Open Access

Stochastic ground-motion simulations for the 2016 Kumamoto, Japan, earthquake

Earth, Planets and Space201668:184

https://doi.org/10.1186/s40623-016-0565-3

Received: 16 June 2016

Accepted: 5 November 2016

Published: 18 November 2016

Abstract

On April 15, 2016, Kumamoto, Japan, was struck by a large earthquake sequence, leading to severe casualty and building damage. The stochastic finite-fault method based on a dynamic corner frequency has been applied to perform ground-motion simulations for the 2016 Kumamoto earthquake. There are 53 high-quality KiK-net stations available in the Kyushu region, and we employed records from all stations to determine region-specific source, path and site parameters. The calculated S-wave attenuation for the Kyushu region beneath the volcanic and non-volcanic areas can be expressed in the form of Q s = (85.5 ± 1.5)f 0.68±0.01 and Q s = (120 ± 5)f 0.64±0.05, respectively. The effects of lateral S-wave velocity and attenuation heterogeneities on the ground-motion simulations were investigated. Site amplifications were estimated using the corrected cross-spectral ratios technique. Zero-distance kappa filter was obtained to be the value of 0.0514 ± 0.0055 s, using the spectral decay method. The stress drop of the mainshock based on the USGS slip model was estimated optimally to have a value of 64 bars. Our finite-fault model with optimized parameters was validated through the good agreement of observations and simulations at all stations. The attenuation characteristics of the simulated peak ground accelerations were also successfully captured by the ground-motion prediction equations. Finally, the ground motions at two destructively damaged regions, Kumamoto Castle and Minami Aso village, were simulated. We conclude that the stochastic finite-fault method with well-determined parameters can reproduce the ground-motion characteristics of the 2016 Kumamoto earthquake in both the time and frequency domains. This work is necessary for seismic hazard assessment and mitigation.

Keywords

Ground-motion simulations Stochastic finite-fault method 2016 Kumamoto earthquake

Introduction

At 16:25 on April 15, 2016 (UTC), a large shallow crustal earthquake (M w 7.1) occurred beneath Kumamoto city in the Kyushu region, Japan. Prior to the mainshock, a moderate foreshock (M w 6.1) at 21:26 on April 14, 2016 (UTC), struck the same region. According to F-net (full range seismograph network of Japan) moment tensor solution, the hypocenters of the mainshock and foreshock were located, respectively, in the Futagawa and Hinagu fault zones, two active right-lateral strike-slip faults in the Kyushu region (Fig. 1). There were more than 1000 aftershocks with an intensity above one degree within the vicinity of Kumamoto prefecture. Peak ground acceleration (PGA) reached as high as 1362 cm/s2 at station KMM16 with an epicentral distance of 2 km. The strong ground motions of the 2016 Kumamoto earthquake sequence caused at least 110 fatalities and more than 2400 injuries. Numerous buildings were damaged seriously, and even collapsed, during this earthquake sequence. In particular, Kumamoto Castle, one of the most popular tourist destinations in Kumamoto prefecture, suffered destructive damage to roofs and stone walls. In addition, numerous landslides were triggered throughout the nearby mountainous areas in the Kyushu region. For example, Great Aso Bridge in Minami Aso village was swept away by a landslide and collapsed into the river. Although two dense strong-motion seismograph networks (K-NET and KiK-net) are installed and operated in Japan, some heavily damaged regions still lack strong-motion stations. Ground-motion simulations for the 2016 Kumamoto earthquake have important implications, not only for seismic hazard assessment, such as slope stability analysis and landslide run-out estimation, but for earthquake-resistant design, such as response spectrum analysis of structures in the damaged regions.
Fig. 1

Epicenters and focal mechanisms of the mainshock and foreshock of 2016 Kumamoto, Japan, earthquake sequence. Red and black beach balls represent the focal mechanisms of the mainshock and foreshock, respectively. Open triangles represent KiK-net stations; the black and red ones are located in the volcanic and non-volcanic areas, respectively. Black solid circles represent Kumamoto Castle and Minami Aso village. The inset shows the tectonic setting of the Kyushu region. The subduction direction of the Philippine Sea Plate into the Eurasian Plate is shown in red triangular fronts; the study area, Kyushu region, is indicated by a red rectangle; boundaries of tectonic plates are shown in black and red solid lines

In this paper, the ground-motion simulations for the 2016 Kumamoto earthquake have been performed using the stochastic finite-fault method based on a dynamic corner frequency. Our major objectives are to determinate region-specific source, path and site parameters, to validate our finite-fault model and to simulate ground motions in severely damaged areas that do not have strong-motion stations. For these purposes, we first determined input parameters including quality factor (Q s), zero-distance kappa (κ 0), which represents the effect of rapid spectral decay at high frequencies, site amplifications in the Kyushu region and the stress drop of the mainshock. Then, the ground-motion simulations were performed and compared with the observations at all stations. Simulated PGA values were also compared with ground-motion prediction equations (GMPEs) suggested by Boore et al. (2014). Finally, we performed blind simulations for Kumamoto Castle and Minami Aso village based on our validated model, where engineered structures suffered severe damages but without ground-motion records.

Methods

The stochastic finite-fault method is widely used in ground-motion simulations of past or scenario earthquakes (Ugurhan and Askan 2010; Ghofrani et al. 2013; Safarshahi et al. 2013; Zengin and Cakti 2014; Mittal and Kumar 2015). Compared with other ground-motion simulation methods, such as the deterministic or hybrid approach, the advantages of the stochastic method are its independence of small earthquake selection and good performance at both low and high frequencies (Motazedian and Atkinson 2005). In this method, near-field ground motions, including the acceleration time series, Fourier amplitude spectra (FAS) and 5%-damped pseudo-acceleration response spectra (PSAs), can be synthesized at the frequency range of engineering interest (Atkinson et al. 2009). In particular, the 5%-damped PSA represents the maximum acceleration caused by a linear oscillator with 5% damping and a specified natural period. In this study, we employ the latest version of the finite-fault code EXSIM12 to simulate the ground motions of the 2016 Kumamoto earthquake. For each station, we simulate surface recordings with ten trials to eliminate the bias resulting from stochastic variability.

Data and processing

We employ strong ground-motion records from the KiK-net borehole and surface seismic network for the 2016 Kumamoto earthquake. A total of 53 KiK-net stations in the Kyushu region recorded this event (Table 1). The quality of each record from these stations is evaluated based on the signal-to-noise ratio (SNR) technique suggested by Ktenidou et al. (2011). All records are proved to be high quality as they pass the strict selection criterion of a SNR threshold of 3. Borehole recordings are used to compute the Q s beneath the volcanic area, whereas surface recordings are used to estimate κ. Site amplification at each station is calculated using the horizontal-component (N–S and E–W) borehole and surface recordings.
Table 1

Information on the strong-motion stations used in this study

Station code

Latitude (°N)

Longitude (°E)

Epicentral distance (km)

PGA (cm/s2)

V S30 (m/s)

FKOH01

33.8849

130.9798

121

60

588.5

FKOH03

33.5608

130.5499

88

135

497.0

FKOH06

33.5925

131.1348

93

75

1001.8

FKOH07

33.3678

130.6354

65

94

282.9

FKOH08

33.4654

130.8285

74

103

535.8

FKOH09

33.8501

130.5432

119

43

566.7

FKOH10

33.2891

130.817

54

89

921.3

KGSH01

32.1554

130.1191

96

49

603.0

KGSH03

31.9812

130.4438

97

37

1196.2

KGSH04

31.8374

130.3602

114

41

280.4

KGSH05

31.8699

130.4958

107

74

477.5

KGSH06

31.6988

130.4594

126

30

454.9

KGSH07

31.714

130.6149

122

47

260.0

KGSH08

31.5618

130.9969

138

10

KGSH09

31.3741

130.4333

162

13

409.1

KGSH10

31.2066

130.6183

177

6

254.9

KGSH12

31.2583

131.0877

173

3

451.6

KMMH01

33.1089

130.6949

36

252

574.6

KMMH02

33.122

131.0629

43

687

576.7

KMMH03

32.9984

130.8301

22

800

421.2

KMMH06

32.8114

131.101

28

180

567.8

KMMH09

32.4901

130.9046

36

246

399.7

KMMH10

32.3151

130.1811

79

195

176.9

KMMH11

32.2918

130.5777

60

88

1292.3

KMMH12

32.2054

130.7371

66

218

409.8

KMMH13

32.2209

130.9096

65

113

402.5

KMMH14

32.6345

130.7521

19

612

248.3

KMMH15

32.1704

130.3647

81

76

499.9

KMMH16

32.7967

130.8199

2

1362

279.7

MYZH04

32.5181

131.3349

83

175

484.4

MYZH05

32.347

131.2668

59

142

1072.5

MYZH08

32.2132

131.5309

67

143

374.4

MYZH09

32.0421

131.0618

95

17

973.0

MYZH10

32.0215

131.29

88

98

494.7

MYZH12

31.8643

130.9454

98

96

319.5

MYZH13

31.7301

131.0791

105

50

251.2

MYZH15

32.3654

131.5893

121

118

445.7

MYZH16

32.506

131.6958

88

45

847.5

NGSH01

33.2116

129.4353

90

42

397.8

NGSH02

33.2122

129.7652

135

23

642.1

NGSH03

33.1256

129.8102

107

39

634.5

NGSH04

32.9553

129.8026

99

40

633.2

NGSH06

32.6999

129.8625

95

30

1421.1

OITH01

33.4122

131.0326

89

70

865.1

OITH03

33.4736

131.6856

71

25

486.0

OITH05

33.1525

131.542

111

89

1269.4

OITH08

32.8392

131.5357

80

86

657.4

OITH10

32.9278

131.8695

69

49

836.9

OITH11

33.2844

131.2118

101

598

458.0

SAGH01

33.508

129.8877

66

37

980.2

SAGH02

33.2656

129.8798

116

70

557.9

SAGH04

33.3654

130.4046

100

149

724.1

SAGH05

33.1806

130.1046

73

32

1000.0

The stations located in the non-volcanic area are shown in italics

Preliminary data processing is implemented for each record. First, we employ the empirical approach with an automatic scheme (Wang et al. 2011) to correct baseline for raw data. The corrected records are band-pass filtered in the frequency range of 0.1–25 Hz with a fourth-order Butterworth filter. Second, the S-wave and noise windows are extracted and tapered at both ends with a 10% Hanning-type window. Finally, FAS are computed for both S-wave and noise windows.

Input parameters

Source parameters

Source information, such as moment magnitude, hypocenter location, fault geometry and subfault size, is required to define the source mechanism in the stochastic finite-fault model. According to the F-net moment tensor solution determined by the National Research Institute for Earth Science and Disaster Prevention (NIED), the moment magnitude of the mainshock is M w 7.1, the hypocenter location is at 32.7545°N, 130.763°E, the focal depth is 11 km, and the strike and dip of the fault plane are 224° and 65°, respectively. The fault plane is divided into 18 × 9 subfaults with dimensions of 5 km × 2.9 km along the strike and dip, following Hayes (2016)’s routine of discretization. The slip distribution (Fig. 2), which directly controls the seismic moment of each subfault, is prescribed on the basis of teleseismic waveform inversion (Hayes 2016). Some source parameters, such as density, rupture propagation velocity and pulsing area percentage, are assigned with commonly used values according to previous studies (Table 2).
Fig. 2

Slip distribution used in the simulations [reproduced from Hayes (2016) with his permission]. The hypocenter location is denoted by a star. The slip amplitudes are shown in color, and motion direction of the hanging wall relative to the footwall is denoted by black arrows

Table 2

Input parameters for the stochastic finite-fault model of the 2016 Kumamoto earthquake

Parameters

Value

Reference

Source

  

Moment magnitude (M w)

7.1

F-net

Hypocenter location

32.754°N, 130.763°E, 11 km

F-net

Strike and dip angle (°)

224 and 65

F-net

Subfault length and width (km)

5 and 2.9

Hayes (2016)

Slip distribution

Prescribed

Hayes (2016)

Stress drop (bars)

64

This study

S-wave velocity (km/s)

3.6 (beneath the volcanic areas)

3.7 (beneath the non-volcanic areas)

Estimated from Zhao et al. (2011), Atkinson and Boore (2006)

Density (g/cm3)

2.8

Atkinson et al. (2009)

Rupture propagation velocity

0.8β

Atkinson and Boore (2006)

Pulsing area percentage

50%

Atkinson and Boore (2006)

Path

  

Geometric spreading, R b : b=

−1.0 (0–100 km)

−0.5 (>100 km)

Zengin and Cakti (2014)

Ground-motion duration, dR, d=

0.0 (0–10 km)

+0.16 (10–70 km)

−0.03 (70–130 km)

+0.04 (>130 km)

Atkinson and Boore (1995)

Quality factor

Q s = (85.5 ± 1.5)f 0.68±0.01 (beneath the volcanic areas)

Q s = (120 ± 5)f 0.64±0.05 (beneath the non-volcanic areas)

This study

Site

  

Site amplification

See Additional files

This study

κ (s)

0.0514 ± 0.0055

This study

S-wave velocity (V s) anomalies are taken into account in this paper. Some studies (e.g., Zhao et al. 2011; Liu and Zhao 2016) report that low-velocity zones exist beneath the volcanic areas in the Kyushu region. For example, Zhao et al. (2011) revealed a −3% V s perturbation at a depth of 5–15 km under active volcanic areas in the Kyushu region using tomography method. In this study, we assume the V s is 3.6 and 3.7 km/s beneath the volcanic and non-volcanic areas, respectively, as constrained by the tomographic results (Zhao et al. 2011) and typical crustal V s profiles (Atkinson and Boore 2006).

We determine the stress drop using an optimization algorithm. It follows the criterion of minimizing the average absolute residual of observed and simulated PSA in terms of common logarithmic form (Ghofrani et al. 2013). The residual is defined as
$${\text{res}}\left( {f,R_{\text{JB}} } \right) = \log_{10} \left( {{\text{PSA}}_{\text{obs}} } \right) - \log_{10} \left( {{\text{PSA}}_{\text{sim}} } \right),$$
(1)
where f is the frequency of ground motion and R JB is the closest horizontal distance to the surface projection of the fault plane (Kaklamanos et al. 2011). The average absolute residual is defined as
$$\left| {\overline{\text{res}} } \right| = \frac{1}{{N_{\text{f}} N_{\text{d}} }}\sum\limits_{n = 1}^{{N_{\text{f}} }} {\sum\limits_{m = 1}^{{N_{\text{d}} }} {\left| {{\text{res}}\left( {f,R_{\text{JB}} } \right)} \right|} } ,$$
(2)
where N f and N d are the number of frequencies and distances, respectively.

Path parameters

In the stochastic finite-fault method, the path spectrum, \(G(R)\exp [ - \pi fR/\beta Q_{\text{s}} (f)],\) depends on geometrical spreading (G(R)) and quality factor (Q s). For the geometrical spreading, we use a popular piecewise function expressed in the following form (Zengin and Cakti 2014),
$$G\left( R \right) = \left\{ {\begin{array}{*{20}l} {R^{ - 1} ,} \hfill &\quad {R < 100\,{\text{km}}} \hfill \\ {(100R)^{-0.5,}} \hfill &\quad {R \ge 100\,{\text{km}}} \hfill \\ \end{array} } \right. .$$
(3)
One objective of this study is to make a reliable estimate of Q s in the Kyushu region. The quality factor, Q s, is an indicator of regional S-wave anelastic attenuation. Aki and Chouet (1975) suggested a power-law form of Q s = Q 0 f η , where Q 0 is the value of Q s at a frequency of 1 Hz and η is the frequency parameter. We use a classical spectral decay method (Anderson and Quaas 1988) to determine it as follows. The FAS recorded at hypocentral distance R, U(f, R), can be expressed as
$$U(f,R) = S \cdot G(R)\exp (-\pi fR/\beta Q_{\text{s}} ) ,$$
(4)
where S is a source-dependent scalar. Equation (4) can be shown in a linear relationship by using natural logarithm on both sides,
$$\ln \left( {U(f,R)/G(R)} \right) = - \frac{\pi f}{{\beta Q_{s} }}R + \ln (S).$$
(5)
For a given frequency, the Q s −1 and its standard error can be calculated from the slope of Eq. (5) with an assumed S-wave velocity (β). The corrected FAS of each horizontal component [the left hand of Eq. (5)] are plotted against hypocentral distance at the frequency range of 1–25 Hz with 1-Hz spacing. We average Q s −1 of N–S and E–W components at each frequency and plot them against the frequency range (Fig. 3). The Q s −1 can be obtained by using standard linear regression.
Fig. 3

Estimate of quality factor (\(Q_{\text{s}}^{ - 1}\)) beneath the volcanic area in the Kyushu region and its standard error at each frequency

Significant lateral Q s heterogeneities in the Kyushu region have been reported by many studies. Low-Q anomalies are revealed by tomography method in the crust and uppermost mantle beneath active volcanic areas, such as Aso, Sakurajima and Kirishima, whereas the subducting Philippine Sea slab exhibits high-Q character (e.g., Pei et al. 2009; Liu and Zhao 2015). Given the strong lateral Q s variations in the Kyushu region, we divide all stations into volcanic area stations and non-volcanic area stations (shown in Fig. 1; Table 1). The Q s beneath the volcanic area is estimated from the borehole recordings of 44 stations located in the volcanic areas, based on Liu and Zhao (2015)’s tomographic results [Fig. S29(a) of their work]. However, the number of stations in the non-volcanic area (9) is inadequate to provide a robust estimate of Q s. Therefore, we choose to estimate the non-volcanic area Q s by combining the volcanic area Q s and Q s perturbation identified from Fig. S29(a) of Liu and Zhao (2015). Specifically, the non-volcanic area Q 0 equals to the volcanic area Q 0 divided by 1 plus the Q s perturbation. For η, we use Oth et al. (2011)’s estimate for the Kyushu region. In addition, we also calculate Q s using all stations to investigate the effect of lateral Q s variations on ground-motion simulations.

Ground-motion duration is another important path parameter to trigger seismic hazards, such as liquefaction. We use a well-known distance-dependent duration model obtained by Atkinson and Boore (1995).

Site effects

Site amplifications and κ 0 are two parameters required to characterize the site response in the stochastic finite-fault method. A corrected cross-spectral ratio technique is used to compute site amplification at each station as follows:
$$S/B^{\prime } = \frac{{\left| {S_{12} (f)} \right|^{2} }}{{S_{11} (f)S_{22} (f)^{\prime } }}(S/B),$$
(6)
where S 11(f) and S 22(f) are the power spectral densities of the surface and borehole recordings, respectively, S 12(f) is the cross-power-spectral density function and S/B refers to the ratio of surface FAS over borehole FAS at a certain station. Note that all variables in Eq. (6) are the geometric mean of two horizontal components smoothed with a Konno–Ohmachi filter (Konno and Ohmachi 1998).
Additionally, kappa filter (κ) is adopted to represent the slope of high-frequency decay of FAS in the stochastic finite-fault method. A model (Anderson and Hough 1984) characterized the shape of FAS at high frequencies, shown as
$$a(f) = A_{0} \exp \left( { - \pi \kappa f} \right)\quad {\text{for}}\,f > f_{\text{e}} ,$$
(7)
where A 0 is a source and propagation path-dependent amplitude and f e is the lower cutoff frequency above which the decay of FAS can be considered as approximately linear observed in a log-linear space. κ can be calculated from the slope λ of FAS over a certain frequency range (Δf) in a log-linear space:
$$\kappa = - \lambda /\pi ,$$
(8)
where λ = Δ(ln a)/Δf. The distance dependence of κ was also observed and suggested by Anderson and Hough (1984) in the linear form of
$$\kappa = \kappa_{0} + \kappa_{R} R,$$
(9)
where κ 0 is the zero-distance kappa, κ R is the slope and R is the epicentral distance. We use the classic routine (Anderson and Hough 1984) mentioned above to determine κ for each horizontal-component record. At each station, we average two horizontal-component κ values and consider it to be the representative. κ 0 [the intercept of Eq. (9)] is determined by extrapolating the κ values to R = 0.

Our optimized finite-fault model consists of the source, path and site parameters. They are summarized in Table 2.

Results and discussion

Region-specific parameters

Region-specific parameters are determined in this paper, including the quality factor (Q s), zero-distance kappa (κ 0), site amplifications and the stress drop of the mainshock.

We determine the frequency-dependent Q s in the Kyushu region by incorporating lateral variations. The Q s −1 beneath the volcanic area is estimated and expressed in the form of Q s −1  = (0.0117 ± 0.002)f −(0.68±0.01) (Fig. 3). In the simulations, it is transformed to Q s = (85.5 ± 1.5)f 0.68±0.01. It is in good agreement with Oth et al. (2011)’s result, Q s = (91 ± 8)f 0.64±0.05, which is derived from a nonparametric spectral inversion scheme and based on a much richer dataset. Additionally, Q s beneath the non-volcanic area is also estimated and shown in the form of Q s = (120 ± 5)f 0.64±0.05. Both Q 0 are consistent with the results of an S-wave attenuation tomography performed by Pei et al. (2009). Therefore, the Q s we estimated provides a convincing proof to describe the complexity of crustal structure in the Kyushu region. In addition, we also obtain the Q s without considering lateral variations in the form of Q s = (102 ± 5)f 0.67±0.01.

Further, the effect of lateral V s and Q s heterogeneities on the ground-motion simulations is investigated. The finite-fault models with and without the lateral V s and Q s heterogeneities are referred to as Model 1 and Model 2, respectively. Ground-motion simulations at all stations are performed with both of them. We select two representative stations to highlight their differences. Station KGSH04 is located near Sakurajima, which is one of seven active volcanoes in the Kyushu region. Station NGSH01 is located in the non-volcanic area. The differences between two models in simulation results are shown in Figs. 4, 5 and 6. In the time domain (Fig. 4), the observed and simulated acceleration time series show good agreement at both stations, but the simulated PGAs of Model 1 are closer to the observed ones. Similarly, in the frequency domain (Figs. 5, 6), Model 1 behaves better than Model 2 in terms of FAS, PSA and their residuals at high frequencies (frequency >1 Hz) or short periods (period <1 s). The differences between two simulation results mainly rise from significantly different values of Q s at high frequencies. Therefore, it indicates that lateral V s and Q s heterogeneities can affect the simulation results in both the time and frequency domains. In the next section, we present and discuss the simulation results based on Model 1.
Fig. 4

Comparison of acceleration time series for two models with different V s and Q s: (left) at station KGSH04 (in the volcanic area); (right) at station NGSH01 (in the non-volcanic area)

Fig. 5

Comparison of FAS and their residuals for two models with different V s and Q s: a at station KGSH04 (in the volcanic area), b at station NGSH01 (in the non-volcanic area)

Fig. 6

Comparison of PSAs and their residuals for two models with different V s and Q s: a at station KGSH04 (in the volcanic area), b at station NGSH01 (in the non-volcanic area)

κ 0 is estimated to be 0.0514 ± 0.0055 s (Fig. 7). Such a high value corresponds to soft rock sites or unstable regions, where high-frequency energy is rarely observed (Ktenidou et al. 2014). In Table 1, 74% of the stations in the Kyushu region are located in class C (soft rock, V S30 = 360–760 m/s) and D (stiff soil, V S30 = 180–360 m/s) sites based on the National Earthquake Hazards Reduction Program (NEHRP) site classes using V S30 as the most important parameter for site classification, where V S30 represents the time-weighted average S-wave velocity over the upper 30 m of the profile (Boore et al. 2014). Thus, the soil conditions in the Kyushu region may result in a high κ 0. The second possible reason is the active tectonic setting. Considerable volcanic activities associated with low-frequency microearthquakes occur in the Kyushu region. Therefore, such an active tectonic (unstable) region may be consistent with a high κ 0. An important application of κ 0 is that it can be used as a low-pass filter to constrain high frequencies, influencing PGA and spectral level in the generation of ground motions when using stochastic method or hybrid method (Ktenidou et al. 2014). Moreover, κ 0 has been included in the functional form of GMPEs explicitly to characterize site attenuation that dominates high frequencies. In summary, the well-determined κ 0 in the Kyushu region contributes to the generation of reliable synthetic ground motions and to the calibration of GMPEs in engineering seismology.
Fig. 7

Distribution of individual kappa (κ) measurements and their standard errors against epicentral distance. The regression line using the standard linear regression is plotted

Site amplification in the Kyushu region is estimated by using the corrected cross-spectral ratios technique (see Additional file 1: Figure S1). Compared with the classic standard spectral ratio technique, the “depth effect” reported by Cadet et al. (2012) is corrected. The amplified waves usually lead to destructive damage to engineered structures at the surface. Therefore, a calibrated estimate of the site response in the target region is essential not only for ground-motion simulations, but for site classification, both of which are necessary for the earthquake-resistant design of engineered structures.

The stress drop based on the USGS slip model (Hayes 2016) is calculated by minimizing the average absolute residual of observed and simulated PSAs. The optimized value of stress drop, 64 bars, is reasonable for a large event (Ugurhan and Askan 2010; Zengin and Cakti 2014). The stress drop determined here contributes to reliable estimates of simulated PSA, because it controls the spectral amplitude at high frequencies (Motazedian and Atkinson 2005).

Model validation

Our finite-fault model using optimized parameters is validated by comparison between the observed and simulated acceleration time series, FAS and 5%-damped PSAs at all stations. To validate the attenuation characteristics of PGAs against distance, GMPEs suggested by Boore et al. (2014) are used. Moreover, the simulated PGAs are also compared with the observations in regional scale. Note that we use horizontal-component geometric mean at the surface as observed ground-motion variables (i.e., FAS and 5%-damped PSA), whereas the simulated ones are the averages of ten trials. For synthetic acceleration time series, we select the one with its peak value closest to the average of ten trials. Comparison of observed and simulated time series, FAS and PSAs at all stations can be found in the Additional files (see Additional files 2: Figure S2, 3: Figure S3, 4: Figure S4). To avoid lengthy comparisons, we select one station at each epicentral distance range of 0–50, 50–100 and larger than 100 km, respectively, for further discussion.

Figure 8 shows the results of observed and simulated acceleration time series at selected stations. In the time domain, the envelopes of the synthetic acceleration time series are very similar to the real ones. It indicates that the observed and simulated acceleration time series match very well.
Fig. 8

Comparison of observed and simulated time series for the selected stations

Figure 9 shows the observed and simulated 5%-damped PSAs and their residuals at selected stations. To quantify the misfit, we calculate the smoothed FAS residuals using Eq. (1) (replacing the PSA with FAS). The maximum absolute residual at high frequencies is as low as 0.45, whereas at low frequencies it is 0.71. The lower value of residual means better agreement of observations and simulations. Thus, the simulated FAS at high frequencies match well with the observed ones, but are overestimated at low frequencies. The good agreement of FAS at high frequencies rises from the exact estimate of the high-frequency cutoff filter, κ 0. The misfit of FAS at low frequencies might be attributed to the uncertainty of the slip distribution. The source spectrum increases as \(CM_{0ij} H_{ij} (2\pi f)^{2}\) (Motazedian and Atkinson 2005). The moment magnitude of each subfault, M 0ij , is assigned as \(M_{0} S_{ij} /\sum\nolimits_{i = 1}^{nl} {\sum\nolimits_{j = 1}^{nw} {S_{ij} } }\) where S ij is the relative slip weight of the ijth subfault. The spectral amplitude at low frequencies is more sensitive to the slip distribution, because the effect of the decay term exp(−πfκ) is not remarkable.
Fig. 9

Comparison of observed and simulated FAS and their smoothed residuals for the selected stations

Figure 10 displays the observed and simulated 5%-damped PSAs and their residuals at selected stations. Note that the PSA residuals are calculated from Eq. (1). The maximum absolute residual at short periods is only 0.35, whereas at long periods it is 0.67. It indicates that the simulated PSAs match the observed ones better at short periods (high frequencies) than that at long periods (low frequencies). It also means the optimized value of the stress drop, 64 bars, is a reliable estimate for the mainshock of the 2016 Kumamoto earthquake, because the stress drop controls the spectral amplitude of high-frequency part (Motazedian and Atkinson 2005). Note that the stress drop is model dependent (Atkinson et al. 2009). If another slip model is applied, the optimized value of the stress drop will be expected to change. The slight misfit of PSA observed at long periods is partly due to the pulsing area percentage. It is reported that a large pulsing area will boost the amplitudes at longer periods and higher energy radiation (Motazedian and Atkinson 2005). The performance of PSA at long periods can be improved by altering the pulsing area. However, strict selection of the pulsing area is beyond the scope of this paper. On the basis of the rule of thumb, we select the commonly used 50% as the value of pulsing area percentage.
Fig. 10

Comparison of observed and simulated PSAs and their residuals for the selected stations

For further validation, observed and simulated PGAs at all station are compared with GMPEs derived from NGA-West2 database (Fig. 11). For the observed PGAs, we use the composite maximum acceleration of three-component records. For the simulated ones, we use the one closest to the average of ten trials. The median trend of GMPEs is plotted as a function of R JB, for a strike-slip earthquake and a generic soil site with V S30 = 310 m/s. In Fig. 11, most of the individual PGAs fall in the region between the upper and lower limits of one standard deviation. It indicates that the attenuation characteristics of the simulated PGAs are also captured well by the GMPEs.
Fig. 11

Comparison of observed and simulated PGAs with GMPEs suggested by Boore et al. (2014)

We then plotted the observed and simulated PGA contour maps in regional scale (Fig. 12). Higher values are expected to concentrate around the epicenter and distributed along the motion direction of the strike-slip faults (NE–SW). The severely damaged regions, with intensity above 5°, locate in the vicinity of Kumamoto prefecture, which is mostly overlapped by simulated high-PGA regions. The underestimation observed in the northeastern region can be attributed to the slip heterogeneity on the fault plane, because the details of slip distribution, such as the locations and slip amounts of asperities, have a significant effect on the near-field ground-motion distribution at the surface (Zengin and Cakti 2014). Nevertheless, the simulated PGA distribution in the Kyushu region shows an overall good agreement with the observed one.
Fig. 12

Comparison of observed and simulated PGA contour maps. The solid star is the epicenter

Our finite-fault model with optimal parameters is validated well through the good agreement of observations and simulations in both the time and frequency domains at all stations. It shows the capacity to perform ground-motion simulations at some critical but not-instrumented sites.

Blind simulations

We then simulate the ground motions of Kumamoto Castle and Minami Aso village caused by the mainshock, which suffered destructive damage. As the site amplifications are unknown, we assign those of KMMH06 and KMMH14 as alternatives based on their V S30 (close to the representatives of the NEHRP class C and D sites) and relative distance to the targets. The simulation results based on our optimized model are shown in Fig. 13. The simulated PSA at Kumamoto Castle can be applied to the response spectrum analysis. Similarly, the simulated acceleration time series at Minami Aso village has applications for seismic hazard analysis, such as slope stability analysis or landslide run-out estimation.
Fig. 13

Simulated time series, FAS and PSA at Kumamoto Castle and Minami Aso village, respectively

Conclusions

The 2016 Kumamoto earthquake caused severe casualty and building damage. Investigating the ground-motion characteristics of this earthquake is essential for seismic hazard analysis and earthquake-resistant design. In this study, we use the stochastic finite-fault method based on a dynamic corner frequency to simulate the strong ground motions of the 2016 Kumamoto earthquake.

To achieve realistic simulation results, the source, path and site parameters in the Kyushu region are calibrated. For source effect, the stress drop of the mainshock is determined to capture the characteristics of high-frequency response spectrum, with an optimized value of 64 bars. For path effect, the low-Q anomalies beneath the volcanic area are revealed by frequency-dependent attenuation relation Q s = (85.5 ± 1.5)f 0.68±0.1. Besides, the S-wave attenuation beneath the non-volcanic area is also estimated and expressed as Q s = (120 ± 5)f 0.64±0.05. For site response, κ 0 with a value of 0.0514 ± 0.0055 s in the Kyushu region characterizes linear decay trend of FAS at high frequencies accurately, contributing to PGA, spectral level of ground motions and the calibration of GMPEs in engineering seismology. In addition, site amplifications in the Kyushu region are also estimated to quantify impedance effect, while seismic waves traverse soil layers near the surface, which is necessary for ground-motion simulations and site classification. Overall, the calibration of region-specific parameters contributes to reliable ground-motion simulations.

In conclusion, the stochastic finite-fault method based on a dynamic corner frequency is able to reproduce the ground-motion characteristics of the 2016 Kumamoto earthquake. Our finite-fault model is validated by the comparison of observations and simulations at all stations and regional scale, which shows good agreements in both the time and frequency domains. Attenuation characteristics of the simulated PGAs are also captured well by the GMPEs. Finally, we simulate the ground motions for two severely damaged regions, Kumamoto Castle and Minami Aso village, with the validated model. The simulation results can be further considered as an input for slope stability analysis, landslide run-out estimation and response spectrum analysis of structures. This work provides a deep insight into seismic hazard assessment and mitigation in the Kyushu region, Japan.

Declarations

Authors’ contributions

LZ conceived this study, ran the simulations, performed data analysis and drafted the manuscript. GC and YW revised the manuscript. HJ carried out the strong-motion data processing. All authors read and approved the final manuscript.

Acknowledgements

Ground-motion data and site information were obtained from the KiK-net at http://www.kyoshin.bosai.go.jp/, the NIED strong-motion seismograph networks, last accessed May 1, 2016. All the figures in this paper were prepared using Generic Mapping Tools (Wessel et al. 2013). The authors would like to thank Dr. R. Wang for providing the baseline correction code. We appreciate the helpful discussions with Z. Jiang, Z. Liu, S. Zhou, W. Wang and W. Feng. In addition, the authors thank Prof. Martha Savage (the editor) and two anonymous reviewers for their helpful comments on the draft manuscript. Also, this work was financially supported by National Science Foundation of China (41474002), Grant-in-Aid for challenging Exploratory Research (Grant No. 15K12483, G. Chen) from Japan Society for the Promotion of Science and Kyushu University Interdisciplinary Programs in Education and Projects in Research Development. These financial supports are gratefully acknowledged.

Competing interests

The authors declare that they have no competing interests.

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors’ Affiliations

(1)
Department of Civil and Structural Engineering, Kyushu University
(2)
Institute of Earthquake Science, China Earthquake Administration
(3)
First Crust Monitoring and Application Center, China Earthquake Administration
(4)
Department of Petroleum and Geosystems Engineering, The University of Texas at Austin

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© The Author(s) 2016