Upscaling from Mineral Microstructures to Tectonic Macrostructures

Abstract

Summary Earth’s plate tectonic behavior arises from lithospheric ductile weakening and shear-localization. The ubiquity of mylonites at lithospheric shear zones is evidence that localization is caused by mineral grain-size reduction. Most lithospheric mylonites are polymineralic, suggesting that the interaction between mineral phases by Zener pinning promotes grain-size reduction and weakening. Yet this interaction only occurs where mineral phases mix at the grain scale. Phase mixing and its effect on microstructure and strength have been shown in deformation experiments and natural field samples. Our theory for the interaction between phase mixing (treated as a stress driven diffusion) with two-phase grain damage has been compared to lab experiments. But using processes at the tiny grain-scale embedded within the small hand-sample and lab scales to model large-scale lithospheric processes, requires an upscaling scheme that captures the physics from micro- to macro-structures. For example, weakening from grain-damage in zones of mixing can lead to banded viscosity structure at the small scale that manifests as viscous anisotropy at the large scale. Here we provide a new framework for self-consistently upscaling from microscopic (grain) scales, to mesoscopic (petrological heterogeneity) scales to macroscopic (tectonic) scales. The first upscaling step models phase mixing and grain-size evolution in a small “mesoscopic” lab-scale volume or “patch”, which is equivalent to a point in the macroscopic space. Within this mesoscale patch, stress driven diffusive mixing is described by an analytical solution for mineral phase fraction, provided a minimalist Fourier representation of phase fraction, and a transformation to the patch frame of reference as well as to the principal stress directions at that point. The orientation and volume fraction of mixed-phase regions can then be extracted from the analytical solution for phase fraction. The grain-size and viscosity in the mixed bands are determined by two-phase grain-damage theory; the unmixed zone properties follow from mono-phase grain damage theory. The mesoscale banded viscosity field leads to a macroscale anisotropic viscosity at that point in space. But, the evolution of properties at each macroscale point involves tracking only a few quantities (phase fraction, grain sizes) rather than modeling each patch of mesoscale space as its own 2-D or 3-D system. For the final upscaling, the anisotropic viscosity field is used in a macroscale lithosphere flow model. We show an example of this scheme for a lithospheric Rayleigh-Taylor drip driven by ridge-push compressive stress, which can cause anisotropic weakening via grain mixing and damage that may help initiate subduction and passive margin collapse.