 Research article
 Open Access
 Published:
Fault model of the 2012 doublet earthquake, near the updip end of the 2011 TohokuOki earthquake, based on a nearfield tsunami: implications for intraplate stress state
Progress in Earth and Planetary Science volume 6, Article number: 67 (2019)
Abstract
On December 7, 2012, an earthquake occurred within the Pacific Plate near the Japan Trench, which was composed of deep reverse and shallow normalfaulting subevents (Mw 7.2 and 7.1, respectively) with a time interval of ~10 s. It had been known that the stress state within the plate was characterized by shallow tensile and deep horizontal compressional stresses due to the bending of the plate (bending stress). This study estimates the fault model of the doublet earthquake utilizing tsunami, teleseismic, and aftershock data and discusses the stress state within the incoming plate and spatiotemporal changes seen in it after the 2011 TohokuOki earthquake. We obtained the vertical extents of the fault planes of deep and shallow subevents as ~45–70 km and ~5 (the seafloor)–35 km, respectively. The downdip edge of the shallow normalfaulting seismic zone (~30–35 km) deepened significantly compared to what it was in 2007 (~25 km). However, a quantitative comparison of the brittle strength and bending stress suggested that the change in stress after the TohokuOki earthquake was too small to deepen the downdip end of the seismicity by ~10 km. To explain the seismicity that occurred at a depth of ~30–35 km, the frictional coefficient in the normalfaulting depth range required would have had to be ~0.07 ≤ μ ≤ ~0.2, which is significantly smaller than the typical friction coefficient. This suggests the infiltration of pore fluid along the bending faults, down to ~30–35 km. It is considered that the plate had already yielded to a depth of ~35 km before 2011 and that the seismicity of the area was reactivated by the increase in stress from the TohokuOki earthquake.
Introduction
It is well known that the stress state within the incoming Pacific Plate near the Japan Trench is characterized by shallow tensile and deep horizontal compressional stresses along a direction perpendicular to the trench axis, separated by a thin aseismic (i.e., stressneutral) “elastic core”, due to the bending of the plate (bending stress, Fig. 1c; e.g., Chapple and Forsyth 1979). It is also well known that the number of normalfaulting earthquakes occurring within the plate and near the trench axis increases, following interplate megathrust earthquakes; this is attributed to the increased horizontal tensile stress caused by the stress release of the interplate coupling (e.g., Christensen and Ruff 1988; Dmowska and Lovison 1988).
Recently, Craig et al. (2014) investigated the vertical variation in the centroid depth and fault mechanisms based on global catalogs (M > ~5) and noted that temporal changes in the transition depths between normal and reversefaulting earthquakes were not detected after the 2011 TohokuOki earthquake. However, Obana et al. (2012, 2014, 2015, 2019) studied ocean bottom seismographs and reported that the downdip limit of shallow normalfaulting earthquakes (M < ~5) within the plate near the trench axis deepened from ~25 to ~35 km after the same earthquake; they interpreted spatiotemporal change in the intraplate stress as having been caused by the release of stress associated with the TohokuOki earthquake. However, the reason for this inconsistency has not been clarified. Furthermore, the relationship between the stress state in the incoming Pacific Plate and the changes in coseismic stress due to the TohokuOki earthquake have not yet been quantitatively assessed in detail.
On December 7, 2012, an Mjma 7.3 earthquake occurred within the Pacific Plate near the Japan Trench, where the extremely large coseismic slip (> ~50 m) was estimated to have occurred during the 2011 TohokuOki earthquake (e.g., Iinuma et al. 2012; star in Fig. 1b). Detailed teleseismic analyses (Lay et al. 2013; Harada et al. 2013) revealed that this earthquake was composed of two M ~7 subevents. According to the global centroid moment tensor (GCMT) solution (http://www.globalcmt.org/; Ekström et al. 2012), the first subevent had a reversefaulting mechanism with a depth of ~60 km (Mw 7.2) and the second had a normalfaulting mechanism (~20 km, Mw 7.2) with a time interval of ~12 s (red CMT solutions in Fig. 1b and c). Hereafter, this earthquake is referred to as the doublet earthquake, and the first and the second subevents are referred to as subevent 1 and subevent 2, respectively. Since the fault mechanisms of the two subevents are consistent with bending stress, the source process of the doublet earthquake should reflect the intraplate stress state after the TohokuOki earthquake. The vertical extents of each fault will be key to discussing the temporal change in the vertical variations of the stress state after the 2011 TohokuOki earthquake.
Rupture processes related to the doublet earthquake have been investigated previously. Lay et al. (2013) and Harada et al. (2013) investigated this earthquake using teleseismic data to estimate the CMT solution and the finite fault model. Teleseismic data is generally a powerful dataset for resolving rupture processes of global earthquakes. However, since the teleseismic signals from each subevent overlapped, it is difficult to decompose the rupture process of the doublet earthquake precisely, especially for the latter, shallower, subevent.
Inazu and Saito (2014) estimated the spatial distribution of the initial seasurface height change (tsunami source) using farfield tsunami data from ~200–2000 km away from the focal area (Additional file 1: Figure S1). In contrast to teleseismic data, tsunami data is useful for constraining the rupture process of the subevent 2, since shallow earthquakes generally excite tsunamis or cause seafloor vertical deformation more effectively than deep earthquakes.
When the 2012 doublet earthquake occurred, offline autonomous absolute ocean bottom pressure gauges (PGs) installed near the focal area (< ~200 km from the source, Fig. 1a) recorded clear tsunami signals. This dataset is useful to constrain the fault model of subevent 2, which was difficult to constrain with teleseismic data. In the present study, we utilize the tsunami and aftershock data and the results of the teleseismic analysis to estimate the finite fault model of the 2012 doublet earthquake, focusing particularly on the vertical extent of the fault planes of each subevent. We also discuss the relationship between the vertical profile of the intraplate seismicity and its spatiotemporal changes associated with the 2011 TohokuOki earthquake.
Methods/Experimental
Tsunami data
We use the nearfield PGs installed by Tohoku University (hereafter TPG; e.g., Hino et al. 2014; Kubota et al. 2017a, 2017b) (green inverted triangles in Fig. 1a). We also use tsunami data obtained by the offKushiro online cabled PGs installed by Japan Agency for MarineEarth Science and Technology (JAMSTEC) (Hirata et al. 2002) (KPGs, pink triangles), by GPS buoys installed by the Port and Airport Research Institute (PARI) (Kato et al. 2005) (yellow squares), and by the Deepocean Assessment and Reporting of Tsunamis (DART) system (Bernard et al. 2014) (blue diamonds). Detailed information is given in Table 1.
To retrieve the tsunami waveforms, we remove the oceantide component using the theoretical tide model (Matsumoto et al. 2000) and apply the filter from Saito (1978). The lowpass filter we applied has a cutoff of 3 min to the TPG records, and the bandpass filter has a passband of 3–60 min to the KPG, GPS buoy, and DART records. We apply the lowpass filter to the TPG records to preserve the offset in the pressure change caused by the vertical deformation of the seafloor.
The filtered records are shown in Fig. 2. TPGs first capture downmotion tsunamis with amplitudes of ~−5 cm and then larger upmotion tsunamis with amplitudes of ~+10 cm. The durations of both the down and upmotion tsunamis are ~5 min (black dashed lines in Fig. 2a). Small fluctuations and changes in the pressure offset are observed at the stations near the focal area (Fig. 2b). Tsunami amplitudes at the DART and the KPG stations are very small (~1 cm, black dashed lines in Fig. 2c and d). At the former, dynamic pressure changes caused by seismic waves (e.g., Kubota et al. 2017b) are also observed. Tsunami signals are also detected by some GPS buoys (e.g., ~15 cm at station 801, Fig. 2e).
Stepbystep approach for fault modeling
To decompose the complex rupture process of the 2012 doublet earthquake, we apply a stepbystep procedure to tsunami, teleseismic, and aftershock data. We first estimate an initial seasurface height distribution of the tsunami (hereafter, the tsunami source model) by inverting tsunami records. Since seafloor crustal deformations, or tsunamis, are very sensitive to shallow earthquakes, we then estimate the fault model of shallow subevent 2 based on the tsunami source model. We also use aftershocks detected around subevent 2 (Obana et al. 2015) to obtain information on the fault geometry. We then calculate the change in residual seasurface height between the tsunami source model and the vertical displacement from subevent 2. Given that this residual distribution is caused by subevent 1, we then estimate the fault model of subevent 1. Furthermore, because there are large tradeoffs between fault size and the focal depth and the amount of slip in a deeper earthquake, we also use the results of teleseismic analyses (Lay et al. 2013; Harada et al. 2013) to obtain prior information on the fault parameters such as fault depth and size for subevent 1.
Tsunami source modeling using nearfield tsunami records
We estimate the tsunami source model by inverting tsunami records via the conventional inversion analysis method (e.g., Tsushima et al. 2012; Inazu and Saito 2014; Kubota et al. 2018a). The details of the procedure are identical to those described in Kubota et al. (2018a). Before estimating the tsunami source model, however, we conduct a preparatory tsunami simulation using the tsunami source model in Inazu and Saito (2014) (Additional file 1: Figure S1). Although the pressure fluctuation at the TPGs was explained roughly, the pressure offset changes at the stations closest to the source (G09, TJT1, JFAST, and GJT3) were not explained at all (Additional file 1: Figure S1). This indicates that the latter is not due to coseismic seafloor deformations. Thus, they are probably due to tilts or rotations in the sensors related to the seafloor strong ground motion (e.g., Wallace et al. 2016; Kubota et al. 2018a).
In calculating the Green’s functions for the tsunami, the unit source elements of the seafloor displacements (Kubota et al. 2015, 2018a) are distributed around the focal area. The horizontal dimension of the unit source elements is 20 km × 20 km at a spacing of 10 km (overlapping with the adjacent elements), distributed along 260 km (in the EW direction) × 240 km (NS) area. To calculate the seasurface displacement from the unit source elements of the seafloor displacement, we consider the spatial filtering effect due to water depth (Saito 2019). In the depth filtering process, we assume a seawater depth of 6 km. To simulate the tsunami, we solve the linear dispersive wave equation in the local Cartesian coordinates (e.g., Saito 2019). The grid spacing is 2 km with a 1 s time step according to interpolation done via ETOPO1 bathymetry data (Amante and Eakins 2009). We assume that the displacements of all unit sources occurred instantaneously and simultaneously. The tsunami propagation velocity expected by the linear longwave theory is expressed as v = (g_{0}H)^{1/2} (g_{0}: gravity acceleration constant, H_{0}: water depth). Given the assumed water depth of 6 km and the average depth of the focal area, the propagation velocity is approximated as ~240 m/s (~15 km/min). Thus, the tsunami propagation distance during the duration of the M~7 earthquake (~10 s) and the time interval between two subevents (~10 s) is about 3 km, which is sufficiently small compared to the extent of the tsunami source model (~100 km, Inazu and Saito (2014)). We consider the static pressure offsets related to the calculation of Green’s function of the PGs for permanent seafloor deformation (Tsushima et al. 2012; Kubota et al. (2018a)). The same filter used for the observed records is applied to the simulated waveforms.
All data is resampled to 15 s intervals for the inversion. We use different time windows for each station, including tsunami main phase (Table 1, thick black lines in Fig. 3). The smoothing constraint is imposed and its weight is determined based on the tradeoff between the weight and reduction in variance between the observed and simulated tsunami waveforms (Additional file 1: Figure S2). Since the G09, TJT1, JFAST, and GJT3 stations are located near the source and are probably affected by seafloor ground shaking (Additional file 1: Figure S1), we exclude these records from the inversion analysis. Since all TPG stations are located landward of the source region, the constraint for the eastern edge of the tsunami source is likely not very good. Therefore, to improve the source constraint further, we also use the DART and KPG records. Since the amplitudes of TPG records are approximately ten times larger than the DART and KPG records, we weight the KPG and DART data at values ten times that of the TPG data.
Fault modeling of subevent 2
Because we found that the subsidence of the tsunami source was generated by the shallow subevent 2 (see Fig. 4 and Tsunami source model subsection in Results and Discussion section), we first estimate a fault model for subevent 2, which best explains the subsidence region of the tsunami source model. We use the gridsearch approach proposed by Kubota et al. (2015, 2018b), which estimates an optimum rectangular planar fault model with uniform slip. Because the shortwavelength component disappeared in the tsunami source model due to the smoothing constraint imposed in the inversion and the spatial smoothing effect used in the deepsea region during the tsunami generation (see Fig. 4 and Tsunami source model subsection in Results and Discussion section), we consider the smoothing effect in fault modeling by the following procedure. First, we calculate the seafloor deformation using a fault model candidate (a set of unknown parameters) (Okada 1992) and then simulate a tsunami. The simulated waveforms are inverted to obtain the initial seasurface height distribution, under the same conditions used in the inversion for the tsunami source model. Finally, we evaluate the goodness of the tsunami waveform fitting from the fault model candidate, by comparing the subsided area of the tsunami source model and the inverted seasurface height.
The geometry of the fault plane is assumed to be on the westdipping plane of GCMT solution (strike = 189° and dip = 50°), which is consistent with the planar structure of the aftershock (Obana et al. 2015). We also assume the rake angle from the GCMT solution (= −90°). Because the aftershock alignment is located ~2 km west from the GCMT centroid, the fault plane is constrained to pass through the point that is 2 km west from the GCMT centroid (hereafter, referred to as the reference point). The unknown parameters are the distance from the reference point to both ends of the fault, along the strike (i.e., length) and dip (width) direction (L_{1}, L_{2}, W_{1}, and W_{2}; see Fig. 5c and d). The search range for these parameters is determined based on the aftershocks and the horizontal extent of the subsidence area of the tsunami source. The fault length (L = L_{1} + L_{2}) is assumed to be greater than the fault width (W = W_{1} + W_{2}), as L > W. The top of the fault plane (defined by parameter W_{2}) is constrained as not to extend above the seafloor. The fault model candidate is assessed through variance reduction (VR) of the subsided areas between the tsunami source model and the fault model candidate:
where \( {x}_i^{\mathrm{source}} \) and \( {x}_i^{\mathrm{candidate}} \) are the displacements of the seasurface at the ith grid point, from the tsunami source model and the fault model candidate assuming the unit slip, respectively. N is the total number of grid points. The slip amount on fault D is determined so that the VR takes the maximal value. We use the grid points within the subsided area of the tsunami source model (blue dashed line in Fig. 5a) to calculate the VR. The search range of the unknown parameters is listed in Table 2.
Fault modeling of subevent 1
In order to estimate the fault model of subevent 1, we use the residual seasurface height between the tsunami source model and the seasurface displacement expected from the fault model of subevent 2 (hereafter, referred to as the residual height distribution). This is because the residual height distribution is expected to correspond to the seasurface displacement due to subevent 1. Because subevent 1 occurred at the deeper part of the incoming plate, it appears to be difficult to constrain the fault parameters such as fault geometry, depth, size, and slip amount only from the residual height distribution. Meanwhile, the residual height will contribute to constrain the horizontal location of the fault. Thus, we use the results of the teleseismic analyses in previous studies (GCMT; Lay et al. 2013; Harada et al. 2013) to obtain prior information on the fault parameters. We fix the centroid depth, fault geometry (strike, dip, and rake angles), and fault dimension (length and width) based on previous teleseismic analyses. We estimate the optimum horizontal location (longitude and latitude) of the fault and the amount of uniform slip on the rectangular fault using the gridsearch approach, as in the fault modeling of subevent 2.
Because Lay et al. (2013) investigated the CMT solution of the 2012 doublet earthquake using the teleseismic Wphase waveforms and showed and discussed the uncertainty of their estimations in detail, we use the CMT solution proposed by them as prior information for our fault modeling. We assume the centroid depth as 60.5 km and the westdipping nodal plane with geometry of strike = 163° dip = 51°, and rake = 57°. The slip distribution of subevent 1 obtained by the teleseismic analysis (Lay et al. 2013; Harada et al. 2013) had a main rupture area with a dimension of L ~ 30 km and W ~ 20 km; therefore, we fix the fault length and width as 30 and 20 km, respectively (L_{1} = L_{2} = 15 km and W_{1} = W_{2} = 10 km). The search range of the horizontal location of the centroid is determined based on the evaluation of the uncertainty of the horizontal location of the Wphase analysis of Lay et al. (2013) (see Figure S2 in Lay et al. 2013). The search range is listed in Table 2.
Results and Discussion
Tsunami source model
We obtained a tsunami source distribution that had a pair of large uplifts and subsidences (Fig. 3a). The observed waveforms (red lines in Fig. 3b) were reproduced well. The GPS buoy waveforms, which were not used for the inversion, were also explained. Furthermore, although the offset changes at the stations near the source (G09, TJT1, JFAST, and GJT3) were not reproduced, the fluctuations in the calculated waveforms were similar to the observations. This is consistent with the idea that these changes were due to the tilting or rotation of the sensors (e.g., Wallace et al. 2016; Kubota et al. 2018a).
To investigate the contribution from each subevent on the tsunami source, we compute the seasurface vertical displacement from the GCMT solution and compared the results with the tsunami source model. We use the equation in Okada (1992), which assumes that the rectangular planar fault on the westdipping nodal plane has a uniform slip. For simplicity, values of length, width, and slip L = 70 km, W = 35 km, and D = 0.7 m, respectively, are used. The spatial pattern of the tsunami source model (Fig. 4a) is similar to that of the combined deformation of subevents 1 and 2 (Fig. 4b) and the subsidence area is similar to that expected from the CMT solution of subevent 2 (Fig. 4d). The uplift of the tsunami source model is not consistent with either subevent 1 nor 2 alone (Fig. 4c and d). Based on this comparison, we conclude that the subsidence is generated by subevent 2 alone and that both subevents contribute to the uplift. The deformation expected from subevent 2 (Fig. 4d) has a sharp displacement peak that was not estimated in the tsunami source model. This is probably because the shortwavelength components disappeared due to the smoothing constraint imposed in the inversion and the spatial smoothing effect used in the deepsea region during the tsunami generation (Saito 2019).
Fault models of two subevents of the 2012 doublet earthquake
We obtained an optimum fault model of subevent 2, which had the highest VR value among all the fault model candidates, with a length of 35 km (L_{1} = 5 km, L_{2} = 30 km), width of 25 km (W_{1} = 15 km, W_{2} = 10 km), and fault slip of 1.1 m (VR = 96 %, Fig. 5). The seismic moment was 5.5 × 10^{19} Nm (Mw 7.1, assuming the rigidity of 60 GPa). The VR values for all fault model candidates (in the descending order) are shown in Fig. 5b. The VR values for the top ten candidates are almost flat and relatively high (Fig. 5d). This indicates that the top ten candidates reasonably reconstruct the subsidence of the tsunami source model. Hence, we inspect the model parameters for these candidates to evaluate the estimation error of the optimum fault model. They are projected onto the vertical crosssection in Fig. 5c and d (thin black lines), and the histograms of the model parameters are shown in Fig. 6. Among the top ten candidates, most models have the downdip limit of the fault plane of W_{1} = 15 km, and all models have fault bottoms shallower than the depth of ~35 km (W_{1} ≤ 20 km, Fig. 6). This indicates that the lower end of the fault of subevent 2 should be less than ~35 km.
We also calculated the seasurface height assuming the faults with smaller dimension with larger slip (Additional file 1: Figure S3). In this calculation, the downdip end of the fault (W_{1}) and slip amount were changed, and the length (L_{1}, L_{2}) and the updip end (W_{2}) of the fault, and seismic moment Mo were fixed to those of the optimum model. In the fault models with W < 15 km (downdip depth of fault is shallower than ~25 km), the locations of the western edge of the subsided area and of the peak displacement are inconsistent with those of the tsunami source model. This indicates the small fault models are implausible. The subsidence of the tsunami source model could be explained when the small faults are located slightly west of the optimum fault location. However, such faults can be rejected because we used the aftershock distribution of Obana et al. (2014, 2015) to constrain the horizontal location of the fault. It is important to use the aftershock distribution for prior information on the fault horizontal location, in order to accurately constrain the downdip depth of the subevent 2 fault.
The subsided area calculated from the optimum fault model was consistent with that of the tsunami source model (Fig. 7a and b). We calculate the residual seasurface height between the tsunami source model (Fig. 7a) and the seasurface displacement expected from the fault model of subevent 2 (Fig. 7b; the residual height distribution).
From the residual height distribution utilizing the results of the teleseismic analyses, we constrained the fault model of subevent 1. The result is shown in Fig. 8. The slip amount on the fault was 2.2 m, and the seismic moment was 7.8 × 10^{19} Nm (Mw 7.2, rigidity of 60 GPa). We obtained the optimum VR of 80%. The VR values are relatively high and flat for the top ten fault model candidates (Fig. 8b). The uncertainty of the horizontal location of the fault center for these candidates is likely to be ± ~10 km (Fig. 8a). This horizontal uncertainty is almost consistent with that estimated by Lay et al. (2013).
Tsunami and teleseismic waveform simulation from optimum fault model
The results of the fault modeling of the 2012 doublet earthquake are summarized in Fig. 9. The seasurface height displacement expected from the optimum rectangular fault models of subevents 1 and 2 (Fig. 9a) is calculated by the superposition of the displacements from each fault model (Figs. 5a and 8a). The distribution is very similar to that of the tsunami source model (Fig. 4). The optimum models have vertical ranges of ~6 (seafloor)–30 km for shallow subevent 2 and ~50–70 km for deep subevent 1 (Fig. 9d and e).
From the combined displacement, we numerically simulate tsunami waveforms (Fig. 10). The simulated waveforms reasonably explained the observed tsunami waveforms well, not only the nearfield TPGs but also the farfield DART, KPG, and GPS buoys (red lines in Fig. 10b). We calculate the VR between the observed and calculated waveforms from Eq. (1), by using the same time window as in the inversion of tsunami records. We finally obtained VR = 79 %.
We also simulate the teleseismic Pwaves using the fault model parameters for comparison with the observed teleseismic waveforms (Fig. 11). We assume pure doublecouple point sources at the centers of the optimum faults of each subevent. We use the calculation programs of Kikuchi and Kanamori (2003). A triangularshaped source time function with the rise time of 6 s is assumed, considering the typical rupture duration of M ~7 earthquakes (Fig. 9b). After simulating the waveforms of each subevent, we stack the simulated waveforms. We assume that the difference of focal times between subevents 1 and 2 was 10 s, which is determined by inspecting the waveform similarity of the observed and stacked waveforms.
We use a 1D multilayered velocity structure model without the water layer, assuming that the source structure was identical to the receiver structure in Table 3 (blue traces in Fig. 11b). The simulated waveforms for each subevent are also shown in Additional file 1:Figure S4. The peak timing and amplitudes of the first upmotion and the subsequent downmotion waves reasonably fitted the observation, although the subsequent phases during 50–80 s did not perfectly match. This is probably because of the assumptions of the velocity structure and simple source time function. We then simulate the teleseismic waveforms incorporating the water layer and oceanic structure, shown in Table 3 (red traces in Fig. 11b). The agreement of the subsequent phases improved compared with the simulation without the water layer. According to the teleseismic analysis by Lay et al. (2013), another smaller normalfaulting subevent was estimated at 40 s after subevent 1. Hence, it is possible that the third smaller subevent also contributed to the generation of the later arrival. It is worth pointing out that it is important to use the teleseismic records to resolve the temporal complexity of the doublet earthquake in detail.
Our fault model explains both tsunami and teleseismic observations. In addition, our fault model of subevent 2 is consistent with the aftershock distribution determined by the ocean bottom seismographs. The rupture area of subevent 2 estimated by Harada et al. (2013) was located at the outertrench region and concentrated in the shallower portion of the plate (z < ~20 km). The horizontal location of subevent 2 centroid by Lay et al. (2013) (Fig. 1b) was also inconsistent with our fault model and with the aftershock locations. The consistency of our fault model with the tsunami, teleseismic waveforms, and aftershocks indicates that the stepbystep procedure used in this analysis can decompose the complex rupture process of the 2012 doublet earthquake. We conclude that we can obtain a more comprehensive fault model of the 2012 doublet earthquake, than the one estimated from the teleseismic data alone.
Importance of nearfield tsunami data for the fault modeling
Inazu and Saito (2014) showed a tsunami source model of the 2012 doublet earthquake using offshore tsunami stations located more than 200 km from the source area (Additional file 1: Figure S1). We compare the tsunami source models of this study with that of Inazu and Saito (2014) (Fig. 12a). The horizontal location of the tsunami source was in agreement with the model of Inazu and Saito (2014), although the amplitudes were lower. The simulated tsunami at the TPG stations using the tsunami source model of Inazu and Saito (2014) is similar to the tsunami peak timing of the observation (Fig. 12b). This indicates that the horizontal location of the tsunami source is reasonably constrained even when using tsunami stations located far from the source (> ~200 km).
However, the dominant period and amplitudes of the simulated waveforms are longer and smaller than the observation. This indicates that the spatial resolution of the farfield tsunami data is not sufficient for the finite fault model, and thus, to constrain the downdip limit of the fault plane of subevent 2. Using the nearfield tsunami data, the constraint of the downdip limit of the fault plane of shallow subevent 2 is improved. This enables us to discuss the intraplate stress regime after the 2011 TohokuOki earthquake.
The fault dimension and depth of subevent 1 estimated in this study are consistent with previous results of the teleseismic waveforms (Lay et al. 2013; Harada et al. 2013). This is because we used the teleseismic analyses as the prior information for fault dimension. In contrast, the horizontal location and fault dimension of subevent 2 differ from the teleseismic analyses. The downdip limit of subevent 2 constrained from the teleseismic analysis (Harada et al. 2013) is considerably shallower (< ~20 km) than that of the constrained from tsunami data (~40 km). Our fault model has better consistency with the aftershock distribution, for both horizontal location and depth range. It is likely that the rupture process of subevent 2 was not resolved well from the teleseismic data, because the teleseismic signal from subevent 2 overlaps with that of subevent 1. By using the nearfield tsunami records, the resolution of subevent 2 rupture was considerably improved.
Temporal change in downdip limit of normalfaulting earthquake
The normalfaulting aftershocks around subevent 2 (Obana et al. 2014, 2015) mainly occurred at depths of ~30 km, which corresponds to the downdip depth of the optimum fault of subevent 2 (Fig. 9b). Some normalfaulting seismicity also occurred at depths of ~35 km, along the downdip direction (Fig. 9b). According to Obana et al. (2014), the estimation error of the aftershocks is less than 5 km (Figure 2 in Obana et al., 2014). Considering the estimation error of the fault model and aftershock distribution, the downdip limit where the shallow normalfaulting seismicity can occur around this region is ~30–35 km (Fig. 13).
We also investigate the temporal change of the intraplate seismicity before and after the TohokuOki earthquake (Fig. 13). The downdip limit of subevent 2 fault (~35 km) is clearly ~10 km deeper, compared with the downdip limit of the normalfaulting seismicity observed in 2007 (< ~25 km, Hino et al. 2009). Because both researches use the arrays of the ocean bottom seismometers installed just above the focal area, which have identical sensitivity and were distributed with almost identical spatial intervals (~10 km), the detectability in both observation periods is expected to be identical and thus the difference between the seismicity depths of the lower limit of the shallow normalfaulting seismicity was confidentially significant. In addition, a few deeper (> ~40 km) events were detected in both observations. This also suggests the misdetection of the deeper shallow normalfaulting event (~30–40 km) before the TohokuOki earthquake is unlikely to occur.
In contrast, the updip limits of the subevent 1 fault (~50 km) and the deep reversefaulting seismicity (~50 km, Obana et al. 2015) are almost equivalent to the deep reversefaulting seismicity before the TohokuOki earthquake (Seno and Gonzalez 1987; Hino et al. 2009), although it is difficult to discuss this in detail because of the very low seismicity. By focusing on the shallow normalfaulting seismicity, we discuss the cause of the deepening of the downdip limit of the normalfaulting seismicity.
The yield strength of the plate is characterized by the brittle rupture at the shallow portion and ductile failure laws at the deeper parts of the plate (Fig. 14a, e.g., Scholtz 1988; Turcotte and Schubert 2002; Hunter and Watts 2016). Based on the Anderson theory of faulting, the brittle strength along the horizontal direction normal to the trench axis τ_{xx}(z) is expressed as (e.g., Turcotte and Schubert 2002):
where ρ_{0} is the crust density, p_{w} is the pore pressure, z is depth (downward is positive), δ is the fault dip angle, and μ is the frictional coefficient. This equation implies that the rock strength is proportional to depth z (green line in Fig. 14a). Further, by assuming the plate as a rigid twodimensional elastic plane (x and zaxes are the subducting direction and vertical direction, respectively), the vertical distribution of the bending stress along the dip direction σ_{xx}(z) is approximated as (e.g., Turcotte and Schubert 2002; Craig et al. 2014; Hunter and Watts 2016)
where E is the Young’s modulus, C is the curvature of plate bending, ν is the Poisson’s ratio, and z_{0} is the stressneutral depth (tensile stress is positive, blue line in Fig. 14a).
At a shallower portion of the plate, where the bending stress exceeds the brittle strength (the blue background area in Fig. 14a), the rock cannot remain elastic and the stress is released, or the rock yields, leading to shallow normalfaulting earthquakes. In contrast, elastic behavior is expected in the depth range where the bending stress does not exceed strength; the range is termed the elastic core (e.g., Craig et al. 2014; Hunter and Watts 2016). The actual deviatoric stress profile within the plate is represented by the red solid line in Fig. 14a. The top of the aseismic elastic core, or the bottom of the vertical range of the normalfaulting seismicity, can be defined as a depth where the bending stress and the frictional strength are equal. As the top of the elastic core is present at a depth of ~30–35 km and the top of the reversefaulting seismicity (the bottom of the elastic core) at ~45 km, the stressneutral plane is expected to be located in the depth range between 30–35 and 45 km. This depth range is almost consistent with the depths where fault mechanisms flip from the shallow normalfaulting to the deep thrustfaulting mechanisms, near the trench axis off NE Japan (~25–40 km, Gamage et al. 2009; Koga et al. 2012).
We compare the vertical profiles of the brittle strength and bending stress. Assuming E = 80 GPa and ν = 0.25, and C = 2 × 10^{7} m^{1} (McNutt and Menard 1982), dσ_{xx}/dz = EC/(1−ν^{2}) is ~15 MPa/km. Assuming the hydrostatic pressure condition p_{w} = ρ_{w}g_{0}z (ρ_{w} = 1030 kg/m^{3}, seawater density) and ρ_{0} = 2700 kg/m^{3} , δ = 50°, and μ = 0.6 (e.g., Byerlee 1978), dτ_{xx}/dz is ~11 MPa/km as per Eq. (2). In this situation, assuming z_{0} = 40 km, τ_{xx}(z) and σ_{xx}(z) are equal at z ~25 km (Fig. 14b). This is consistent with the downdip limit of normalfaulting seismicity observed before the TohokuOki earthquake (Hino et al. 2009). However, considering dσ_{xx}/dz = ~15 MPa/km, the stress increment of ~300 MPa is needed to deepen the top of the elastic core from 25 to 35 km (orange arrow in Fig. 14b). This value is too large compared to the coseismic stress change around subevent 2 expected from the fault model of the TohokuOki earthquake by Iinuma et al. (2012), Δσ_{xx} ~20 MPa. The expected depth change of the downdip limit of the normal faulting seismicity is only a few km (Fig. 14c).
It must be considered that τ_{xx}(z) and σ_{xx}(z) are equal at ~30–35 km depth before the TohokuOki earthquake (Fig. 14c). In order that the normalfaulting earthquakes occur at a depth of 35 km, the brittle strength must be reduced compared to the typical frictional condition (Fig. 14b). If we assume z_{0} = 40 ± 5 km (Fig. 13), the frictional coefficient of the fault around the lower end of the fault of subevent 2 is μ ~0.07 ± 0.06 so that τ_{xx}(z) and σ_{xx}(z) are equal at z = 35 km (Fig. 14c). Even when the top of the elastic core is assumed to be at z = 30 km, the expected frictional coefficient μ is ~0.2 (Additional file 1: Figure S5). These values are much smaller than that of the typical rocks but comparable to that estimated for the other incoming plate (Craig et al. 2014).
Reduction of friction has often been reported in studies on inland earthquakes (e.g., Yoshida et al. 2018); this reduction can be attributed to the existence of the pore fluid (e.g., Bell and Nur 1978). Based on the active seismic survey in the outerrise region of the Japan trench (e.g., Fujie et al. 2018), the significant seismic wave velocity reduction and high V_{p}/V_{s} area were detected at the shallow part of the subducting plate (< 5 km), which are interpreted as being the results of pore fluid penetration through the preexisting bending faults in the shallower part of the plate (e.g., Peacock 2001). Considering these studies, it is suggested that that the strength reduction within the plate might be related to the pore fluid. Numerical modeling by Faccenda et al. (2009) demonstrated that the pore fluid can infiltrate the plate as deep as the lower limit of the normal faulting seismicity observed in this study. Cai et al. (2018) also reported the serpentinized mantle wedge associated with water infiltration into the subducting plate (down to ~35 km) at the Mariana subduction zone.
However, the majority of the seismicity at depths of 30–35 km is located around the subevent 2’s fault (Fig. 9) and less in the other portions of the plate. This localization of seismicity suggests that the pore fluid, or the strength reduction, is localized within the plate, as also suggested by Faccenda et al. (2009) and Obana et al. (2019).
The activation of the normalfaulting seismicity at depths of 25–35 km after the TohokuOki earthquake can be interpreted as follows: the plate at 25–35 km depths had yielded before the TohokuOki earthquake, leading to intrinsically aseismic region; a stress increment by the TohokuOki earthquake enhanced the horizontal tensile stress in a broad depth range near the top of the elastic core, which activates seismicity. Less normalfaulting seismicity at depths of 25–35 km during observation from April to June 2007 (Hino et al. 2009) may be representative of the longtermaveraged deformation. It is expected that the stressing rate due to the bending deformation is lower near the stressneutral depth, where nulldeformation is expected, than the shallowest part of the incoming oceanic plate.
On the other hand, if EC/(1−ν^{2}) is small, the static stress change by the TohokuOki earthquake can contribute to deepening the elastic core or the lower limit of the shallow normal faulting seismicity. Supposing that the elastic core is deepened by 10 km due to the coseismic static stress change Δσ_{xx} of ~20 MPa by the TohokuOki earthquake, EC/(1−ν^{2}) must be ~0.5 MPa/km, which is smaller than the typical elastic condition described above by an order of magnitude. However, it is unlikely that the Young’s modulus or the plate curvature are significantly reduced by an order of magnitude even if supposing the existence of the pore fluid or estimation error of the curvature. Thus, this hypothesis seems unlikely. Although it might be possible that the EC/(1−ν^{2}) is small compared to that assumed in this study, its contribution to deepening the elastic core associated with the TohokuOki earthquake is not highly significant.
Conclusions
In this study, we estimated the fault model of the intraplate doublet earthquake that occurred on December 7, 2012 (subevent 1: a deep reversefaulting earthquake; subevent 2: a shallow normalfaulting earthquake) strategically utilizing offshore tsunami, aftershocks, and the teleseismic records based on the stepbystep analysis procedure. First, the initial seasurface height distribution was estimated by inverting the offshore tsunami records and comparing it with the seafloor deformation from the CMT mechanism. It was found that the subsidence and uplift areas were generated by subevent 2 and both subevents, respectively. Then, the fault model of each subevent was estimated based on the initial seasurface height model, using information from previous studies. As a result, the vertical extent of the fault plane of subevent 2 was obtained as ~5 km (i.e., the seafloor) to 35 km. Finally, we simulated the tsunami and teleseismic waveforms from the fault model, which explained the observation well.
We compared the tsunami source model obtained from the nearfield tsunami data acquired at less than 200 km from the epicenter and that from the farfield (> 200 km) data. We found that the horizontal location of the tsunami source was reasonably constrained, even from the farfield tsunami data alone. However, to constrain the finite fault model in more detail, it is necessary to use the nearfield tsunami records. We also discussed the stress state within the plate and its spatiotemporal change after the 2011 TohokuOki earthquake. We found that the downdip limit of the shallow normalfaulting earthquakes was obviously deepened compared with that observed in 2007, from 25 to 35 km. However, comparing the coseismic stress change by the TohokuOki earthquake and the amount of the bending stress within the plate, the plate down to ~35 km in depth should have already yielded before the TohokuOki earthquake, and the top of the elastic core been located at ~35 km. Furthermore, as the bending stress around the top of the elastic core was much smaller than the rock strength expected from the empirical relationship, the frictional strength in the range of the normalfaulting earthquakes is expected to be significantly reduced. The significant strength reduction of the plate suggests pore fluid infiltration down to ~35 km, along the bending faults.
Availability of data and materials
TPG data is available in Additional file. KPG data were obtained from the Submarine Cable Data Center (SCDC), JAMSTEC (http://www.jamstec.go.jp/scdc/top_e.html). Teleseismic data were downloaded from the Data Management Center (DMC) of Incorporated Research Institutions for Seismology (IRIS) (http://ds.iris.edu/ds/nodes/dmc/tools/event/3650366). GPS buoy data were obtained by a request to PARI. The data from DART, which is jointly operated by NOAA and JMA, was provided upon request by Eddie Bernard and Yong Wei from Science Applications International Corporation (SAIC). Aftershock data was provided by Koichiro Obana.
Abbreviations
 CMT:

Centroid moment tensor
 DART:

Deepocean Assessment and Reporting of Tsunamis
 GCMT:

Global Centroid Moment Tensor
 JAMSTEC:

Japan Agency for MarineEarth Science and Technology
 KPG:

Pressure Gauge Installed off Kushiro
 PARI:

Port and Airport Research Institute
 PG:

Pressure gauge
 TPG:

Pressure gauge installed by Tohoku University
 VR:

Variance reduction
References
Amante C, Eakins BW (2009) ETOPO1 1 ArcMinute Global Relief Model: Procedures, Data Sources and Analysis. National Geophysical Data Center, NOAA, Boulder, Colorado, doi:doi.org/10.7289/V5C8276M
Bell ML, Nur A (1978) Strength changes due to reservoirinduced pore pressure and stresses and application to Lake Oroville. J Geophys Res Solid Earth 83:4469–4483. https://doi.org/10.1029/JB083iB09p04469
Bernard E, Wei Y, Tang L, Titov V (2014) Impact of nearfield, deepocean tsunami observations on forecasting the 7 December 2012 Japanese tsunami. Pure Appl Geophys 171:3483–3491. https://doi.org/10.1007/s0002401307208
Byerlee J (1978) Friction of rocks. Pure Appl Geophys 116:615–626. https://doi.org/10.1007/BF00876528
Cai C, Wiens DA, Shen W, Eimer M (2018) Water input into the Mariana subduction zone estimated from oceanbottom seismic data. Nature 563:389–392. https://doi.org/10.1038/s4158601806554
Chapple WM, Forsyth DW (1979) Earthquakes and bending of plates at trenches. J Geophys Res 84(B12):6729–6749. https://doi.org/10.1029/JB084iB12p06729
Christensen DH, Ruff LJ (1988) Seismic coupling and outer rise earthquakes. J Geophys Res Solid Earth 93:13421–13444. https://doi.org/10.1029/JB093iB11p13421
Craig TJ, Copley A, Jackson J (2014) A reassessment of outerrise seismicity and its implications for the mechanics of oceanic lithosphere. Geophys J Int 197:63–89. https://doi.org/10.1093/gji/ggu013
Dmowska R, Lovison LC (1988) Intermediateterm seismic precursors for some coupled subduction zones. Pure Appl Geophys 126:643–664. https://doi.org/10.1007/BF00879013
Ekström G, Nettles M, Dziewoński AM (2012) The global CMT project 20042010: Centroidmoment tensors for 13,017 earthquakes. Phys Earth Planet Inter 200–201:1–9. https://doi.org/10.1016/j.pepi.2012.04.002
Faccenda M, Gerya TV, Burlini L (2009) Deep slab hydration induced by bendingrelated variations in tectonic pressure. Nat Geosci 2:790–793. https://doi.org/10.1038/ngeo656
Fujie G, Kodaira S, Kaiho Y, Yamamoto Y, Takahashi T, Miura S, Yamada T (2018) Controlling factor of incoming plate hydration at the northwestern Pacific margin. Nat Commun 9:3844. https://doi.org/10.1038/s4146701806320z
Gamage SSN, Umino N, Hasegawa A, Kirby SH (2009) Offshore doubleplaned shallow seismic zone in the NE Japan forearc region revealed by sP depth phases recorded by regional networks. Geophys J Int 178:195–214. https://doi.org/10.1111/j.1365246X.2009.04048.x
Harada T, Murotani S, Satake K (2013) A deep outerrise reversefault earthquake immediately triggered a shallow normalfault earthquake: The 7 December 2012 offSanriku earthquake (M_{W} 7.3). Geophys Res Lett 40:4214–4219. https://doi.org/10.1002/grl.50808
Hino R, Azuma R, Ito Y, Yamamoto Y, Suzuki K, Tsushima H, Suzuki S, Miyashita M, Tomori T, Arizono M, Tange G (2009) Insight into complex rupturing of the immature bending normal fault in the outer slope of the Japan Trench from aftershocks of the 2005 Sanriku earthquake (Mw = 7.0) located by ocean bottom seismometry. Geochem, Geophys Geosyst 10:Q07O18. doi: 10.1029/2009GC002415
Hino R, Inazu D, Ohta Y, Ito Y, Suzuki S, Iinuma T, Osada Y, Kido M, Fujimoto H, Kaneda Y (2014) Was the 2011 TohokuOki earthquake preceded by aseismic preslip? Examination of seafloor vertical deformation data near the epicenter. Mar Geophys Res 35:181–190. https://doi.org/10.1007/s1100101392082
Hirata K, Aoyagi M, Mikada H, Kawaguchi K, Kaiho Y, Iwase R, Morita S, Fujisawa I, Sugioka H, Mitsuzawa K, Suyehiro K, Kinoshita H, Fujiwara N (2002) Realtime geophysical measurements on the deep seafloor using submarine cable in the Southern Kurile subduction zone. IEEE J Ocean Eng 27:170–181. https://doi.org/10.1109/JOE.2002.1002471
Hunter J, Watts AB (2016) Gravity anomalies, flexure and mantle rheology seaward of circumPacific trenches. Geophys J Int 207:288–316. https://doi.org/10.1093/gji/ggw275
Iinuma T, Hino R, Kido M, Inazu D, Osada Y, Ito Y, Ohzono M, Tsushima H, Suzuki S, Fujimoto H, Miura S (2012) Coseismic slip distribution of the 2011 off the Pacific Coast of Tohoku Earthquake (M9.0) refined by means of seafloor geodetic data. J Geophys Res 117:B07409. doi: https://doi.org/10.1029/2012JB009186
Inazu D, Saito T (2014) Two subevents across the Japan Trench during the 7 December 2012 off Tohoku earthquake (Mw 7.3) inferred from offshore tsunami records. J Geophys Res Solid Earth 119:5800–5813. https://doi.org/10.1002/2013JB010892
Ito A, Fujie G, Miura S, Kodaira S, Kaneda Y, Hino R (2005) Bending of the subducting oceanic plate and its implication for rupture propagation of large interplate earthquakes off Miyagi, Japan, in the Japan Trench subduction zone. Geophys Res Lett 32:L05310. https://doi.org/10.1029/2004GL022307
Kato T, Terada Y, Ito K, Hattori R, Abe T, Miyake T, Koshimura S, Nagai T (2005) Tsunami due to the 2004 September 5th off the Kii peninsula earthquake, Japan, recorded by a new GPS buoy. Earth Planets Space 57:297–301. https://doi.org/10.1186/BF03352566
Kikuchi M, Kanamori H (1991) Inversion of complex body waves—III. Bull Seismol Soc Am 81:2335–2350
Kikuchi M, Kanamori H (2003) Note on teleseismic bodywave inversion program. http://www.eri.utokyo.ac.jp/ETAL/KIKUCHI/.
Koga S, Ito Y, Hino R, Shinohara M, Umino N (2012) Focal mechanisms of small earthquakes within the Pacific Plate near the Japan Trench. Zisin 2(64):75–90 (in Japanese with English abstract). https://doi.org/10.4294/zisin.64.75
Kubota T, Hino R, Inazu D, Ito Y, Iinuma T (2015) Complicated rupture process of the Mw 7.0 intraslab strikeslip earthquake in the Tohoku region on 10 July 2011 revealed by nearfield pressure records. Geophys Res Lett 42:9733–9739. https://doi.org/10.1002/2015GL066101
Kubota T, Hino R, Inazu D, Ito Y, Iinuma T, Ohta Y, Suzuki S, Suzuki K (2017a) Coseismic slip model of offshore moderate interplate earthquakes on March 9, 2011 in Tohoku using tsunami waveforms. Earth Planet Sci Lett 458:241–251. https://doi.org/10.1016/j.epsl.2016.10.047
Kubota T, Saito T, Ito Y, Kaneko Y, Wallace LM, Suzuki S, Hino R, Henrys S (2018b) Using tsunami waves reflected at the coast to improve offshore earthquake source parameters: Application to the 2016 Mw 7.1 Te Araroa earthquake, New Zealand. J Geophys Res Solid Earth 123:8767–8779. https://doi.org/10.1029/2018JB015832
Kubota T, Saito T, Suzuki W, Hino R (2017b) Estimation of seismic centroid moment tensor using ocean bottom pressure gauges as seismometers. Geophys Res Lett 44:10907–10915. https://doi.org/10.1002/2017GL075386
Kubota T, Suzuki W, Nakamura T, Chikasada NY, Aoi S, Takahashi N, Hino R (2018a) Tsunami source inversion using timederivative waveform of offshore pressure records to reduce effects of nontsunami components. Geophys J Int 215:1200–1214. https://doi.org/10.1093/gji/ggy345
Lay T, Duputel Z, Ye L, Kanamori H (2013) The December 7, 2012 Japan Trench intraplate doublet (Mw 7.2, 7.1) and interactions between neartrench intraplate thrust and normal faulting. Phys Earth Planet Inter 220:73–78. https://doi.org/10.1016/j.pepi.2013.04.009
Matsumoto K, Takanezawa T, Ooe M (2000) Ocean tide models developed by assimilating TOPEX/POSEIDON altimeter data into hydrodynamical model: A global model and a regional model around Japan. J Oceanogr 56:567–581. https://doi.org/10.1023/A:1011157212596
McNutt MK, Menard HW (1982) Constraints on yield strength in the oceanic lithosphere derived from observations of flexure. Geophys J Int 71:363–394. https://doi.org/10.1111/j.1365246X.1982.tb05994.x
Obana K, Fujie G, Kodaira S, Takahashi T, Yamamoto Y, Sato T, Yamashita M, Nakamura Y, Miura S (2015). SeismSSicity and structure of the incoming Pacific plate subducting into the Japan Trench off Miyagi. Abstract T43G01 presented at 2015 AGU Fall Meeting, San Francisco, CA, 14–18 Dec 2015.
Obana K, Fujie G, Takahashi T, Yamamoto Y, Nakamura Y, Kodaira S, Takahashi N, Kaneda Y, Shinohara M (2012) Normalfaulting earthquakes beneath the outer slope of the Japan Trench after the 2011 Tohoku earthquake: Implications for the stress regime in the incoming Pacific plate. Geophys Res Lett 39:L00G24. doi: https://doi.org/10.1029/2011GL050399
Obana K, Fujie G, Takahashi T, Yamamoto Y, Tonegawa T, Miura S, Kodaira S (2019) Seismic velocity structure and its implications for oceanic mantle hydration in the trench–outer rise of the Japan Trench. Geophys J Int 1629–1642. doi: https://doi.org/10.1093/gji/ggz099
Obana K, Kodaira S, Nakamura Y, Sato T, Fujie G, Takahashi T, Yamamoto Y (2014) Aftershocks of the December 7, 2012 intraplate doublet near the Japan Trench axis. Earth, Planets Sp 66:24. https://doi.org/10.1186/188059816624
Okada Y (1992) Internal deformation due to shear and tensile faults in a halfspace. Bull Seismol Soc Am 82:1018–1040
Peacock SM (2001) Are the lower planes of double seismic zones caused by serpentine dehydration in subducting oceanic mantle? Geology 29:299–302. https://doi.org/10.1130/00917613(2001)029<0299:ATLPOD>2.0.CO;2
Saito M (1978) An automatic design algorithm for band selective recursive digital filters. Butsuri Tanko 31:112–135 (in Japanese)
Saito T (2019) Tsunami Generation and Propagation. Springer Japan, Tokyo. https://doi.org/10.1007/9784431568506
Scholz CH (1988) The brittleplastic transition and the depth of seismic faulting. Geol Rundschau 77:319–328. https://doi.org/10.1007/BF01848693
Seno T, Gonzalez DG (1987) Faulting caused by earthquakes beneath the outer slope of the Japan Trench. J Phys Earth 35:381–407. https://doi.org/10.4294/jpe1952.35.381
Tsushima H, Hino R, Tanioka Y et al (2012) Tsunami waveform inversion incorporating permanent seafloor deformation and its application to tsunami forecasting. J Geophys Res 117:B03311. https://doi.org/10.1029/2011JB008877
Turcotte DL, Schubert G (2002) Geodynamics, 2nd ed. Cambridge University Press. https://doi.org/10.1017/CBO9780511807442
Wallace LM, Araki E, Saffer D et al (2016) Nearfield observations of an offshore Mw 6.0 earthquake from an integrated seafloor and subseafloor monitoring network at the Nankai Trough, southwest Japan. J Geophys Res Solid Earth 121:8338–8351. https://doi.org/10.1002/2016JB013417
Wessel P, Smith WHF (1998) New, improved version of generic mapping tools released. Eos, Trans Am Geophys Union 79:579. https://doi.org/10.1029/98EO00426
Yoshida K, Hasegawa A, Yoshida T, Matsuzawa T (2018) Heterogeneities in stress and strength in Tohoku and its relationship with earthquake sequences triggered by the 2011 M9 TohokuOki earthquake. Pure Appl Geophys. https://doi.org/10.1007/s0002401820739
Acknowledgements
We thank the reviewer Thorne Lay and another anonymous reviewer, as well as the editor, Frantisek Gallovic, for their reviews and insightful comments. We thank Koichiro Obana for providing aftershock data and Keisuke Yoshida for providing stress change data due to the TohokuOki earthquake. We thank Eddie Bernard, Yong Wei, Science Applications International Corporation (SAIC), and JMA for providing DART data. We also thank JAMSTEC and PARI for providing the KPG and GPS buoy data, respectively. We also thank Editage (www.editage.jp) for English language editing. The figures in this paper were prepared using Generic Mapping Tools (Wessel & Smith 1998). TK thanks Koichiro Obana and Tatsuhiko Saito for insightful discussions. Without the constructive comments and enormous encouragement from Yusaku Ohta, this paper would not have been published.
Funding
This work was supported by the research project “Research concerning Interaction between the Tokai, Tonankai and Nankai earthquakes” of the Ministry of Education, Culture, Sports, Science and Technology, Japan, by JSPS KAKENHI [Grant Numbers JP20244070, JP26000002, and JP 19K14818], and by the Sasakawa Scientific Research Grant [20192037] of the Japan Science Society.
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TK designed the study, analyzed the data, interpreted the results, and drafted the manuscript. RH contributed to fault modeling, data interpretation, and revision of the manuscript. DI contributed to tsunami modeling and revising the manuscript. SS took part in the installation and retrieval of the pressure data. All authors approved the final manuscript.
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Correspondence to Tatsuya Kubota.
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Kubota, T., Hino, R., Inazu, D. et al. Fault model of the 2012 doublet earthquake, near the updip end of the 2011 TohokuOki earthquake, based on a nearfield tsunami: implications for intraplate stress state. Prog Earth Planet Sci 6, 67 (2019). https://doi.org/10.1186/s406450190313y
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Keywords
 Ocean bottom pressure gauge
 Doublet earthquake
 Intraplate earthquake
 2011 TohokuOki earthquake
 Bending stress
 Fault modeling