Elastic anisotropy of polycrystalline ice with transversely isotropic and orthotropic symmetry

Abstract

Ice crystals in glaciers and ice sheets have hexagonal crystallographic symmetry, and are mechanically anisotropic. A preferred orientation of ice crystals develops as stress increases, and this is important for understanding and modeling glaciers and ice sheets. The elastic stiffness tensor of a polycrystalline aggregate of ice crystals is expressed in terms of the coefficients in an expansion of the crystal orientation distribution function in generalized Legendre functions. Expressions for the components of the elastic stiffness tensor in terms of these coefficients allow information on the crystal orientation distribution function to be obtained from elastic wave velocity measurements, without the need to assume a particular idealized fabric. This approach enables more complete information on the orientation distribution function to be determined from ultrasonic, sonic and seismic data. Application of the method to published ultrasonic velocity measurements on samples from the Dye 3, Greenland, deep ice core shows that a description of the ice fabric in terms of a second-rank fabric tensor is insufficient to describe the elastic anisotropy of polycrystalline ice.