites IBUH01 and HKD127 are approximately 183 and 189 m/s, respectively. On the other hand, the Pwave velocities in the upper 10 m beneath the two sites are approximately 571 and 982 m/s, respectively. The maximum amplitude of the upgoing pulses was relatively larger at the site HKD127 than that at the IBUH01 site. The maximum and minimum PGAs at the site IWTH25 were 3866 and 1703 cm/s^{2}, respectively. We examined the PSlogging data at the site IWTH25 and found that the shallow soil layers are stiffer than those at the sites HKD127 and IBUH01; the average Swave and Pwave velocities in the upper 10 m of the soil column beneath the site IWTH25 were approximately 465 and 1073 m/s, respectively. Yamada et al. (2009) noted that the sites that showed asymmetric waves were relatively stiff sites. These observations may suggest that the local site geology is one of the important factors to understand the mechanisms of asymmetric waves observed on vertical component recordings during strongmotions, and stiff sites may lead to stronger asymmetrical pulses with large vertical accelerations during strongmotions. We explore the characteristics of nonlinear site response using the singlestation HtoV spectral ratio technique at selected sites of the KiKnet and KNET in the next section.
HtoV spectral ratios at surface KiKnet and KNET sites
In this paper, we obtained the HtoV spectral ratios of surface recordings at the KiKnet and KNET sites depicted in Fig. 3. The spectral ratios were obtained as the vector sum of two horizontal components Fourier spectral amplitudes divided by the corresponding Fourier spectral amplitudes of the vertical component. The HtoV spectral ratios for the weak and strongmotions at the KiKnet sites are plotted in Fig. 12 along with the StoB spectral ratios for horizontal components during the mainshock. The sites are arranged in the same order as that in Figs. 5 and 7. Figure 12 shows that the two types of mean spectral ratios for the weakmotions (HtoV: black lines, and StoB: blue lines) are generally different. In the same way, the corresponding ratios during the mainshock (HtoV: red lines, and StoB: green lines) are also different. These results are generally expected as the StoB spectral ratios are dependent on both site geology and depth of the downhole sensor (e.g., Steidl et al. 1996) while the HtoV spectral ratios are mainly controlled by the site geology (e.g., Kawase et al. 2011).
The peak frequencies for the two types of spectral ratios for weakmotions are plotted in Fig. 13a. It can be seen that the peak frequencies are comparable except at few sites, where the peak frequencies are higher for StoB spectral ratios. The site IBUH05 is exceptional; the weakmotions StoB spectral ratios had peak at frequency ~ 14.5 Hz while the weakmotions HtoV had peak at frequency ~ 2.7 Hz. The StoB spectral ratios during the strongmotions suggested nonlinear site response, and the reasonable shift of peak frequency was recognized (from ~ 14.5 to 12 Hz) (see Fig. 5g). The HtoV spectral ratios during the strongmotions also indicated a small degree of nonlinear site response, and the spectral ratios were smaller in relation to weakmotions at frequencies larger than about 10 Hz, but the shift of peak frequency was not evident (see Fig. 12g). The lack of clear peak for HtoV spectral ratios for the weakmotions as well as the strongmotions may be one of the possible reasons for the large discrepancy of the peak frequencies between the two types of spectral ratios at the site IBUH05. The DNL values for the mainshock based on the two types of spectral ratios are plotted in Fig. 13b, and they may be considered similar considering the reasonable scattering of the spectral ratios. Similarly, the peak frequencies for the two types of spectral ratios during the mainshock are comparable at most sites as shown in Fig. 13c. Here, we note that the larger DNL value at the site IBUH01 based on the HtoV spectral ratios is partially due to the effect of nonlinear amplification on the vertical component recording at the surface (see Fig. 7a). The above result suggests that the HtoV spectral ratio method may not be suitable to reliably extract the degree of change in site response such as the reduction in spectral amplification factors at higher frequencies if the vertical components experienced nonlinear site response. However, as evident in Fig. 13b, c, the data points that deviate largely from equality are not systematic between the StoB and HtoV methods for strongmotions. The HtoV spectral ratio method is still able to detect the nonlinear site response in similar ways to that of StoB spectral ratio method of horizontal components, which was primarily due to the different ranges of frequencies that were affected on the horizontal and vertical component ground motions. The horizontal motions were affected up to relatively lower frequencies than those for vertical motions by the nonlinear site response (for example, see Figs. 5a, c, h and 7a, c, h for sites IBUH01, HDKH01, and IBUH06, respectively).
Here we discuss the nonlinear site response at the KNET sites. The HtoV spectral ratios at the selected 16 sites of KNET are plotted in Fig. 14. All the sites recorded horizontal vector PGA of 200 cm/s^{2} or larger. The peak ground motions for the mainshock, predominant frequencies during the mainshock and weakmotions, and the DNL values at the KNET sites are provided in Table 3. The sites, namely HKD127, HKD125, HKD128, HKD103, HKD126, HKD124, HKD129, HKD105, HKD184, HKD131 (Fig. 14a, b, c, d, e, f, h, i, j, l), showed the shift of predominant frequencies and reduction in higherfrequency spectral ratios in different amounts, suggesting that the sites experienced various degrees of nonlinear site response. The horizontal vector PGAs were between 387 cm/s^{2} and 1318 cm/s^{2}, and the DNL values ranged between 3.3 (HKD125, Fig. 14b) and 13.4 (HKD126, Fig. 14e) at the sites. The site HKD126 with maximum DNL value of 13.4 showed a marked reduction in spectral ratios at frequencies higher than about 2 Hz during the mainshock, and the shift of predominant frequency was from 3.06 Hz to 0.53 Hz. The DNL value at the site HKD127 (Fig. 14a) was 13.1, and the shift of predominant frequency was from 7.78 to 2.06 Hz. As the site HKD127 experienced nonlinear site response on the vertical component as discussed in the previous section, the DNL value based on HtoV spectral ratios may not be suitable to infer the degree of nonlinearity at the site. However, by analogy with the site IBUH01, the information on the shift of predominant frequency is useful for the identification of soil nonlinearity. The other six sites, namely HKD185, HKD104, HKD181, HKD130, HKD182, HKD106 (Fig. 14g, k, m–p), had DNL values between 2.6 (HKD182 and HKD106) and 3.8 (HKD182), and the sites did not show clear shift of predominant frequencies except an apparent shift of frequencies between about 1 and 10 Hz at the site HKD182. The horizontal vector PGAs ranged between 206 and 356 cm/s^{2} at the sites except at HKD185 that recorded 562 cm/s^{2}. Despite the large PGA, the DNL value at HKD185 was 3.4. The spectral ratios as well as the DNL values at the sites HKD105 and HKD184 (Fig. 14i, j), for example where the PGAs were smaller than those at the site HKD185, indicated the nonlinear site response at the sites. Accordingly, the nonlinear site response is not related by simple relation with the PGAs at the surface, and rather, it signifies that the nonlinear site response is primarily controlled by soil stiffness and input ground motions at the bottom of the soil layers discussed briefly in the next section.
The peak frequencies of StoB spectral ratios of horizontal components during strongmotions (mainshock) and weakmotions at the KiKnet sites and those of HtoV spectral ratios at KNET sites are plotted in Fig. 15. It is evident in the figure that the peak frequencies of the spectral ratios for the mainshock are mostly lower than those for the weakmotions except at a site (HKD129). The weakmotion spectral ratios at the HKD129 site are comparable to the spectral ratios during the mainshock at frequencies between about 0.5 and 10 Hz, and the ratios are almost flat between those frequencies as shown in Fig. 14h. Therefore, the difference between the weakmotion and strongmotion peak frequencies at the HKD129 site is mainly due to similar spectral ratios. Figure 15 suggests that the larger DNL values are related to larger PGAs and lower Vs30 values. However, the Vs30 values do not always indicate the plausibility of nonlinear site response sufficiently as discussed briefly in the next paragraph.
Among the sites analyzed in this study, two KiKnet sites, namely IBUH02 and HDKH05, have Vs30 values exceeding 500 m/s (see Table 2). The IBUH02 site clearly showed signatures of nonlinear site response (see Fig. 5b); the Vs30 value at the site is 542 m/s, and horizontal vector PGA was 707 cm/s^{2}. A site with such high Vs30 value is generally expected to undergo linear site amplification. However, a close examination of the PSlogging data at the site showed that the Vs30 is 130 m/s for the top 2 m of soil layer and 280 m/s for the next 5 m, which overlies the stiffer layers having Vs value of 810 m/s and larger. The above findings may suggest that the top layers having smaller Vs values overlying the more competent large impedance layers may experience significant nonlinear site response, and hence, the Vs30 values may not be a good indicator for nonlinear site response in every case. The HDKH05 site showed a small degree of nonlinear site response (see Fig. 5p) despite smaller input motions (the horizontal vector PGA was approximately 68 cm/s^{2} at the surface and 26 cm/s^{2} at a depth of 100 m) and large Vs30 value of 766 m/s. A close examination of the PSlogging data at the site showed that the Vs30 is 250 m/s for the top 2 m of soil layer, 470 m/s for the next 4 m, and larger than 1000 m/s for the underlying layers. These velocity models together with the above observations corroborate that the layers having Swave velocities smaller than about 300 m/s are strongly susceptible to nonlinear site response during strongmotions.
An ad hoc equation for nonlinear site amplification
We found that the most sites at fault distances shorter than about 50 km experienced nonlinear site response during the mainshock, and it was confirmed that the sites gained the motions in the frequency bands that corresponded to the enhancement of amplification due to nonlinear site response. Even though both the PGA and PGV are affected by nonlinear site response, it is mostly the PGV that is amplified because the relatively longerperiod ground motions get enhanced due to nonlinear site response. Kamiyama (1992) obtained a nonlinear site amplification model at a site statistically as a function of maximum particle velocity at a virtual rock site. Abrahamson and Silva (1997) obtained nonlinear site amplification terms in their GMPE as a function of rock site PGA. More recent studies (e.g., Walling et al. 2008; Kamai et al. 2014) proposed the rock site PGA as one of the input motion parameters as well as the Vs30 to address the unequal nonlinear site response at different site conditions. The studies mentioned above indicate that the strength of input motions at the base of a soil site may be represented in terms of the corresponding PGA or PGV for a virtual rock site at the site of interest. In this study, we followed the recent trend of using PGA as a reference motion to incorporate nonlinear site response in GMPEs. Over the last 40–50 years, an enormous amount of literature has been accumulated in the numerical simulation of nonlinear site response. For an overview of quantification of nonlinear site response by numerical simulations, we refer the paper by Régnier et al. (2016) and the references therein.
Here we derived a correction formula for the PGVs with reference to the median values obtained from GMPEs. We first obtained the rock site PGAs at the selected sites using the GMPE by Si and Midorikawa (1999). These PGAs and Vs30 values at the sites were treated as independent variables, and the residuals for PGVs plotted in Fig. 2d were fitted against the two variables. Finally, we obtained the following relation (Eq. 3) between PGV residuals, input PGAs (rock site PGAs ≥ 50 cm/s^{2}), and Vs30 values (between 110 and 540 m/s approximately) by linear regression:
where \( {\text{obsPGV}} \) is the observed PGV (larger of two components), \( {\text{prePGV}} \) is the predicted PGV taking account of Vs30 in GMPE by Si and Midorikawa (1999), \( {\text{PGA}}_{\text{rock}} \) is the predicted PGA at a virtual rock site at the distance of site of interest using the GMPE for PGA in Si and Midorikawa (1999). To confine the equation within the range of nonlinear response, we obtained the equation using the data points at which the DNL values were 4 or larger at the both KNET and KiKnet sites. This resulted in the rock site PGAs ≥ 50 cm/s^{2} and Vs30 values smaller than about 540 m/s in the above analysis. The standard deviation of the residuals for Eq. 3 is 0.1304 in base10 logscale. The obtained coefficients for PGA and Vs30 are generally in good agreement with the expected results that the PGV should decrease with the increase in Vs30 values and should increase with the increase in input motions. The PGV residuals are plotted against rock site PGAs in Fig. 16; a linear relationship can be easily seen between the two variables. The data points are colorcoded by Vs30 and DNL values. The lines representing the correction values for PGVs in base10 logscale are also plotted in the figure for Vs30 values of 150 m/s (gray line) and 450 m/s (black line). It can be seen that the main contributor to the correction value is the input PGA, and this finding is similar to the previous results (e.g., Campbell and Bozorgnia 2008, 2014). The PGVs plotted in Fig. 2b were corrected by Eq. 3 at sites where input PGAs ≥ 50 cm/s^{2} were calculated, and these new values are plotted in Fig. 17. It can be seen that the same GMPE describes the data well after the corrections for the nonlinear site response.
Since Eq. 3 is derived for a specific data set for a single event and limited site conditions, we consider the correction coefficients an ad hoc result. We continue to investigate the relationships for other events as an effort toward our longterm goal of accomplishing the reliable prediction of ground motions for seismic hazard analysis and earthquake early warnings in our future studies.
Discussions and conclusions
We analyzed the strongmotion data of the 2018 Mw 6.6 Hokkaido eastern Iburi earthquake to understand the peak ground motions and characteristics of nonlinear site response during the earthquake. We compared the observed PGAs and PGVs with the values from the GMPEs by Si and Midorikawa (1999), which have been widely used for seismic hazard evaluation in Japan. We found that the data at fault distances larger than about 50 km were generally explained by the ground motion prediction equations very well. In contrast, in the regions of high seismic intensity at smaller distances and soft sites, the equations underestimated the data substantially. The underestimation was more evident to PGVs.
We computed and analyzed the StoB spectral ratios of horizontal components, StoB spectral ratios of vertical components, and HtoV spectral ratios of surface recordings for the mainshock and weakmotions at 16 KiKnet sites. Only the HtoV spectral ratios were analyzed at the equal number of KNET sites because the KNET sites consisted of sensors only at the surface. We obtained DNL values following the method of Noguchi and Sasatani (2008) using the spectral ratios between 0.5 and 20 Hz. The threshold DNL value of 4 for HtoV spectral ratio method and 2.5 for StoB spectral ratios of horizontal components as suggested by Noguchi and Sasatani (2011) generally served as a good criterion to identify nonlinear site response in this study. Furthermore, in the present study, we found that a DNL value of 3.5 or larger may indicate a nonlinear site response based on the StoB spectral ratios of vertical components for the time window that corresponds to Swaves on horizontal components.
By comparing the weakmotions and strongmotions (mainshock) spectral ratios, we found that the sites having relatively smaller Vs30 values in regions of stronger input motions experienced a larger degree of nonlinear site response. These results were consistent with previous results regarding the commonly reported conditions for nonlinear site response. We found that a few sites might have experienced nonlinear site response on horizontal components having PGAs as low as about 70 cm/s^{2} depending on the site condition. In the earlier literature and the engineering community in general (e.g., Kramer 1996, p. 318), a decrease in PGAs at soil sites during strongmotions in comparison with weakmotions has been well accepted. More recent studies supported by many data (e.g., Campbell and Bozorgnia 2008, 2014) have emphasized the nonlinear amplification of ground motions at wide frequencies that depends on the input PGAs. We found that, during the 2018 Mw 6.6 Hokkaido eastern Iburi earthquake, the nonlinear amplification was larger by one order of magnitude at the IBUH01 site, and at the other several sites which experienced large intensities (e.g., IBUH03, HDKH01, HDKH04, HKD126, HKD128), the increase in amplification at lower frequencies in relation to the linear case was substantial. Indeed, amplifications decreased during strongmotions at the predominant frequencies of the linear case at the sites mentioned above, and at the site IBUH03, the horizontal vector PGA at the surface was somewhat smaller than that at the borehole at a depth of 153 m (651 cm/s^{2} vs 795 cm/s^{2} approximately). Contrarily, the horizontal vector PGV was significantly amplified at the site IBUH03 (surface 151 cm/s vs borehole 39 cm/s). We think that the nonlinear amplification was one of the main causes of high JMA intensities and underestimation of the observed PGVs at smaller fault distances. These observations suggest for greater attention to nonlinear site response in seismic hazard analyses.
It is noteworthy to mention here that the sites IBUH01 and HKD127 experienced nonlinear site response on both the horizontal and vertical component ground motions at the surface. It is still not all out about the threshold motions and mechanisms that cause the generation of large amplitude asymmetric pulses, but the relatively stiffer site condition appears to be one of the factors in addition to the large vertical input motions at the base rock. Our analyses based on the StoB spectral ratios of vertical components suggested that most sites that showed nonlinear site response on horizontal components did not show nonlinear site response on vertical components. These findings suggested that the HtoV spectral ratio method is equally useful as the StoB spectral ratio method to identify nonlinear site response at least in a statistical sense. However, we note that some sites might have experienced nonlinear site response on vertical components for vertical PGAs as low as approximately 80–200 cm/s^{2}. This means that the DNL values obtained from the HtoV method are not reliable if the site experienced nonlinear site response on vertical components. Larger DNL values as obtained in this study imply the larger reduction in higherfrequency components. Therefore, caution should be maintained to estimate the spectral amplifications at higher frequencies during strongmotions based on the HtoV spectral ratio method. Interestingly, the shift of predominant frequency to lower one was quite similar between the StoB and HtoV spectral ratio methods even at a site that experienced nonlinear site response on the vertical component. In our analysis, this was because the horizontal motions were affected up to lower frequencies than those for vertical motions by the nonlinear site response.
By considering the PGAs at virtual rock sites as reference input motions, we obtained an ad hoc equation to account for nonlinear site amplification for PGVs with reference to the GMPEs in Si and Midorikawa (1999). We found that the input motions largely control the deviations from the median predictions given the identical site conditions. For a given input motion, the larger deviation was found for the softer site condition, but that deviation was relatively smaller for a proportional change in input motions. Since we did not investigate how much of the nonlinearity and other effects such as the rupture propagation effects had been already included in the GMPEs in Si and Midorikawa (1999) and the residuals analyzed in this study, the equation for correction of nonlinear site amplification should be taken as a general guide rather than the true estimate.
Availability of data and materials
The strongmotion (KNET and KiKnet) recordings and PSloggings used in this study were downloaded from the Web sites: http://www.kyoshin.bosai.go.jp/. The moment magnitude was taken from the Web site: http://www.fnet.bosai.go.jp/event/joho.php?LANG=en. The strongmotion recordings at the JMA sites were retrieved from https://www.data.jma.go.jp/svd/eew/data/ltpgm_explain/data/past/20180906030805/index.html, in Japanese. The hypocenter location and JMA magnitude of the mainshock were taken from the Web site: https://www.data.jma.go.jp/svd/eqev/data/bulletin/hypo_e.html. The hypocenter information of the aftershocks plotted in Fig. 1c, d was taken from https://hinetwww11.bosai.go.jp/auth/JMA/jmalist.php. For other specific information such as the list of recordings used in the study, contact author for data requests.
Abbreviations
 3D:

threedimensional
 BA:

backarc
 DNL:

degree of nonlinearity
 FA:

forearc
 Fnet:

fullrange seismograph network
 GCMT:

global centroid moment tensor
 GMPE:

ground motion prediction equation
 HtoH:

horizontaltohorizontal
 HtoV:

horizontaltovertical
 JIVSM:

Japan integrated velocity structure model
 JMA:

Japan Meteorological Agency
 JST:

Japan Standard Time
 KiKnet:

Kiban Kyoshin network
 KNET:

Kyoshin network
 Mj:

JMA magnitude
 Mw:

moment magnitude
 NEHRP:

National Earthquake Hazards Reduction Program
 NIED:

National Research Institute for Earth Science and Disaster Resilience
 Pwave:

primary wave
 PGA:

peak ground acceleration
 PGV:

peak ground velocity
 StoB:

surfacetoborehole
 Swave:

secondary wave/shear wave
 USGS:

United States Geological Survey
 UTC:

coordinated universal time
 VtoV:

verticaltovertical
 Vs30:

average Swave velocity in the upper 30 m of the soil layer
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Acknowledgements
We would like to thank the Japan Meteorological Agency for providing us with hypocenter information for the earthquakes used in this study and the strongmotion data. We would also like to thank Wessel and Smith (1998) for providing us with Generic Mapping Tools, which were used to make some figures in the manuscript. We would like to express our sincere thanks to the guest editor Dr. Nobuo Takai and three anonymous reviewers for their constructive comments which helped us to improve the manuscript significantly.
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YPD analyzed the data and drafted the manuscript. TKs, WS, and SA provided helpful comments. All authors read and approved the manuscript.
This study was supported by “Advanced Earthquake and Tsunami Forecasting Technologies Project” of NIED.
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Correspondence to Yadab P. Dhakal.
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Additional file
Additional file 1. Comparison of the surface and borehole PGVs at the site IBUH03 for the mainshock and a small event.
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Keywords
 Nonlinear site response
 Degree of nonlinearity
 Ground motion prediction equations
 Spectral ratios
 Peak ground acceleration
 Peak ground velocity
 The 2018 Hokkaido eastern Iburi earthquake