Analytical parametrization of self-consistent polycrystal mechanics: Fast calculation of upper mantle anisotropy

Progressive deformation of upper mantle rocks via dislocation creep causes their constituent crystals to take on a non-random orientation distribution (crystallographic preferred orientation or CPO) whose observable signatures include shear-wave splitting and azimuthal dependence of surface wave speeds. Comparison of these signatures with mantle flow models thus allows mantle dynamics to be unraveled on global and regional scales. However, existing self-consistent models of CPO evolution are computationally expensive when used with 3-D and/or time-dependent convection models. Here we propose a new method, called ANPAR, which is based on an analytical parametrization of the crystallographic spin predicted by the second-order (SO) self-consistent theory. Our parametrization runs ≈2-6 × 10⁴ times faster than the SO model and fits its predictions for CPO and crystallographic spin with a variance reduction >99 per cent. We illustrate the ANPAR model predictions for the deformation of olivine with three dominant slip systems, (010)[100], (001)[100] and (010)[001], for three uniform deformations (uniaxial compression, pure shear and simple shear) and for a corner-flow model of a spreading mid-ocean ridge.