Figure 1a shows the permanent seismic stations used in this study by colored markers with other stations by open markers. Some stations had short-period seismometers, and some had broadband seismometers (Fig. S1.1). All seismic stations recorded continuously with a sampling rate of 100 Hz. We analyzed the frequency range from 1 Hz to 15 Hz. This paper mainly presents the SBL in 3.5-7 Hz because the variation of interest was the most visible. Although many reported volcanic tremors have dominant frequencies around 1 Hz 38, frequency bands above several Hz are also informative 39,40.
We analyze the data from May 1, 2008 to December 31, 2018. All stations except SMW were operated with the same instruments individually in the key periods discussed in this study (Fig. S1.1). At SMW station, we used data from short-period (1 Hz) seismometers before August 1, 2010, and a broadband seismometer afterward. We confirmed that the SBL growth before the 2011 eruption was captured by both sensors consistently (Fig. S1.2). When we discuss temporal variation at the individual stations, we do not correct for the site amplification effects in this study.
Temporal SBL variation
We calculated daily SBL in 3.5-7 Hz band and smoothed them by week to reduce the short-term effect (See Methods). Figure 2c presents the smoothed SBL of the five stations (colored circles in Fig. 1a). We observe characteristic variations indicated with arrows, which are prominent and correlated at the two stations closest to the crater (SMN and SMW) as well as temporally related to the deep inflation-deflation behaviors (arrows with corresponding colors and styles in Fig. 2a). These variations are compared with the eruptive events in the next paragraph. We also noticed the elevated SBL every summer at all the stations, which is the most evident at SMW. Figure 2d and 2e present the stacked and normalized power spectra in the quiet time windows every night, which we refer to as \({P}_{SBL}\) (see Methods), at SMN and SMW, respectively. We see the spectral structures change with the characteristic variations of SBL.
As the light-blue arrows in Fig. 2c indicate, SBL grows simultaneously at SMN and SMW toward the 2017 eruption. The growth is visible also at more distant stations after July 2017 (KRS station malfunctioned). Then, SBL becomes apparently larger than usual at all the stations, growing from the 2017 eruption to the 2018, dropping after the main phase of the 2018 eruption. The growth of SBL is also observed before the 2011 eruption (the red arrow in Fig. 2c). The SBL increase and slight inflation of the deep source are observed in 2013 and 2014 without an eruption (the dashed orange arrows in Fig. 2a and 2c). The elevated SBL in this period has different features from those prior to the 2011 and 2017 eruptions. The increase is stepwise, the SBL ratio of SMN to SMW is apparently larger (Fig. 2c), and \({P}_{SBL}\) is poor in low-frequency components and has varying peaks (Fig. 2d and 2e).
We also note the SBL variations toward the end of eruptive periods. Although the deep inflation resumed after the co-eruption drop, it did not accompany SBL growth. After the main phase of the 2018 eruption, SBL stayed at the level prior to the 2017 eruption but abruptly went back to a lower level at the end of May 2018, while the recovery inflation continued for several months (the dashed-green arrows in Fig. 2a and 2c). The 2017-2018 eruption ceased with two minor events in June 2018 (Fig. 1b). In the 2011 eruption, the close stations had problems after the main phase. Nevertheless, the other stations suggest that SBL remained relatively high with a peak at the end of the 2011 eruptive period and declined at the end of the year, when the recovery inflation stopped (the dashed red arrows in Fig. 2a and 2c).
All the above-mentioned features are not apparent in daily RSEM or RSAM (Fig. S4). On the other hand, the RSEM is more sensitive to non-volcanic signals, including the 2016 Kumamoto-Oita earthquake sequence and their aftershocks, whose hypocenters distribute at 60–170 km from Shinmoe-dake 41.
Clustering analysis results
To approach the causes of the smoothed SBL variations described above, we performed clustering classification 42,43 of \({P}_{SBL}\) (see Methods). The current clustering method emphasizes the similarity in overall trend of spectra rather than local features like positions and shapes of spectral peaks. Besides, the number of clusters is arbitrary. Below we give similar names and colors to clusters that appear in similar periods.
The daily SBL values belonging to different clusters are distinguished by the colors in Fig. 3a and 3c, and monthly fractions of each cluster are shown in Fig. 3b and 3d. Note that the smoothed SBL in Fig. 2c represents the lower envelop of the daily SBL. The characteristic variations of the smoothed SBL are represented mainly by green, red, and black clusters (enclosed by the magenta rectangles in the legends of Fig. 3). The blue and yellow clusters exhibit short-term day-by-day fluctuation or SBL in the quiet periods and thus are regarded unrelated to the long-term SBL growth of current interest. Some components of the red and black clusters also exhibit short-term fluctuation in 2008-2010, which we discuss later.
The green cluster at SMW (Gw) mainly appears in summer with high SBL and correlates with the local precipitation (Fig. 3e). Although the specific mechanism for this is not known, the increased water flow may generate higher levels of noise, especially at station SMW that is located near a running river. The Gw cluster is also observed in 2013-2014 independently of the precipitation. At SMN, the green cluster (Gn) exclusively appears in this period. Therefore, the high SBL in this period is regarded as non-precipitation feature. In contrast, the transient increase in SBL at SMW in September 2011 (around ④) does not include the green clusters nor correlates with the precipitation. We can infer that the increase is not caused by precipitation either, although the stations were not fully functioning in this period.
The red clusters increase as SBL grows between the 2017 and 2018 eruptions and prior to the 2011 eruption both at SMN (Rn1 and Rn2) and SMW (Rw1 and Rw2). The growth of SBL prior to the 2017 eruption mainly consists of the black clusters (Kn at SMN and Kw at SMW). Both Kn and Kw increase with high precipitation as well, indicating that the SBL that grows prior to the 2017 eruption has some similarity to the precipitation noise. Besides, the black clusters sparsely appear from 2008 to the 2011 eruption and generates scattered SBL values. However, the SBL behavior prior to the 2017 eruption is distinct due to the large values, the growing nature that is independent of the precipitation, and the spectral features that have not been distinguished by the current clustering method but are visually apparent (Fig. 2d). The red and black clusters also constitute the SBL in the decaying period of the 2018 eruption from March to May 2018. From the beginning to the 2011 eruption, the red clusters are always present at both stations, some of which generate daily scattered variations. This may be partly because the different sensors before and after the 2011 eruptions (Fig. S1.1) may have affected the clustering analysis. On the other hand, it is also possible that the red clusters reflect the fact that the volcano was always active in that period with several phreatic eruptions.
Signal locations
The SBL remains high from the 2017 eruption to the 2018 eruption (from ⑤ to ⑥ in Fig. 2c). This is due to the continuous volcanic tremors beneath Shinmoe-dake. The tremor dominates the daytime human noise and is detectable with conventional methods. We estimate the tremor source locations using the same method as in the previous study for the 2011 eruption (the amplitude-based source location in the frequency band 3.5-7 Hz)39. The tremor sources for the 2011 eruption (Fig. 4b)39 and the 2017།2018 eruptions (Figs. 4c) are distribute over a similar region beneath Shinmoe-dake.
Referring to these confirmed tremors, we investigate the SBL ratio between SMN and SMW stations, where the SBL elevation prior to the eruptions is apparent. Figure 4a reveals that the SMW/SMN ratio is significantly larger in the precursory periods (black arrows) than during the tremor periods (pink arrows) and during the elevated SBLs in 2013-2014 without subsequent eruptions (a green arrow). The logarithmic plot of SBL (Fig. 2c) also indicates that the ratios of SBLs at SMN and SMW to the other stations are larger in the precursory periods than in the other periods. From these ratios, we infer that the precursory SBL sources are shallower and more to the west than the tremors. To determine the source locations, we need to investigate the SBL distribution with more stations around the sources, which will be the goal of our future study.