Relation Between High-frequency Seismic Source Amplitudes of Eruption Tremors and Eruption Volume Flux

We studied high-frequency seismic signals of eruption tremors during recent eruptions at Ontake and Kirishima in Japan, Tungurahua in Ecuador, and Nevado del Ruiz in Colombia and quantified their seismic source amplitudes (A_s). A_s corresponds to the average amplitude of envelope waveforms in 5-10 Hz corrected for geometrical spreading and medium attenuation based on the assumption of isotropic S-wave radiation. We found that plume height (H) of those eruptions is scaled by A_s and H is described by two relations depending on the value of A_s, which are power law and exponential relations for H > 6 km and H < 6 km, respectively. We also found that eruption volume flux (Q) estimated from tiltmeter data at Kirishima is related to A_s. Especially, the proportionality between A_s and Q holds only when we use seismic data at stations located more than 1 km from the crater. We considered that the relation between A_s and Q depends on seismic wavefields as follows. Assuming an S-wave velocity of 1400 m/s, the wavelength of S waves is 200 m in 5-10 Hz. The scattering mean free path of S waves is estimated to be about 500 m at various volcanoes. When stations are located more than 1 km from the crater, the wavefields are regarded as far-fields and multiple scattering occurs, resulting in isotropic radiation of S waves. In this case, A_s estimates correspond to the moment rate function. However, such simple relation may not hold in near-fields at stations less than 1 km from the crater. Next, we considered the seismic source model of tremor to explain the above proportionality between A_s and Q. We assumed that jet flows exit from the vent of a vertical crack conduit. When the length of the conduit is proportional to its aperture and tremor frequencies are almost constant in a wide range of flow conditions, we can theoretically derive the proportionality between A_s and Q for far-field S-waves with isotropic radiation. For a vertical cylindrical conduit, the proportionality between A_s and Q can be also derived when the conduit length is proportional to its radius. These results indicate the proportional relation between high-frequency seismic source amplitudes of eruption tremors and eruption volume flux.