Introduction

The Hidaka mountain range in central Hokkaido, Japan, is formed by the Hidaka arc–arc collision zone (e.g., Iwasaki et al. 2004), with the eastern boundary fault zone of Ishikari lowland on the west side and the Tokachi plain fault zone on the east side. The 2018 Hokkaido eastern Iburi earthquake (Mw 6.6) occurred at 03:08 JST on September 6, 2018, in this arc–arc collision zone. The Japan Meteorological Agency (JMA) magnitude (MJMA) was 6.7, and the hypocentral depth was 37 km. The maximum JMA seismic intensity of 7 was observed in Atsuma town. During this earthquake, 41 people died mainly owing to a large landslide in Atsuma town. Several buildings damaged by the strong ground motion were mainly concentrated around the Mukawa district in Mukawa town. At the Kyoshin network (K-NET) Mukawa (HKD126) and JMA Atsuma Shikanuma (JMA47004) strong motion stations, the strong motion records indicated a strong power that was able to destroy timber frame buildings. It is important to investigate the cause of such dangerous ground motion despite a not shallow and moderate-sized earthquake.

In this study, we focused on the cause of the strong ground motion characteristics of HKD126. Therefore, we examined the difference in the velocity structures of HKD126 and a temporary station “MKW01” that was installed on a hill close to HKD126. To analyze the velocity structures, temporary strong motion observations, microtremor array observations, and multichannel analysis of the surface wave method (MASW) with an active source were carried out. Furthermore, the strong motion amplification characteristics were discussed with estimated S-wave velocities (Vs).

Features of strong ground motions around the epicentral area

We selected stations around the epicentral area (Fig. 1). The horizontal velocity waveforms derived from acceleration records are shown in Fig. 2. It can be clearly seen that the 1–2 s period waves are included in the waveforms at JMA47004 and HKD126. We calculated the horizontal velocity response spectra (h = 0.05); the horizontal response spectrum was obtained using the maximum of the vector sum of the two horizontal-component response histories for a specific natural period. These horizontal velocity response spectra of the main shock recorded at four epicentral stations are compared with that of the 1995 Kobe earthquake at JR Takatori station (Hyogo-prefecture: Nakamura et al. 1996), as shown in Fig. 3. The velocity response at HKD126 and JMA47004 indicate that the range of 1–2 s period is dominated. The response spectra of the Kiban Kyoshin network (KiK-net) Oiwake (IBUH01) and K-NET Hayakita (HKD128) are completely different from those of HKD126 and JMA47004. These records at the northern stations IBUH01 and HKD128 are dominated by a shorter period, around the range of 0.5–1.0 s (Fig. 3). We further investigated the difference in the amplitude of the horizontal components of the velocity waveforms at HKD126 and JMA47004 (Fig. 2); the EW components amplitude are larger than the NS components. These stations are located near the nodal plane of the focal mechanism; therefore, the difference may be owing to the radiation patterns of the seismic source. In general, strong ground motions are affected by the nonlinear response of the surface soft soil. The strong motion record of HKD126 was examined in terms of the nonlinear effects using the degree of nonlinear effect (DNL) method (Noguchi and Sasatani 2008). The DNL was calculated using the horizontal to vertical Fourier spectral ratio of weak motion records and the strong motion one of the surface records for 10.24 s of the S-wave part (Noguchi and Sasatani 2008). The DNL value (Fig. 4) was 13.7, which indicates that large nonlinearity occurred by the threshold DNL value of 4 (Noguchi et al. 2016). The predominant period of 1–2 s might have changed from the short-period side owing to this large nonlinearity.

Fig. 1
figure 1

Location map of the study area. The white triangles denote the station used for this study. The red and yellow stars denote the epicenters of the 2018 Hokkaido eastern Iburi earthquake and aftershocks which were determined by JMA. Hokkaido and the study area (rectangle) are shown in the top right inset

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Fig. 2
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Ground velocities at four stations. The horizontal velocity waveforms were derived from the acceleration records of selected sites with a 0.05 Hz low-cut filter. The stations correspond to Fig. 1

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Fig. 3
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Horizontal velocity response spectra. The horizontal velocity response spectra for four stations and one notable station (JR Takatori) are shown. The horizontal response spectra were obtained according to the maximum of the vector sum of the two horizontal-component response histories for a specific natural period using the damping factor h = 0.05. The JR Takatori record was observed by the Railway Technical Research Institute (RTRI) (Nakamura et al. 1996)

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Fig. 4
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S-wave horizontal-to-vertical spectral ratios at HKD126. The red line represents the spectral ratio for main shock; a blue line with the light blue shadow represents the average spectral ratio and the standard deviation for weak motions

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Minor building damage occurred over a wide area, including the Sapporo metropolitan area. However, the heavy damage of the timber frame buildings that were destroyed by the strong ground motion was directly concentrated in the Mukawa district of Mukawa town. We could not determine the building damage clearly around JMA47004 because there were few buildings around this station. HKD126 is located near the heavily damaged area. From previous studies, it is clear that the 1–2 s periods have a potential influence on the timber flame building damage (e.g., Sakai et al. 2004). The response spectrum of the JR Takatori station record which has JMA seismic intensity of 7 was known as the Damage belt (e.g., Kawase 1996) during the 1995 Kobe earthquake. From this comparison, we can observe that the records at HKD126 and JMA47004 have dominated period ranges of 1–2 s similar to the record at JR Takatori.

Characteristics of strong ground motions at HKD126 and MKW01 stations

We installed a seismometer at a hill to know the effect of the surface geology at HKD126 on the strong ground motion. The Headquarters for Earthquake Research Promotion (2018) provide site amplification factors, for example, engineering geomorphologic classification and AVS30 (average S-wave velocity in the upper 30 m) in the Japan Seismic Hazard Information Station (J-SHIS). A black marsh, delta and coastal lowland, natural levee, and abandoned river channel of the engineering geomorphologic classification are distributed around HKD126 site. We considered this classification to select the site of a temporary station at a hill in Mukawa town (MKW01), which was located approximately 4 km north from the HKD126 (Fig. 5). The observation was carried out from September 10, 2018, to December 16, 2018, for approcimately 3 months. The seismometers used are an over dumping moving coil type accelerometer (Mitutoyo JEP-6A3 2 V/g). The data loggers are 24-bit (Hakusan LS-8800) in 100 Hz sampling with 12 V load batteries. The internal clock signal of each instrument was calibrated with a GPS timing signal every 1 h. The sensor was fixed with a two-pack type epoxy-based adhesive on the paved road. The photograph of the setup is shown in Fig. 6. The velocity waveforms and acceleration Fourier spectra of the Mw 4.5 (September 14, 2018, Event 1 in Fig. 1) aftershock at the two stations HKD126 and MKW01 are shown in Fig. 7. We observed a significant difference in the amplitudes of the waveforms, spectral amplitudes, and predominant frequency of the spectra. The differences between the NS and EW components were affected by the source wave radiation pattern similar to those for the main shock.

Fig. 5
figure 5

Locations of temporary strong motion and microtremor observations sites. The red triangles denote the temporary strong motion stations (MKW01-06), the blue circles and lines denote the microtremor array observation points, and the light blue circles denote the single station microtremor observation points (HV01-10). The base map was obtained from the geospatial information authority of Japan (GSI)

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Fig. 6
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Photographs of the setting situation. The temporally strong motion station (left: MKW01). The microtremor observation (right)

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Fig. 7
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Horizontal ground velocities and acceleration Fourier spectra at two stations in Mukawa town for the Mw 4.5 earthquake (Event 1: September 14, 2018). The velocity waveforms (left and center) were derived from the acceleration records. The strong motion stations (HKD126 and MKW01) and the epicenter of Event 1 are shown in Fig. 1. The right panel shows their acceleration spectra

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The significant differences of these near two sites necessitate the estimation of the velocity structures of both sites, which will reveal the cause of the destructive strong ground motion during the main shock at HKD126.

Estimation of S-wave velocity structures

We present the details regarding the methods for exploring and the results of the estimation of the Vs structures in this section.

Methods

To determine the difference in waveforms recorded at HKD126 and MKW01, we performed microtremor array (radii = 40–2000 m) observations at three sites around HKD126. To determine the variety of the engineering bedrock depth, we selected another site Aoba (AOB) as the mid-point between HKD126 and MKW01; the locations of these three sites are indicated in Fig. 5. We used servo-type velocity seismometers (Lennertz Le-3D/5 s) and 24-bit data loggers (Hakusan LS-7000XT) set in 100 Hz sampling with GPS time calibration. The locations of the observation sites and array sizes are summarized in Table 1. The example of the measurement setup is shown in Fig. 6. We selected the low noise section from the entire data to examine the phase velocities of Rayleigh waves using the spatial autocorrelation (SPAC) method (Okada 2003). Furthermore, we used small arrays (radius = approximately 1–7 m) at HKD126; for this case, we used an over dumping moving coil accelerometer (Mitutoyo JEP-6A3 2 V/g). The large array (LL: radius = 2000 m) phase velocity data were used for the three sites, as we could not set up the large array for the sites. This assumption of the common use for all site is obtained from the low variations of seismic bedrock depth in J-SHIS on this area. And phase velocities of the large array (L: radius = 400 m) at AOB were used for the MKW01 estimation.

Table 1 Array sizes and locations for the microtremor array observations
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We also carried out MASW on the high-frequency phase velocity at HKD126 and MKW01. We set 24 geophones of 4.5 Hz vertical component spaced 1 m apart with GEODE (Geospace Technologies) and an 8 kg wood hammer. The phase velocities of MASW were examined by the frequency-wave number method (e.g., Park et al. 1999). The phase velocities determined using MASW in the high-frequency range were combined with the phase velocities determined using the SPAC method in the low-frequency range (Fig. 8).

Fig. 8
figure 8

Phase velocities of Rayleigh waves at HKD126. The open circles denote the observed phase velocities using the SPAC method and the open squares denote those obtained using the MASW method. The solid lines denote the theoretical phase velocities for the AIST, J-SHIS V2 and Hatayama et al. (2007) models. The right panel shows the details of the low velocity part

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There are existing models for this area: the Japan Seismic Hazard Information Station (Fujiwara et al. 2012) version 2 model (J-SHIS V2), the Geological Survey of Japan, the National Institute of Advanced Industrial Science and Technology (AIST) model (Yoshida et al. 2007), and the Hatayama et al. (2007) model. First, we examined the underground Vs structure at HKD126 with the observed phase velocity from the SPAC and MASW methods. The observed phase velocities were compared with the theoretical phase velocities for existing Vs structures [Hatayama et al. (2007), AIST, and J-SHIS V2 models]. The phase velocity of the Hatayama et al. (2007) model which was estimated to simulate the 7–8 s period ground motions during the 2003 Tokachi-oki earthquake accurately explains the observed data (Fig. 8). Therefore, we inserted a 400 m/s layer (assuming the engineering bedrock) and used the Vs model of Hatayama et al. (2007) in the higher velocity part (over 400 m/s). Furthermore, we added a shallower layer to explain the 1-s period amplification referring, to the soil column of HKD126. These existing models are shown in Fig. 9. These Vs layer orders were used commonly for HKD126 and AOB and MKW01.

Fig. 9
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Estimated S-wave velocity structures at three sites. The existing structures are also indicated for each site. a HKD126, b AOB, c MKW01

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We estimated Vs by fitting selected phase velocities to the dispersion curve of the fundamental mode of the Rayleigh waves using the genetic algorithms inversion method (Yamanaka and Ishida 1996). We used the following parameters in this method: the number of generations is 50, the population is 40, the crossover ratio is 70%, and the mutation ratio is 1%. The material densities and P-wave velocities for each layer were estimated using the empirical relationship between them and the Vs obtained by Ludwig et al. (1970). The search range of the genetic algorithms is fixed as follows and shown in Table 2. For the deep part (Vs > 400 m/s), the Vs values are fixed and the depth of the top of the 400 m/s layer was fixed with a hot spring drilling near HKD126 (Yamaguchi 1960; Oka 2004). For the shallower part, the thickness of each layer is fixed by the boundary of the soil column of HKD126 (Table 2).

Table 2 Search range for inversion
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Results

HKD126

The observed phase velocity and theoretical dispersion curve of the estimated Vs structure at HKD126 are compared in Fig. 10a and the estimated Vs structure is shown in Fig. 9a and Table 3. The theoretical dispersion curve well explains the observed value in the range of 0.2–10 Hz. The estimated Vs at the shallowest layer is 70 m/s, which is similar to the PS-logging data at HKD126 (Vs = 60 m/s). After constructing the Vs structure of HKD126, we used this structure to examine the other two sites.

AOB

AOB, the mid-point between HKD126 and MKW01, was selected on a flat plain, as HKD126 is located on a flat plain as well, to determine the variation. For the search range of Vs and thickness of each layer, we referred to from the HKD126 site. We selected AOB site to determine the variety of the engineering bedrock depth in the flat plain. We have not performed small SPAC and MASW methods around the AOB site because of the place for setting; therefore, the phase velocity is estimated to be less than 2 Hz. The observed phase velocities and theoretical dispersion curve of the estimated Vs structure at AOB are compared in Fig. 10b and the estimated Vs structure is shown in Fig. 9b and Table 3.

Table 3 Estimated S-wave velocities and layer thickness at three sites
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Fig. 10
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Observed and theoretical phase velocities of the Rayleigh waves at three sites. The black circles denote the observed phase velocities. The red solid line denotes the theoretical phase velocities for the estimated Vs structure model. a HKD126, b AOB, c MKW01. The gray solid lines denote the original observed phase velocities

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MKW01

Because the temporary station MKW01 site was on the hill (Fig. 5), it did not have a wide area to carry the wide SPAC arrays. The geomorphologic classification of MKW01 borders between terrace covered with volcanic ash soil and hill. We used phase velocities of the AOB large array (L: radius = 400 m) which was set on a lower flat field. The observed phase velocities of the arrays (radii = 120, 40 m) are connected to the those of the large array. Additionally, we used the phase velocity observed by MASW over 10 Hz. The phase velocities using the small SPAC array and the MASW converge to 200 m/s. Therefore, we removed two shallow layers (Vs = 70 m/s) from the estimated profile of HKD126 to invert the Vs structure. The observed phase velocities and the theoretical dispersion curve of the estimated Vs structure are compared in Fig. 10c and the estimated Vs structure is shown in Fig. 9c and Table 3.

Although there is no phase velocity of 1–10 Hz due to the problem of array size, theoretical dispersion curve and observed phase velocities correspond well in other frequency ranges (Fig. 10c).

Single station microtremor linear array observation

The single station microtremor observations were performed along the temporary strong motion high-density linear array (Fig. 5) using the same instruments that were employed for SPAC arrays.

The data processing for datasets was as follows. Each dataset were divided into 40.96 s windows tapered with a 5% cosine function. The Fourier spectra were smoothed using a 0.1 Hz Parzen window. The Fourier spectra of the NS and EW component were averaged (root mean square) to obtain the horizontal component Fourier spectrum. Then the spectral ratios between the horizontal components and the vertical components were calculated. Finally, the spectral ratios of the horizontal component to the vertical component (H/V) were calculated using the arithmetic mean of 10 selected low noise sections. The H/V spectral ratio at HKD126 is shown in Fig. 11, along with the theoretical ratio of the constructed velocity structure. A contour diagram of the spectral ratio for the linear array is shown in Fig. 12. Their peak frequencies do not have large variations around 1 Hz in the flat plane area; however, a drastic change occurs near MKW01 in the frequency range of 1–10 Hz.

Fig. 11
figure 11

Horizontal to vertical Fourier spectral ratios of the single station microtremor observations at the HV10 site, along with the theoretical ratio

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Fig. 12
figure 12

Contour diagram of the horizontal to vertical Fourier spectral ratios of the single station microtremor observations. Left to right in this figure correspond to south to north

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Discussions

The constructed and existed structures are compared in Fig. 9 for each site. In Hatayama et al. (2007), the Vs = 1300 m/s layer appears at a depth greater than 300 m; however, it appears within 200–300 m in the estimated Vs structures. This layer at HKD126 is shallower than the MKW01 layers, and the depth of the AOB layer lies in between. This tendency of the depth variation is the same as that of the seismic bedrock and the subsurface structure depth variation of the AIST and J-SHIS V2 models (Fig. 9). However, the similar value Vs layer of the J-SHIS V2 and AIST structures have many varieties (Fig. 9). Conversely, with respect to the shallow part, the engineering bedrock depth of MKW01 is shallower than that of HKD126. The seismic bedrock of AOB is at medium depth among the other sites; however, the surface soft soil deposit at AOB is detected to be thicker, down to about 13 m, than that at HKD126. The appearance of a second peak in the high-frequency range around HV05 matches these results (Fig. 12).

We have calculated the theoretical amplification factor of the SH-wave with the Vs structure, which was constructed as mentioned above (Fig. 13). We assumed that the input motion is a plane SH-wave at a depth of 1 km depth with an incident angle of 0°. The amplification factor of 1 Hz at AOB is the largest among the three sites. Further, the amplification factors of AOB and HKD126 are five times larger than that of MKW01 at a frequency of around 1 Hz. The reason for this tendency is the low Vs in the shallow part of the two sites; the engineering bedrock (400 m/s) of the two sites are deeper than that of MKW01.

Fig. 13
figure 13

Theoretical site amplification factor of the SH-wave for three sites. The theoretical site amplification factor calculated with the estimated Vs structures in Fig. 9 and Table 2. The SH-wave was assumed to input for 1.3 km/s layer with an incident angle of 0°

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We performed strong motion high-density linear array observation from December 1, 2018, to December 16, 2018, at six stations along the lines of HKD126 to MKW01 in Mukawa (Fig. 5) to investigate the variation of the strong ground motion in the target area. The instruments used for this observation were the same as those for MKW01. The observed velocity waveforms of the transverse component during the aftershock (Event 2 in Fig. 1: Mw 3.9, 9 December 2018) are shown in Fig. 14. The spectral ratios of the S-wave at the five stations were divided by the spectra at MKW01 (Fig. 15). These records were not affected by the nonlinear effect of soft soil, because their amplitudes were low.

As this study area is located in the collision zone, the deep crustal structure is complex (Miyamachi et al. 1994; Iwasaki et al. 2004) and the shape of the seismic bedrock is also complex (Hatayama et al. 2007). In the deep underground structures of the J-SHIS and AIST models, the seismic bedrock is slightly inclined to the northern side. The depth of the Vs = 1300 m/s layer estimated in this study tends to incline to the north (Fig. 9). This may implicate the seismic bedrock variation in the deeper structure.

Among the observed spectral ratios of the five sites, the amplitudes of northern sites (MKW02, MKW03, MKW04) are larger than those of the southern sites (MKW05, MKW06) in the frequency range of 0.5–1 Hz. The theoretical spectral amplitudes in Fig. 13 are consistent with these observed spectral ratios. However, the amplitude of the observed spectral ratio of HKD126 (MKW05) is not larger than that of AOB (MKW02, 03). The cause of this difference between theory and observations might have to be discussed with other data (e.g., drilling data) in detail (Fig. 14).

Fig. 14
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Transverse component velocity waveforms for the Mw 3.9 earthquake (Event 2: 09 December 2018). These velocity waveforms were derived from the acceleration records of a temporary line array observation (MKW01-06) in Mukawa town with a 0.05–5 Hz bandpass filter. The line array is shown in Fig. 5 and the epicenter of Event 2 is shown in Fig. 1

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Fig. 15
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Spectral ratios for the Mw 3.9 earthquake (Event 2: 09 December 2018). The spectral ratios are derived from the S-wave part Fourier spectra of each station divided by the MKW01 spectra

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The theoretical amplification factor of MKW01 is slightly larger than others at 0.3 Hz. We cannot recognize this phenomenon in the observed spectral ratios (Fig. 15); however, the spectral amplitude of MKW01 is larger than that of HKD126 at a frequency of approximately 0.3 Hz (Fig. 7). If we use the larger amplitude records, we can examine the effect of the seismic bedrock depth variation in detail. However, it is difficult to discuss this complex tendency through the results of our measurements.

The predominant periods during the main shock are longer than the predominant periods of theoretical and weak motion records (Fig. 4); this might be the effect of nonlinearity. The strong ground motion of the 1–2 s period during the main shock at HKD126 was mainly amplified by this shallow Vs structure, and this predominant range was shifted for long periods possibly due to the nonlinear effect.

Concluding remarks

Severe building damage occurred around the HKD126 strong motion station during the 2018 Hokkaido eastern Iburi earthquake. This damage was caused by the 1–2 s ground motion which was the dominant period in the velocity spectra. We conducted temporary strong motion, microtremor, and MASW observations in Mukawa town to investigate the underground structure. The estimated Vs structure that was inverted from the phase velocity using the microtremor array and MASW observations explained the strong ground motion characteristics during the main shock observed at HKD126. For the strong ground motion of the main shock, we confirmed that the shallow underground velocity structure was responsible for approximately 1 s at HKD126. For future studies, examining the nonlinear effect for HKD126 in detail is important. To do this, we must consider more ground motion records from a wider area for obtaining a detailed three-dimensional velocity structure.