A three-dimensional microgeodynamic model of melt geometry in the Earth's deep interior

This article presents a three-dimensional microgeodynamic model of grain-melt geometry in partially molten rocks. The isotropic unit cell of the partially molten rock is characterized by a face-centered-cubic symmetry, consisting of rhombic dodecahedral grains. The variation of surface tension between grain-grain and grain-melt contacts excites a coupled viscous flow within grains and the interstitial melt, leading to a steady state grain-melt geometry. We obtain the fractional area of intergranular contact, contiguity, from these models as a function of melt volume fraction, between melt fractions of 0.05 and 0.25. Comparison with previous results indicates that the contiguity in three-dimensional models is lower than in two-dimensional models. The contrast between two-and three-dimensional values of contiguity increases at high melt volume fractions. We apply our model to the ultralow-velocity zones (ULVZs) and the very low velocity province (VLVP) in the Earth's core-mantle boundary. The observed seismic signature of the ULVZ and VLVP can be explained by peridotite melt volume fractions between 0.08 and 0.12 and between 0.01 and 0.05, respectively, in a matrix of elastic properties similar to the Preliminary Earth Reference Model.