Analytical Parameterization of Self-Consistent Polycrystal Mechanics: Fast Calculation of Upper Mantle Anisotropy

Progressive deformation of upper mantle rocks via dislocation creep causes their con- stituent crystals to take on a non-random orientation distribution (crystallographic pre- ferred orientation or CPO) whose observable signatures include shear-wave splitting and azimuthal dependence of surface wave speeds. Comparison of these signatures with man- tle 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 in 3-D and/or time-dependent convection models. Here we propose a new method, called ANPAR, which is based on an analytical parameterisation of the crystallographic spin predicted by the second-order (SO) self-consistent theory. Our pa- rameterisation runs ≈2-6 x 10⁴ times faster than the SO model and fits its predictions for CPO and crystallographic spin with a variance reduction > 99%. We illustrate the AN- PAR model predictions for the deformation of olivine with three dominant slip systems, (010)[100], (001)[100] and (010)[001], for three uniform deformations (uniaxial com- 2 Neil J. Goulding et al. pression, pure shear, simple shear) and for a corner-flow model of a spreading mid-ocean ridge.