Analytical parameterization of self-consistent polycrystal mechanics

Tuesday, 16 December 2014: 8:45 AM
Neil M Ribe, University of Paris-Sud 11, Orsay, France, Neil Goulding, University of Bristol, School of Earth Sciences, Bristol, United Kingdom, Olivier Castelnau, PIMM Laboratoire Procédés et Ingénierie en Mécanique et Matériaux, Paris, France, Andrew Walker, University of Leeds, School of Earth and Environment, Leeds, United Kingdom and James M Wookey, University of Bristol, School of Earth Sciences, Bristol, BS8, United Kingdom
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.