Earth’s various layers – from the inner core to the cryosphere – exhibit mechanical anisotropy, meaning their properties depend on the direction in which forces are applied. In the upper mantle, the primary source of anisotropy is the crystallographic preferred orientation (CPO) of olivine that is a result of sub-grain rotation during plastic deformation. The alignment of olivine grains allows the anisotropic behavior of single olivine crystals to add up leading to a macroscopic scale anisotropic viscosity (AV) linked to the CPO.

The role of anisotropic viscosity has been examined in various geodynamic scenarios. However, due to the computational complexity of the problem, there has not been a comprehensive integration of olivine CPO development with the linked anisotropic viscous behavior into geodynamic models. Here, we present an approach that directly derives anisotropic viscosity parameters from the orientation distribution (texture) of olivine grains.

Olivine polycrystals exhibit an orthotropic symmetry within the CPO’s reference frame, i.e., when the models' reference frame is aligned with the mean orientation of the olivine symmetry axes. In this case, AV can be characterized by six independent parameters, which are related to the Hill plastic yield criteria (Hill, 1948; Signorelli et al., 2021).  To determine these independent parameters, existing micromechanical models are employed, enabling the calculation of the stress required to achieve a specific strain rate on an aggregate. By applying the micromechanical model to a given texture, we can evaluate different strain rates and use the anisotropic constitutive equation (e.g. Signorelli et al., 2021) to fit the calculated strain rates with those employed in the micromechanical model, thereby identifying the best-fitting anisotropic parameters. However, simply applying this method inside a geodynamic model is too computationally costly. Thus, we built a large database (>10 000 entries) of textures occurring in geodynamic simulations, describing each texture with a set of scores derived from the orientation matrices of the three olivine symmetry axes. For each texture we applied the micromechanical model by Hansen et al., (2016), and used a minimum search function to find the best fitting AV parameters. Finally, linear regression models were utilized to establish a straightforward mapping of anisotropic parameters directly from a combination of textures scores. To determine which combination of texture scores provides the best outcome, we tested the results against both laboratory data and on a simple shear (numerical) experiment.

The approach presented here is advantageous for integrating anisotropic viscosity into 4D geodynamic models because it allows for a direct determination of the viscosity tensor from the evolving rock texture, saving a large amount of computational time.

Hansen, L.N., Conrad, C.P., Boneh, Y., Skemer, P., Warren, J.M., and Kohlstedt, D.L., 2016a, Viscous anisotropy of textured olivine aggregates: 2. Micromechanical model: Journal of Geophysical Research: Solid Earth

Hill, R., 1948, A theory of the yielding and plastic flow of anisotropic metals: Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences

Signorelli, J., Hassani, R., Tommasi, A., and Mameri, L., 2021, An effective parameterization of texture-induced viscous anisotropy in orthotropic materials with application for modeling geodynamical flows