Introduction

Two large events during the 2016 Kumamoto earthquakes caused a great deal of damage in Kumamoto and Oita Prefectures, Kyushu Island, Japan. The largest foreshock (M JMA6.5; indicated by the green star in Fig. 1a) occurred at 21:26 on April 14, 2016 (JST: UTC + 9 h), and then, the mainshock (M JMA7.3; indicated by the yellow star in Fig. 1a) took place at 01:25 on April 16, 2016 (JST). The epicenter of the mainshock was located near the intersection of the Futagawa and Hinagu faults, which are reported to be active faults (Nakata and Imaizumi 2002). During the mainshock, a moderate event (M JMA5.7; indicated by the sky blue star in Fig. 1a) was induced near the Yufu-dake volcano, Oita Prefecture (e.g., Yoshida 2016). After the mainshock and the induced event, the aftershock activity extended toward the NE, where the active volcanoes, Mt. Aso, Mt. Kuju, Mt. Yufu-dake, and Mt. Tsurumi-dake, are located (Fig. 1a).

Fig. 1
figure 1

a Tectonic background and b events and stations used in this study. Green, yellow, and sky blue stars indicate the epicenters of the largest foreshock (M JMA6.5), the mainshock (M JMA7.3), and the induced event (M JMA5.7), respectively. White stars denote the epicenters of events larger than M JMA 5.0 for one month following the foreshock. Black circles indicate the epicenters of events with 2.0 ≤ M JMA < 5.0 occurring for one month following the foreshock. Active and quaternary volcanoes are shown as red and peach triangles, respectively. Purple lines denote active faults (Nakata and Imaizumi 2002). Black lines are contours of altitude with intervals of 300 m. The red square corresponds to the area shown in Fig. 2. Colored circles and inverse triangles show the events and stations used in this study. The color and size of each circle indicate the depth and the magnitude of the event, respectively

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Kyushu Island is located in southwest Japan. The Philippine Sea (PHS) plate is subducting beneath this region along the Nankai Trough. The active volcanoes mentioned above are located along the volcanic front on Kyushu Island. The sequence of the 2016 Kumamoto earthquakes and the induced event occurred through this volcanic area in the central Kyushu Island, across which the Beppu–Shimabara graben lies oriented NE–SW. Along the graben, a shear zone (western extension of the median tectonic line) is present under the north–south extensional stress regime where both normal faulting and strike-slip earthquakes have occurred (Matsumoto et al. 2015). The Futagawa and Hinagu faults are in the southwestern portion of the shear zone.

The quality factor Q expresses the degree of anelasticity of rocks and depends on the temperature and water content (e.g., Karato 2003). Generally, P- and S-wave Q (\(Q_{\text{P}}\) and \(Q_{\text{S}}\)) show that the condition \(Q_{\text{S}} > Q_{\text{P}}\) is found in the crust (e.g., Rautian et al. 1978; Modiano and Hatzfeld 1982), whereas the condition \(Q_{\text{P}} > Q_{\text{S}}\) dominates in the asthenosphere (e.g., Anderson et al. 1965). Several three-dimensional Q tomographic studies have been conducted for southwestern Japan, including Kyushu Island (Liu and Zhao 2014, 2015; Saita et al. 2015; Komatsu and Oda 2015). These results revealed the low-Q zones upwelling from the top of the high-Q PHS slab to the active volcanoes. Liu and Zhao (2015) showed that low-Q zones in the crust are located in or around the active faults. They interpreted that large crustal earthquakes might be caused by fluids due to dehydration on the PHS slab. Mamada and Takenaka (2004) investigated the \(Q_{\text{S}}\) structure around the source region of the 1997 Northwestern Kagoshima earthquakes in southern Kyushu with the coda normalization method and found that the focal region of these earthquakes have lower Q than outside of the focal region. Most recently, Wang et al. (2017) estimated the 3-D attenuation and velocity structures in the source region of the 2016 Kumamoto earthquakes from the data including events before and after these earthquakes and found that the Kumamoto earthquakes occurred in a high-Q and high-velocity zone in the upper crust underlain by a low-Q, low-velocity, and high-Poisson’s ratio area in the lower crust and upper mantle.

Komatsu and Oda (2015), our previous study, estimated the 3-D P-wave attenuation structure beneath southwest Japan, including Kyushu. The obtained tomographic image illustrates that a low-\(Q_{\text{P}}\) zone exists around the Beppu–Shimabara graben and active volcanoes, while a high-\(Q_{\text{P}}\) zone exists in the PHS slab. In this study, we estimate the \(Q_{\text{P}}\) and \(Q_{\text{S}}\) structures beneath the source region of the 2016 Kumamoto earthquakes and discuss the relationship among \(Q_{\text{P}}\), \(Q_{\text{S}}\), and geophysical phenomena (fluid content, thermal structure, seismicity, and rupture process).

Data and methods

The study area is the central part of Kyushu Island, which is situated at 31.5°N–34.1°N and 129.4°E–132.4°E (Fig. 1b). We use seismograms recorded by 80 stations within the High Sensitivity Seismograph Network Japan (Hi-net) deployed by the National Research Institute for Earth and Disaster Resilience (NIED) (Okada et al. 2004). We select 743 crustal and intra-slab events (M JMA 3.0–6.0) occurring in and around Kyushu Island in the period from June 2002 to May 2012 (Fig. 1b). Note that the period is before the Kumamoto earthquakes took place. These events were also used in the study of the three-dimensional P-wave attenuation structure beneath southwest Japan (Komatsu and Oda 2015).

We first determine the path-averaged attenuation factor \(t^{*}\) from the waveform data through a spectral analysis. The seismic displacement spectra of P- and S-waves for event i observed at station j may be expressed as

$$U_{ij} \left( f \right) = \varOmega_{0i} S_{i} \left( f \right) \cdot { \exp }\left( { - \pi ft_{ij}^{*} } \right) ,$$
(1)
$$S_{i} \left( f \right) = \frac{1}{{1 + \left( {\frac{f}{{f_{ci} }}} \right)^{2} }},$$
(2)

where f is the frequency, \(\varOmega_{0i}\) is a frequency-independent term related to the seismic moment, and \(f_{ci}\) is the corner frequency of the source spectrum \(S_{i} \left( f \right)\) (Scherbaum 1990; Eberhart-Phillips and Chadwick 2002). The attenuation factor \(t_{ij}^{*}\) contains information on Q along the ray path from the hypocenter i to station j. In order to determine \(t_{ij}^{*}\), Eq. (1) is rewritten as

$${ \log }\left| {U_{ij} \left( f \right)/S_{i} \left( f \right)} \right| = \left( { - \pi t_{ij}^{*} { \log }e} \right)f + { \log }\varOmega_{0i} .$$
(3)

Since there is a trade-off between the \(f_{ci}\) included in \(S_{i} \left( f \right)\) and \(t_{ij}^{*}\) (e.g., Scherbaum 1990; Ko et al. 2012), before evaluating \(t_{ij}^{*}\), we independently estimate \(f_{ci}\) using a procedure exploited by Somei et al. (2014), which is based on the S-wave coda spectral ratio method (e.g., Aki and Chouet 1975) (see Additional file 1: Section 1 and Figure S1 for the description and example of the \(f_{c}\) estimation).

In evaluating \(t^{*}\) based on Eq. (3), the original velocity records are transformed into the displacement records, and the displacement spectra are estimated from the signals in a window of 3 s duration, beginning 0.5 s before the P- or S-wave arrivals. The P-wave spectrum is calculated from the vertical component seismogram, while the S-wave spectrum is obtained by the square root of the sum of the squared NS and EW spectral amplitudes of the S-wave. Here, \(\varOmega_{0i}\) and \(t_{ij}^{*}\) are determined for the frequency range of 3–30 Hz by fitting Eq. (3) to the observed spectrum, where we used the P- and S-wave corner frequencies estimated by Komatsu and Oda (2015) (see Additional file 1: Fig. S2 for examples of the waveforms and spectra). Consequently, 11512 P-wave \(t^{*}\) and 11820 S-wave \(t^{*}\) data were obtained.

The attenuation factor \(t^{*}\) for the P- or S-wave propagating into a three-dimensionally heterogeneous structure may be represented as

$$t^{*} = \mathop \int \limits_{\text{ray path}}^{{}} \frac{{{\text{d}}s}}{{v_{{\left( {x,y,z} \right)}} Q_{{\left( {x,y,z} \right)}} }} ,$$
(4)

where \(v\) is the seismic velocity (Thurber 1983), and the integration is performed along a ray path between the event and the station. When a three-dimensional grid is placed in the target space, Eq. (4) is discretized into a linear equation of \(Q^{ - 1}\) at the grid nodes in the vicinity of the ray path (Thurber 1983; Komatsu and Oda 2015). Since a set of the linear equations is obtained for all event–station pairs, we can conduct \(Q\) tomography from the \(t^{*}\) data by solving it for \(Q^{ - 1}\) of the grid nodes. The grid intervals are set to be 0.125° in the lateral directions and 5–50 km along the depth direction. These intervals are smaller than those used by Liu and Zhao (2014, 2015), Saita et al. (2015), Komatsu and Oda (2015), and Wang et al. (2017). For calculation of the ray paths of the P- and S-waves, we employ a 1-D velocity structure, which is based on the JMA2001 model (Ueno et al. 2002). The crustal velocity structure consists of two homogeneous layers (V P = 6.02 km/s and V S = 3.53 km/s for the upper crust; V P = 6.70 km/s and V S = 3.89 km/s for the lower crust), each of which is 15 km in thickness. The P- and S-wave ray paths and travel times are calculated with a ray tracing technique developed by Zhao et al. (1992, 1994). We use a nonnegative least squares method (Lawson and Hanson, 1974) for the \(t^{*}\) inversion to obtain the \(Q^{ - 1}\) structures for the P- and S-waves, so that the \(Q^{ - 1}\) values estimated at grid nodes are always positive.

Results

To see how correctly the \(Q_{\text{P}}\) and \(Q_{\text{S}}\) structures are restored by inversion of the \(t^{*}\) data, we perform checkerboard resolution tests (CRTs) (e.g., Zhao et al. 1992) using synthetic \(t^{*}\) data produced from a structure where \(Q^{ - 1}\) = 0.001 and 0.007 (Kita et al. 2014) are alternately assigned to the size of 0.25° [longitude] × 0.25° [latitude] × 10–75 km [depth direction] at depths of 2–250 km. The synthetic \(t^{*}\) values are calculated along the same ray paths as those of the real analysis of the observed \(t^{*}\) data. Random noise with a standard deviation of 0.001 s is then added to the synthetic \(t^{*}\). The \(Q^{ - 1}\) values at grid nodes are determined by inversion of the synthetic \(t^{*}\) data using the same velocity structure as the actual tomography (Additional file 1: Figure S3). After inverting this dataset, we examine the results of the CRTs by resolvability R (Zelt 1998; Saiga et al. 2010) (see Additional file 1: Section 2). When the resolvability R of \(Q^{ - 1}\) value recovered at each grid is larger than 0.75, the \(Q^{ - 1}\) structure is judged to be restored with high resolution (Saiga et al. 2010). We also carry out another set of restoring resolution tests (RRTs) (e.g., Zhao et al. 1992). The RRTs are similar to the CRTs, except for the input model that is constructed from the obtained \(Q^{ - 1}\) structure (Additional file 1: Figure S4). The results for the CRTs and the RRTs illustrate that the structures are well restored down to 20 km (Additional file 1: Figures S3 and S4).

Figure 2 shows the lateral variation of \(Q_{\text{P}}\) and \(Q_{\text{S}}\) at 7, 12, and 17 km depths in the crust. The area shaded by gray indicates a low resolution region, where resolvability R is smaller than 0.75 in the CRTs (Additional file 1: Figure S3). In the source region of the 2016 Kumamoto earthquakes (area of 130.5°E–131°E and 32.5°N–33°N), high-\(Q_{\text{P}}\) and high-\(Q_{\text{S}}\) areas exist at 7 and 12 km depths, where large aftershocks (white stars) occurred. There also exists a localized low-\(Q_{\text{P}}\) patch in which the epicenters of the largest foreshock (green star) and mainshock (yellow star) are located. In the lower crust, a low-\(Q_{\text{P}}\) zone is distributed beneath the source region. Beneath the active volcanoes (Mt. Aso, Mt. Kuju, Mt. Yufu-dake, and Mt. Tsurumi-dake indicated by the red triangles in the range 131°E–131.5°E), the low-\(Q_{\text{P}}\) and low-\(Q_{\text{S}}\) zone extends toward the lower crust (Fig. 2 and Additional file 1: Figure S5).

Fig. 2
figure 2

Lateral distribution of estimated \(Q_{\text{P}}^{ - 1}\) and \(Q_{\text{S}}^{ - 1}\) in the crust. The region shaded by gray shows low resolution, where the resolvability R is smaller than 0.75. See the caption of Fig. 1 for explanation of the lines and symbols

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For comparing \(Q_{\text{P}}\) with \(Q_{\text{S}}\) in the crust, we also estimate the \(Q_{\text{P}} /Q_{\text{S}}\) structure directly using the S-wave \(t^{*}\) data and the estimated \(Q_{\text{P}}^{ - 1}\) structure (Pozgay et al. 2009). In the estimation of \(Q_{\text{P}} /Q_{\text{S}}\), for \(Q_{\text{P}}^{ - 1}\) smaller than 0.0005, we assume \(Q_{\text{P}}^{ - 1}\) = 0.0005. The resolution of \(Q_{\text{P}} /Q_{\text{S}}\) is evaluated from both the CRTs for \(Q_{\text{P}}\) and \(Q_{\text{S}}\). This result shows that, in the crust, \(Q_{\text{S}}\) is basically larger than \(Q_{\text{P}}\) (Additional file 1: Figure S6). This trend is consistent with the relationship between \(Q_{\text{P}}\) and \(Q_{\text{S}}\) reported in previous studies (e.g., Rautian et al. 1978; Modiano and Hatzfeld 1982).

Figure 3 displays \(Q_{\text{P}}\) and \(Q_{\text{S}}\) structures on the vertical cross sections along three lines: line A–B (from Mt. Yufu-dake to Mt. Aso), line B–C (along the Futagawa fault), and line C–D (along the Hinagu fault). Low-\(Q_{\text{P}}\) and low-\(Q_{\text{S}}\) zones exist beneath Mt. Yufu-dake (in depth of 5–15 km along line A–B) and between Mt. Kuju and Mt. Aso (in depth of 10–15 km along line A–B) and reach a depth of 25 km beneath Mt. Kuju (line A–B). In these low-\(Q_{\text{P}}\) and low-\(Q_{\text{S}}\) areas, the lower limit of the seismicity is shallower than that in the source region along lines B–C and C–D. Many aftershocks occurred between the high- and low-\(Q_{\text{P}}\) patches beneath the area from Mt. Kuju to Mt. Aso, while beneath Mt. Yufu-dake, aftershocks locally took place in a low-\(Q_{\text{P}}\) and low-\(Q_{\text{S}}\) zone. In the source region, two high-\(Q_{\text{P}}\) and high-\(Q_{\text{S}}\) zones are located in the upper crust, where many aftershocks occurred. Low-\(Q_{\text{P}}\) patches, where aftershock activity is lower than that in the source region, also exist in both edges of the high-\(Q_{\text{P}}\) zones.

Fig. 3
figure 3

Vertical cross sections of \(Q_{\text{P}}^{ - 1}\) and \(Q_{\text{S}}^{ - 1}\) structures and topography along lines A–B, B–C, and C–D. The region shaded by gray shows low resolution, where the resolvability R of the CRTs is smaller than 0.75. The Conrad and Moho discontinuities in the model are drawn by dashed lines. Green, yellow, and sky blue stars indicate the hypocenters of the largest foreshock (M JMA6.5), the mainshock (M JMA7.3), and the induced event (M JMA5.7), respectively. White stars denote the hypocenters of events larger than M JMA5.0 for 1 month following the foreshock. Black dots indicate the events with 2.0 ≤ M JMA < 5.0 occurring for 1 month following the foreshock. See the caption of Fig. 1 for explanation of the triangle symbols

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Discussion

The \(Q_{\text{P}}\) and \(Q_{\text{S}}\) structures in the upper crust are different between the volcanic region along line A–B and the source region along lines B–C and C–D (see Fig. 3). In the volcanic region, low-\(Q_{\text{P}}\) and low-\(Q_{\text{S}}\) zones are distributed beneath active volcanoes, where the lower limit of seismicity is shallower than that in the source region as mentioned in the previous section (Fig. 3). Matsumoto et al. (2016) estimated the \(D_{95}\) depth distribution in Kyushu, which indicates the bottom depth of the seismogenic layer. The \(D_{95}\) depth in the volcanic region is shallower than that in the source region. Cho and Kuwahara (2013) estimated the thermal structure at the bottom of the seismogenic layer and revealed the existence of higher temperature in the volcanic region. The shallowing of the seismogenic zone around volcanoes might be due to weakening associated with the presence of magma.

In the source region, high-\(Q_{\text{P}}\) and high-\(Q_{\text{S}}\) zones are distributed in the upper crust except near the epicenters of the largest foreshock and mainshock (Fig. 2). Near the epicenters, a localized low \(Q_{\text{P}}\) exists. In the lower crust, a low-\(Q_{\text{P}}\) area is widely distributed below the source area. Most recently, Wang et al. (2017) also estimated the 3-D attenuation structure in the source region of the 2016 Kumamoto earthquakes and illustrated that the source region of the Kumamoto earthquakes is covered with a high-\(Q\) zone in the upper crust underlain by a low-\(Q\) zone in the lower crust, which is similar to the present study. Horiguchi and Matsuda (2013) investigated the 3He/4He ratio in water from various hot springs in central Kyushu. In Fig. 4, we plot their measured 3He/4He on the lateral variation of \(Q_{\text{P}}\) at 17 km depth in the lower crust. It is found that a high-3He/4He point exists close to the epicenter of the mainshock. Since the 3He-rich fluids in the lower crust are thought to come from the upper mantle, the high 3He/4He ratio could be evidence of the high fluid content in the crust. In addition, Aizawa et al. (2017) estimated the resistivity structure in central Kyushu and showed that a high conductivity anomaly in the lower crust is distributed below the NW parts of the Futagawa and Hinagu faults. This indicates that the lower crust below the source region includes fluids from the upper mantle. The localized low-\(Q_{\text{P}}\) zone near the mainshock epicenter in the upper crust might be associated with the effect of fluids injected from the lower crust to the faults where the fault friction could be reduced.

Fig. 4
figure 4

Ratio of 3He/4He observed by Horiguchi and Matsuda (2013), which is plotted on the estimated \(Q_{\text{P}}\) structure at 17 km depth shown in Fig. 2. Circles are color coded according to 3He/4He ratios in Ratm. Gray stars indicate the largest foreshock, mainshock, and induced event. The small circles are the epicenters of the aftershocks. The black triangles denote the active volcanoes

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To discuss the details of the variation of the \(Q_{\text{P}}\) and \(Q_{\text{S}}\) around the source region, we show the \(Q_{\text{P}}\) and \(Q_{\text{S}}\) structures along the source fault planes estimated by Kato et al. (2016) and the Geospatial Information Authority of Japan (2016) (GSI). Figure 5 shows a surface projection of the two fault planes, of which the strike and dip angles are N 235°E and 60° for the Futagawa fault, and N 205°E and 72° for the Hinagu fault, respectively. Figure 6 displays the \(Q_{\text{P}}\) and \(Q_{\text{S}}\) structures along the planes shown in Fig. 5. The two areas enclosed by the black dashed lines are the Futagawa and Hinagu segments of the fault source. The localized low-\(Q_{\text{P}}\) patch, including the hypocenters of the largest foreshock and mainshock, is put between two high-\(Q_{\text{P}}\) and high-\(Q_{\text{S}}\) patches (along strike, 0–20 km in the Futagawa segment and 5–25 km in the Hinagu segment). As mentioned above, a high 3He/4He ratio is observed close to the mainshock epicenter. This suggests that around the mainshock epicenter, fluids in the lower crust might enter faults in the upper crust, i.e., the seismogenic layer, and reduce the friction of the faults to trigger earthquakes. In the high-\(Q_{\text{P}}\) and high-\(Q_{\text{S}}\) patch in the Futagawa segment, the large-slip area of the mainshock (surrounded by the red dashed line in Fig. 6) estimated by Asano and Iwata (2016) is located. Such a large-slip area located in a high-\(Q\) zone is seen for other large earthquakes (e.g., Liu et al. (2014) for the 2011 Tohoku earthquake; Rietbrock (2001) for the 1995 Kobe earthquake). The high-\(Q_{\text{P}}\) and high-\(Q_{\text{S}}\) zone might be attributed to the strongly coupled area along the Futagawa fault segment. The aftershock activity in the high-\(Q_{\text{P}}\) and high-\(Q_{\text{S}}\) zone vanishes beneath the southwest side of Mt. Aso. This is near the boundary between the high-Q P zone and the volcanic low-\(Q_{\text{P}}\) zone. Yagi et al. (2016) estimated the source rupture process of the mainshock using teleseismic records and showed that the northeast edge of the large-slip area is located in this region, suggesting that the high-temperature area around the magma chamber of Mt. Aso contributes to the termination of the rupture during the mainshock. The low-\(Q_{\text{P}}\) region beneath Mt. Aso may give new evidence for this suggestion.

Fig. 5
figure 5

Map of the Futagawa and Hinagu fault planes. The solid red rectangles show the areas of the planes used in Fig. 6 projected onto the surface, and the red dashed rectangles indicate the source fault planes of the mainshock and foreshocks estimated by Kato et al. (2016) and GSI (2016). Active faults (Nakata and Imaizumi 2002) are plotted by the purple lines. Black circles denote the events (M JMA ≥ 2.0) that occurred for 1 month following the foreshock. See the caption of Fig. 1 for explanation of the star and triangle symbols

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Fig. 6
figure 6

\(Q_{\text{P}}^{ - 1}\) (upper) and \(Q_{\text{S}}^{ - 1}\) (lower) distribution along the planes shown in Fig. 5. Two dashed squares indicate the source fault planes estimated by Kato et al. (2016) and GSI (2016). The region enclosed by the red dashed line is the large-slip area (≥3.0 m) of the mainshock estimated by Asano and Iwata (2016). See the captions of Figs. 3 and 5 for an explanation of the symbols

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Conclusions

We estimated the 3-D \(Q_{\text{P}}\) and \(Q_{\text{S}}\) structures around the source region of the 2016 Kumamoto earthquakes. In the volcanic region, low-\(Q_{\text{P}}\) and low-\(Q_{\text{S}}\) patches were located around active volcanoes. Many of aftershocks occurred between the high- and low-\(Q_{\text{P}}\) patches beneath the area from Mt. Kuju to Mt. Aso, and beneath Mt. Yufu-dake, aftershocks locally took place in a low-\(Q_{\text{P}}\) and low-\(Q_{\text{S}}\) zone. In the source region, two high-\(Q_{\text{P}}\) and high-\(Q_{\text{S}}\) zones exist along the Futagawa and the Hinagu fault segments in the upper crust, and numerous aftershocks occurred in these zones, while in the lower crust, a low-\(Q_{\text{P}}\) zone exists entirely below the source region, which might be caused by the presence of fluids from the mantle. The large-slip area of the mainshock inferred from a source inversion is located in the high-\(Q_{\text{P}}\) and high-\(Q_{\text{S}}\) zone of the Futagawa fault segment in the upper crust. The eastern edge of this zone adjoins a low-\(Q_{\text{P}}\) zone beneath Mt. Aso. This suggests that the high-temperature area around the magma chamber might have contributed to the termination of the rupture of the mainshock.