Introduction

The Hokkaido district in Japan belongs to the northeastern Japan subduction zone. Due to the oblique subduction of the Pacific slab, the Kuril arc is dragged to the west and collides to the northeastern Japan arc at the central part (e.g., Kimura 1996). This arc–arc collision makes characteristic structures; they are seen as the surface topographies, such as the Hidaka mountain range (HMR), and the surface geology. In this region, some destructive earthquakes have occurred at depths of greater than 30 km, which is abnormally deep; the 1970 Hidaka earthquake (M6.7, 55 km depth), the 1982 Urakawa-oki earthquake (M7.1, 40 km depth) and the 2018 Hokkaido Eastern Iburi earthquake (M6.7, 37 km depth; hereafter we call 2018 Iburi Earthquake).

Heterogeneities with respect to seismic wave velocity (e.g., Kita et al. 2010, 2012) and attenuation (e.g., Takahashi 2012; Kita et al. 2014) were investigated in this region. These studies revealed that heterogeneous structures resulted from the arc–arc collision developed at the west side of the HMR and suggested that these structures relate to occur the 1970 Hidaka and the 1982 Urakawa-oki earthquakes (e.g., Kita et al. 2012). The 2018 Iburi Earthquake and its aftershocks occurred at the abnormal depths of the crust. Thereby, the 2018 Iburi Earthquake would be the earthquake linking the arc–arc collision and its forming structures (e.g., Kita et al. 2012). Because attenuation structures can compare between locations of hypocenter and heterogeneity without a trade-off, such as between the hypocenter and the velocity models, it will significantly improve our understanding on why the earthquakes occur at the abnormal depths in the Hokkaido district.

In this study, therefore, we estimate the S-wave attenuation (Qs) structures of the Hokkaido district in precisely by the method using the spectrum inversion method (e.g., Nakamura and Uetake 2002). As a result, we could reveal very low-Qs at the west of the HMR at depths of 0–50 km and high-Qs zone along the HMR, as well as results for Qp (Kita et al. 2014). Around the 2018 Iburi Earthquake and its aftershocks, we find that boundary between the low-Qs and the high-Qs zones, indicating that attenuation property abruptly changes around the source area of the 2018 Iburi Earthquake.

Method and data

For the present study, we determine the three-dimensional (3D) S-wave attenuation (Qs) structure beneath the Hokkaido district of northern Japan using the tomographic inversion method.

The National Research Institute for Earth Science and Disaster Resilience (NIED) operates nationwide strong-motion observation networks in Japan: K-NET (1045 stations) and KiK-net (698 stations). We collect 89,388 seismograms recorded at 457 stations of the networks from 1329 earthquakes which occur during May 1996–Nov. 2018. The magnitude of the earthquakes is 4.0–7.5. We limit epicentral distances when collecting the seismograms: \(\le\) 100 km and \(\le\) 500 km for the earthquakes occurred at depths of 0–30 km and 30–200 km, respectively. The stations and the earthquakes used in this study are shown in Fig. 1. Nonlinearity effects on the ground motion would be apparent when it becomes 100 Gal or stronger (e.g., Beresnev and Wen 1996; Noguchi and Sasatani 2011). Thus, we only adopt seismograms that the maximum acceleration is less than 100 Gal. A time length for calculating spectral amplitude changes depending on the magnitude of earthquakes and 180 s from S-wave arrival is the maximum. In our tomographic analysis, we estimate site effects simultaneously with spatial variation in Qs and effects with respect to sources. In our tomographic analysis, we estimate effects with respect to site and source simultaneously with spatial variation in Qs. The site effects express near surface amplifications of amplitude and can be characterized by AVS20 (Fujimoto and Midorikawa 2006; Boore et al. 2011): average S-wave velocity from ground surface to 20-m depth (Fig. 1a). In Nakamura (2009), the number of station groups is six in whole of Japanese island. There are significant and local variations in near surface conditions reflecting the surface geology around the HMR (Kimura 1996); for example, the Yufutsu Plain in the eastern Iburi has very soft ground due to thick sediments (e.g. IBUH03 of KiK-net station). In this study, therefore, we increase to eight station groups that are equally divided by the AVS20 on the logarithmic scale (Fig. 1a).

Fig. 1
figure 1

Distributions of a stations and b earthquakes used in this study. Colored symbols indicate average S-wave velocity from the ground surface to a depth of 20 m (AVS20). b White star indicates the epicenter of the 2018 Hokkaido Eastern Iburi Earthquake

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We use 3D tomographic inversion method provided by Nakamura (2009) which bases Nakamura et al. (2006). We briefly introduce the method here.

Supposed that acceleration spectral amplitude at \(i\)-th station and \(j\)-th earthquake, \(\alpha_{ij}\), is written (Nakamura 2009) as

$$\begin{aligned} \alpha_{ij} \left( f \right) &= Sa_{j} \left( f \right) \times {Ge} \times \sqrt {\frac{{\rho_{\text{SB}} \beta_{\text{SB}} }}{{\rho_{j} \beta_{j} }}} \\ &\quad\times g_{l} \left( f \right) \times \exp \left[ { - \pi f \sum_{k} \frac{{T_{k} }}{{Q_{k} \left( f \right)}} } \right] , \end{aligned}$$

where \(f\) is frequency, \(Sa_{j}\) is the source acceleration spectrum, \({Ge}\) is the geometrical spreading factor, \(g_{l}\) indicates site amplification effects at \(l\)-th station group. \(\rho_{\text{SB}}\) and \(\beta_{\text{SB}}\) are the density and velocity at the seismic basement (SB), respectively, and are replaced by those at the surface, 0-km depth, of the JMA2001 one-dimensional (1D) model (Ueno et al. 2002) in this study. The density and velocity at the depth of \(j\)-th earthquake are denoted as \(\rho_{j}\) and \(\beta_{j}\), respectively. \(Q_{k}\) denotes quality factor of S-wave attenuation at \(k\)-th block and \(T_{k}\) is time spent of a ray in the block. The summation on the exponential term is made along the ray of S-wave. \(\alpha_{ij}\) is calculated from NE component seismogram at 1–10 Hz with every 1 Hz.

We perform iterative inversion using the ARTB algorithm (Herman, 1980) to determine Qs structure by minimizing residuals between observed and calculated spectrum of ground accelerations. We describe the source acceleration spectrum following the notation of Boore (1983):

$$\begin{aligned} Sa_{j} \left( f \right) &= \frac{{M_{0j} R_{\theta \varphi } F}}{{4\uppi\rho_{j} \beta_{j}^{3} }} \times S\left( f \right) \times P\left( f \right) = \frac{{M_{0j} R_{\theta \varphi } F}}{{4\pi \rho_{j} \beta_{j}^{3} }} \\ &\quad\times \left( {2\pi f} \right)^{2} \left( {1 + \frac{f}{{f_{cj} }}} \right)^{ - 2} \times \left( {\frac{f}{{f_{\hbox{max} } }}} \right)^{ - n} , \end{aligned}$$

where \(M_{0}\) is the seismic moment, \(R_{\theta \varphi }\) is the radiation pattern, and \(F\) is the reduction factor taking account for the energy partitioning into two horizontal components. \(S\) represents the source spectral model and \(f_{c} = 4.9 \times 10^{6} \beta_{j} \times \sqrt[3]{{\Delta \sigma /M_{0j} }}\) is the corner frequency where \(\Delta \sigma\) denotes the stress drop.

We initially assume the similar conditions of Nakamura (2009) to the variables: \(R_{\theta \varphi } = 0.65\), \(F = 0.71\), \(\Delta \sigma = 100 \left[ {\text{bar}} \right]\), \(f_{ \hbox{max} } = 12 \left[ {\text{Hz}} \right]\), and \(n = 3.5\). Seismic moments of earthquakes are those determined by the F-net of the NIED. The site amplification effects are started from \(g_{l} = 2\) for a station group (blue stars in Fig. 1) on the hard rock, \({\text{AVS}}20 > 1000 \left[ {\text{m}/\text{s}} \right]\), whereas \(g_{l} = 3\) for the other station groups, where the \({\text{AVS}}20\) is \(\le 1000 \left[ {{\text{m}}/{\text{s}}} \right]\) or unknown. The quality factor, \(Q\), of \(100f^{0.78}\) is adapted to the initial model of the inversion. We impose dumping factors representing variances of an observation/estimation error in the data, the source spectrum, the site amplification effects, and the attenuation models: \(\sigma_{\alpha } = 0.20\), \(\sigma_{Sa} = 1.0\), \(\sigma_{g} = 0.34\), and \(\sigma_{Q} = 10f^{0.78}\). The values of dumping factors are after Nakamura (2009). The relaxation parameter of ARTB is \(\lambda = 0.1\). The relaxation parameter value is after Kamiya et al. (1989) and was used by Nakamura and Uetake (2002), Nakamura et al. (2006), Nakamura (2009). In the study area of 138° E–142° E and 34° N–38° N, the blocks take the size of 0.1° × 0.1° × 10 km. The JMA 2001 1D model (Ueno et al. 2002) is employed as the 1D S-wave velocity structure for calculating ray paths and travel times. The number of blocks where rays hit is 26,278. The total number of model parameters, that is, \(Q_{\text{s}}\) in each block, the source strength and site amplification effect, is 28,614. Resultant images of \(Q_{S}\) structure are obtained after the global 300th iteration of ARTB in this study.

For check validity of our \(Q_{S}\) model, the checkerboard resolution test is carried out. \(Q_{S}\) of 100 and 400 are alternately assigned to blocks in horizontal and depth directions. The geometries of stations and earthquakes are the same in the inversion. Source spectrum and site amplification effects are fixed in this trial. \(Q_{S} = 160\) is given in the calculation space as the starting model. We defined a restoration index, \(\text{RI}\), to evaluate reproducibility in the trial:

$${\text{RI}} = \left| {\frac{1}{{Q_{\text{CB}}^{\text{inp}} }} - \frac{1}{{Q_{\text{CB}}^{\text{est}} }}} \right| ,$$

where \(Q_{\text{CB}}^{\text{inp}}\) is assigned value (100 or 400) and \(Q_{\text{CB}}^{\text{est}}\) estimated value. Namely, this index \({\text{RI}}\) gives small value when the assuming anomalies are well reconstructed.

Results

The estimated Qs structures at 10 Hz are demonstrated in Fig. 2. In the figure, we only display the structures where the input anomalies are well recovered (\({\text{RI}} < 0.001\)) in the resolution test (Additional file 1: Figure S1). Thus, spatial variations of Qs are mainly revealed from the forearc region to around the volcanic front in and around Hokkaido. The results in the other frequency bands (1–9 Hz) are displayed in Additional file 2: Figure S2, which provides similar Qs distributions while characteristics of spatial variations of Qs are emphasized in high-frequency bands.

Fig. 2
figure 2

S-wave attenuation (Qs) structures at depths of 0–90 km in and around Hokkaido, Japan. The frequency, \(f\), is 10 Hz. The well-resolved area, where the restoration index, RI, is greater than 0.001. White circles denote the earthquakes used in this study. Black triangles are volcanoes

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Figure 2 clearly shows that the estimated Qs structures at depths of 0–30 km have strong lateral variations. For example, the remarkable low-Qs (high-attenuation) and high-Qs (low-attenuation) zones spreading north to south are found at the central Hokkaido. This north–south distribution of Qs is continuously estimated at depth by about 50 km beneath the forearc region. Low-Qs areas also appear at depths of 20–50 km beneath the volcanoes. Although validities of estimated Qs would be declined, these low-Qs areas beneath the volcanoes seem to extend towards the backarc region with depths. It would represent the upwelling flow in the mantle wedge which has been retrieved as low-velocity (e.g., Nakajima et al. 2001; Kita et al. 2014; Shiina et al. 2018) and high-attenuation (Nakamura and Uetake 2004; Takahashi 2012; Nakajima et al. 2013; Liu et al. 2014) anomalies in P and S waves in the Hokkaido and the Tohoku district, Japan. At the forearc side from the volcanoes, the high-Qs zones are widely estimated at the depths of 30–40 km or deeper. This suggests that S-wave attenuation in the Pacific slab and mantle wedge beneath the forearc region tend to be weak.

It is known that attenuation effects can be modeled by the scattering attenuation and the intrinsic absorption (e.g., Hoshiba 1993; Takahashi et al. 2009; Sato et al. 2012). Carcolé and Sato (2010) mentioned characteristics in the two types of Qs using the multiple lapse time window analysis. For comparing results at the HIROO2 and the KUSHI2 in Carcolé and Sato (2010) at a range from 1 Hz to 10 Hz, we average Qs values from blocks that are posited within an epicentral distance of 100 km from the target stations (the inset map of Fig. 3) and depths of 0–40 km. The averaged Qs in the frequency bands of interests are almost comparable to the sum of the scattering and the intrinsic effects constrained by Carcolé and Sato (2010). Therefore, we reveal the total effects on Qs and its spatial variations in this study.

Fig. 3
figure 3

Comparisons of Qs values obtained in this study and Carcolé and Sato (2010). The Qs values of this study (black circles) are computed as average values within 100 km in horizontal and 0–40 km in depth directions from stations of the KUSHI2 and the HIROO2. Total Qs (red open circles) of Carcolé and Sato (2010) is the sum of intrinsic Qs (blue crosses) and the scattering Qs (brown circles)

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The earthquakes used in this study tend to locate on the high-Qs areas (Fig. 2). Because magnitudes of the earthquakes are 4.0 or larger, this indicates that the earthquakes with moderate to large magnitude occur within the media of which the total attenuation is small. Around earthquakes at depths by about 50 km corresponding to the arc crust and the uppermost mantle; moreover, high-Qs and the low-Qs boundaries are frequency imaged.

Discussion

At the central Hokkaido, the obtained low- and high-Qs zones mark belt-like distributions in the north–south direction (Fig. 2). There are remarkable at depths of 0–20 km. Moreover, in the west side of the Hidaka mountain ranges (HMR), these distributions of Qs are found at depths by about 50 km (Figs. 2 and 4), that is, the low-Qs zones seem to extend to near the upper boundary of the Pacific slab. In the areas marking the low-Qs values, reductions of seismic wave velocity (e.g., Kita et al. 2012; Shiina et al. 2018) and P-wave attenuation (Kita et al. 2014) were retrieved.

Fig. 4
figure 4

Vertical cross-sections of Qs structures at 10 Hz. The black curves represent the upper boundary of the Pacific slab (Nakajima et al. 2009). Dashed lines in the inset map denote separate characteristics of surface topography, such as geological boundary or the Hidaka mountain ranges (HMR)

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These north–south spreading heterogeneities seem to consistent with the geological boundary at the ground surface, in particular at the depths of 0–10 km. By comparing between Fig. 2 and the inset map of Fig. 4, the high-Qs zone is estimated along the HMR and the low-Qs belt imaged next to the west of the HRM well matches to the Sorachi-Yezo belt. In the east side of the HMR, lateral variations in Qs seeming to match to the geological boundary within the Tokoro and the Yubetsu belts. These correlations between heterogeneous structure and the surface geology have been discussed (e.g., Iwasaki et al. 2004; Kita et al. 2010). Thereby, our results support these interpretations from the spatial variation of Qs; complex structures are developed around the central Hokkaido and it would relate to the collisions between the Kuril and northeastern Japan arcs.

The Qs values at depths of 0–20 km mark remarkably low along the coastline of the west side of the HMR (Fig. 2). Across this arc–arc collision zone, Iwasaki et al. (2004) investigated the shallow crustal structure of the P-wave velocity (Vp) in detail. According to their constructed Vp model, the low-Vp, < 4.5 km/s, layers are lying near the ground surface in the west side of the HMR. These layers were interpreted as the thick sedimentary layers, and associating features are identified in other geophysical measurements, such as S-wave velocity (e.g., Nishida et al. 2008), P-wave attenuation (Kita et al. 2014), and electric resistivity (Yamaya et al. 2017). Kinoshita and Ohike (2002) reported that the sediments would affect to reductions of Qs from the studies around the Kanto district, Japan. Thereby, the remarkable low-Qs values would be derived from presences of the thick sedimentary layers. At the results of 10 Hz, low-Qs values concentrating to near the ground surface are additionally detected in the east side of the HMR (Fig. 4b–d). Iwasaki et al. (2004) showed the presences of low-Vp layers in the east side too. Thus, the low-Qs zone in the east side of the HMR may also represent the sedimentary layer; however, it would be thinner than in the west side because decreases of Qs are not clear in the low-frequency bands (Additional file 1: Figure S1).

Figure 5b shows the Qs structure elongated around the arc–arc collision zone from Fig. 4b and compares to the crustal structure interpreted by Iwasaki et al. (2004), displayed in Fig. 5a. As discussed above, the low-Qs values are imaged near the ground surface and there are almost consistent with sedimentary layers. However, it is seen that the low-Qs values in the west side of the HMR appear outside from the sedimentary layers (distances of about 110–140 km in Fig. 5b). On the other hand, relatively high-Qs values (distances of 140–160 km; the Region A in Fig. 5c) estimated as sandwiched the low-Qs zones near the ground surface continuously distribute to the deep potions in the east side of the HMR. These Qs structures would represent the obduction of the mid/lower crust of (e.g., Tsumura et al. 1996; Iwasaki et al. 2004) and/or the mantle wedge materials beneath the Kuril arc (e.g., Kita et al. 2010). Although effect of the thick sediment layers may affect Qs in the area, the Qs reductions concentrated near surface are extended in the areas where the sedimentary layers would not be present in the southern part of the cross-sections. This expects that the low-Qs in the Region A indicate that S waves would be attenuated in the frontal areas of the collision zone. The low-Qs zone depth-extending in parallel to the high-Vp values (the Region A) is possibly consistent with the development of high-attenuation properties at the frontal areas of the collision zones. Along the HMR, metamorphic materials, such as the serpentine, are often exposed (e.g., Okamoto et al. 2015). Large amplitude decays which would be due to the serpentine were discussed from seismic observations (e.g., Nakamura et al. 2006; Nakajima et al. 2013). Whereas many faults will be formed in the collision zone and they emphasize S-wave attenuation. Therefore, we expect that the low-Qs values estimated at the distance of 110–140 km in Fig. 5b reflect either or both heterogeneities present in the frontal areas of the collision zone.

Fig. 5
figure 5

Comparisons and interpretations of the estimated Qs structure in this study. a The crustal structure across the collision zone between the Kuril and the northeastern Japan arcs interpreted by Iwasaki et al. (2004). b, c The Qs estimated structure in this study and its interpretations. A location of the cross-section is included in Fig. 4b. The vertical length is enlarged by 2. The color scale is the same in Fig. 4

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The main shock of the Ibrui Earthquake and its aftershocks locate in the western edge of the remarkable low-Qs zone beneath the area including the Sorachi-Yeno belt (Fig. 2). In other words, Qs values are abruptly changed in laterals around the source area of the Iburi Earthquake. The boundary between the high-Qs and the low-Qs zones is intersected near vertical, as well as the distribution of the earthquakes (Fig. 4b, c). We also find the tendency for the stress drop to increase with depth from the obtained source parameter of the aftershocks of the Iburi Earthquake. This trend is consistent with the results of Nakano and Kawase (2019).

In this study, estimated Qs values express the total effect of seismic attenuation, that is, the sum of scattering and intrinsic effects. From the refraction/wide-angle reflection surveys (e.g., Iwasaki et al. 2004), the stratified-like structures were proposed in the source region, as seen in Fig. 5a. It is expected that compositions within a layer will be almost homogeneous, implying intrinsic effect difficult to vary in each layer. For the horizontal layers, thus, the laterally varied Qs values would represent spatial changes of the scattering attenuation. In this case, the low-Qs zones will suggest localizations of small faults or cracks and the Iburi Earthquake and its aftershocks seem to occur in areas adjacent to the fractured zones. Alternatively, the lateral changes of Qs can also be simply implicated that near vertical structural boundary lies in the source area. Namely, it is speculated that the northeastern Japan arc may penetrate to the mantle wedge with a high angle and the boundary between the attenuation properties will reflect the material boundary, such as the Moho discontinuity. Because the earthquake sequences of the Iburi Earthquake also distribute in vertically, these earthquakes may be used these structural boundaries if there are formed in this area, likewise to the discussions in Kita et al. (2012) for the 1970 Hidaka and 1982 Urakawa-oki earthquakes.

The Qs structures estimated in this study provide that the Iburi Earthquake and its aftershocks activate in an area where Qs values are laterally changed. The earthquakes relating to the Iburi earthquake locate on the high-Qs zones. These correlations between the hypocenter locations and the heterogeneity in Qs can be seen in the entire study region. The Qs structure is constructed for 1D velocity model and compared to the hypocenters determined for the 1D model in this study. On the other hand, some studies (e.g., Nishida et al. 2008; Kita et al. 2012) pointed out the large lateral variations in seismic wave velocity around the source area of the Iburi Earthquake. The Qs values estimated in this study may be perturbed if the S-wave velocity are varied in 3D. Therefore, investigations of Qs model, as well as determination of the hypocenters, around the source area of Iburi Earthquake taking 3D structure of seismic wave velocity into account will provide further detailed features with respect to the Qs structure, and thus will improve insight into the links between the structural heterogeneity and the generation mechanism of the Iburi Earthquake, including ongoing processes in the arc–arc collision zones at the central Hokkaido, Japan.

Conclusions

In this study, we constructed Qs structures in and around Hokkaido, Japan. At the central Hokkaido, lateral variations of Qs were determined. The belt-like anomalies of Qs spreading north to south almost matched to the surface geology, and those Qs patterns were retained at depths by about 50 km. Therefore, we considered that these characteristic distributions of Qs reflected the complex structures resulted from the collision between the Kuril and the northeastern Japan arcs at the central Hokkaido.

Around the source area of the 2018 Hokkaido Eastern Iburi Earthquake, Qs values were abruptly changed, and it showed the near vertical boundary of the Qs values. The main shock and its aftershocks are located on the high-Qs zones and seem to be arraigned along the boundary of the Qs. These consistencies of distributions of between the Qs and the earthquake locations propose the presence of strong heterogeneity in the source areas of the 2018 Hokkaido eastern Iburi Earthquake and the heterogeneity closely linked to the generation of the main shocks and following aftershocks.