Waveform inversion of the ultra-long-period seismic event associated with ground tilt motion during an eruption of Mount Kusatsu–Shirane, Japan, on January 23, 2018

We conducted waveform inversions of an ultra-long-period (~ 240-s) event associated with the phreatic eruption of Mount Kusatsu–Shirane on January 23, 2018. We used broadband seismic and tilt records from three stations surrounding the eruption site. The horizontal components of the broadband seismic records were severely contaminated by tilt motions. We applied a waveform inversion algorithm to account for both the translational and tilt motions. To reduce the number of free parameters, we assumed a tensile crack source and conducted grid searches for the centroid location and orientation of the crack. The results showed a rapid inflation of 10 5 m 3 of the crack, followed by a slow deflation starting 8–11 s prior to the onset of the eruption. The source location and crack orientation were not uniquely determined. The most likely source is a north–south-opening sub-vertical crack near the eruptive craters. This ultra-long-period event may represent volcanic fluid migration from depth to the surface through a vertical crack during the eruption. Graphical abstract