Critical investigation of calculation methods for the elastic velocities in anisotropic ice polycrystals

Abstract

Crystallographic texture (or fabric) evolution with depth along ice cores can be evaluated using borehole sonic logging measurements. These measurements provide the velocities of elastic waves that depend on the ice polycrystal anisotropy, and they can further be related to the ice texture. To do so, elastic velocities need to be inverted from a modeling approach that relate elastic velocities to ice texture. So far, two different approaches can be found. A classical model is based on the effective medium theory; the velocities are derived from elastic wave propagation in a homogeneous medium characterized by an average elasticity tensor. Alternatively, a velocity averaging approach was used in the glaciology community that averages the velocities from a given population of single crystals with different orientations. In this paper, we show that the velocity averaging method is erroneous in the present context. This is demonstrated for the case of waves propagating along the clustering direction of a highly textured polycrystal, characterized by crystallographic c axes oriented along a single maximum (cluster). In this case, two different shear wave velocities are obtained while a unique velocity is theoretically expected. While making use of this velocity averaging method, reference work by Bennett (1968) does not end with such an unphysical result. We show that this is due to the use of erroneous expressions for the shear wave velocities in a single crystal, as the starting point of the averaging process. Because of the weak elastic anisotropy of ice single crystal, the inversion of the measured velocities requires accurate modeling approaches. We demonstrate here that the inversion method based on the effective medium theory provides physically based results and should therefore be favored.