The OBX-750 recorded angles of roll and pitch of the housing and heading (azimuth) at an interval of 1 min during a seismic recording. It was found that the recorders were positioned stably on the seafloor during the observation (Fig. 3). For the OBXA, the heading had a large change after the deployment. At this large change of heading for the OBXA, the pitch and roll varied, and there is a possibility that the buoy on the sea surface had pulled the recorder slightly. A strong wind with a maximum speed of 10 m/s was observed on the coast during the large change of heading for the OBXA. When a small change of attitude occurred before the recovery of the OBXC, a strong wind was also recorded. The temperature of the recorders was registered at every 1 min for the entire recording period (Fig. 3). This temperature decreased rapidly after the deployment, to reach approximately 17 °C, and although it was generally stable, there was a small variation that is thought to correspond with a change in sea water temperature.

Fig. 3
figure3

Temporal variation of attitudes and temperature of the recording packages. Upper: roll, pitch and heading angles are plotted with time for two recording units. OBXA (the southern station) and OBXC are estimated for installation on the seafloor covered with sand and rocks, respectively. Angles are generally stable during the observation, although the attitude of OBXA largely changed on June 5, 2019. It is possible that the recording package was pulled. Lower: temporal changes of temperature for both units are also small, except for June 6th for OBXC. A small variation in temperature of the unit lowers the error of the timing, which is based on a crystal oscillator in the unit

We can convert the three-component orthogonal seismic data from the OBX-750 to three-component data for up–down, north–south, and east–west directions using information from the attitude of the recorder. Because the attitude was measured at an interval of 1 min, we divided the seismic data into 1-min batches and applied the conversion (Fig. 4). The conversion of the seismic data was useful for identifying the arrival of the P- and S-waves. After the conversion of the seismic data, we estimated the ambient seismic noise spectra of the records obtained on the shallow seafloor.

Fig. 4
figure4

Example of seismograms from the anchored-buoy OBSs and temporal land seismic stations for an earthquake. Three-component records are shown. The records of the OBSs have been converted from original records using information from tiltmeters and the azimuth meter. No filter has been applied. The estimated coordinates of the epicenter of the event are 38.66° N, 139.44° E. The depth and magnitude of the event are 9.9 km and 3.7, respectively. The station is labeled above the vertical component. Black bars on the north–south component indicate the scale of amplitude in velocity. Root-mean square averages of amplitude for the first 0.5 s are shown by numerals. Solid and open inverted triangles indicate P- and S-wave arrivals, respectively

A large ambient seismic noise was expected due to the shallow water depth. We evaluated the noise levels in the shallow water using the direction-corrected data obtained from the anchored-buoy OBS that we had developed. First the velocity records of the seismometers were differentiated to transform to acceleration. The power spectra of the corrected data were estimated with a time window of about 33 s at intervals of 1 min for all observation periods. We calculated their average using smoothing in the frequency domain. A total of 11,411 spectra were obtained, and we calculated the probability density functions (McNamara and Buland 2004; McNamara and Boaz 2006) of the power spectra (Fig. 5). The ambient seismic noise levels of the anchored-buoy OBSs were positioned between the Low Noise Model and the High Noise Model in the frequency range less than 10 Hz (Peterson 1993). Although there is no information for typical noise levels in the frequency range higher than 10 Hz, the ambient noise levels of both vertical and horizontal components are comparable to those obtained in the deep ocean. The noise levels of the anchored-buoy OBSs could be compared to those of the close land stations, and the noise levels were equivalent (Fig. 5). This means the detectability of the anchored-buoy type OBSs is comparable with those of land seismic stations. Because the seismometers in the OBX-750 are moving coil type with a natural frequency of 15 Hz, the noise levels decreased in the frequency range lower than 15 Hz. In addition, we estimated temporal noise level variation for vertical and horizontal components using the obtained spectra. All spectra at an interval of 1 min were plotted as a function of time (Additional file 1: Fig. S2). Although the noise levels sometimes became greater, the level was generally stable. There is a possibility that boats were operating near the stations when the noise in the records became greater. We could compare the noise levels of the anchored-buoy OBSs to maximum wind speed observed by a weather station installed close to our seismic network (AMeDAS, JMA) and maximum wave height observed by GPS buoy off Yamagata Prefecture (NOWPHAS) operated by Port Bureau, Ministry of Land, Infrastructure, Transport and Tourism (Additional file 1: Fig. S2). The noise levels around 10 Hz seem to correlate to the wind speed and the wave height. Consequently, we were able to confirm that observation using the developed anchored-buoy system for the shallow seafloor because the noise levels were low enough on the records for small earthquake observation throughout the observation period. Reflecting the low and stable noise level, many aftershocks were unexpectedly recorded by the anchored-buoy OBSs including microearthquakes with magnitudes of less than 1.0 (Additional file 1: Fig. S3).

Fig. 5
figure5

The probability density function of ambient seismic noise spectra from three-component records of the anchored-buoy OBSs. The original data from the OBSs have been converted to the records for up–down, north–south and east–west directions using information on the attitude of the packages. Data from 14:31 on July 5, 2019, to 12:14 on July 13, 2019, were used for the estimation. We estimated spectra every 1 min with a time window of 32.768 s, and probability was estimated using 11,411 spectra. Although the seismic sensors of the anchored-buoy OBS have a natural frequency of 15 Hz, the sensor response was not compensated for the estimation. The High Noise Model and Low Noise Model of Peterson (1993) are shown in frequencies lower than 10 Hz. Black, gray, and white lines indicate averages of seismic noise spectra for the same period from the records of the land stations, E.NZMY, E.KNSY, and E.YAMY, respectively. A 15-Hz high-pass filter was applied for data from the land stations to compare those from the anchored-buoy OBSs. The ambient noise levels of the anchored-buoy OBSs are sufficiently small to pick up arrivals and comparable to the land stations, in spite of shallow water depths. It is believed that the flat shape of the recorder is effective for reducing ambient noises

The time of the individual records by the anchored-buoy OBSs was adjusted using comparative information between GNSS timing and the clock in the recorder. After the time adjustment, all seismic data were combined into multi-station waveform data files with a duration of 1 min. Our network consisting of the anchored-buoy OBSs, permanent and temporary land stations had a total of 16 seismic stations (Additional file 1: Table S1). Then the arrival times of the P- and S-waves were read manually from the records of the anchored-buoy OBSs and land stations on a computer display (Urabe and Tsukada 1991), based on the event list determined by the JMA (Fig. 4). In addition, some small aftershocks that had not been listed in the JMA catalogue were also processed. We could pick up the arrival time and largest amplitude for a total of 181 aftershocks. For large events, we also read the polarities of the first arrivals to determine the focal mechanism of the events.

An exact velocity structure under the region is necessary for the location of the aftershock with spatial high-resolution. A seismic survey using OBS, multichannel hydrophone streamer, and airguns was performed in 2010 (Sato et al. 2014). The profile was laid from the coastal area to the Yamato Basin in the Japan Sea and intersected the source region of the 2019 mainshock. Because the active region of the aftershocks was relatively narrow, a one-dimensional velocity structure seemed to be enough for the hypocenter location. Since the source area is close to the coast of Japan’s main island, the existing seismic survey cannot determine the velocity structure with high resolution for that region (Sato et al. 2014). We estimated a simple, one-dimensional seismic wave velocity structure for the hypocenter location from the results of the marine seismic survey by extrapolation (Fig. 6). From the results of the seismic survey, the crust seemed to have a thickness of approximately 25 km and comprised a sedimentary layer, upper and lower crust. The sedimentary layer had a constant P-wave velocity of 2.0 km/s, the upper crust had P-wave velocities of 3.0–6.8 km/s and a thickness of 13.5 km, and the lower crust had P-wave velocities of 7.0–7.8 km/s. For the S-wave structure, we assumed a Vp/Vs ratio of 1.73 for all layers. A P-wave velocity in the uppermost mantle was assumed to be 8.0 km/s. We constructed a one-dimensional velocity structure whereby the velocity would increase continuously with depth for the preliminary location. Then we transferred the continuous velocity structure to the velocity structure, whereby each layer had constant velocities for another location program. The velocity and thickness of the uppermost layer should have varied beneath each seismic station. Therefore, a compensation of calculated travel time for the location was necessary for high resolution.

Fig. 6
figure6

P-wave velocity structure models for the hypocenter locations. The red and blue lines denote the P-wave velocity models for the preliminary location using absolute travel times and the DD method, respectively. The models are constructed by extrapolation from the existing refraction experiment carried out using the OBSs and airguns through the source region

We first located hypocenters of the aftershock using the location program with absolute travel times and the maximum-likelihood estimation technique (Hirata and Matsu’ura 1987). Thick sedimentary layers with low seismic velocity were estimated below the seismic stations and the anchored-buoy OBSs in particular. First, the hypocenter location was carried out using P- and S-wave arrival times with assumed values of station correction for the velocity structure. We calculated the average of differences between observed and estimated travel time using the velocity structure (O-C times) for each station from the results of the location, and the averages of O-C times were added to the previous station correction. Then the hypocenter location was performed again using the new values of the station correction. This procedure was repeated three times and we obtained appropriate values of each station correction (Additional file 1: Fig. S4). Next, we relocated the hypocenter using the double-difference (DD) method (Waldhauser and Ellsworth 2000) to obtain more precise positions for the aftershocks. Because the location program for the DD method accepts a velocity structure with constant velocity in layers, we used the velocity structure that was consistent with that of the first location using absolute travel times. We estimated the magnitude of the aftershocks by the maximum amplitudes of the seismic data obtained from the land stations (Watanabe 1971).

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