A possible restart of an interplate slow slip adjacent to the Tokai seismic gap in Japan
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The Tokai region of Japan is known to be a seismic gap area and is expected to be the source region of the anticipated Tokai earthquake with a moment magnitude of over 8. Interplate slow slip occurred from approximately 2001 and subsided in 2005 in the area adjacent to the source region of the expected Tokai earthquake. Eight years later, the Tokai region again revealed signs of a slow slip from early 2013. This is the first evidence based on a dense Global Positioning System network that Tokai long-term slow slips repeatedly occur. Two datasets with different detrending produce similar transient crustal deformation and aseismic slip models, supporting the occurrence of the Tokai slow slip. The center of the current Tokai slow slip is near Lake Hamana, south of the center of the previous Tokai slow slip. The estimated moments, which increase at a roughly constant rate, amount to that of an earthquake with a moment magnitude of 6.6. If the ongoing Tokai slow slip subsides soon, it will suggest that there are at least two different types of slow slip events in the Tokai long-term slow slip area: that is, a large slow slip with a moment magnitude of over 7 with undulating time evolution and a small one with a moment magnitude of around 6.6 with a roughly linear time evolution. Because the Tokai slow slip changes the stress state to one more favorable for the expected Tokai earthquake, intense monitoring is going on.
KeywordsPlate subduction zone GPS Interplate earthquake Transient deformation Slow slip event Tokai seismic gap Tokai slow slip Low-frequency earthquake
Global Positioning System
In this tectonic setting, the dense Global Positioning System (GPS) network (GEONET) in Japan detected transient movements in the Tokai region from early 2001, which disappeared around 2005 (e.g., Ozawa et al. 2002; Miyazaki et al. 2006; Liu et al. 2010). This transient was interpreted as a long-term slow slip on the plate interface near Lake Hamana, central Japan, adjacent to the Tokai seismic gap (e.g., Ozawa et al. 2002; Ohta et al. 2004; Miyazaki et al. 2006; Liu et al. 2010; Tanaka et al. 2015). The previous Tokai slow slip gradually stopped and did not trigger the anticipated Tokai earthquake. After the discovery of the Tokai slow slip by GEONET, it was proposed that the Tokai long-term slow slip occurred during the periods of approximately 1978–1983 and 1987–1991 on the basis of baseline measurements by an electromagnetic distance meter or based on leveling data (e.g., Kimata et al. 2001; Ochi 2014). This hypothesis is consistent with other slow slip events around Japan, such as the Bungo slow slip and the Hyuga-nada slow slip (e.g., Ozawa et al. 2013; Yarai and Ozawa 2013), in that they have occurred quasi-periodically.
Since the 2011 M w9 Tohoku earthquake, eastward postseismic deformation has been the dominant source of crustal deformation in the Tokai region (see Fig. 1b). Around 12 years after the start of the previous Tokai slow slip, GEONET has been detecting a similar transient signal in the Tokai region since early 2013, which is mixed with the postseismic deformation due to the 2011 Tohoku earthquake. This transient movement suggests the possibility of the restart of the Tokai slow slip on the interface between the Amurian plate and the Philippine Sea plate. In addition to the crustal deformation detected by GEONET, a strain meter in the Tokai region also shows transient deformation (Miyaoka and Kimura 2016).
Because there is a possibility that the ongoing slow slip will lead to the anticipated Tokai earthquake, it is important to monitor the state of the current Tokai slow slip. In this study, we estimate the spatial and temporal evolution of the possible Tokai slow slip by applying square-root information filtering following the time-dependent inversion technique and compare it with the previous event. We also discuss the relationship between the low-frequency earthquakes and the estimated slow slip model and the influence of the latter on the expected Tokai earthquake.
GPS data were analyzed to obtain daily positions with Bernese GPS software (version 5.0). We adopted the F3 solution (Nakagawa et al. 2008), which uses the final orbit and earth rotation parameters of the International GNSS Service (IGS) and provides a higher S/N ratio than the previous F2 position time series (Hatanaka et al. 2003). We used the east–west (EW), north–south (NS), and up–down (UD) components at approximately 400 GPS sites in the Tokai, Kanto, and Tohoku regions.
Postseismic deformation due to the 2011 Tohoku earthquake has strong potential to contaminate and bias our search for slow slip in the Tokai region. We therefore attempt to remove its influence in two different ways, each generating a different dataset. First, we invert two fault patches (one for the Tokai slow slip and one for the Tohoku afterslip). In this analysis, we attributed all the postseismic deformation of the Tohoku earthquake to afterslip on the plate interface in the Tohoku region and did not take viscoelastic relaxation into account. This first approach assumes that the postseismic deformation due to viscoelastic relaxation can be partly modeled by afterslip modeling. However, it is a fact that viscoelastic relaxation contributes to the postseismic deformation due to the Tohoku earthquake (e.g., Sun et al. 2014). Thus, we need another approach to estimate the effects of viscoelastic relaxation and afterslip on the plate interface to support the results of the analysis with two fault patches. For this purpose, second, we attempt to remove the Tohoku postseismic deformation by considering exponential and logarithmic trends in the position time series in the analysis with one fault patch for the Tokai slow slip.
Analysis with two fault patches
The degree of the polynomial functions n and the overtone of the trigonometric functions m were estimated on the basis of Akaike information criterion (AIC) (Akaike 1974). After removing the annual components, we estimated the linear trend for the data between January 1, 2008, and January 1, 2011, during which no transient displacements occurred, and removed it from the data without annual components. We consider that the adopted steady state for this period is satisfactory for emphasizing the results, because the previous 2001–2005 slow slip and the current slow slip were clearly detected as a deviation from this adopted steady state. After this detrending, we smoothed the position time series by averaging over 3 days to reduce errors. Thus, this first detrending does not take into account the postseismic deformation due to the 2011 Tohoku earthquake, which is the main difference from the following second detrended dataset. We call this dataset the first detrended dataset.
We applied square-root information filtering (Ozawa et al. 2012) to the first detrended dataset following the inversion technique of McGuire and Segall (2003) for the period between January 1, 2013, and October 25, 2015. To reduce the computational burden, we used position time series with an interval of 3 days. Because we used detrended data, the estimated aseismic interplate slip is the deviation from the steady state for the period between January 1, 2008, and January 1, 2011.
We used 389 GPS sites in the filtering analysis for the first detrended dataset (see Fig. 1a). We weighted the EW, NS, and UD displacements with a ratio of 1:1:1/3 considering the standard deviations estimated from ordinary Kalman filtering.
We used two fault patches for the upper boundary of the Pacific plate along the Japan Trench and that of the Philippine Sea plate along the Suruga trough (Fig. 1). Because postseismic deformation occurred after the 2011 Tohoku earthquake as mentioned above, we attributed the cause of all postseismic deformation to afterslip on the Tohoku fault patch. In this case, we do not take the viscoelastic response due to the Tohoku earthquake into account because we consider that the effect of the viscoelastic response to ground deformation occurs on a spatially large scale and is similar to the afterslip effect at this point. That is, the contribution of the viscoelastic response to the surface deformation in the Tokai region may be partly compensated by our afterslip model on the first fault patch, which is the upper surface of the Pacific plate after the Tohoku earthquake.
We incorporated the inequality constraint that the slip is within 40° of the direction of the plate motion following the method of Simon and Simon (2006). In this filtering analysis, we incorporated the spatial roughness of the slip distribution (McGuire and Segall 2003). Hyperparameters that scale the spatial and temporal smoothness were estimated by approximately maximizing the log-likelihood of the system (Kitagawa and Gersch 1996; McGuire and Segall 2003). The optimal values of the spatial and temporal smoothness of the Tohoku fault patch are approximately 1.0 and 0.001, while those of the Tokai fault patch are approximately 0.004 and 0.001, respectively.
In the above analysis, a fault patch and a slip distribution on a fault patch are represented by the superposition of spline functions (Ozawa et al. 2001). The fault patch for the Tokai region consists of 11 nodes in the T-direction and 15 nodes in the S-direction (see Fig. 1b) (Ozawa et al. 2001). These directions are defined in Fig. 1b. The spacing of knots on the fault patch is approximately 20 km in the Tokai region. The plate boundary model is from Hirose et al. (2008). With regard to the fault patch in the Tohoku region, we used 12 nodes in the T-direction and 10 nodes in the S-direction with spacing of approximately 80 and 40 km in the T-direction and S-direction, respectively (see Fig. 1a). This Tohoku fault patch is used only in the analysis with two fault patches. Although the spacing between the parallel trench nodes is larger than that between the normal trench nodes, the results for the afterslip on this Tohoku fault patch are similar to those of Ozawa et al. (2012), in which the grid spacing is shorter. Thus, we consider that the fault patch adopted for the Tohoku region can satisfactorily describe the afterslip of the Tohoku earthquake. The plate boundary model is from Nakajima and Hasegawa (2006) and Nakajima et al. (2009). The coefficients of the spline functions that represent the slip distribution on the fault patches are estimated in this inversion (Ozawa et al. 2001).
Analysis with one fault patch
We used 129 GPS sites in the Tokai region of the second detrended dataset for the time-dependent inversion analysis (Fig. 1b). This is because it is not necessary to take into account the postseismic deformation due to the 2011 Tohoku earthquake for the second detrended dataset, although we have to take it into account in the first detrended dataset.
In the second detrended dataset, we used the same fault patch between the Philippine Sea plate and the Amurian plate beneath the Tokai region as that in the first detrended dataset without the Tohoku fault patch, because we consider that the effects of the viscoelastic relaxation and afterslip due to the 2011 Tohoku earthquake are nonexistent in the second detrended dataset owing to the removal of the exponential and logarithmic trends.
The spatial and temporal smoothness of the second detrended dataset is set to the same values as those of the Tokai fault patch in the analysis with two fault patches so that we can approximately compare the results of this analysis with those of the analysis with two fault patches.
Analysis of the previous Tokai slow slip
In addition, we created a third detrended dataset using the same method as for the first detrended dataset but with a different period of estimation for the annual components. That is, we estimated the annual components of the EW, NS, and UD position time series separately for the period up to January 1, 2011, together with a polynomial function from the raw position time series at each station. We estimated the linear trend for the same period as for the first and second datasets and removed it from the position time series without annual components. We used 86 GPS sites in the following inversion. Using this third detrended dataset, we estimated an approximate model of the previous Tokai slow slip for the period between January 1, 2001, and January 1, 2008, by the same method as for the second detrended dataset because there are no other signals, such as those corresponding to postseismic deformation due to the 2011 Tohoku earthquake, for this period. We consider that the postseismic deformation due to the 2004 off Kii peninsula earthquakes (M w > 7) (see Fig. 1a) does not significantly affect the previous Tokai slow slip model. The estimated optimal spatial and temporal parameters are approximately 3.0 and 1.0, respectively.
Results and discussion
Analysis with two fault patches
Although we estimated the afterslip on the Pacific plate in the Tohoku region together with the slip on the Philippine Sea plate in the Tokai region, we will not discuss it in this paper because our focus is on the Tokai slow slip. The characteristic features of the estimated afterslip on the Pacific plate in the Tohoku region are similar to the results of Ozawa et al. (2012) (Additional file 2).
Analysis with one fault patch
Comparison between the two models
We obtained almost the same results using the two different detrended datasets. With regard to the estimated model based on the first detrended dataset, we cannot rule out the existence of a systematic error resulting from the postseismic deformation since the 2011 Tohoku earthquake. However, we believe that any such systematic error would be small considering the difference in the spatial scale of the viscoelastic relaxation effect mentioned above. Furthermore, because our model based on the second detrended dataset, which excludes the exponential and logarithmic time evolution corresponding to viscoelastic relaxation and afterslip, respectively, shows similar results for the location and time evolution of aseismic slip to those obtained from the first detrended dataset, we consider that slow slip is now occurring on the west boundary of the Tokai seismic gap area, without signs of decay. This finding is consistent with the strain meter observations in this region by Japan Meteorological Agency, which also indicate interplate slow slip near Lake Hamana (Miyaoka and Kimura 2016). Although the start time of the current slow slip event is unclear, we assumed that it started in early 2013 at the latest on the basis of the approximate start time of the transient in Figs. 2 and 6 and the moment release rate shown in Figs. 5b and 9b. For the second detrended data, we also changed the regression periods for the logarithmic and exponential functions to March 12, 2011–March 12, 2012, and March 12, 2011–March 12, 2014, respectively, and found that the characteristic feature of a slip area appearing that was centered on Lake Hamana was not changed.
The reason why the two different detrended datasets gave similar results is that the postseismic deformation due to the 2011 Tohoku earthquake can be well explained by both the kinematic afterslip model and the logarithmic and exponential functions, which are based on the physics of the rate- and state-dependent friction law and viscoelasticity. However, it remains unclear why the kinematic afterslip model and the logarithmic and exponential functions produced similar postseismic deformation. We cannot rule out the possibility that the estimated logarithmic and exponential functions may reflect an actual process of afterslip and viscoelastic relaxation involved in the postseismic deformation due to the Tohoku earthquake. This problem remains to be solved in a future study.
Comparison between the previous and current slow slips
Because the previous Tokai slow slip reached a moment magnitude of over 7, we cannot rule out the possibility that the present stage may correspond to the initial stage of the time evolution of the Tokai slow slip. The estimated moment release of the current Tokai slow slip seems to have increased almost linearly since early 2013, as shown in Figs. 5b and 9b and in Fig. 12 in the long term, while the moment release rate of the previous Tokai slow slip changed in the long term. At this point, the current Tokai slow slip seems to be following a different time evolution from that in the previous event (Fig. 12).
At the time of the previous Tokai slow slip, the center of the slip area was located near Lake Hamana in the early period, then moved north over time (e.g., Ozawa et al. 2001; Miyazaki et al. 2006) (see Additional file 3). Thus, there is a possibility that the ongoing slow slip will move northward over time with an increase in the slip magnitude. However, if the current aseismic slip stops in the near future, it will indicate the coexistence of relatively small slow slip events in the Tokai long-term slow slip area. Our previous Tokai slow slip model reproduces the observations well as shown in Fig. 10.
Relationship with low-frequency earthquakes
Non-volcanic low-frequency tremors have been discovered in the Nankai trough subduction zone in Japan (Obara 2002). These low-frequency tremors include low-frequency earthquakes whose hypocenters can be determined by identification of coherent S-wave and P-wave arrivals (Katsumata and Kamaya 2003). Low-frequency earthquakes occur at a depth of approximately 30–40 km on the plate interface in the Tokai region. Low-frequency tremors that contain low-frequency earthquakes occur in the Tokai region with a recurrence interval of approximately 6 months accompanied by aseismic slip, which continues for 2–3 days, and release a seismic moment corresponding to M w ~ 6 (Hirose and Obara 2006). This relationship between low-frequency tremors or earthquakes and slow slip events has also been observed in many other areas (e.g., Rogers and Dragert 2003; Shelly et al. 2006). Thus, we can expect low-frequency tremors or earthquakes with higher activity owing to the influence of the current Tokai slow slip. However, such a relationship has not been observed this time, although there was a correlation between the low-frequency earthquake activity in the Tokai region and the previous Tokai slow slip (Ishigaki et al. 2005). We consider that low-frequency earthquakes are not being activated by the current slow slip because the central part of the slow slip area is located away from the low-frequency earthquake area (Figs. 5a, 9a) and its magnitude is still small, suggesting little change in the stress in the low-frequency earthquake area. Although short-term slow slip events of M w6 in the Tokai region trigger low-frequency tremors or earthquakes (Hirose and Obara 2006), the area of induced low-frequency tremors or earthquakes overlaps with the short-term slow slip area, indicating a large change in stress in this case.
The short-term slow slip with a maximum moment magnitude of M w6 in the low-frequency earthquake area (Hirose and Obara 2006) does not affect our optimal Tokai slow slip model owing to its small moment magnitude compared with the current Tokai event and the center location of our current Tokai model.
Influence on the expected Tokai earthquake
There is a possibility that the 2011 Tohoku earthquake and its postseismic deformation have affected the seismic activity of the Japanese archipelago. In studies on the Coulomb failure stress change (ΔCFS) due to the Tohoku earthquake, Toda et al. (2011) showed seismic excitation throughout central Japan after the Tohoku earthquake and Ishibe et al. (2015) reported changes in seismicity in the Kanto region that were correlated with ΔCFS. Furthermore, slow slip events off the Boso peninsula, east Japan, have shown a shorter recurrence interval after the Tohoku earthquake (Ozawa, 2014). Our Tohoku coseismic model (Ozawa et al. 2012) produces a ΔCFS of approximately 3 kPa near Cape Omaezaki in the Tokai seismic gap. Furthermore, the two estimated models of the current Tokai slow slip produce ΔCFS of approximately 3 kPa near Cape Omaezaki (see Fig. 1b). We assumed a rigidity of 30 GPa, Poisson’s ratio of 0.25, and a friction coefficient of 0.4 in these calculations (Harris 1998). Considering these points, we cannot rule out the possibility that the ongoing slow slip will trigger the anticipated Tokai earthquake, although the previous event did not cause the expected earthquake. Thus, it is very important to intensively monitor the ongoing Tokai slow slip using the dense GPS network in Japan.
It has been proposed that the Tokai slow slip occurs with a recurrence interval of 9–14 years, although the truth of this hypothesis is difficult to establish because of the scarcity of data (e.g., Kimata et al. 2001; Ochi 2014). Thus, our finding, obtained using the dense GPS network in Japan, confirms that the Tokai slow slip has occurred repeatedly on the west boundary of the Tokai seismic gap and changed the stress state in favor of the anticipated Tokai earthquake. Although the start time of the current event is not clear, the recurrence interval of the Tokai slow slip is approximately 12 years if we assume it to be early 2013. Our estimated models of the current Tokai slow slip indicate differences from the previous event regarding the following points. First, the magnitude of the current event is approximately 6.6, which is very small compared with the M w of over 7 for the previous event, and increasing at a roughly constant rate. Second, the center of the slip area is located south of that in the previous event. Third, the moment release rate is very small compared with that in the previous event. We cannot clearly state whether the current slow slip will become similar to the previous Tokai slow slip or whether it will be a different type of slow slip from the above points.
SO performed all the data analysis, prepared the graphical material, and wrote the manuscript. MT proposed the detrending method using a function consisting of logarithmic and exponential functions and estimated the time constants of the logarithmic and exponential functions. MT and HY supervised SO and helped to improve the manuscript. All authors read and approved the final manuscript.
We are grateful to our colleagues for helpful discussions. Prof. Teruyuki Kato of the Earthquake Research Institute, the University of Tokyo, advised us about detrending. Prof. Sagiya of Nagoya University provided us with helpful information. The hypocenter data of low-frequency earthquakes are from Japan Meteorological Agency. The data used in this paper are available by contacting email@example.com.
The authors declare that they have no competing interests.
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