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.