Keywords

1 Introduction

Local site conditions influence the characteristics of strong ground motion strongly. The early investigations can be traced to [1,2,3], as old as earthquake engineering [4]. Attempts to evaluate the effect of soil column, named as site response [5], have a long history, and much effort has been expended, from both theoretical and experimental points of view. The most common theoretical methods are linear full resonance (FR), quarter-wavelength (QWL), equivalent linear and nonlinear [6]. Pioneer works appeared in the first half of the twentieth century [7, 8]. Following these, lots of works came up [9,10,11,12,13].

FR and QWL are widely used, the former is the theoretical prediction of site amplification that accounts for the constructive and destructive interference of all reverberations in layered media, and the latter is an approximation. A few comparisons of QWL amplifications and FR amplifications have appeared [5, 14]. In the case of the mainshock of the 2016 Kumamoto earthquake, we compare the site response from these two methods and the combination of them. With the help of the pairs of borehole and surface strong-motion records at two KiK-net stations, we compare synthetic and observed ground motions on the surface, by inputting our synthetic ground motions on buried bedrock using EXSIM [15].

2 Method for Ground Motion Synthesis

On April 14, 2016, an MJMA6.5 earthquake occurred in the Kumamoto area of Japan (32.74°N, 130.81°E), with the focal depth of 11 km, and caused Japan Meteorological Agency (JMA) intensity 7 in Mashiki. 28 h later, the MJMA7.3 mainshock (32.75°N, 130.76°E) occurred, with the focal depth of 12 km, and caused JMA intensity 7 in Mashiki and Nishihara [16]. The Headquarters for Earthquake Research Promotion judged that the MJMA6.5 earthquake occurred on Takano-Shirahata section of the Hinagu fault zone, while the mainshock occurred on the Futagawa section of the Futagawa fault zone [16]. During the MJMA6.5 event, strong ground motions on surface and in the borehole were recorded at 146 KiK-net stations, PGAs larger than 500gal were observed around the epicentre and the maximum PGA of 1580gal was recorded at KMMH16 station with the epicentral distance of 7 km; for the mainshock, KiK-net obtained strong ground motion data at 328 stations on surface and in the borehole, and the maximum PGA of 1362gal was recorded at KMMH16 station [17].

After this event, several rupture processes of the mainshock were provided [18,19,20,21,22,23]. We borrow the source model from [20], which is divided into 21 subfaults along the strike direction and 9 subfaults along the dip direction, each with a size of approximately 2 × 2 km. Stress drop is set as 70bars, κ0 is 0.05 s [24], the other parameters used in synthesis are from [25].

Surface-borehole records at a far-field station FKOH01 and a near-fault station KMMH03 from the mainshock are collected. The processed data, using baseline correction and 0.1–25 Hz band-pass filter with a fourth-order Butterworth filter. Horizontal ground motions at these two borehole stations are synthesized by EXSIM [15]. Density of soil layers is calculated by the relation between density and P-wave velocity [26], as Eq. (1).

$$ \rho = 0.23V_{P}^{0.25} $$
(1)

Observed and synthetic full wave Afull on the buried bedrock is transmitted to upward wave Aup by Eq. (2), which is the relationship between the acceleration Fourier amplitude spectra.

$$ \frac{{A_{{{\text{up}}}} }}{{A_{{{\text{full}}}} }} = \frac{{E_{N} }}{{E_{N} + F_{N} }} = \frac{{e_{N} }}{{e_{N} + f_{N} }} $$
(2)

where, EN and FN are the amplitude coefficients of upward and downward waves on the buried bedrock. Aup is the input on the buried bedrock to evaluate the site response.

We consider the site response in three ways. The first one is to multiply the input Fourier spectra by FR from the bottom to the ground surface. The second one is to multiply the input Fourier spectra by the amplification spectra from the bottom to the ground surface, which are calculated by QWL approximation initially proposed by [12]. We propose to apply QWL for the amplification from hard rock surface to engineering rock surface, and FR for the amplification of ground motion in soil layers. The input Fourier spectra are multiplied by the product of QWL amplification spectra and FR (QWL × FR), the QWL amplification spectra are from the bottom to −13 m and −80 m for two station respectively, and the FR are from −13 m to −80 m to the ground surface. The input position is consistent with the depth of the buried bedrock surface, and the detailed velocity structure of site is involved.

3 Ground Motion Synthesis at Two KiK-Net Stations

When we input the transmitted upward waves from synthetic and observed borehole full waves, the surface ground motions at station FKOH01 are shown in Fig. 1a–c and Fig. 2, respectively, compared with the observed surface ground motions in two horizontal directions as Fig. 1d and e.

Fig. 1
Five waveforms of F R, Q W L, Q W L times F R, E W, and, N S are plotted in the acceleration in centimeters per second squared versus time in seconds' graphs.

Ground motions at FKOH01 surface station, inputted by synthetic ground motions

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Fig. 2
Three waveforms of F R, Q W L, and Q W L times F R are plotted in the acceleration in centimeters per second squared versus time in seconds' graphs.

Ground motions at FKOH01 surface station, inputted by observed borehole ground motions

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In Fig. 1, the waveforms of synthetic and observed motions on surface are difference; the durations of strong motion are close; the PGAs from FR in Fig. 1a, QWL in Fig. 1b and QWL × FR in Fig. 1c are 45.6 gal, 45.6 gal and 50.9 gal, the observed PGAs in two horizontal directions are 56.6 gal and 49.0 gal. In Fig. 2, the waveforms are similar, especially in EW direction; the PGAs from FR in Fig. 2a, QWL in Fig. 2b and QWL × FR in Fig. 2c are 53.5 gal, 55.2 gal and 68.7 gal.

The results at station KMMH03 are shown in Fig. 3 and Fig. 4, respectively.

Fig. 3
Five waveforms of F R, Q W L, Q W L times F R, E W, and N S are plotted in the acceleration in centimeters per second squared versus time in seconds' graphs.

Ground motions at KMMH03 surface station, inputted by synthetic ground motions

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Fig. 4
Three waveforms of F R, Q W L, and Q W L times F R are plotted in the acceleration in centimeters per second squared versus time in seconds' graphs.

Ground motions at KMMH03 surface station, inputted by observed borehole ground motions

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The surface waveforms inputted by the upward waves of synthetic motions (Fig. 3a–c) are difference with those inputted by observed motions (Fig. 4a–c); the durations of synthetic motions are shorter; the PGAs from FR in Fig. 3a, QWL in Fig. 3b and QWL × FR in Fig. 3c are 363.2 gal, 399.8 gal and 365.5 gal, the observed PGAs in two horizontal directions are 227.6 gal in Fig. 3d and 786.6 gal in Fig. 3e. In Fig. 4, the waveforms are close and the durations of strong motions are similar; the PGAs from FR in Fig. 4a, QWL in Fig. 4b and QWL × FR in Fig. 4c are 217.5 gal, 262.2 gal and 215.6 gal.

The 5% damped acceleration response spectra, from the three methods of FR, QWL and QWL × FR, are compared with those of records on these two surface stations, as shown in Figs. 5 and 6, corresponding to the upward-wave inputs of synthetic and observed ground motions.

Fig. 5
Two multi-line graphs plot the S A versus time in seconds for the synthetic motions and the observed motions for E W, N S, F R, Q W L, and Q W L times F R. Both graphs exhibit a gradually increasing and then decreasing trend.

Acceleration response spectra at FKOH01 surface station

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Fig. 6
Two multi-line graphs plot the S A versus time in seconds for the synthetic motions and the observed motions for E W, N S, F R, Q W L, and Q W L times F R. Both graphs exhibit a ragged gradually increasing then abruptly decreasing trend.

Acceleration response spectra at KMMH03 surface station

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In Fig. 5a, the response spectral amplitudes from the three methods are close to the records at periods 0.15–5 s. In Fig. 5b, the results from the three methods are closer to the records, especially at periods higher than 0.5 s, which implies that all three ways to consider site effect is feasible. In Fig. 6, the difference between the two-horizontal spectra is large, our results fit with the EW spectrum. The spectra are close at periods lower than 1.5 s in Fig. 6a, the spectral amplitudes from three methods are lower at periods 1.5–4 s, while those are higher at periods 7–10 s; in Fig. 6b, the spectra fit well at periods higher than 0.5 s, while the spectral amplitudes from three methods are lower at periods less than 0.2 s.

4 Conclusions

Ground motions at two KiK-net stations, FKOH01 and KMMH03, in the mainshock of 2016 Kumamoto Earthquake, are synthesized, in which borehole ground motions are from EXSIM and site response is considered by three methods of FR, QWL and QWL × FR. Our results are compared with both the borehole and the surface records in two horizontal directions to illustrate the feasible of the three methods.

By inputting the upward waves of synthetic borehole motions, the surface motions from these three methods are different; the durations of strong motion are close. By inputting the upward waves of observed motions, the waveforms are close and the durations of strong motions are similar. Further comparison shows that PGAs from QWL × FR are larger than those from QWL, which are larger than that from FR, at FKOH01, the relative error is 3.2–28.3%; at KMMH03, PGAs from QWL are larger than those from QWL × FR, and the latter are close to those from FR, the relative error is 0.9–20.5%. A similar trend is observed in the comparison of response spectra.