  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
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 parameterisation runs approximately 2-3 x 10^4 times faster than
the SO model and fits its predictions for CPO and crystallographic spin with a
variance reduction > 99%. We illustrate the ANPAR model predictions for three
uniform deformations (uniaxial compression, pure shear, simple shear) and for a
corner-flow model of a spreading ridge.
