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An optimization problem is proposed for inferring physical properties of polycrystals given ultrasonic (elastic) wave velocity measurements, made across multiple sample orientations. The feasibility of the method is demonstrated by inferring both the effective grain elastic parameters and the grain c-axis orientation distribution function (ODF) of ice-core samples from Priestley glacier, Antarctica. The method relies on expanding the ODF in terms of a spherical harmonic series, which allows for a non-parametric estimation of the sample ODF. Moreover, any linear combination of the Voigt (strain) and Reuss (stress) homogenization scheme is allowed, although for glacier ice, the exact choice is found to matter little for bulk elastic behaviour, and thus for inferred physical properties, too. Finally, the accuracy of the inferred grain elastic parameters is discussed, including the well-posedness and shortcomings of the inverse problem, relevant for future adoptions in glaciology, geology and elsewhere.

We investigate the errors caused by neglecting the crystal-orientation fabric when inferring the basal friction coefficient field, and whether such errors can be alleviated by inferring an isotropic enhancement factor field to compensate for missing fabric information. We calculate the steady states that arise from ice flowing over a sticky spot and a bedrock bump using a vertical-slab numerical ice-flow model, consisting of a Weertman sliding law and the anisotropic Johnson flow law, coupled to a spectral fabric model of lattice rotation and dynamic recrystallisation. Given the steady or transient states as input for a canonical adjoint-based inversion, we find that Glen's isotropic flow law cannot necessarily be used to infer the true basal drag or friction coefficient field, which are obscured by the orientation fabric, thus potentially affecting vertically integrated mass fluxes. By inverting for an equivalent isotropic enhancement factor, a more accurate mass flux can be recovered, suggesting that joint inversions for basal friction and the isotropic flow-rate factor may be able to compensate for mechanical anisotropies caused by the fabric. Thus, in addition to other sources of rheological uncertainty, fabric might complicate attempts to relate subglacial conditions to basal properties inferred from an inversion relying on Glen's law.

We introduce a transfer matrix model for radio-wave propagation through layered anisotropic ice that permits an arbitrary dielectric permittivity tensor in each layer. The model is used to investigate how crystal orientation fabrics without a vertical principal direction affect polarimetric radar returns over glaciers and ice sheets. By expanding the c-axis orientation distribution in terms of a spherical harmonic series, we find that radar returns from synthetic fabric profiles are relatively insensitive to the harmonic mode responsible for a nonvertical principal direction; however, only for normally incident waves. Consequently, the strength of this mode might be relatively difficult to infer in glaciers and ice sheets, which in turn has implications for the ability to determine the full second-order structure tensor, needed to infer the local flow regime, flow history, or to represent the directional viscosity structure of glacier ice for ice-flow modeling.

The crystal structure within an ice sheet evolves in response to deformation; hence ice-crystal fabric records ice-flow history. However, the complexity of crystal-fabric evolution, and the lack of model results with which to compare data, limit the usefulness of fabric measurements, particularly in areas with complex ice dynamics. Here, we use an ice-flow model to identify characteristic fabrics associated with ice-stream onset, with the goal of aiding interpretation of fabric measurements. Using time-dependent model simulations, we identify how crystal fabric may be used to diagnose changes in an ice stream's speed or lateral position. Consistent with previous work, we find that fabric within an ice stream is generally a vertical girdle, though horizontal shear can lead to a horizontal single maximum. Transient simulations demonstrate that effects from changes in flow may be recorded in the crystal fabric for thousands of years after an ice stream activates and more than ten thousand years after an ice stream stagnates. Both transient and steady effects on fabric are sufficiently large as to be measurable in ice cores or with polarized radar, suggesting that in certain scenarios fabric could be used to identify past flow changes. These results could be used to design radar surveys in areas where ice streams are known to deactivate, such as the Siple Coast in Antarctica, or where they may migrate laterally or widen, such as in Northeast Greenland.

Bulk directional enhancement factors are determined for axisymmetric (girdle and single-maximum) orientation fabrics using a transversely isotropic grain rheology with an orientation-dependent non-linear grain fluidity. Compared to grain fluidities that are simplified as orientation independent, we find that bulk strain-rate enhancements for intermediate-to-strong axisymmetric fabrics can be up to a factor of ten larger, assuming stress homogenization over the polycrystal scale. Our work thus extends previous results based on simple basal slip (Schmid) grain rheologies to the transversely isotropic rheology, which has implications for large-scale anisotropic ice-flow modelling that relies on a transversely isotropic grain rheology. In order to derive bulk enhancement factors for arbitrary evolving fabrics, we expand the c-axis distribution in terms of a spherical harmonic series, which allows the rheology-required structure tensors through order eight to easily be calculated and provides an alternative to current structure-tensor-based modelling.