Seismic attenuation in partially molten rocks

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.