Analytical and numerical models of viscous anisotropy: a toolset to constrain the role of mechanical anisotropy for regional tectonics and fault loading

To what extent mechanical anisotropy is required to explain the dynamics of the lithosphere is an important yet unresolved question. If anisotropy affects stress and deformation, and hence processes such as fault loading, how can we quantify its role from observations? Here, we derive analytical solutions and build a theoretical framework to explore how a shear zone with linear anisotropic viscosity can lead to deviatoric stress heterogeneity, strain-rate enhancement, as well as non-coaxial principal stress and strain rate. We develop an open-source finite-element software based on FEniCS for more complicated scenarios in both 2-D and 3-D. Mechanics of shear zones with transversely isotropic and orthorhombic anisotropy subjected to misoriented shortening and simple shearing are explored. A simple regional example for potential non-coaxiality for the Leech River Schist above the Cascadia subduction zone is presented. Our findings and these tools may help to better understand, detect and evaluate mechanical anisotropy in natural settings, with potential implications including the transfer of lithospheric stress and deformation through fault loading.