High-frequency seismic source amplitude of eruption tremor and its relations to plume heights, volumes, and durations of Plinian eruptions

We studied the high-frequency seismic signals of eruption tremors during recent eruptions at various volcanoes and quantified their seismic source amplitudes (A_s) and cumulative source amplitudes (I_s) in the 5-10 Hz based on the assumption of isotropic S-wave radiation. A_s and I_s correspond to the maximum and the cumulative value of amplitudes at the source during eruption tremor. We previously found that the power law relation between A_s and I_s holds and eruption plume height (H) can be scaled by A_s. We also found that A_s is proportional to the eruption volume rate. These results suggest that the eruption volume (V) is proportional to I_s. In this study, we further investigated the relation among A_s, V and duration (T) of Plinian eruptions.

Using the estimated values of A_s and I_s, we calculated the envelope width (p) as I_s/A_s, which is related to the duration of a seismic envelope waveform. We found that p is proportional to 0.4 power of A_s and I_s, respectively. We also found that envelope waveforms of eruption tremors can be approximated as trapezoids, where A_s and T correspond to their heights and lower bases, respectively. Moreover, the ratios of upper to lower bases for these envelope waveforms are roughly constant. In this case, the proportionality between p and T holds. Therefore, T is proportional to 0.4 power of V. This proportional relation was consistent with the estimates of T and V for various Plinian eruptions compiled by Mastin et al. (JVGR, 2009). Therefore, the scaling relation between durations of eruption tremors and eruption volumes of Plinian eruptions holds over a wide range of eruption size.

We showed that A_s is related to eruption plume heights, volumes and durations. This suggests that quantitative information about eruption can be obtained from A_s. Especially, the plume height can be estimated from A_s in real-time. Therefore, we developed the estimation system of eruption plume height using A_s continuously estimated in every 1 min. Our test results indicate that plume heights of recent eruptions at Kirishima and Aso in Japan and Nevado del Ruiz in Colombia are reproduced by this system although there are some errors between estimates and observations. Our system may be useful to provide eruption information in real-time.