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 and Kodaira, 2009; Todd et al., 2018) sides. The simultaneous occurrences of LFTs and other slow earthquakes are often observed. For example, spatiotemporal coincidence of LFTs and very low frequency earthquakes (VLFEs; e.g., Yamashita et al., 2015) and another type of slow earthquake has been observed in the Hyuga-nada region (Yamashita et al., 2015) and the Nankai subduction zone (Kaneko et al., 2018; Toh et al., 2018). Such a relationship between different types of slow earthquake phenomena suggests that this series of different dominant frequencies is a united broadband phenomenon (Ide, 2008; Ide, 2019), and it is important to use as many types of slow earthquakes to detect the broadband phenomenon and their spatiotemporal associations.
Recently, slow earthquakes were detected along the Japan Trench subduction zone that hosted the 2011 Tohoku-Oki earthquake (Mw 9.1). Matsuzawa et al. (2015) identified VLFEs by inspecting onshore broadband seismograms since 2005 and showed that they are concentrated within several small areas based on correlation with manually identified template events. Baba et al. (2020) also used onshore broadband seismograms since 2003 and estimated the distribution of VLFEs by using the waveform correlation with synthetic interplate events. Tanaka et al. (2019) and Nishikawa et al. (2019) detected remarkable LFT activity near the Japan and Kuril trenches that are distributed along the plate-boundary depth of 10–20 km. These discoveries were made possible by the new cabled seafloor observation network for earthquakes and tsunamis along the Japan Trench (S-net) that cover east off NE Japan by 150 seismometers. Knowledge about the activities of LFTs prior to the deployment of the S-net in 2016 is, however, quite limited in time and space because near-source ocean bottom seismograms (OBSs) are required to detect weak signal radiation. Using temporal OBS observations, Ito et al. (2015) and Katakami et al. (2018) identified the LFT activity for ~ 1.5 months immediately before the 2011 Tohoku-Oki earthquake near its hypocenter. Ohta et al. (2019) reported the LFT activities coexisting with the shallow 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.
Observations
A total of five free-fall and pop-up type OBSs were deployed at the northern rim of the aftershock area of the 2011 Tohoku-Oki earthquake and observation was made from April 11 to October 25, 2011 (Fig. 1a) to monitor the temporal expansion of the aftershock area immediately after the occurrence of the mainshock. Three-component velocity seismograms from geophones with a natural frequency of 4.5 Hz geophones were recorded at 100 Hz sampling. During the observation, Matsuzawa et al. (2015) identified seven VLFEs located near the OBS array; we call them VLFE #1–7 in the order of their occurrences.
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 identified 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 significantly 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 confirmed 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, deficits in the high-frequency component can also be identified 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 identified 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 deficit 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 et al., 2015; Ohta et al., 2019; Nishikawa et al., 2019). Based on the similarities of the peak amplitude patterns (Figure S2) and of the PSDs (Figure S3) among the LFTs #1–7, we searched for seismograms having these characteristics. To this end, we quantified 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) filter, 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 confirmed 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 define 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 identified here.
Newly detected LFTs
By inspecting continuous OBS waveforms based on two parameters, AI and RSS_spectra, we identified 131 LFTs (Figure S4), which are other than the events associated with the known VLFEs. The newly identified 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 fulfilling 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 significantly 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 define 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 defined 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 difficult to identify using the other criteria, AI, as they require large S/N among all the five 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 significant impact on the discussion on the identified LFTs during our OBS observations.