Electrical conductivity and permeability of partially molten mantle rocks: results from digital rock physics experiments

Abstract:

Estimates of overall melt content beneath mid-ocean ridges inferred from magnetotelluric tomography (MT) studies vary widely between 1 and 10 vol. %. Much of this variation may arise from a lack of understanding about how melt geometry influences the bulk electrical conductivity of partially molten mantle rock, especially at low melt fraction. We present results from experiments in which we numerically calculate the electrical conductivity and permeability using high-resolution, three-dimensional melt geometries of olivine-basalt systems obtained via synchrotron X-ray microtomography (SXμT).

Starting materials consist of San Carlos olivine and Fo₉₀ basalt mixed in various proportions to achieve nominal melt fraction of 0.02 to 0.20 when melted. Samples were prepared by isostatically pressing samples at 1.5GPa and 1350°C for a minimum of 1 week (Zhu et al., 2011; Science) and then quenched, turning the melt to basaltic glass. Samples were imaged using SXμT at the Advanced Photon Source at Argonne National Labs to obtain three-dimensional, 700 nm-per-pixel digital reconstructions. Grayscale data was segmented using Avizo^® software (Miller et al., 2014; EPSL), and binary images were used as computational domains in numerical experiments to determine bulk electrical conductivity and permeability.

Numerical experiments were carried out on several statistically representative subvolumes per sample using finite difference techniques. Olivine and melt are treated as conductive and insulative phases, respectively. To calculate conductivity, Laplace’s equation is solved for the electric potential, assuming zero electric flux across phase boundaries. Ohm’s Law yields the bulk conductivity of the sample. To calculate permeability, Stokes’ equations are solved using the artificial compressibility method on a staggered grid. Darcy’s law then gives the permeability of the subvolume.

We fit permeability and electrical conductivity values to power laws in order to establish empirical relationships with melt fraction. We compare with experimental studies. By linking permeability and electrical conductivity to melt content, we are able to better guide interpretations of geophysical data and constrain melt connectivity and transport at mid-ocean ridges.