Plume height, duration and volume of sustained explosive eruptions inferred from eruption tremor amplitudes

Seismic source amplitudes determined by using the amplitudes of high-frequency (5-10 Hz) tremor signals generated by sustained explosive eruptions have been shown to be related to eruption plume height by power-law and exponential relations and to eruption volume flux by a proportional relation. We further examined these relations and extended this source quantification approach to investigate eruption duration by using the envelope width, defined by the ratio of the cumulative source amplitude to the source amplitude. We first confirmed that the relationship between source amplitude and plume height proposed by a previous study holds for small eruptions at Nevado del Ruiz (Colombia), although slight modifications were required. We then showed that the relations of envelope width with source amplitude and with cumulative source amplitude of eruption tremor associated with sub-Plinian eruptions at Kirishima (Japan) and Tungurahua (Ecuador) could be described by a power law. The source amplitude functions of these tremors were characterized by three periods and could be approximated by a trapezoidal shape. A power-law function fitted to the relation between eruption volume and eruption duration obtained from these relations was similar to that estimated by fitting a power-law function to previously reported eruption volume and duration data of well-documented silicic and andesitic eruptions. Our results suggest that eruption duration may systematically vary with eruption volume when the conduit is stably open during the second period of the trapezoidal source amplitude function. This study demonstrated that source amplitudes can be used for real-Time predictions of both plume height and eruption duration, which in turn may be used to estimate ashfall distributions and tephra transport for local residents and aviation operations.