Low-Frequency Tremors Immediately After the 2011 Tohoku-Oki Earthquake Detected by Near-Trench OBS Observations

Hidenobu Takahashi (  hidenobu@dc.tohoku.ac.jp ) Tohoku Daigaku https://orcid.org/0000-0002-3938-4721 Ryota Hino Tohoku University: Tohoku Daigaku Naoki Uchida Tohoku University: Tohoku Daigaku Takanori Matsuzawa National Research Institute for Earth Science and Disaster Resilience Yusaku Ohta Tohoku University: Tohoku Daigaku Syuichi Suzuki Tohoku University: Tohoku Daigaku Masanao Shinohara Tokyo University


Introduction
Studies have detected various types of slow earthquakes all over the world, and their activity on subduction interfaces is expected to have a strong relationship with the generation processes of massive interplate earthquakes (e.g., Obara and Kato, 2016). Low-frequency tremors (LFTs) are a slow earthquake phenomenon characterized by unclear P-and S-wave arrivals with a dominant frequency of 2-8 Hz and smaller amplitudes than those of regular earthquakes with similar seismic moments. LFTs are usually active at the margins of seismogenic zones, both at the downdip (e.g., Obara, 2002;Frank et al., 2014) and updip (e.g., Obana  afterslip of the 2011 earthquake ~ 5 years after the occurrence of the mainshock, from October 2016 to September 2017, in the southern Japan Trench. It is expected that LFTs are occurring more frequently than VLFEs and thus the LFTs are suitable to detect the broadband phenomena. The activity of LFTs in the very early postseismic period after huge interplate earthquakes is of particular interest, as it may allow us to detect more slow earthquake episodes, investigate relationship between slow earthquakes and understand its temporal evolution in the vicinity of the Tohoku-Oki earthquake. However, so far, no detailed studies based on near-source observations have been made for the period. In this study, we inspected the seismograms obtained by the OBS observations made immediately after the 2011 Tohoku earthquake in the northern Japan Trench, ~ 250 km away from its hypocenter and at the northern rim of the early aftershock distribution. Within the observation period, several VLFEs were located near the OBS array by Matsuzawa et al. (2015), and it is expected that the OBSs detected LFTs associated with the VLFEs. Since the small repeating earthquakes (SREs) were also activated in the area at that time (Uchida and Matsuzawa, 2013), this provides a unique opportunity to investigate the relationship among the LFTs, VLFE, and SREs in the early postseismic period of the massive interplate earthquake in the periphery of its rupture area. The OBS seismograms around the origin times of the VLFEs show gradual increases in horizontal amplitudes with unclear P-and S-wave arrivals (Figs. 1b and S1). Note that the VLFEs (Mw 3.4-3.6) have peak amplitudes below 0.1 Hz, and they were identi ed based on the onshore broadband seismograms (Matsuzawa et al., 2015). The timings of the peak amplitudes of the OBS seismograms seem to be delayed as the epicentral distances from the VLFEs increase. The amplitudes decreased in the order of the epicentral distances. The order of the timing of the peak amplitude as well as the spatial decay of the amplitudes resemble those of SREs (Uchida and Matsuzawa, 2013), regular earthquakes on the plate boundary, close to the VLFE epicenters. As an example, the seismograms of an SRE (hereafter SRE-A; M3.9) whose epicenter is closest to VLFE #5 are shown in Fig. 1. Although SRE-A shows much larger amplitude and clearer P-and S-wave onsets than the seismograms at the VLFE timing, the orders of arrival times and of peak amplitudes at different OBSs are similar (Fig. 1). The amplitude variations among the OBSs are also similar for all the seismograms at the time of the other VLFEs ( Figure S2). This characteristic suggests that these recorded signals radiated from sources that are very close to the hypocenter of SRE-A.
Although the source locations of the seven events are expected to be close to SRE-A, seismograms of the newly observed events are signi cantly different in their frequency contents from that of SRE-A. Figure 1c shows the power spectral density (PSD) of the horizontal records of LFT #5 and that of SRE-A at the station AO.S05, which is nearest to the VLFE #5. The PSD of the events has different decay pattern in the frequency range 1-4 Hz from that of SRE-A. It is con rmed that the other six events associated with the VLFEs also present a similar shape of PSDs ( Figure S3).
As high-frequency signals are attenuated because of the path effect, de cits in the high-frequency component can also be identi ed in the seismograms of remote regular earthquakes. For example, the PSD below 6 Hz of the seismogram of an earthquake of ~ 160 km in the epicentral distance resembles the PSDs of the events identi ed at the VLFE timings ( Figure S3). However, the spatial variation of the observed amplitudes is clearly different from those of the events associated with the VLFEs (Figures S1 and S2). Therefore, we can distinguish local low-frequency events from remote earthquakes. As demonstrated by Toh et al. (2018), amplitude variations at different OBS stations are important for interpreting the locations of low-frequency events.
Based on these observations, the similarity in amplitude variation with a local SRE and the evident de cit of high-frequency energy, we interpret the events detected at the timing of the known VLFEs are seismic waves that radiated from LFTs whose sources are close to those of the VLFEs and the SRE. Hereafter, we call these events LFT #1 to LFT #7 according the number of associating VLFEs.

Searching for additional LFTs
In the previous section, we showed that short-period OBSs deployed near the known VLFE epicenters recorded LFTs associated with the VLFEs. Here, we try to explore undetected LFTs that is not associated with the VLFEs, because it is expected that the frequency of LFTs is more than that of VLFEs (e.g., Ghosh  Figure S2) and of the PSDs ( Figure S3) among the LFTs #1-7, we searched for seismograms having these characteristics. To this end, we quanti ed these two characteristics. We introduce a quantity termed "Amplitude Index" (AI, Text S1 for detailed explanation) to measure the similarity of the peak amplitude pattern of sampled seismograms with those of LFTs #1-7. AI measures discrepancy between the peak amplitude distribution of samples and the average distribution for the seven LFTs. Sample seismograms were taken from continuous seismograms using a sliding time-window of 30 s with a time interval of 15 s, after applying a band-pass (2-4 Hz) lter, because the signals of LFTs are most pronounced in this frequency band. As a measure of similarity of PSDs, we calculated residual sum of squares (RSS_spectra, Text S1) between a PSD of a sample waveform and the PSD of LFT #5, which was observed with the highest signal-to-noise ratio (S/N). Sample PSDs were calculated from the seismograms extracted using sliding time-windows identical to the AI calculation. RSS_spectra were calculated in a frequency band of 1-4 Hz. Both AI and RSS_spectra take smaller values when a sampled seismogram resembles more to those of the LFTs. Figure 2 shows the two-hour spectrograms including for LFT #5 with temporal variations of AI and RSS_spectra. It is con rmed that both AI and RSS_spectra have the smallest values at the time of LFT #5. For the seismograms obtained in the six days when the seven LFTs associated with the VLFEs were detected, both the AI and RSS_spectra are obviously small in the seven windows, including that of LFTs #1-7, compared with the rest of the seismograms as expected (Fig. 3). It must be noted that the RSS_spectra of LFT #1 is relatively large possibly due to the smallest signal levels ( Figure S1 and S3).
LFT #6, which is more depleted in the low (~ 1 Hz) frequency components than the others ( Figure S3) and is slightly deviated from the others in terms of peak amplitude distribution ( Figure S2), has larger AI and RSS_spectra. In this study, we excluded these two events to de ne the thresholds of RSS_spectra and AI for making LFT detection more conservative. As a result, we set the thresholds as 0.675 and 0.17 for AI and RSS_spectra, respectively based on the AI and RSS_spectra for LFT#2-5 and #7 (Fig. 3).
Although it is expected that AI of SRE-A would be as small as those of LFTs, judging from closeness of the epicenters of SRE-A to that of VLFE #5, its AI is no smaller than the criteria (Fig. 3). Instead, we detected another SRE (SRE-B; M2.7) showing AI smaller than the threshold of LFT detection. Appearance of its seismograms and characteristics of PSDs is similar to those of SRE-A (Figs. 1, S1, S2 and S3), indicating that SRE-B is a regular earthquake located very close to the sources of the LFTs. As to the seismogram of a remote earthquake, RSS_spectra is smaller, but AI is larger than the thresholds (Fig. 3).
Therefore, we can distinguish LFTs from local regular earthquakes and remote earthquakes by using these two quantities. During the six days, there is a seismogram satisfying the criteria of the LFT detection as indicated by a triangle in Fig. 3. The corresponding record appears in Fig. 2 as an event at ~ 10 min before LFT #5. The newly detected event is similar to that of LFT #5 in the seismograms and it can be regarded as an LFT. There are a few events satisfying the LFT-detection threshold of RSS_spectra but not AI (e.g., events at 87 min and 100 min in Fig. 2). Slightly larger AI but acceptably small RSS_spectra of these events indicate that these events are LFTs having different source locations from the group of LFTs that we have identi ed here.

Newly detected LFTs
By inspecting continuous OBS waveforms based on two parameters, AI and RSS_spectra, we identi ed 131 LFTs ( Figure S4), which are other than the events associated with the known VLFEs. The newly identi ed LFTs have similar AI and RSS_spectra ( Figure S4) and waveform characteristics ( Figure S5) with the known LTFs. For most of the events, the windows ful lling the criteria are isolated, but sometimes, two successive windows satisfy the thresholds. However, both AI and RSS_spectra were not small enough in three or more successive windows. This suggests that the duration of LFTs detected here are not signi cantly larger than 60 s, that is, twice the window length. This result is consistent with the average duration of the LFTs in the northern Japan Trench (44 s) reported by Nishikawa et al. (2019).
As we de ne RSS_spectra such that the similarity of the absolute PSDs to that of LFT #5 is evaluated, the detected events should have a similar size to that of LFT #5 as clearly recorded by the OBSs. With the present threshold using the RSS_spectra de ned here, the LFT events of different event magnitudes would be missed, if they exist. Here we discuss a possibility of missing events by the proposed method applied to our OBS records. The smaller events are di cult to identify using the other criteria, AI, as they require large S/N among all the ve OBS stations. Therefore, we examined the PSDs of all the events larger than LFT #5 to detect the possible large LFT events. Here, we measure magnitudes of the events by averaging the power in the 2-4 Hz frequency range. Among the events having acceptably small AI, there are only few that are larger than LFT #5, which is regarded as a template of our LFT search ( Figure S6). Most of them, including SRE-B, have steeper slopes of PSD than LFT #5 indicating that these are regular earthquakes rich in high-frequency content. Nevertheless, we detected a small number of large events with a small PSD slope, relatively rich in low-frequency content. Waveforms of these events resemble those of LFT #5, except for one (d in Figure S6) corresponding to a P-coda part of a remote M 3.8 regular earthquake. These low-frequency events may be LFTs slightly larger than that of LFT #5. Based on the inspection, we regard that LFT #5 is the largest LFT in the area, and missing LFTs larger than that of LFT #5 does not have a signi cant impact on the discussion on the identi ed LFTs during our OBS observations.

Discussion
Since our method of searching for LFTs relies on the similarities of the spatial pattern of the observed seismograms, it is expected that the sources of all the detected LFTs must be concentrated within a small area including those accompanied by the seven VLFEs that are used as references. Notably, the signal amplitude distribution of the SRE-B resembles those of the LFTs (Figure S2), and thus, ensures that the AI of SRE-B is as small as the AIs of the LFTs (Fig. 3). Since the similarity of the amplitude variations requires the closeness of the hypocenters as well as of the focal mechanisms, our observation suggests that the detected LFTs are the thrust faulting events in the vicinity of the SRE-B, a regular interplate earthquakes.
We relocated the SREs around SRE-B by P-wave arrivals at ve OBS stations to con rm how their epicenter locations and AI values are correlated. As a result, the AIs of the SREs other than SRE-B were signi cantly larger than that of the threshold for the LFT detection ( Figure S7), except one SRE (SRE-B'), which belongs to the sequence of SRE-B, considered as re-rupture of the identical source area for SRE-B. Based on the relocated epicenters, the SREs with AIs larger than the LFT detection threshold are distant from SRE-B by more than ~ 5 km. This suggests that we can differ among epicenter locations using AI with resolution of ~ 5 km and that newly detected LFTs occurred within ~ 5 km from regular interplate earthquakes (SRE-B and SRE-B'). Our result con rms the close collocation of LFTs and the regular occurrence of earthquakes along the Japan Trench subduction zone. In contrast, such coexistence of LFTs and regular earthquakes is rarely observed in the Nankai subduction zone (e.g., Obara Fig. 1a. Interestingly, the recent LFT activity also showed evident temporal uctuation with a periodicity of approximately 60-100 days (Fig. 4), which is similar to that of the LFTs in 2011. To examine the signi cance of the periodicity, we calculated the Schuster p-value (Ader and Avouac, 2013), the probability that a given periodicity is observed from a sequence without periodicity by chance ( Figure  S8). We observed statistically signi cant periodicities in the LFTs cataloged by Nishikawa et al. (2019) ( Figure S8). From the statistical signi cance, the possible range of the period is 60-100 days. The LFTs in 2011 also exhibit a decrease in p-value in the similar period range, but the value is not su ciently small. This is possibly because of the short data period, 193 days, which is much shorter than that of Nihiskawa's catalog (720 days). However, we suggest that LFT-activity preserves a similar pattern in temporal uctuation from just after the Tohoku-Oki earthquake until 2016-2018. The temporal invariance in the uctuation period probably show that it is controlled not by the rate of the postseimic slip that decay in the ~ 7 years but by structure near the plate interface. A possible reason for the temporal variations of the LFT-activity is the acceleration and deceleration of the interplate slow slip associated with similar slow slip events such as in Cascadia (Dragert et al., 2004, Rogers et al., 2003 and southwestern Japan (Obara and Ito, 2005). Since the activities of the SREs are considered good indicators of the in situ fault slip rate (e.g., Uchida and Matsuzawa, 2013), we compared them (Fig. 4). During either period, immediately after and more than ve years after the Tohoku-Oki earthquake, the SREs and VLFEs tend to occur during the periods of increased LFT activities; however, high LFT activities do not necessarily accompany SREs and VLFEs. The activities of the identi ed SREs and VLFEs, which are less frequent than those of the LFTs, may be less sensitive to the small-sized slow slip events than those of the LFTs. LFTs can be better indicators to monitor the change in rate of the aseismic slip on the plate interface owing to their higher activity than those of SREs and VLFEs.

Conclusions
We detected several LFTs immediately after the 2011 Tohoku-Oki earthquake in the northern periphery of its aftershock area by temporal OBS observations. Some of the discovered LFTs occurred simultaneously with the VLFEs detected by onshore broadband seismic observations; however, the LFT activity occurred almost continuously throughout the ~ 6 months study period with temporal variation in the strength of the activity. The duration of the identi ed LFTs is estimated to be less than 60 s, which is consistent with the reported duration for the recent LFTs in the area. These LFTs are considered to occur in the vicinity of a sequence of small repeating earthquakes, which are regular interplate earthquakes. The pattern of the temporal uctuation of the LFT activity in 2011 resembles that of LFTs during 2016-2018, suggesting that frequent small-scaled slow slip events have repeatedly occurred in intervals of 60-100 days since 2011. These similarities indicate that event duration and temporal variation of the activities have been stable through the postseismic period suggesting structural control of the activity interval. Not all the LFT activities were accompanied by SRE and/or VLFE activities, suggesting that the activities of the LFTs may be more sensitive to small aseismic slip events. Near-eld OBS observations by cabled systems as well as pop-up type instruments above the megathrust zone are important to clarify the nature of slow deformation in a shallow subduction zone.

Availability of data and materials
The OBS data used in this article are available online (Now we prepared them in Zenodo).
27. Yamashita, Y., Yakiwara, H., Asano, Y., Shimizu, H., Uchida, K., Hirano, S., Umakoshi, K., Miyamachi, H., Nakamoto, M., Fukui, M., Kamizono, M., Kanehara, H., Yamada, T., Shinohara, M., Obara    Results of waveform classi cation using AI and RSS_spectra for the six days, when the reported VLFEs occurred. Hexagons are LFT #1-7, a diamond is SRE, and a square is the remote earthquake. Symbol colors show the maximum amplitude at station AO.S05 at the corresponding time window. Thresholds of RSS_spectra and AI are shown by vertical and horizontal lines, respectively. AI and RSS_spectra calculated for SRE-A and a remote earthquake are also shown, although these earthquakes happened on different days. RSS_spectra of LFT #5 is not exactly zero in the gure, because the time window including LFT #5 in the event searching is slightly different from that for the reference PSD calculation.