Analytical parameterization of self-consistent polycrystal mechanics

Seismic anisotropy in the upper mantle is primarily due to the crystal preferred orientation (CPO) of olivine crystals, and reflects the space- and time-dependence of the deformation experienced by mantle rocks. Existing models (VPSC, Second Order, D-Rex, etc.) for the evolution of CPO make predictions in good agreement with laboratory experiments, but are too computationally intensive to be incorporated into 3-D mantle flow codes, especially when the flow is time-dependent. Using the state-of-the-art Second Order (SO) self-consistent model as our benchmark, we show that its predictions of crystallographic spin as a function of crystal orientation can be parameterized analytically in a surprisingly simple way that reduces the computational cost by orders of magnitude. The parameterization allows for different strengths of the three dominant olivine slip systems, as well as a macroscopic strain rate tensor having an arbitrary orientation relative to the finite-strain ellipsoid that encodes the prior deformation history. The parameterization agrees almost perfectly with the SO model (variance reduction greater than 99.7%), but with a computational cost that is smaller by a factor 2.10⁴. We will illustrate the predictions of the parameterization using several geophysically relevant flow fields.