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Study of the explosive eruption jets with the experimental and theoretical approaches

Nataliya Galina, Ayuta Tsuge, Ryuki Tada, Kiwamu Nishida, Mie Ichihara

Abstract

Often the seismic waves from an explosive eruption are generated by a nearly vertical single force Fs which is usually interpreted as the reaction force F due to the ejection of materials during an eruption. Analysing this single force Fs may allow to evaluate the mass discharge rate ṁ and the style of the eruption. In this work we started with investigating the relationship between the mass discharge rate  and reaction force  using an experimental setup to measure the single force Fs during water ejection from a plastic bottle. A series of experiments using different initial pressure and varying the cross-sectional area of the jet was performed. As a result, we report on the reaction force F = 3⁄2 ṁv, although traditionally the reaction force F has been considered as ṁv. The next step of this study was calculating synthetic waveforms and their comparison with the real seismograms recorded during 2022 Hunga Tonga--Hunga Haʻapai eruption. The far-field seismic wavefield can be expressed as a convolution of the single force Fs(t) with the Green's function. The last one was calculated as a response of a homogeneous elastic half-space to a vertical point force applied to the surface. As for the single force Fs(t), we upscaled the time series from the experiments to the duration of a real eruption. Finally, the computation result was compared with the one obtained using the single force Fs(t) in the general form of a triangular pulse.