Observation of Shallow Slow Earthquakes by Distributed Acoustic Sensing Using Offshore Fiber‐Optic Cable in the Nankai Trough, Southwest Japan

Off Cape Muroto area, along the Nankai Trough in southwest Japan, is a typical area with adjacent occurrences of slow and megathrust earthquakes. High‐resolution monitoring of slow earthquakes is necessary to understand tectonic conditions. In the off Muroto area, distributed acoustic sensing (DAS) measurement, which provides high‐density strain data, has been conducted using offshore fiber‐optic cable. We observed shallow tremors, a type of slow earthquakes, using DAS measurement for the first time. The characteristics of the tremor signals recorded by DAS were longer durations than those recorded in seismographs and composed of several phases with apparent velocities of several hundreds of m/s to several km/s that are coherent only in tens of meters. By combining DAS and seismograph data, we located these tremors around a subducted seamount peak. Therefore, spatial relationship between slow earthquakes and structural characteristics is suggested. This is a pioneering study of slow earthquake observation using DAS.

have been detected in the updip of the coseismic slip area (e.g., Nakano et al., 2018;Takemura et al., 2019;Tamaribuchi et al., 2022;Yokota & Ishikawa, 2020) by both onshore and offshore data (e.g., Dense Ocean floor Network system for Earthquakes and Tsunamis 2 (DONET2); Aoi et al., 2020;Kaneda et al., 2015;National Research Institute for Earth Science and Disaster Resilience, 2019). Thus, this area is a typical example of adjacent occurrences of slow and megathrust earthquakes. In addition, a seamount is subducted in this area (e.g., Kodaira et al., 2000); therefore, the geometry of the plate boundary is characteristic. However, the detection and locations of shallow slow earthquakes by previous studies in this area are limited and scattered ( Figure 1) because of the difficulty of offshore observation due to the long distances from the onshore network, noisy offshore data, and the limited spatial distributions of the offshore data. Therefore, shallow slow earthquake activity has not been understood with a high resolution compared to deep slow earthquake activity, which occurs in the downdip area. In addition, characteristics of tremor signals have not been discussed well by the dense observation. To investigate the distribution of shallow slow earthquake activity and detailed characteristics of their waveforms, observations with offshore data are required.
Recently, distributed acoustic sensing (DAS) measurement has been widely used for the observations of regular earthquakes (e.g., Lindsey et al., 2017;Shinohara et al., 2022;Zhan, 2019), infragravity waves (Williams et al., 2019), hydroacoustic signals , and the extraction of P-waves from ambient noise (Tonegawa et al., 2022). DAS measurements use an optic fiber cable as a strain or strain rate sensor array. The strain or strain rate data can be obtained at many locations along the fiber-optic cable with intervals of meter scale and at a high sampling rate (500-1,000 samples per second). Therefore, DAS measurements enable high-density spatiotemporal observations. Although DAS measurement is commonly used to observe regular earthquakes, there are few studies of slow earthquake observations with the DAS measurement. Currently, the Japan Agency for Marine-Earth Science and Technology conducts real-time DAS observations off Cape Muroto, using an offshore fiber-optic cable along the dip direction. As the fiber-optic cable exists near the shallow slow earthquake area, the spatial distribution of slow earthquake activity can be investigated with high-density DAS data.
To clarify detailed characteristics of waveforms and the distribution of shallow slow earthquakes off Cape Muroto, we used DAS measurement to observe shallow tremors. As this is the first study of tremor observation using DAS, we have discussed the characteristics of strain waveforms recorded by DAS and compared the  Tamaribuchi et al. (2022). Yellow dots are epicenters of shallow very low frequency earthquakes detected by Nakano et al. (2018) and Yamamoto et al. (2022). The purple rectangle represents an estimated slow slip event fault plane in 2017-2018 (Yokota & Ishikawa, 2020). Dashed black lines and solid green lines represent the sections of the Muroto cable that are not used and used for the distributed acoustic sensing measurements in this study, respectively. White and gray diamonds show the locations of DONET stations used and not used for this study, respectively. Letters A, B, F, and G represent the node names of DONET2. The brown ellipse shows the location of a subducted seamount (Kodaira et al., 2000). Red polygons indicate the anticipated megathrust source regions (Earthquake Research Committee, 2001). The white dashed line indicates the Nankai Trough. Background color scale denotes the bathymetry (ETOPO1; Amante & Eakins, 2009). waveforms of DAS and seismometers. We then investigated the hypocenters of shallow tremors by using the data from the DAS and DONET2 broadband seismometers. Finally, we have presented the advantages, challenges, and prospects of slow earthquake observations using DAS measurement. This study can be a pioneering study of slow earthquake observations using DAS.

Data
For the DAS observation, we used the Muroto cable with a total length of 128 km. Details of the Muroto cable are described in Ide et al. (2021) and Matsumoto et al. (2021). The DAS measurement is conducted by AP Sensing with a sensing length of 55 km along the cable from the coast. The gauge length, the sensor spacing, and the sampling rate of the original data are 40.8 m, 5.1 m, and 500 Hz, respectively. In the DAS measurement, the temporal change in strain rate converted from the differential phase at each channel is recorded. We prepared decimated data by stacking and averaging the waveforms of successive 10 channels to downsample to 51-m channel spacing and decimating to 100 Hz sampling. The temporal change in strain rate has been continuously recorded by the DAS measurement since 29 January 2022.

Characteristics of Tremor Signals Measured Using DAS
The plots of the DAS strain rate records at all channels of the decimated data in a frequency range of 2-10 Hz demonstrate a signal propagating from south to north during the period from January 30 to 8 February 2022 ( Figure 2a). During this time window, tremor signals were shown to simultaneously occur in the broadband seismograms of DONET2 in the same frequency range (Figures S1a-S1c in Supporting Information S1). Therefore, the signal in the DAS records shown in Figure 2a is considered a tremor signal. We found 29 tremor signals during the period by visually checking the plots of DAS records from January to March 2022 (Data Set S1).
We investigated the detailed characteristics of the tremor signals by plotting the temporal strain change, which was obtained by integrating the raw strain rate data ( Figure 2b). A tremor signal is composed of several phases with variable apparent velocities, each with a duration of several seconds. These phases were coherent within only tens of meters ( Figure S2 in Supporting Information S1). This characteristic may be caused by structural heterogeneity in the sediment with a scale of ∼10 m. The apparent phase velocity of these phases is evaluated to be the range between several hundreds of m/s and several km/s (Text S1 and Figure S3 in Supporting Information S1). The minimum value of the apparent phase velocity is 0.3 km/s. The amplitudes of tremor signals in the frequency range of 2-10 Hz observed in the original channels were ∼1 nstrain ( Figure 2b and Figure S1b in Supporting Information S1). Assuming a plane wave, the velocity waveforms can be calculated by multiplying the apparent phase velocity by the strain waveform (e.g., Daley et al., 2016;Shinohara et al., 2022;Wang et al., 2018). The apparent phase velocity is evaluated to be the range between several hundreds of m/s and several km/s; therefore, the velocity amplitude is estimated to be several hundreds to thousands m/s. The amplitudes of the broadband seismograms at the A-node and G-node stations of DONET2, which are the nearest stations to the DAS cable, are 500 and 4,000 nm/s, respectively (Figure S1c in Supporting Information S1). If the tremor shown in Figure 2 occurs in the area where shallow tremors and VLFEs were located in previous studies, the hypocentral distance of DAS cable is closer to A-node stations than G-node stations. The converted DAS amplitude of tremor signals with the phase velocity of hundreds of m/s is closer to velocity amplitudes in A-node stations than those with the phase velocity of several km/s. It suggests that tremor signals are dominantly composed of phases with velocity of hundreds of m/s.
As the tremor signals of DAS records are not coherent, we calculated the envelopes of strain waveforms from DAS records and velocity waveforms of broadband seismograms from DONET2 data to investigate the outline of tremor signals. After applying band-pass filtering with a frequency range of 2-8 Hz, we obtained envelope waveforms by squaring, low-pass filtering below 0.2 Hz, and resampling at one sample per second in a method similar to that of Ide (2010).
Generally, the duration of a tremor signal in DAS channels (40-60 s) is longer than that in horizontal components of DONET2 broadband seismometers with the similar hypocentral distances (30-50 s) (Figure 2c and Figure S4 in Supporting Information S1). The reason for long duration of tremor signals in DAS channels can be caused by large amplitudes of S-coda waves. A possible reason is the difference in angle sensitivities between the DAS and horizontal components of seismometers. If we consider an S-wave with an incident angle of θ along a cable on the x-axis, the displacement in the x-direction is sinθ times. Accordingly, the maximum amplitude occurs when the incident angle of an S-wave is 90°. On the other hand, the apparent velocity of this cable is 1/cosθ of the actual velocity; therefore, the weight of the strain of the S-wave is sinθ cosθ (=sin2θ). Accordingly, the maximum amplitude of the strain occurs when the incident angle is 45°. Therefore, DAS may measure scattered coda waves that are incident obliquely to the cable as large amplitudes. Another possible reason is the low phase velocity in the S-coda waves. If phase velocities of later S-coda waves of tremors are low, the velocity amplitudes of these phases in DONET are measured small. However, it cannot be denied that small-scale structural heterogeneities in the sediment affect the duration and shape of tremor signals in the envelopes of DAS channels apart from the nature of DAS measurement. To investigate the cause of differences in tremor signals between the DONET2 and DAS channels, observation of tremors in DAS and seismometers at the same position, simulation of strains in DAS channels, or detail investigation of phase velocity of tremor signals are required in the future works.

Method of Locating Tremors
We located 29 tremors observed by DAS measurement using DAS strain data and horizontal velocity waveforms of DONET2 broadband seismometers. As shown in Figure 2b, the tremor signals were not coherent; therefore, we used the envelopes obtained by the procedure described in Section 2.2 for the tremor location. We used the strain data of 55 DAS channels with intervals of 1 km and two horizontal components of broadband seismograph data of stations in the DONET2 A, B, F, and G nodes (Figure 1). First, we manually picked the rising of envelopes of tremor signals in the DAS channels and horizontal channels of the DONET2 stations (Figure 2c and Figure S4 in Supporting Information S1), considering that the rising of the envelope corresponds to the arrival of S-wave. In some channels, the arrival of the tremor signals in the envelopes is unclear. In such a case, we did not pick the arrival. We set grids with 0.01° intervals on the top of the Philippine Sea plate (Nakanishi et al., 2018) and located tremor events at grid points where the residual between the observed and synthetic travel times was the smallest by the grid search. The residual is calculated using the following equation: where obs and syn are the observed and synthetic travel times at ith channel, respectively, and N DAS and N DONET are the number of DAS and DONET2 channels where the arrival of the tremor signals can be picked, respectively. As the number of DAS channels is larger than that of the DONET2 channels, we introduced weight factor w i to the weight of the DAS and DONET2 channels to 1:1 in Equation 1. The weight factor w i is defined as = DONET DAS + DONET for DAS channels and = DAS DAS + DONET for DONET2 channels. The origin time was searched in the range from 30 s before to 5 s after the arrival times of the channels where the picked arrival time was first. Synthetic travel times were calculated based on a one-dimensional S-wave velocity structure model representing the area near the Nankai Trough (Nakano et al., 2013). To verify the effect of DAS data, we located the same tremor event using the same method with only DONET2 data (Data Set S2). In this case, the weight factor w i is 1 for all channels.
In this study, we did not use the envelope correlation method, which is frequently used for tremor locations. Due to the variation in tremor signal duration and shape, the correlation coefficients between channel pairs are generally small; therefore, the travel time differences obtained by envelope correlation are not often consistent with those obtained by arrival times.

Method of Locating VLFEs Correlated With Tremors
In the broadband seismometer data from G-node stations, VLFE signals were also found in a frequency range of 0.02-0.05 Hz at the same time as tremor signals observed by DAS ( Figure S1d in Supporting Information S1), although VLFE signals were not found in data from the A-node stations. For 25 of the 29 tremors observed by DAS, the VLFE signals were temporally correlated. We located these VLFEs and determined their centroid moment tensor (CMT) solutions using the DONET2 data and the same method of Yamamoto et al. (2022) (the SWIFT system; Nakano et al., 2018). The parameter setting, calculation of synthetic waveforms, and used one-dimensional velocity structure (Nakano et al., 2013) are the same as Yamamoto et al. (2022). The location and CMT solutions of these VLFEs are shown in Data Set S3.

Results
Most of the tremors were located northeast of the G-node of DONET2 around 134.7°E and 32.8°N (Figure 3a and Figure S5 in Supporting Information S1). Generally, the residual of tremor location is 2-3 s. According to the residual distribution ( Figure S6 in Supporting Information S1), the resolution of the epicenters was considered to be 0.1-0.2°. Based on the residual distribution of the analysis with only DONET2 data, the location has a large uncertainty in the east-west direction north of the G-node ( Figure S6b in Supporting Information S1). This uncertainty can be reduced by combining DAS and DONET2 data, because the DAS cable extends north of the G-node. The location estimated from DONET2 and DAS data tends to be slightly (∼0.05°) more distant from the G-node than the location estimated from only DONET2 data. It is possible that the seismic wave velocity may be slower at the DAS channels; therefore, the arrival of the tremor signals may be delayed. Although there are tremors which were located outside the Nankai Trough, the residual of these tremors is large (>5 s); therefore, the uncertainty of locations of these tremors can be large.
Many VLFEs which temporally correlated with tremors observed by DAS were also located northeast of the G-node (Figure 3a). Although the spatial distribution of tremors and VLFEs partly overlapped, some of the VLFEs that temporally correlated with tremors were located 0.1-0.2° closer to the G-node than tremors.
Although it is not clear whether VLFEs and tremors occur at the same hypocenter, tremors and VLFEs spatiotemporally correlated at a resolution of 0.1-0.2°. Most of VLFEs were located only by G-node stations; therefore, the distance between the epicenters of the VLFEs and the G-node may have a large uncertainty. Regarding the tremor locations, although there is an uncertainty of 2-5 s when manually picking, the difference between calculated and picked arrival time is generally smaller than 3 s ( Figure S4 in Supporting Information S1). Considering the S-wave velocity (∼3 km/s), this uncertainty corresponds to ∼10 km (∼0.1°). The discrepancy between tremor and VLFE locations may be due to this uncertainty. Given the uncertainty of the tremor locations, it can be certain that most of tremors occur in the northeast of the G-node.

Correlation Between Tremor Distribution and Structures
To discuss the tectonic environment of slow earthquake activity, we compared the cumulative number of tremors and VLFEs with the seismic reflection survey data of Line SIN144 (Nakamura et al., 2022; Figure 3). The number of tremors changes abruptly at 15 km along the profile SIN144. This profile is along the dip direction ( Figure 3a); therefore, the downdip limit of tremor activity can be identified. The range of large numbers of tremors and VLFEs were similar along the profile at a resolution of 5 km (Figure 3b).
Most of tremors occur near the peak of a seamount, and few tremors and VLFEs occur in the downdip of the peak (Figure 3b). The relationship between shallow slow earthquake activity and subducted seamounts or ridges has been discussed in previous studies (e.g., Takemura et al., 2022;Toh et al., 2020). Sun et al. (2020) suggested that the updip of the seamount peak is a stress shadow with low effective normal stress, whereas the downdip is a high effective normal stress area. In the off Cape Muroto area, tremors and VLFEs possibly occur in the stress shadow area of the updip area. On the other hand, accumulated stress can be released by high-speed ruptures of megathrust earthquakes in the downdip of the seamount peak. The spatial relationship between slow earthquakes and the seamount peak off Cape Muroto is consistent with Sun et al. (2020).

Advantages, Challenges, and Prospects of Slow Earthquake Observation by DAS
Seismic observation using DAS measurement is a recent technology. This is the first study to observe tremor signals using the DAS measurement; therefore, the advantages and disadvantages have not previously been discussed extensively. In this section, we discuss the advantages, challenges, and prospects of slow earthquake observations using DAS measurement.
A major advantage of DAS measurement is its spatially dense observation. In this study, the characteristics of tremor signals that consist of several phases with velocity in the orders of several hundreds of m/s to several km/s and are coherent only in tens of meters are first clarified by DAS observation. The observation of tremors by DAS may reveal the detailed propagation characteristics of tremor signals.
However, it is difficult to locate events using DAS measurement with one linear cable. Like this study, a combination of DAS and other seismic network data is required. This disadvantage can be mitigated when the cable shape has a bending point. DAS array analysis using multiple cables in various directions can also be effective.
By comparing the DAS and DONET2 data, we found that the signal-to-noise ratio of DAS data was not higher than that of DONET2 data; therefore, detection ability cannot be improved by using DAS data. Thus, there are no events that are observed only in DAS data. In this observation, the sensing length of the DAS measurement did not reach the slow earthquake area. In addition, we could not find VLFE signals in the frequency range of 0.01-0.1 Hz in the DAS data for the observation period. In future works, conducting DAS measurement just above the slow earthquake area with an improved noise level in the lower frequency band by a more stable laser could enable the detection of more tremors and VLFEs. This could further enhance the spatial resolution of slow earthquakes including their depths. By clarifying the tectonic environment and broadband characteristics of slow earthquakes in more detail using DAS observation, it is possible to approach the mechanisms of the occurrence of slow earthquakes.
As described in Section 2.2, the duration of tremor signals in DAS channels tended to be longer than those in the DONET2 data. In addition, the amplitude of the P-wave of regular earthquakes measured by DAS is relatively small owing to the high apparent velocity and near-vertical incident angle (Lior et al., 2021). Thus, the sensitivity of incident angles and high-amplitude phases can differ between DAS and seismometers. To apply the methods that have been used in seismology to the DAS data, it may be necessary to improve the methods that consider the properties of DAS measurement. The characteristics of DAS measurement should be investigated in future studies.

Conclusions
We observed shallow tremors by DAS measurement off Cape Muroto, southwest Japan, from January 30 to 8 February 2022. Although DAS measurement has recently been used for seismic observation, slow earthquake observations using DAS have been rare. The durations of tremors observed in the DAS channels were generally longer than those observed in DONET2 stations. In detail, tremor signals are composed of several phases with apparent velocities in the range of several hundred of m/s to several km/s, and these phases are coherent within only in tens of meters. We located these tremors by manually picking the rising of the envelopes of tremor signals at 2-8 Hz and searching for the point with the residual between synthetic and observed arrival times was the smallest. These tremors occur northeast of the G-node of DONET2 and are spatiotemporally correlated with VLFEs. Most of these tremors are at the peak of the subducted seamount along the dip direction; therefore, a spatial relationship between slow earthquakes and a seamount is suggested.
Overall, the dense observation of DAS measurement enabled us to reveal the detailed characteristics of tremor signals. In this observation, the number of events was small and VLFEs were not observed in the low frequency band. In future works, DAS measurement with a longer sensing length and lower noise level in the VLFE frequency band is required. As the longer duration of tremor signals in DAS channels may be caused by the sensitivity of the incident angle or lower velocity of S-coda phases, the cause of the difference between the waveforms of DAS and seismometers should also be investigated.