Reconstructing Surface Eruptive Sequence of 2018 Small Phreatic Eruption of Iwo-Yama Volcano, Kirishima Volcanic Complex, Japan by Infrasound Cross-correlation Analysis


 The Iwo-yama volcano of the Kirishima Volcanic Complex in Japan had a small phreatic eruption in April 2018, which formed multiple vents. The activity was recorded by two infrasound sensors and two monitoring cameras which had been installed within 1 km of the vents. This study identified infrasonic signals from the multiple vents by a cross-correlation analysis between the two infrasound sensors. The analysis successfully revealed the signals from two main eruption craters and constrained the infrasound onsets at the individual vents in the two craters. We combined the results with the images from the cameras and reconstructed the sequence of the small phreatic eruption of Iwo-yama. Notably, the intense eruption accompanying remarkable infrasound delayed several hours to the eruption onset at each of the two craters. This study provides a sequence of the activities of the multiple vents in a phreatic eruption, which will be useful for understanding the phreatic eruption mechanism and hazard assessments.

In phreatic eruptions, multiple vents are frequently formed one after another at the ground surface (e.g., Yukutake et al. 2017). Identifying multiple vent activities is essential for understanding the transition process of phreatic eruptions and hazard assessments. The 2018 eruption of the Iwo-yama volcano of the Kirishima Volcanic Complex (KVC) in Japan is a case of phreatic eruptions with successive vent formations. Two infrasonic sensors and monitoring cameras recorded the events within 1 km of the vents. In this study, we used an acoustic cross-correlation analysis between the two infrasound sensors to reveal the activities of the individual vents. We also referred to the monitoring images and then, reconstructed the sequence of the small phreatic eruption at the Iwo-yama volcano.

Data
Infrasonic data Infrasonic data were collected at KU.EBQ7 station, 387 m southwest of the summit of Iwo-yama, and KU.KREB station, 842 m west of the summit (Fig. 1a). Infrasound was recorded using a Hakusan SI104 microphone (Hakusan Corporation, Japan) at KU.EBQ7 (hereafter referred to as MC1) at 200-Hz sampling frequency and a Hakusan SI102 microphone at KU.KREB (MC2) at 100 Hz. Both microphones have at responses in a frequency range above 0.05 Hz. All the time-series data were logged continuously by 24-bit digitizers.

Monitoring camera
Monitoring camera data were provided by the Kagoshima Local Meteorological O ce of the Japan Meteorological Agency (JMA). There were two video cameras around Iwo-yama volcano. The Iwo-Yama-Minami monitoring camera (CAM1), was located 204 m to the south of the summit and the Ebinokogen monitoring camera (CAM2), was located 930 m to the west (Fig. 1a). Because these are visible light cameras, volcanic activity during night could not be captured. The sampling rate was approximately 6 s.
The vents formed in front of either one of the cameras, and therefore, their activities were successfully captured during the daytime.
Overview of the 2018 small phreatic eruption of Iwo-yama KVC is composed of ~ 20 volcanoes and is located in the southern part of Kyushu Island, Japan (Fig. 1a).
Iwo-yama is one of the active cones of KVC, holding subsurface hydrothermal systems and surface geothermal activities (Tsukamoto et al. 2018). From April 19-21, 2018, a small phreatic eruption occurred at Iwo-yama and emitted an ash-steam mixture up to 500 m from the vents. During this eruption, infrasonic signals were recorded by the observation sites near the vents (Fig. 1a). The eruptive activity was localized in two areas, which were the Iwo-yama South Craters (hereinafter, South Crater), consisting of several sub-craters, and Iwo-yama West Crater (hereinafter, West Crater) (Tajima et al. 2020). The craters were composed of several vents, namely S1 to S7 in South Crater and W1 to W7 in West Crater (Fig. 1b). The eruption began at vents S1 and S5 in South Crater from 15:39 on April 19, 2018, and the other vents were subsequently formed and merged into three sub-craters (Tajima et al. 2019). These were vents S1-S3 to the crater Y3, S4-S6 to the crater Y2a, and S7 to the crater Y2b (Fig. 1b). Hereafter, we refer to these three sub-craters (Y2a, Y2b, and Y3) as vents because our analysis does not have resolution to discriminate individual vents (S1-S7) in South Crater. At approximately 16:30 on April 20, steaming began 500 m to the west of South Crater, and the vents (W1-W7) formed before the morning of April 21.
The vents W3 and W4 grew to a crater, around which ashy deposits and ejecta were observed. It is considered that the ejection occurred in the evening of April 20 (Tajima et al. 2020). However, the eruption time in the West Crater area was not logged by the video recordings as it was nighttime. After the eruption, vigorous fumarolic activity and hot water swelling from the vents continued for over a year. Figure 2 shows the waveform and spectrogram of the infrasound recorded by MC2, and the snapshots taken by the monitoring cameras that captured surface phenomena at the two crater areas. During the entire period from 15:00 on April 19 to 7:00 on April 21 (Figs. 2a and 2b), tremor-like infrasound, with an amplitude of up to ~ 1 Pa consisting of two frequency bands, 1-7 Hz and 7-20 Hz, was observed. The eruption onset in South Crater was clearly captured by CAM1 (Figs. 2c and 2d) and was recognized by the sudden increase in the infrasound amplitude (Figs. 2a and 2b). The West Crater area was recorded by CAM2, where faint fumaroles began rising at approximately 16:30 on April 20 (Figs. 2e and 2f). However, the time of the small eruption from vents W3 and W4 could not be con rmed with the monitoring camera recordings. We aim to distinguish the acoustic signals of West Crater from those of South Crater.

Cross-correlation analysis
We conducted an acoustic cross-correlation analysis between two microphones, MC1 (KU.EBQ7) and MC2 (KU.KREB); the distance between MC1 and MC2 is 585 m. Walsh et al. (2019) used a similar method for analyzing the phreatic eruption of White Island, New Zealand. They showed that the lag time of infrasound obtained by a cross-correlation analysis was consistent with the eruption vent locations inferred from the seismic tremor amplitude distribution and concluded that the eruption signals originated from a single vent. In this study, we attempted to distinguish and constrain the activity of multiple vents.
We investigated the temporal change of the cross-correlation coe cient where P1 and P2 are the acoustic signals recorded at points x1 and x2, respectively, and τ is the lag time of P1 to P2. We calculated R(t,τ)using time windows of a xed length of 5 s starting at t and sliding with 60% overlaps. The result is graphically displayed on the t-τ axis. The function R(t,τ) has a peak at a particular lag time that corresponds to the acoustic travel time difference between the two observation points when a coherent acoustic signal exists. Depending on the signal's lag time and spectral features, the t-τ plot has a characteristic pattern that helps in identifying the signal. We separately performed correlation analyses in two frequency bands, 1-7 and 7-20 Hz, referring to the spectrogram (Fig. 2b).

Estimation of expected lag time
Herein, the candidate source locations (South Crater and West Crater) are known, and therefore, the expected lag times are estimated. For simplicity, we assumed linear and isotropic propagation for acoustic waves. The expected lag time was then calculated as (d1-d2)/C, where d1 and d2 are the travel distances of the signal from the source to the observation points x1 and x2, respectively, and c is the atmospheric sound speed. The atmospheric sound speed is calculated by assuming an ideal gas, where γ is the heat capacity ratio (1.4), R g is the gas constant of air (287 J/kg/K), and T is the atmospheric temperature in K (Johnson 2003). The atmospheric temperature uctuates with time. The wind speed and direction also affect the sound propagation velocity c. Although there was not a meteorological station present around Iwo-yama, the low-frequency noise level in the infrasound data suggested that the wind was weak. Therefore, we ignored the wind effect and calculated the theoretical temperature at an altitude of 1300 m from hourly temperature data collected at the Kakuto station (228 m a.s.l.) of JMA, which is the closest meteorological observation site. The estimated atmospheric temperature ranged from 272-296 K, and the resultant sound speed ranged from 330.7-345.0 m/s during the period from 15:00 on April 19 to 7:00 on April 21. Using these values, we estimated the possible ranges of the expected lag times. Assuming the source at South Crater (Y2a, Y2b, and Y3), the expected lag times are 1.46-1.57 s. If the source is located at West Crater (W3 and W4), the expected lag time is 0.70-0.74 s. The values for all the vents and craters are shown in Table A1 of Additional File 1. Figure 3 shows the results of the cross-correlation analysis. The top panel (Fig. 3a) shows the waveforms ltered at 1-7 Hz and 7-20 Hz. The middle and bottom panels show t-τ plots of the cross-correlation coe cient in the frequency ranges of 1-7 Hz (Fig. 3b) and 7-20 Hz (Fig. 3c), both of which exhibit high correlation values around τ =1.5 s after 15:39:45 on April 19. This lag time is equivalent to that expected for infrasound from South Crater, which con rms that its eruptive activity continued over the analyzed period after the onset. The correlation values in the lower-frequency band increase at 19:19:40 (Fig. 3b), similar to the amplitude values (Fig. 3a). Simultaneously, CAM1 captured the widening of the Y2a vent, which began at 18:40:51, with increased ash plumes from the vent (Additional File 2: Fig. A1). We consider that an intense eruption, accompanying remarkable low-frequency infrasonic signals, began at 19:19:40 after the vent widening. From around 3:57 on April 20, the correlation values around τ =1.5 s in the higher-frequency band intensi ed again (Fig. 3c). Besides, subtle peaks in τ <0.9 s, indicating West Crater signals, appear around 21:00 on April 20 in the 7-20 Hz band; however, the correlation pattern is unclear to constrain the onset (Fig. 3c).

Results And Discussion
We improved the resolution using the following procedure: The data were resampled up to 500 Hz by linear interpolation to increase the lag time resolution. We then calculated the cross-correlation coe cients for 5 s-long time windows sliding in 2 s, and progressively stacked them every 20 s. The results for the higher-frequency band are shown in Fig. 4, and the results for the lower-frequency band are provided in Additional File 3.
By analyzing the South Crater signals, the lag time of the initial stage of the eruption is 1.55 s, whereas that after the reincrease (3:57 on April 20) is 1.50 s. (Fig. 4b). Referring to the expected lag times of the South Crater signals (Table A1), we consider that the shortening of the correlation peak lag time by 0.05 s indicates the source shift from Y2a to Y3. The lag time starts shortening simultaneously with the vent widening at 18:40:51, and before the low-frequency power increase at 19:19:40 (Fig. 3b). The images from CAM1 also show increased ash plumes from Y3 with the widening of Y2a (Fig. A1). We interpret that Y3 was activated with the vent widening and then, from around 3:57 on April 20, became the main source of the higher-frequency infrasonic signals.
At West Crater, there is no clear correlation in the corresponding range τ before 21:00 (Fig. 4c), although CAM2 recorded faint steam clouds from around 16:30. A possible reason is that the signal was below the detection level, or was buried in the strong signal from South Crater. At 21:05:20 ± 10 s, a correlation peak appears around τ =0.83 s (Fig. 4c), which corresponds to vent W6 (Additional File 1: Table A1). The correlation decays after 22:00. Another peak then appears around τ =0.72 s from 21:42:20 ± 10 s ( Fig. 4c), which we infer as the onset of the small eruption from vents W3 and W4 that erupted ash and ejecta.
The relationships between the correlation peak time lags and the source positions are subject to uncertainties regarding the atmospheric temperature and the local wind speed. We checked the validity of the interpretations described above. For South Crater, the peak at τ =1.55 s is related to Y2a with the atmospheric sound speed and temperature of 336 m/s and 281 K, respectively. If the signal is from Y3, the atmosphere should have 326 m/s and 265 K, respectively. Alternatively, if the peak at τ =1.50 s is made by Y2a, it requires 347 m/s and 300 K. These values are outside the range of the estimated atmospheric temperature. It is also unrealistic that the temperature increased by nearly 20 K from 4 pm to 4 am; neither can we assume that the wind speed increased more than 10 m/s when considering the lowfrequency noise level of the infrasound data (Fig. 3a). For West Crater, if the peak at τ =0.83 s corresponds to W3 and W4 instead of W6, the sound speed and the atmospheric temperature need to be as low as 292 m/s and 212 K, respectively. If the peak at τ =0.72 s is vent W6, it requires extremely large values of 390 m/s and 379 K. Neither the wind can generate such propagation speeds.
We reconstructed the sequence of the multiple-vent activities of the 2018 small phreatic eruption of Iwoyama (Fig. 5). South Crater began an eruption at 15:39 on April 19, mainly from Y2a (and Y2b). The vent widened from 18:40 to 19:19, following which the eruption intensi ed, accompanying lower-frequency infrasonic signals. Vent Y3 was activated with the Y2a widening and became the main source of higherfrequency infrasonic signals from 3:57 on April 20. The steam-emitting vents appeared in the West Crater area around 16:30 on April 20, and the eruptions accompanying infrasonic signals occurred from 21:05 successively, in multiple vents. These observations suggest that the intense eruptions with remarkable infrasonic signals started with several hours of delay after the onset of steaming or the appearance of the vents.
Several hours of delay in the vent formation accompanying ash falls with intensi ed seismic tremor after the infrasound onset was also observed in the 2015 small phreatic eruption of the Hakone volcano, Japan (Yukutake et al. 2017). The delay has been interpreted as the time for the hydrothermal uid to reach the ground surface from a subsurface open-crack source, while the infrasound began concurrently with the crack opening by strain transfer (Yukutake et al. 2018). The time delay between the onset of surface phenomena and the intense eruptions can be a common feature of small-scale phreatic eruptions. Our results add another case and will be useful for considering the mechanism of the transition process of small-scale phreatic eruptions and assessing the hazards of eruptions that form multiple vents.
We found two types of signals in the frequency range and their temporal uctuations and interpret this as the re ection of the dynamics and transition of the eruptive activity. At the West Crater area, the geological survey found ash deposits and fragments around W3 and W4 (Tajima et al. 2020), but only traces of mud ows from W6 (Tajima et al. 2019). Conversely, the signal from W6 exhibits a clearer correlation than that from W3 and W4 (Fig. 4c), indicating that the former has more signi cant power. It is noticed that the infrasonic power does not necessarily represent the amount of ash emission. The generation mechanism of infrasound accompanying phreatic eruptions is only partially understood (e.g., Jolly et al. 2016), and we plan to investigate the source process of the infrasonic signals at Iwo-yama in future work.

Conclusions
We reconstructed the sequence of the multiple-vent activities of the 2018 small phreatic eruption of the Iwo-yama volcano in Japan by conducting an acoustic cross-correlation analysis between two infrasound sensors. We identi ed infrasound signals from South Crater that were associated with the eruption onset and the vent widening that had been observed by the monitoring camera. We also constrained the timing of the signi cant eruptive activity at the individual vents in both South Crater and West Crater during the nighttime, which had not been con rmed visually. The results suggest that the intense eruptions with remarkable infrasound delay several hours to the steaming onsets or the vents' appearance. In addition, it is observed that intense infrasound does not necessarily accompany a large amount of ash emission, as is the case with W6. Our results demonstrate a case of the transition processes of phreatic eruptions that form multiple vents. These ndings will be useful in constraining the mechanism and assessing eruption hazards.