On the Limitations of Using Polarimetric Radar Sounding to Infer the Crystal Orientation Fabric of Ice Masses

Nicholas M Rathmann,David A Lilien,Tamara A Gerber,Dorthe Dahl‐Jensen,Tun Jan Young,Aslak Grinsted

doi:10.1029/2021gl096244

Nicholas M Rathmann, David A Lilien + Show 4 more

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https://doi.org/10.1029/2021gl096244

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Abstract

AbstractWe 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.

Highlights

Single crystals of ice and olivine are both viscously (Bai et al, 1991; Duval et al, 1983) and elastically (Gammon et al, 1983; Kumazawa & Anderson, 1969) anisotropic
In line with existing transfer matrix models for fabric profiles that strengthen with depth (e.g., Young, Martín, et al, 2021), a reduction in the vertical spacing between nodes in δPHH and φHV is found, and δPHV displays a depth-constant 90° periodicity
By expanding the grain c-axis distribution in terms of a spherical harmonic series, we found that radar returns over glacier ice are, for normal incidence, insensitive to whether or not a vertical principal fabric direction exists

Summary

Introduction

Single crystals of ice and olivine are both viscously (Bai et al, 1991; Duval et al, 1983) and elastically (Gammon et al, 1983; Kumazawa & Anderson, 1969) anisotropic. The permittivity tensor of a given layer is diagonal if 〈c ⊗ c〉 is isotropic or has a vertical principal direction and is rotated into its horizontal eigenbasis. In the general case of obliquely incident waves in birefringent media with nonzero off-diagonal elements in the permittivity tensor, the total radiation consists of four partial plane waves, and mode coupling takes place at interfaces (Yeh, 1980). Layered models that allow for arbitrary dielectric tensors, and arbitrary orientation fabrics, involve the manipulation of 4 × 4 matrices. Let the wave be incident on an anisotropic layer below that is horizontally homogeneous and has a permittivity of ε0ε and a scalar permeability of μ0μ.

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