Seismic signals during explosive eruptions have been correlated to eruption size or eruption volume flux for individual eruptive episodes.However, the universality of these correlations has yet to be confirmed. We quantified the sources of high-frequency seismic signals associated with sub-Plinian and Vulcanian eruptions at Kirishima (Japan), Tungurahua (Ecuador) and other volcanoes in Japan using a simple approach based on highly scattered seismic waveform characteristics. We found that eruption plume heights scale to seismic source amplitudes and are described by two relations depending on the value of source amplitudes: powerlaw and exponential relations for plume height > 6 km and <6 km, respectively. Though conceptually similar, our scaling relations differ from the previously proposed relation based on reduced displacement. By comparing seismic and geodetic data during sub-Plinian eruptions at Kirishima, we found that the source amplitude is proportional to eruption volume flux. Combining these relations, we show that our scaling relation for Plinian eruptions is consistent with predictions from plume dynamics models. We present a source model to explain the proportionality between the source amplitude and eruption volume flux assuming a vertical crack or a cylindrical conduit as the source. The source amplitude can be estimated in seconds without any complicated data processing, whereas eruption plumes take minutes to reach their maximum heights. Our results suggest that high-frequency seismic source amplitudes are useful for estimating plume heights in real time.
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