Because the correlation pattern was identified only during the eruption (Fig. 2e), it was thought to reflect the occurrence of an infrasound signal associated with the eruptive activity. A slight shift of the node in the correlation pattern from the theoretical position of τ = 0 was observed as seen in Fig. 2d. Yokoo and Ichihara (2012) indicated that the node in the correlation pattern could be shifted from the theoretical position when a seismic single in the same frequency range as that of an infrasound signal overlapped in a ground velocity record (Additional file 3). This shift of the node may be an effect of the volcanic tremor signal observed during this period (Yukutake et al. 2017). The correlation coefficients as shown in Fig. 2b, d range from approximately −0.2 to 0.2, which is low compared to examples from other volcanoes (e.g., Ichihara et al. 2012; Matoza and Fee 2014). Ichihara et al. (2012) demonstrated that during a subplinian eruption, the correlation pattern becomes less clear even if the infrasonic amplitude is very large. This is a result of the strong seismic waves that are not coupled to the infrasonic signals. The low correlation coefficients at Hakone may be explained by contamination from relatively high-amplitude seismic signals generated by VT earthquakes or the volcanic tremor.
During the first 30 s after the onset of the rapid tilt change, the tilt record represents a reverse polarity with respect to that expected from the crack opening, i.e., a tilt downward in the NE direction at the KZR station (Fig. 3d). Thereafter, the polarity aligned with the crack opening, i.e., a tilt downward in the SW direction at the KZR station. Honda et al. (2017) demonstrated that the tilt change showing reverse polarity in the initial phase was caused by an apparent transient response of the tiltmeter, as described in Kokubo (2013), rather than a real contraction of the source. Therefore, it is suggested that the opening of the crack started simultaneously with the emergence of the correlation pattern.
The relationship between the correlation pattern and the tilt changes (Fig. 3) shows that the surface phenomena, such as rapid emission of volcanic gas, occurred concurrently with the crack opening beneath the Owakudani region even though we cannot estimate the exact scale of the upwelling. The result also suggests that the increase in the infrasound amplitude was not caused by an incidence of seismic waves. The upper end of the open crack estimated by Honda et al. (2017) is approximately 150 m beneath the surface of the Owakudani region, which is approximately 1000 m above sea level. Honda et al. (2017) indicated that the residual becomes three times larger than that of the best model when the upper end of the open crack is fixed at a depth of 50 m below the surface. The open crack model estimated by the ground deformations based on InSAR data (Doke et al. 2017) has an upper end at a similar elevation of 830 m above sea level. Because the surface area above the open crack is mostly covered with dense vegetation, it is difficult to detect subtle surface displacements via field survey. However, field surveys at Owakudani, which is a barren area because of the fumarolic activity, and along trekking courses, where the soil is exposed, did not observe any surface displacement to indicate the emergence of the open crack at the surface (Mannen, personal communication). Therefore, it is reasonable to believe that the opening of the crack did not reach the ground surface but stopped approximately 150 m below the surface. If we assume that the sudden opening of the crack reflects an intrusion of highly pressurized hydrothermal fluid, the instantaneous response of the infrasound signal to the rapid tilt change cannot be explained by the diffusion of the pressurized fluid from the open crack. The diffusion of the fluid from the upper end of the crack to the surface (approximately 150 m) takes a longer time given the hydraulic diffusivity of the porous media of 0.5–1.0 m2/s, which was estimated on the basis of the hypocenter migration of the earthquake swarms in the Hakone volcano and corresponds to a migration velocity of several tens of meters per hour (Yukutake et al. 2011). The delay in the fluid diffusion or the following heat transfer from the open crack may correspond to the timing of vent formation (Mannen et al. 2015) and the increase in the volcanic tremor amplitude (Yukutake et al. 2017) that occurred several hours after the onset of the rapid tilt change.
We then considered the relation of the strain transfer caused by the crack opening to the instantaneous response of the infrasound signal. The strain change due to the crack opening propagates to the surface nearly instantaneously in contrast to the diffusion of the fluid because the crack is very near the surface. Figure 4 shows the spatial distribution of the volumetric strain changes at the surface of the Owakudani region (at an elevation of 1000 m) using the crack model of Honda et al. (2017). The final static strain changes because of the crack opening were calculated using the formula of Okada (1992). This result indicates that a positive (dilatational) volumetric strain change of more than 25 μ acted on the area around the vents at the end of the rapid tilt change. This value of the strain change corresponds to a depressurization of approximately 0.16 MPa, which is 1.6 times greater than the atmospheric pressure near the surface if we set the rigidity to 3.9 GPa as calculated assuming an S-wave velocity of 1.4 km/s in the surface layer of the Hakone caldera (Oda 2008) and a rock density of 2.0 g/cm3. If we use the other crack model estimated using the InSAR data (Doke et al. 2017) to calculate the strain change, a large volumetric strain area of more than 25 μm is also produced around the vents (Additional file 4: Figure A4). The detailed distribution of the volumetric strain changes is expected to change when considering the differences between the fault models, the heterogeneity of the displacement, and the effect of topography. However, it is certain that dilatational volumetric strain changes comparable to an order of magnitude of 10 μm acted on a broad area in the Owakudani geothermal region because of the opening of the crack. It is reasonable to believe that groundwater near the boiling temperature pre-existed beneath the Owakudani geothermal region prior to the eruption because fumarolic activity was previously observed. Even though a dynamic time sequence of strain change was not considered here, the infrasonic wave coincident with the rapid tilt changes may be attributed to the emission of vapor caused by groundwater boiling due to depressurization resulting from the strain transfer (Fig. 5).
Figure 3 indicates that the increase in the seismic amplitude occurred approximately 20 s before the occurrence of the infrasonic wave. The VT earthquakes that occurred near the onset of the rapid tilt changes were distributed near an elevation of 0 km (approximately sea level) beneath Owakudani (Fig. 4). The result suggests that the pressure of the hydrothermal fluid at depth initially increased, thus triggering the VT earthquakes at depth and subsequently opening the shallow crack (Fig. 5).
On the other hand, Yukutake et al. (2017) reported discrete impulsive infrasonic waves coincident with the increase in the volcanic tremor amplitude. The corresponding signal was detected as the correlation patterns at 06:57 and 10:32 on June 30 and from 04:05 to 06:00 on July 01 (Fig. 2f). The last period contains the most pronounced impulsive signal activity. During this period, the largest vent (15-1 in Fig. 1b) formed (Mannen et al. 2015). Yukutake et al. (2017) suggested that the impulsive infrasonic waves were generated by the bursting of a gas slug at the surface vent during groundwater boiling, which was likely caused by heat transfer from the open crack.