A microstructure-based parameterization of the effectivetransverse isotropic elasticity tensor of snow, firn, and porous ice

Effective elastic properties of snow, firn, and porous ice are key for
various applications and influenced by ice volume fraction and
different types of anisotropy. The geometrical anisotropy of the ice-matrix created by temperature gradient metamorphism in low-density
snow and firn and the crystallographic anisotropy commonly created
upon deformation in high-density, porous ice. Towards a quantitative-distinction of the impact of the different anisotropies on elasticity,
we derived a parametrization for the effective elasticity tensor over
the entire range of volume fractions as a function of density and
geometrical anisotropy. We employed FEM simulations on 395 X-ray
tomography microstructures of Lab, Alpine, Arctic, and Antarctic
samples. We employed an empirical two-parameter modification of the
anisotropic Hashin Shtrikman bounds to obtain a closed-form
parametrization accounting for density, anisotropy, and the correct
limiting behavior for bubbly ice. We compare our prediction to
previous parametrizations derived in limited density regimes and we
utilize the Thomson parameter to compare the geometrical-elastic
anisotropy to the crystallographic-elastic anisotropy of
monocrystalline ice. Our results suggest that a coupled treatment of
geometrical and crystallographic effects would be beneficial for a
careful interpretation of acoustic measurements in deep firn.