Linking the flow-induced tremor model to the seismological observation: application to the deep harmonic tremor at Hakone volcano, Japan

Abstract

Abstract Decades ago, Julian (J Volcanol Geotherm Res 101:19–26, 1994. https://doi.org/10.1029/93JB03129 ) proposed the lumped parameter model of non-linear excitation of an elastic channel vibration by fluid flow as a mechanism of volcanic harmonic tremor. Since then, his model and similar flow-induced oscillation models have been applied or considered to explain volcanic tremors and low-frequency earthquakes. Here we extended Julian’s model to allow quantitative comparison with observation data and applied it to deep harmonic tremor observed at Hakone volcano, Japan. We formulated the model in terms of the channel volume and linked the solution to the volumetric moment tensor. We also incorporated the turbulent flow effect to deal with both magma and super-critical fluid as the working fluid. Assuming the realistic material parameters at the tremor source depth ( $$\sim$$ ∼ 30 km) beneath Hakone, we searched for the conditions in which tremor was generated at an observed frequency ( $$\sim$$ ∼ 1 Hz). It is shown that both magma and super-critical fluids can generate realistic tremors with similar channel sizes of several-meter long and several-centimeter wide. We convolved the model solution with the Green’s function at each seismic station to compare the model with the data. The result showed that Julian’s model could produce synthetic tremor waveforms very close to the observed ones. Although the source waveform had only a single peak at each cycle, the convolved waveform exhibited an apparent secondary peak, like the observed waveforms. While the previous models generated such waveforms exhibiting alternative large and small peaks by a non-linear effect of period-doubling before the chaos, our model did not show such transitions, at least with the investigated parameters. Although most of the parameters and physical values of the solutions were in the realistic ranges, the only problem was the presumed low elasticity of the channel as small as $$10^5$$ 10 5 Pa to generate oscillation at $$\sim$$ ∼ 1 Hz. We proposed that not the rock property alone but the channel structure consisting of rock and compressible fluids could generate the low effective elasticity. To fully validate our model, the mechanism of such small elasticity should be identified, which is our future work. Graphical Abstract

Keywords

• Volcanic tremor
• Flow induced oscillation
• Non-linear oscillation