Introduction

Determining earthquake focal mechanisms is important for understanding the earthquake source mechanisms and tectonic stress fields. The off Ibaraki region (Fig. 1a), northeastern Japan, in the Japan Trench subduction zone, is expected to be characterized by a heterogeneous stress field. In addition to the Pacific Plate subducting beneath the northeastern Japan from the east, the Philippine Sea Plate is subducting on the Pacific Plate. The northeastern edge of the Philippine Sea plate has been estimated in this region (green line in Fig. 1a, e.g., Uchida et al. 2010; Nakahigashi et al. 2012). Tectonic loading from the 2 subducting plates complicates the stress field. On the incoming Pacific Plate seaward of the trench, a chain of seamounts exists. Mochizuki et al. (2008) has identified a subducting seamount with a width of ~ 50 km and a height of ~ 3 km in this region. The influence of subducting seamounts on the stress field and seismicity is not yet clear, although it has long been discussed through geological or numerical experiments (e.g., Wang and Bilek 2011, 2014; Sun et al. 2020). Moreover, this region lies around the southern limit of the 2011 off the Pacific coast of Tohoku earthquake (hereafter, we referred to as “the 2011 Tohoku-oki earthquake”) with \({\mathrm{M}}_{\mathrm{w}}\) 9.0. The largest \({\mathrm{M}}_{\mathrm{w}}\) 7.6 aftershock (the 2011 Ibaraki-oki earthquake) occurred approximately 30 min after the 2011 Tohoku-oki earthquake. Static stress changes caused by large earthquakes also affect the stress field and seismicity around the fault area (e.g., Hasegawa et al. 2012; Yoshida et al. 2014). Thus, the off Ibaraki region is an important study area for the seismicity and the stress field related to plate subduction, seamounts, and large earthquakes.

Fig. 1
figure 1

a Study area with the slip distribution of the 2011 Tohoku-oki earthquake within a grey square (Lay et al. 2011), as well as the 2011 Ibaraki-oki earthquake within a black square (Kubo et al. 2013). The grey triangles show the stations of the OBS array in the off Ibaraki region. The blue circle shows the subducting seamount (Mochizuki et al. 2008). The green line shows the northeastern limit of the Philippine Sea Plate (Uchida et al. 2010). b Distribution of seismicity and OBS stations. The white triangles show OBS stations. The circled white triangles show the stations which were recovered approximately 2 weeks after the 2011 Tohoku-oki earthquake occurred. The colored circles show the earthquake hypocenters determined by JMA with their color indicating their depth. The red rectangle represents the region, where the Green’s functions were calculated. c Seismic velocity structure model along profile A–A’ in (b). The region shallower than ~ 10 km was constructed by Yamaya et al. (2021), and deeper by Koketsu et al. (2012)

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Despite these situations, focal mechanism catalogs were not sufficient with respect to their spatio-temporal densities and resolutions in the off Ibaraki region, which decreases the statistical stability and the resolution in the analysis of the stress field. In Japan, focal mechanism catalogs of regional centroid moment tensor (CMT) solutions (e.g., F-net moment tensor (MT): Fukuyama et al. 1998; Kubo et al. 2002; Accurate and QUick Analysis system for source parameters (AQUA) CMT: Matsumura et al. 2006) and first-motion solutions compiled by the Japan Meteorological Agency (JMA) have been routinely determined and contributing to studying the stress field. Some studies redetermined CMT solutions in the Tohoku region to discuss the stress field before and after the Tohoku-oki earthquake (e.g., Asano et al. 2011; Lister et al. 2018). However, any of the systems cannot determine focal mechanisms for \({\mathrm{M}}_{\mathrm{w}}\le\) 3.5 offshore earthquakes. In addition, even for earthquakes with \({\mathrm{M}}_{\mathrm{w}}\) of 3.5–4.0, it is difficult to determine the focal mechanisms of all detected offshore earthquakes. This is because of the low signal-to-noise ratio for low-frequency (e.g., 0.02–0.05 Hz) surface waves and high-frequency first-arrivals at onshore stations. This limited capability of analyzing small earthquakes reduces the number of obtained focal mechanisms, which decreases their spatio-temporal densities. The only use of onshore network data also reduces the spatial resolution of hypocenter determination in offshore regions owing to their far epicentral distances and insufficient azimuthal coverage. In addition, the spatial resolutions of those MT/CMT solutions based on low-frequency surface waves are not sufficient owing to their wavelengths.

Other than the established focal mechanism catalogs, studies using temporally deployed short-period ocean bottom seismometers (OBSs) generally determined first-motion focal mechanisms (e.g., Shinohara et al., 2012; Obana et al. 2021). However, only a few first-motion focal mechanisms were determined in the off Ibaraki region by a series of OBS observations, including the OBS array used in the present study (Shinohara et al. 2012). This limitation is possibly because of a low signal-to-noise ratio due to S and coda waves of the intense aftershock activity, which obstructs manual phase identifications for reading the first-motion polarities. These technical difficulties in estimating the focal mechanisms for offshore small-to-moderate earthquakes must be overcome to elucidate the detailed aftershock activity and stress field in the off Ibaraki region.

Therefore, we apply CMT inversions to high-frequency (0.4–1.0 Hz) body-wave data obtained from a dense array of short-period OBSs. CMT inversion can include information on the amplitudes and phases, in addition to the first-motion polarities. Moreover, manual phase identification is not required in typical grid-search CMT methods. Despite the advantages of CMT inversion, analysis of waveform data from OBS networks, such as CMT inversion, has still been limited in offshore region. Oceanic sediments and seawater layers strongly affect seismic wave propagation (e.g., Shapiro et al. 1998; Nakamura et al. 2015; Noguchi et al. 2016; Volk et al. 2017). Especially in subduction zones or large sedimentary basins with heterogeneous bedrock topography, 3-D seismic velocity structure models are needed to obtain accurate CMT solutions (e.g., Hejrani et al. 2017, 2019, 2020; Takemura et al. 2020; Wang and Zhan 2020; White et al. 2019). To accurately obtain CMT solutions of offshore earthquakes with smaller magnitudes, the use of an appropriate seismic velocity structure model and analysis of higher frequency seismograms should be incorporated. Such CMT analysis has become possible through recent developments in detailed seismic velocity models, numerical simulation codes of seismic wave propagation, and computational resources.

In this study, we conduct CMT inversions of MW2.5–4.5 aftershocks of the 2011 Tohoku-oki earthquake in the off Ibaraki region. To achieve higher spatial resolutions of CMT solutions, we use P-wave data filtered with 0.4–1.0 Hz from the dense OBS array and Green’s functions with a 3-D seismic velocity structure model. The dense array and higher frequency analysis significantly increase the spatial resolution of the CMT solutions. The obtained CMT solutions reflect heterogeneous stress field in the off Ibaraki region related to tectonic loading from the Pacific Plate and the Philippine Sea Plate, the subducting seamount, and the 2011 Ibaraki-oki earthquake.

Data

This study used velocity seismograms from a dense array with 30 OBSs deployed in the off Ibaraki region, in northeastern Japan along the Japan Trench subduction zone (Fig. 1a). The OBS array is composed of three-component short-period (1 Hz) seismometers (LE-3Dlite, Lennartz) with station intervals of approximately 6 km (Fig. 1b). First, 24 OBSs near the array center were deployed on October 17, 2010, and the surrounding 11 OBSs were added on February 14, 2011. After the observation started, on March 11, the 2011 Tohoku-oki earthquake occurred. Three of the OBSs were recovered about 2 weeks after the 2011 Tohoku-oki earthquake to investigate the aftershock activity. Of the OBSs, 28 were recovered in September 2011, but one of the recovered OBSs had an erroneously low amplitude level, likely due to a malfunction of its recorder.

To conduct CMT inversions of small-to-moderate earthquakes in the off Ibaraki region, we selected earthquakes with JMA-scale magnitudes (\({\mathrm{M}}_{\mathrm{JMA}}\)) of 2.5–4.0 that occurred within the region covering from 141.3°E to 142.1°E and from 35.7°N to 36.4°N. We used the earthquakes that occurred following the 2011 Tohoku-oki earthquake and before September 17, 2011.We note that the seismicity was low in this region before the 2011 Tohoku-oki earthquake, according to the JMA and F-net MT catalogs.

Methods

For CMT inversion in this study, we used the seismic records of P-waves on the vertical component. The signal-to-noise ratios on the horizontal components were insufficient for the P-waves. We adopted a frequency range of 0.4–1.0 Hz (i.e., P-wave wavelengths of 2–5 km assuming P-wave velocity of 5 km/s). This is because observed seismograms from our short-period OBSs have little sensitivity at a frequency lower than 0.4 Hz, and the determined CMTs from higher frequency seismograms can be expected to have higher spatio-temporal resolutions (e.g., Hejrani & Tkalčić, 2020; Wang & Zhan 2020). At a frequency higher than approximately 1.0 Hz, the incoherently scattered wavefield becomes dominant (e.g., Takemura et al. 2016; Sato et al. 2012). We did not use S-waves, because most seismograms were saturated for earthquakes with \({\mathrm{M}}_{\mathrm{w}}>3.5\).

Green’s functions were calculated using the Open-source Seismic Wave Propagation Code (OpenSWPC; Maeda et al. 2017) based on the staggered-grid finite difference method (FDM). We used the reciprocal method to obtain Green’s functions at 30 stations from 494710 assumed source grids efficiently. The reciprocal method has been used in previous CMT inversion studies, where the number of the source grid points was significantly larger than that of the stations (e.g., Hejrani et al. 2017; Okamoto et al. 2018; Wang and Zhang. 2020). The source grids were set at an interval of 0.01° (~ 0.6 km) within the regions from 141.3°E to 142.1°E and from 35.7°N to 36.4°N (Fig. 1b). Those along the depth were distributed from 0 to 45 km with an interval of 0.5 km. In the reciprocal calculations, a model volume of \(90\times 90\times 50 {\mathrm{km}}^{3}\) was discretized with a uniform grid interval of 0.025 km. We calculated 40 s of Green’s functions using 32,000 time-steps. We assumed the source time function as a Küpper wavelet with a duration of 0.1 s, which exhibits a flat response in our frequency range (see Fig. 4 of Maeda et al. 2017). Some of the target earthquakes with \(\ge {\mathrm{M}}_{\mathrm{W}}4.0\) may have source time functions with durations of about 1.0 s, which may affect seismogram durations in our target frequencies. Using our synthetic waveforms and a moment–duration relationship (Eq. (1) of Ekström et al. 2012), we confirmed that the effects of finite-duration source time functions are expected to be negligible for earthquakes with \({\mathrm{M}}_{\mathrm{w}}<4.5\) (Additional file 1: Fig. S1). The reciprocal calculations of Green’s functions were conducted using the Oakforest-PACS system at the Information Technology Center, The University of Tokyo. Each calculation needs 5.1 Tbyte memory and a wall-clock time of 2.5 h with 512-node (33792 cores) parallel computing.

Beneath this region, the Pacific Plate is subducting from the east. Offshore seismic surveys (e.g., Tsuru et al. 2002; Mochizuki et al. 2008) and ambient noise studies (e.g., Yamaya et al. 2021) suggest the existence of ~ 2 km oceanic sediments at shallower depths. To accurately model seismic wave propagation at the off Ibaraki region, we used a 3-D seismic velocity structure model. We constructed the 3-D model (Fig. 1c) by combining structures beneath the lower crust from the Japan Integrated Velocity Structure Model (JIVSM; Koketsu et al. 2012) and above the lower crust from a detailed local structure (Yamaya et al. 2021). The JIVSM is widely used for CMT inversions from low-frequency (\(<\sim 0.25\) Hz) seismograms (e.g., Okamoto et al. 2018; Takemura et al. 2020, 2021) for evaluating long-period hazard maps for Japan (https://www.jishin.go.jp/evaluation/seismic_hazard_map/lpshm/12_choshuki/). Here, we note that the Pacific Plate of the JIVSM roughly agrees with other studies of active-source seismic surveys (e.g., Tsuru et al. 2002; Mochiuki et al. 2008; Nakahigashi et al. 2012). Yamaya et al. (2021) resolved the fine-scale S-wave velocity structure of the sediments and the upper crust of the off Ibaraki region with resolutions of ~ 0.1–1.0 km vertically and ~ 10 km horizontally. Our sedimentary structure model can be downloaded from https://doi.org/10.5281/zenodo.6999136. The lowest S-wave velocity in our calculations is 0.34 km/s, and consequently, our FDM calculations can precisely simulate seismic wave propagation for our CMT inversion. Such high-resolution 3-D structures possibly increase CMT resolutions (e.g., Hejrani & Tkalčić, 2020; Wang & Zhan 2020). We assumed P-wave velocity and density structures through the empirical scaling law using Eqs. (1) and (9) in Brocher (2005). Although this scaling law does not consider unconsolidated sediments, the predicted P-wave velocity from the very low S-wave velocity (0.34 km/s) is 1.57 km/s. This obtained P-wave velocity is consistent with those obtained by active-source surveys at the off Ibaraki region (e.g., Mochizuki et al. 2008) and by the Ocean Drilling Program at Japan Trench off northeast Japan (Shipboard Scientific Party 2000). We also assumed the anelastic attenuation Q values using the empirical scaling law by Eqs. (5) and (7) in Brocher (2008). Other technical details (e.g., seawater, air layer, and boundary conditions) are the same as shown in Maeda et al. (2017).

We applied the P-wave time windows for the CMT inversions as follows: for each source grid, we selected the P-wave arrivals of the synthetic seismograms when these absolute amplitudes first exceeded 5% of the maximum absolute amplitude. Then, we determined a 3-s time window starting 1.5 s before the P-wave arrival. We applied the same time window to the observed seismograms. The data saturated within 5 s from the beginning of the time window were excluded from the analysis. Because the lower frequency data (\(<\) 0.4 Hz) are less sensitive to the earthquake signal than the instrumental noise at the short-period OBS, we convolved the synthetic seismograms with the instrumental response function. We note that we did not remove the instrumental response with deconvolution, because the increased instrumental noises for lower frequency components were significantly enhanced, and consequently, earthquake signals were contaminated by these noises.

To constrain the grid-search range of the centroid location for CMT inversion, we determined an initial centroid location. The initial centroid location and time were roughly determined from the P-wave arrival times by a grid search. For this purpose, we automatically detected the arrival times of observed seismograms using the kurtosis gradient functions (e.g., Langet et al. 2014) applied to the waveform data filtered between 4.0 and 10.0 Hz (Additional file 1: Fig. S2). The redetermined hypocenters and origin times were consistent with those of Shinohara et al. (2011, 2012), but differed from those routinely determined by JMA, which relied solely on onshore stations.

We selected Green’s functions at the source grids located horizontally within a 0.24°\(\times\) 0.24° rectangle centered on the initial hypocenter and vertically within depths of 1–45 km. The grid search for centroid time was conducted at every 0.1 s within -1 to 1 s from the initial centroid time, which is the redetermined origin time. Note that we did not apply any station corrections, such as shifting the time window differently for each station as used in the previous studies of hypocenter relocations with the OBSs (e.g., Shinohara et al. (2011, 2012).

A moment tensor inversion was conducted for each spatial and temporal grid. In this study, we fixed the isotropic component of the moment tensor to be zero. Following Sipkin (1982), the seismogram of the \(k\)th station is written as

$$\begin{array}{c}{u}_{k}\left(t\right)=\sum_{n=1}^{5}{m}_{n}*{G}_{kn}\left(t\right), \end{array}$$
(1)

where \({m}_{n}\) is the \(n\)th component of the moment tensor, and \({G}_{kn}\left(t\right)\) is Green’s functions. We solved this equation using the least-squares method and then calculated the variance reduction (VR) between the observed and synthetic seismograms, which is written as

$$\begin{array}{c}VR = \left[1-\frac{{\sum }_{k=1}^{N}\int {\left({u}_{k}^{\mathrm{obs}}\left(t\right)-{u}_{k}^{\mathrm{syn}}\left(t\right)\right)}^{2}dt}{{\sum }_{k=1}^{N}{\int \left({u}_{k}^{\mathrm{obs}}\left(t\right)\right)}^{2}dt}\right]\times 100 \%, \end{array}$$
(2)

where \({u}_{k}^{\mathrm{obs}}\left(t\right)\) and \({u}_{k}^{\mathrm{syn}}\left(t\right)\) are the observed and synthetic seismograms, respectively, and \(N\) is the number of the used stations.

We discarded possibly occurring cycle-skipping solutions when the difference in arrival times between t he observed and synthetic seismograms was larger than 0.35 s. The arrival times of the observed seismograms were estimated following Langet et al. (2014) as noted above. As already mentioned, those for the synthetic seismograms were measured when these absolute amplitudes first obtained 5% of a maximum absolute amplitude. Then, we determined the best CMT solution with the highest \(\mathrm{VR}\) (\({\mathrm{VR}}_{\mathrm{best}}\)) from the remaining CMT solutions, which were obtained without cycle-skipping.

Finally, for the obtained CMT solutions, we estimated the uncertainties of the moment tensor solutions using a bootstrap method (e.g., Efron 1992; Zhan et al. 2012). We randomly selected stations that were used in CMT inversions, which allowed for overlapping and made 10000 sets of bootstrap samples. We performed the CMT inversion for each bootstrap samples, with a hypocenter fixed at the best CMT solution. We estimated the 68% confidence interval of the Kagan angle (Kagan 2007) from the distribution of these CMT solutions.

Results and discussion

We discarded CMT solutions whose \({\mathrm{VR}}_{\mathrm{best}}\) was less than 40% (Fig. 2a, c) and whose 68% confidence interval of the Kagan angle by bootstrap results was larger than 30° (Fig. 2b, d). We obtained 536 CMT solutions for \({2.5\le \mathrm{M}}_{\mathrm{w}}\le 4.5\) earthquakes. In addition, 87 of our CMT solutions achieved \({\mathrm{VR}}_{\mathrm{best}}\) larger than 80%, although we did not use any station corrections, such as shifting the time windows or changing the amplitude factors. We obtained relatively small values of \({\mathrm{VR}}_{\mathrm{best}}\) for earthquakes with smaller (\({\mathrm{M}}_{\mathrm{w}}\le 3.5\)) moment magnitudes because of the lower signal-to-noise ratio, even when the centroids were close to the OBS array. Successive occurrences of aftershocks within very short intervals following the 2011 Tohoku-oki earthquake could also cause noise in our single-event CMT inversion. The 68% confidence interval of the Kagan angle did not depend on the moment magnitude but on the spatial location. This Kagan angle tends to be large for earthquakes that occurred far from the OBS array because of the insufficient azimuthal coverage of the OBS stations.

Fig. 2
figure 2

a Moment magnitudes of the obtained CMT solutions against the VRs, and (b) the 68% confidence interval of Kagan angle by bootstrap results. c Spatial distribution of the VRs and d of the 68% confidence interval of Kagan angle

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We significantly increased the spatial resolution using high-frequency data. Figure 3 shows an example of the inversion results for an earthquake that occurred on 9:06, March 16, 2011 (JST). Our solution was consistent with the F-net MT solution. The spatial distribution of VRs shows that the centroid was well-constrained, with ~ 1 km for VRs exceeding 90% of \({\mathrm{VR}}_{\mathrm{best}}\) (e.g., Kubota et al. 2017). In low-frequency CMT analyses using a 3-D seismic velocity model (e.g., Figs. 3 and 4 in Takemura et al. 2020), higher VRs appeared within depth ranges larger than 10 km. The depths with higher VRs from our CMT method were also constrained for earthquakes of other focal mechanisms (Additional file 1: Figs. S3–6).

Fig. 3
figure 3

Result of the CMT inversions for the earthquake (\({\mathrm{M}}_{\mathrm{w}}4.0\)) that occurred at 9:06, March 16, 2011 (JST). a Centroid location of the earthquake and the OBS array. The red star shows the horizontal location of the best centroid with 14.5 km depth. The red focal mechanism shows the moment tensor of the best CMT solution. The black star indicates the horizontal location of the F-net MT solution with 11.0 km depth. The black focal mechanism shows the moment tensor of the F-net MT solution. The grey triangles show the stations of the OBS array. b Horizontal resolution of the CMT solution. The color of the focal mechanisms shows the VR. The region surrounded by the black line shows VR more than 90% from our best. c Depth resolution with longitudinal direction, and (d) with latitudinal direction

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Fig. 4
figure 4

Comparison of observed and synthetic seismograms for the earthquake (\({\mathrm{M}}_{\mathrm{w}}=4.0\)) that occurred at 9:06, March 16, 2011 (JST). The black and red lines show observed and synthetic seismograms, respectively. The station numbers are shown in Fig. 1b. The white-colored area shows the used time windows. Note that we did not use station #05, because the raw seismogram before applying the bandpass filter was saturated in 5 s from the beginning of the time window

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The synthetic seismograms of our best CMT solution well-reproduced the observed seismograms (Fig. 4), not only for the P-wave in our 3-s CMT time windows but also for subsequent waves. For this earthquake, we did not use station #05 because of the saturation immediately after the time window, as noted in Sect. 3, but the direct P-wave observed in station #05 was reproduced by our CMT solution. Since Eq. (2), which minimize the VR overall, was used, some stations have the small VRs for each station (Additional file 1: Fig. S7). Such stations have a small amplitude and, therefore, a small contribution in Eq. (2).

We also calculated the VRs with various dip, strike, and rake angles to examine the estimation errors of the focal mechanisms (e.g., Takemura et al. 2020). Synthetic seismograms were calculated assuming double-couple sources and fixing centroids and seismic moments. Figure 5 illustrates the experiment. Although there is a trade-off between the rake and strike angles for this thrust earthquake, the dip angle was constrained. Higher VRs for dip angle in dip-rake and dip-strike planes ranged from 8\(^\circ\) to 24\(^\circ\), where the VRs were larger than 90% of the maximum. The optimal dip angle is 16 \(^\circ\). For other types of mechanisms, similar characteristics of VR distributions were obtained (Additional file 1: Figs. S8–9).

Fig. 5
figure 5

Distribution of the VRs for the earthquake (\({\mathrm{M}}_{\mathrm{w}}=3.8\)) that occurred at 14:36, March 12, 2011 (JST), shown in the left top panel. Synthetic seismograms were calculated assuming double-couple sources, and fixing centroids and seismic moments. The strike, dip, and rake for the cross sections are the thrust fault of the obtained CMT solution

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The spatial distributions of the obtained CMT solutions are illustrated in Fig. 6. In the northeastern region, most of our CMT solutions of the earthquakes had thrust mechanisms (Figs. 6a–c, group A). Their mechanisms (dip and strike angles) and depths were consistent with the plate interface of the JIVSM, which suggests that these earthquakes can be considered as interplate earthquakes. We found several shallow (10–15 km) earthquakes of normal-fault mechanisms at approximately 141.8°E and 36.1°N (Fig. 6a, c, group B). These normal-fault earthquakes are located shallower than thrust earthquakes. Although F-net MT solutions did not have sufficient depth resolution to distinguish between groups A and B, our high resolution centroid revealed the evident separation between the source regions of these normal-fault (group B) and interplate earthquakes (group A). In the other region, fewer earthquakes of thrust mechanisms occurred at the plate interface. Instead, in the northern region, our CMT solutions had strike-slip mechanisms at 25–35 km depths (Fig. 6a, b, group C), which are deeper than the plate interface. In the southwestern region, the earthquakes were characterized by normal-fault mechanisms within a depth range of 25–35 km (Fig. 6a, d, group D), which are also deeper than the plate interface. The earthquakes in the southernmost region are characterized by various types of mechanisms (Fig. 6a, e, group E). The group-E earthquakes are widely distributed in the vertical direction, in contrast to most group-A earthquakes, which are considered as the interplate earthquakes.

Fig. 6
figure 6

a Spatial distribution of the obtained CMT solutions. The color of the focal mechanisms shows their depth. b–e Cross sections with the profiles of A–A’, B–B’, C–C’, and D–D’, respectively. The thin lines show the bathymetry, the upper surface and oceanic Moho of the Pacific Plate, and the upper surface of the Philippine Sea Plate (Koketsu et al. 2012)

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Comparison with previous focal-mechanism catalogs

We obtained 536 CMT solutions from \({2.5\le \mathrm{M}}_{\mathrm{w}}\le 4.5\) earthquakes, whereas 209 F-net MT solutions were available in our analyzed period. The small number of F-net MT solutions is because F-net routine system based on the analysis of low-frequency (\(\le\) 0.05 Hz) surface waves could not include \({\mathrm{M}}_{\mathrm{w}}\le 3.5\) earthquakes. In our CMT inversion, using high-frequency data enabled us to obtain CMT solutions for smaller earthquakes.

For the 54 earthquakes with larger moment magnitudes, the CMT solutions were obtained in both the F-net MT analysis and this study. Although the spatial resolutions of F-net MT solutions are not high owing to the use of low-frequency waves, their focal mechanisms are expected to be less sensitive to the heterogeneous structure. To examine the stability of our CMT solutions, we calculated the Kagan angle between the F-net MT and the corresponding CMT solutions. We also compared our CMT solutions with AQUA CMT and Asano et al. (2011). Because the numbers of AQUA and Asano’s solutions within our target period are only 5 and 11, respectively, we only focused on comparisons between our CMT and F-net MT solutions. Since F-net routine MT analysis provides lower depth resolution and is conducted on the fixed epicenter determined by JMA, we focused only on the differences in the focal mechanisms between F-net MT and our CMT solutions. The obtained Kagan angles were smaller than 30\(^\circ\) for most earthquakes, which suggests that our CMT solutions are consistent with F-net MT solutions (Fig. 7). However, large Kagan angles were obtained at approximately 142.1°E and 36.1°N. In addition to the insufficient azimuthal coverage, the focal depths of these earthquakes were presumably shallow, considering the subduction geometry. Thus, focal sphere coverage may be insufficient for accurate CMT estimation. In the following discussion, we discarded the CMT solutions obtained in this region.

Fig. 7
figure 7

Spatial distribution of Kagan angles. The colors of the moment tensors suggest the difference in Kagan angles between F-net MT and obtained CMT solutions. a Kagan angles with obtained and b with F-net MT solutions

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Our centroid distribution mostly agrees with the hypocenters of Shinohara et al. (2011, 2012) as shown in Additional file 1: Fig. S10a, c. The hypocenters were determined using the P- and S-wave arrival times. It is known that the only use of the P-wave arrival times yields a lower depth resolution. However, our depths were consistent, although we did not include S-waves. This might be the result of including information on the amplitudes and a well-constrained 3-D structure model (Yamaya et al. 2021). The number of CMT solutions is larger than that of first-motion focal mechanisms by Shinohara et al. (2012), who used more OBS stations. Our CMT solutions were more consistent with the subducting Pacific Plate than their first-motion solutions. Directly following the 2011 Tohoku-oki earthquake, it was more difficult to read the first-motion polarities because of the coda waves from successive aftershocks. The intense aftershock activity caused a low signal-to-noise ratio, which obstructed manual phase identification for reading the first-motion polarities. Misreading of the first-motion polarities cause large uncertainty in the focal mechanisms, especially for the strike-dip mechanisms (Hardebeck and Shearer 2002). Our CMT inversion that includes the amplitude information in addition to the first-motion polarities might provide better constraints to the focal mechanisms without reading the first-arrival polarities. Correlations or other parameters in various catalogs are shown in Additional file 1: Figure S10.

Tectonic interpretations

Owing to the high-frequency analysis and the dense OBS array, we increased the number of CMT solutions for the aftershocks in the off Ibaraki region. Their spatial resolutions were also improved compared with conventional low-frequency CMT analysis. Consequently, the densities and accuracies of the focal mechanisms increased in both space and time. In this section, we discuss the tectonic interpretations of the aftershocks following the 2011 Tohoku-oki earthquake.

Most of the aftershocks occurring in the northern region of the OBS array are characterized by thrust mechanisms (group A in Fig. 6). To discuss the lateral distribution of the interplate earthquakes, we selected earthquakes with the thrust mechanisms whose Kagan angles with a typical interplate earthquake (strike \(=195^\circ\), dip \(=13^\circ\), rake \(=90^\circ\)) are less than 30 \(^\circ\). The selected earthquakes can be interpreted as interplate earthquakes (Fig. 8a). Their distributions were consistent with the region, where the active seismicity at the plate interface was obtained (Nakatani et al. 2015). These thrust earthquakes occurred in locations separated from the large slip area of the 2011 Ibaraki-oki earthquake (e.g., Kubo et al. 2013). The low seismicity of the thrust earthquakes at the large slip area of the 2011 Ibaraki-oki earthquake suggests that this earthquake released sufficient accumulated strain at the plate interface and consequently prohibited thrust earthquakes within the large slip area. These thrust earthquakes were also observed in locations separated from the tectonic tremors, which were estimated to occur at the up-dip side of the subducting seamount (e.g., Nishikawa et al. 2019; Kubo and Nishikawa 2020). Tectonic tremors are slow earthquakes that are observed in the high-frequency (2–8 Hz) range (summarized in Obara & Kato 2016). These separations of interplate regular and slow earthquakes have also been reported in various subduction zones (e.g., Dixon et al. 2014; Takemura et al. 2020; Plata-Martínez et al. 2021). Slow earthquakes tend to be concentrated in the regions with weak locking strengths (e.g., Takemura et al. 2019). Our results agree that the tremor region can be considered as a weak locked zone, and consequently, accumulated stress may be insufficient to activate thrust-type regular earthquakes.

Fig. 8
figure 8

a Spatial distribution of the thrust mechanisms. The black squares show the tectonic tremors detected by Nishikawa et al. (2019). The slip area of the 2011 Ibaraki-oki earthquake (Kubo et al. 2013) is also shown. The cyan circle shows the subducting seamount (Mochizuki et al. 2008). The green line shows the northeastern limit of the Philippine Sea Plate (Uchida et al. 2010). b Spatial distribution of the non-thrust mechanisms. The color of the focal mechanisms shows their type: red mechanisms are normal faults, blue mechanisms are reverse faults, and green mechanisms are strike-slip faults. c Cross section of the E–E’ line, in which the point E is at 140.9\(^\circ\) E and 34.9\(^\circ\) N

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We colored the mechanism types not classified as the interplate earthquakes according to Frohlich (1992), as shown in Fig. 8b. The strike-slip mechanisms (group C) were obtained in the northern region, which is the northern part of the fault area of the 2011 Ibaraki-oki earthquake (\({\mathrm{M}}_{\mathrm{W}}\) 6.8). From the east to the west region of this group, the northwest–southeast orientation of the maximum compressional axes rotates to the northeast–southwest. The systematically rotated principal axes seem to reflect the static stress change caused by the 2011 Ibaraki-oki earthquake. Previous studies have suggested that large earthquakes can rotate the orientation of the principal stress axes around their fault areas (e.g., Asano et al. 2011; Hasegawa et al. 2011; 2012; Yoshida et al. 2014). Recently, the spatio-temporal changes in the principal stress axes of focal mechanisms have revealed the initial differential stresses, which inform the fault strengths or the coupling strength at plate boundaries (e.g., Hardebeck and Okada 2018). Further investigation may provide us with insights into the original stress state before the 2011 Ibaraki-oki earthquake.

We obtained normal-fault earthquakes at depths greater than 20 km in the western region (group D in Fig. 8b, c). These centroid depths are deeper than the plate interface. We note that the F-net MT solutions also listed such normal-fault earthquakes with \({\mathrm{M}}_{\mathrm{w}}\ge 3.5\) following the 2011 Tohoku-oki earthquake. We propose a possible effect of subduction of the Philippine Sea Plate on these normal-fault earthquakes. In this region, the northeastern edge of the Philippine Sea Plate has been estimated (e.g., Uchida et al. 2010; Nakahigashi et al. 2012). For other subduction zones, normal-fault earthquakes have been reported in the incoming oceanic plate prior to subduction. This is possibly due to the tensional stress field caused by plate bending of the subducting plate (e.g., Ranero et al. 2005). Especially in the Tohoku region, studies revealed that the overriding North American Plate might cause plate bending of the Pacific Plate beneath (e.g., Gamage et al. 2009; Obana et al. 2012, 2021). Similarly, the overriding Philippine Sea Plate might also cause plate bending of the Pacific Plate beneath, and consequently normal-fault earthquakes occur within the subducting Pacific Plate.

The most southern region, where the subducting seamount is imaged (e.g., Mochizuki et al. 2008), has various focal mechanisms (group E in Fig. 8b). Bootstrap analysis supported that the stable estimation of various focal mechanisms (Fig. 2d). Previous studies have also determined various types of focal mechanisms in the regions surrounding the subducting seamount (e.g., Bilek and Engdahl 2007). These observations suggest that a subducting seamount generates 3-D complex fractures in the overriding and subducting plates (e.g., Wang and Bilek 2011, 2014; Contreras-Reyes et al. 2015; Chesley et al. 2021). The existence of complex fractures is consistent with the complex topography of the upper crust of the overriding plate (Yamaya et al. 2021).

Our study found shallow (10–15 km) earthquakes of normal-fault mechanisms, which may also highlight the effect of the subducting seamount (group B in Fig. 8b). These earthquakes are tightly clustered, and the thrust fault earthquakes (group A) occurred at several kilometers below this cluster (Fig. 6c). The fault mechanisms of groups A and B were mostly reversed. It is known that such reversal fault slips (thrust and normal-fault earthquakes) with short separation distances rarely occur, but the first-arrival polarities also support this occurrence (Fig. 9).

Fig. 9
figure 9

Reversal fault pairs. a Black and red stars show locations of the thrust and normal-fault mechanisms for the earthquakes that occurred on April 12 and 30, 2011 (JST), respectively. The depths were 15 km and 12 km, respectively. b Raw seismogram comparison between the earthquakes. Black lines show the raw seismograms for the thrust mechanism, and red lines show the reversal amplitudes of those for the normal-fault mechanism

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We propose the effect of the subducting seamount on the generation of these normal-fault earthquakes. Recent numerical studies simulating mechanical coupling and hydrological processes have suggested that a simple shape of a subducting seamount can create a tensional stress field in the overriding plate (e.g., Sun et al. 2020). The compression of the overriding plate by a subducting seamount can increase the normal stress. In more detail, the observed normal-fault earthquakes are localized compared to the lateral size of the subducting seamount. A chain of seamounts existing on the incoming Pacific Plate seaward of the trench have a more complex shape than that assumed in the simulation by Sun et al. (2020). A more detailed shape of the seamounts may need to be considered to explain the localized normal-fault earthquakes.

Influence of array configuration on CMT inversion

In this study, we used a dense OBS array with a station interval of approximately 6 km. This station interval is smaller than that of a typical OBS array of 10–20 km. To examine the effect of array density, we conducted CMT inversion by changing the array density. The obtained CMT solution from the sparse array (12 km interval) agrees with that obtained using the dense OBS array (Fig. 10a). However, the CMT results exhibited high VRs over wider areas compared to those of the original dense array (Figs. 10b–d). This wider spatial distribution of the high VRs suggests that the CMT solutions determined by the sparser array reduce the spatial resolution to 5 km, which is five times longer than that of the original dense array. In this resolution, we could not discuss the depth distribution between the earthquakes of groups A and B.

Fig. 10
figure 10

Result of the CMT inversions for the earthquake that occurred at 9:06, March 16, 2011 (JST), using sparse OBS stations. Notations are the same as Fig. 3

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Despite the low spatial resolution, the CMT analysis with the sparser array can provide accurate focal mechanisms, using P-wave arrival times to reject the cycle-skipping solutions. This examination suggests that CMT solutions can be obtained with short-period OBS arrays with typical station intervals. The analysis of OBS data to obtain focal mechanisms has conventionally been only using the first-arrival polarities, but CMT inversion can take the place of the first-arrival analysis. Recent developments in detailed seismic velocity structure models, numerical simulation codes of seismic wave propagation, and computational resources have enabled us to conduct CMT inversions without reading first-arrival polarities. Our CMT inversion can be conducted without precise first-arrival pickings. Using our CMT inversion, the systematic monitoring of offshore small-to-moderate earthquakes can be accomplished.

As OBS networks of both temporary and permanent placement have been developed along subduction zones (e.g., Cascadia Initiative: Toomey et al. 2014; DONET, S-net: Aoi et al. 2020), CMT analysis of the OBS networks will reveal more detailed stress fields beneath the ocean in the future. In this study, we only used P-waves, because S-waves are mostly saturated owing to the insufficient dynamic range of the OBSs. These saturated data compelled us to exclude S-waves from the analysis, but in general, incorporating S-waves will allow us to better constrain CMT solutions. Improving wider dynamic ranges of the OBSs or including other types of the seismometers, such as seismic accelerometers, will provide us to use both P- and S-waves in waveform analysis.

Conclusions

We determined CMT solutions of the aftershocks of the 2011 Tohoku-oki earthquake using the dense array of short-period OBSs in the off Ibaraki region. Our method based on Green’s functions in the 3-D seismic velocity structure model can obtain CMT solutions for offshore earthquakes with \({\mathrm{M}}_{\mathrm{w}}\) of 2.5–4.5. Our CMT solutions included smaller magnitude earthquakes than those obtained by the conventional low-frequency CMT method. Consequently, we obtained 536 CMT solutions, which were larger than those in the catalogs of previous publications. Our CMT solutions reflect the complex stress field in the off Ibaraki region.

The obtained CMT solutions are as follows: (1) thrust-type interplate earthquakes in locations separated with the fault area of the 2011 Ibaraki-oki earthquake and the tectonic tremors; (2) intraslab strike-slip earthquakes located north of the fault area of the 2011 Ibaraki-oki earthquake; (3) intraslab normal-fault earthquakes, which suggest a tensional stress field at the subducting Pacific Plate due to the plate bending by the overriding Philippine Sea Plate; (4) earthquakes with various focal mechanisms above the subducting seamount, which suggest 3-D complex fractures caused by the subducting seamount; and (5) shallow normal-fault earthquakes possibly caused by the subducting seamount. Our CMT inversion using short-period OBSs can be applied to other offshore regions, which has sufficient potential to reveal the detailed stress fields in offshore regions.