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 \(10^5\) 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

中文翻译：

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将流致震颤模型与地震观测联系起来：在日本箱根火山深谐波震颤中的应用

几十年前，Julian (J Volcanol Geotherm Res 101:19–26, 1994. https://doi.org/10.1029/93JB03129) 提出了流体流动对弹性通道振动非线性激励的集总参数模型作为一种机制火山谐波震颤。从那时起，他的模型和类似的流致振荡模型已被应用或考虑解释火山颤动和低频地震。在这里，我们扩展了朱利安模型，以便与观测数据进行定量比较，并将其应用于在日本箱根火山观测到的深谐波震颤。我们根据通道体积制定了模型，并将解与体积矩张量联系起来。我们还结合了湍流效应来处理岩浆和超临界流体作为工作流体。箱根地下\(\sim\)  30 km），我们搜索了以观测到的频率（\(\sim\) 1 赫兹）。结果表明，岩浆和超临界流体都可以产生逼真的颤动，其通道尺寸相似，为几米长和几厘米宽。我们将模型解与每个地震台的格林函数进行卷积，以将模型与数据进行比较。结果表明，朱利安模型可以产生与观测波形非常接近的合成震颤波形。尽管源波形在每个周期只有一个峰值，但卷积波形呈现出明显的二次峰值，就像观察到的波形一样。虽然以前的模型通过混沌之前的倍周期非线性效应生成了这样的波形，显示出交替的大峰和小峰，但我们的模型没有显示出这样的转变，至少在研究的参数下是这样。\(10^5\)  Pa 产生\(\sim\)  1 Hz 的振荡。我们提出，不仅是岩石性质，而且由岩石和可压缩流体组成的通道结构也会产生低有效弹性。为了充分验证我们的模型，应该确定这种小弹性的机制，这是我们未来的工作。

图形概要