Attenuation in partially melted material

Expressions for the complex moduli are derived for two models that simulate the structure of partially melted material. In one model, isolated lens-shaped inclusions of melt form the liquid phase, whereas in the other model the liquid phase is a continuous film of melt surrounding approximately spherical solid grains. The response of the two models to propagating waves is found to be similar. Q−1 in ice and Woods metal is inversely proportional to frequency ω, in agreement with published observations. The relationship between attenuation and frequency for partially melted rock in the mantle cannot be established definitely because of uncertainties in the critical frequency, which is proportional to the ratio of the bulk modulus of the liquid phase to the viscosity of the liquid phase.