Stability of daily coordinate time series
First, we assessed the stability of the estimated time series to evaluate the quality of SoftBank's GNSS data. Figure 2a–c shows the standard deviation (SD) between September 22 and 30, 2020, for the three components (east–west [EW], north–south [NS], and up–down [UD]) in Miyagi prefecture. To create the figure, we assumed September 21, 2020 (day of year, 265) as the reference day for all stations. There were no significant earthquake events during this period. The averaged SD of all SoftBank time series was 1.7, 1.6, and 5.3 mm for the EW, NS, and UD components, respectively. Similarly, the averaged SD of all GEONET time series was 1.6, 1.4, and 5.9 mm for the EW, NS, and UD components, respectively. The calculated SDs were approximately the same for each network.
Furthermore, box-and-whisker plots were developed for each observation network to compare the daily time series variability of all stations (Fig. 2d–i). Outliers were defined as data exceed 1.5 times the interquartile range (IQR) value. When we evaluated the day-to-day variability, the number of outliers was slightly higher for the SoftBank network. The number of outliers for the EW, NS, and UD components was 19, 8, and 17, respectively, for GEONET, and 22, 16, and 13 for SoftBank, respectively. The range of the upper and lower quartiles between the networks was similar. These results suggest that the stability of the time series of the SoftBank network data may be sufficient to monitor crustal deformation.
Figure 3 shows the displacement between the averages for September 21–30, 2020, and March 21–30, 2021. Note that the duration was approximately half a year. A significant trenchward displacement and clear uplift in the forearc region appeared in the horizontal and vertical components, respectively. These characteristics mainly reflect the viscoelastic relaxation of the 2011 Tohoku-Oki earthquake (e.g., Suito 2017). Almost all sites showed a consistent displacement with their surroundings. However, several sites showed anomalous displacements. To determine whether these data represent crustal deformation properly, they need to be examined more rigorously using extended time series.
Detectability of coseismic displacement
Figure 4 shows the horizontal coseismic displacement of the 2021 off-Fukushima earthquake. A westward coherent displacement appeared along the coastline. In contrast, several outliers at the SoftBank sites were also confirmed. For example, the BHC0 site, 50 km away from the coastline, showed a westward displacement of approximately 20 mm, although the surrounding sites showed almost zero displacement (Fig. 4).
Figure 5 shows the displacement time series of BH7H and BHC0. We compared these SoftBank GNSS sites and nearby strong-motion seismometer sites (NIED K-net FKS007 and FKS019, sampling frequency: 100 Hz) (Fig. 5). The distance between the SoftBank GNSS and NIED K-net sites is 4.3 km for BH7H and FKS007, and 5.9 km for BHC0 and FKS019, respectively (Fig. 4). In the comparison between the two time series, the strong-motion seismometer time series was integrated twice. For FKS019, a large undulation clearly appeared in the integrated time series in the EW and NS component (Fig. 5b). Thus, a high-pass filter with a corner frequency of 0.05 Hz was applied for the integrated time series of FKS019 in the EW and NS components. The displacement waveforms of BH7H and FKS007 are basically consistent with each other. But the waveform of FKS007 suffered from a low-frequency bias caused by the integration while the shaking of BH7H lasts longer until the latter half of the time series. The latter may reflect a resonance of the cell phone base station caused by the strong motion or other local site effects.
Figure 5b shows the time series of BHC0 and FKS019, where BHC0 showed a displacement different from that of the surrounding sites based on the daily coordinate analysis. The EW components in BHC0 exhibited a permanent westward displacement after the S-wave arrival. This result suggested that the westward displacement of the GNSS antenna may not have occurred by coincidence because of variations in the analysis, but may have been caused by the westward displacement of the GNSS antenna. In addition, the amplitude of the displacement time series due to the seismic wave was clearly larger in BHC0 than in FKS019. These results may suggest that the mounting of BHC0 to the ground is unstable. There are previous studies on these unexpected abnormal displacements that differ from surrounding sites during and after an earthquake. Ohta et al. (2008b) found a localized abnormal coseismic and postseismic displacement in a GEONET site after the 2007 Chuetsu-Oki earthquake (MJMA 6.8) in central Japan. They installed another campaign GNSS site near the GEONET site to evaluate the displacement. Based on short baseline analysis, they concluded that a small-scale landslide occurred after the mainshock due to strong shaking. Such monumentation instability may also occur in private sector GNSS networks such as SoftBank. In GEONET, tiltmeters are installed inside the pillars (Munekane 2013), against which a comparison can be made for unexpected displacement caused by strong shaking. In the case of SoftBank, it is necessary to utilize a screening approach that takes advantage of a very dense network and its inconsistency with the surrounding observation sites. For example, it is considered that an algorithm should be developed to exclude specific sites that show an amount and direction of displacement that is obviously not in accordance with the surrounding GNSS sites within a certain threshold. The stability of mounting might also be investigated by exhaustively examining the relationship between the noise level and wind speed in kinematic time series based on long-term observation data. On the basis of such quality inspection, the SoftBank network can be used to observe not only static offsets by an earthquake, but also dynamic displacement.