Extrinsic viscous anisotropy in two-phase aggregates, fabric parametrisation and application to mantle convection

Earth's mantle rocks are poly-aggregates where different mineral phases coexist.  These rocks may often be approximated as two-phase aggregates with a dominant phase and less abundant one (e.g. bridgmanite-ferropericlase aggregates in the lower mantle). Severe shearing of these rocks leads to a non-homogeneous partitioning of the strain between the different phases. The resulting bulk rock is mechanically not isotropic, and the elastic and the viscous tensor depend on the volume fraction and viscosity contrast between the mineral phases and the fabric.

Here we employ three-dimensional mechanical models to reproduce and parametrise fabrics typical of mantle rocks and quantify the evolution of the viscous tensor. These fabrics are produced by shearing a mechanically heterogeneous medium comprised by randomly distributed isotropic inclusions embedded in: i) a weak inclusion-strong matrix aggregate where strain is mainly accommodated by the weak phase, that flattens and yields a penetrative foliation; and, ii) a strong inclusion-weak matrix where strain is mainly accommodated by the matrix, in this case, the strong phase deforms primarily parallel to the direction of the flow, producing cigar-shaped inclusions.

Finally, we combine the fabric parametrisation of a two-phase aggregate with the Differential Effective Medium (DEM) theory to study the evolution of the viscous tensor and its effects in mantle dynamics. The results of two-dimensional models of thermal convection show that a viscosity contrast of one order of magnitude between the two mineral phases is enough to deflect mantle plumes and produce convection patterns that differ considerably from the ideal isotropic media.