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.
•Seismic properties of partially melted rocks are analysed as function of temperature, pressure and tectonic stress•Arrhenius equation and octahedral stress are used to calculate the rock viscosity to obtain the grain-boundary relaxation•The properties are obtained with the CPA and Walsh models, Hill average, and Krief-Gassmann and Hashin-Shtrikman equations