Abstract We compare viscoelastic models to obtain the seismic properties of a partially molten rock as a function of temperature, pressure and tectonic stress. Invoking the correspondence principle, the material of the inclusions is represented by a Maxwell mechanical model, where the Arrhenius equation and the octahedral stress criterion define the Maxwell viscosity. One of the most advanced models is the self-consistent or coherent-potential approximation (CPA), which considers oblate spheroidal inclusions of arbitrary aspect ratio and high concentration. The physical mechanism behind the Arrhenius equation is grain-boundary relaxation, and melt occurs beyond a critical temperature. The seismic properties (stiffness, wave velocity and dissipation factor) are obtained with the CPA, Hill, Hashin-Shtrikman, Walsh and Krief-Gassmann equations. The latter model and the Hashin-Shtrikman average make no assumption on the shape of the inclusions. All the models show similar trends, predicting relaxation peaks at seismic frequencies and at the brittle-ductile transition.

中文翻译：

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部分熔融岩石中的地震衰减

摘要 我们比较粘弹性模型以获得部分熔融岩石的地震特性作为温度、压力和构造应力的函数。调用对应原理，夹杂物的材料由麦克斯韦力学模型表示，其中阿伦尼乌斯方程和八面体应力准则定义麦克斯韦粘度。最先进的模型之一是自洽或相干电位近似 (CPA)，它考虑了任意纵横比和高浓度的扁球状包裹体。阿伦尼乌斯方程背后的物理机制是晶界弛豫，超过临界温度就会发生熔化。地震特性（刚度、波速和耗散因子）通过 CPA、Hill、Hashin-Shtrikman、Walsh 和 Krief-Gassmann 方程获得。后一个模型和 Hashin-Shtrikman 平均值对夹杂物的形状不作任何假设。所有模型都显示出相似的趋势，预测了地震频率和脆韧转变处的松弛峰值。