Matrix model for polarized electromagnetic wave propagation through ice based on Fujita et al. (2006). The model uses Jones vectors to represent any single polarization state with updates to the polarization based on both anisotropic transmission (birefringence) and scattering. By assuming that the radar wavelength is longer than the scale of the anisotropic ice crystals we can approximate the ice as an effective medium.
Fujita, S., Maeno, H., & Matsuoka, K. (2006). Radio-wave depolarization and scattering within ice sheets: A matrix-based model to link radar and ice-core measurements and its application. Journal of Glaciology, 52 (178), 407–424. doi: 10.3189/172756506781828548
See other work which uses a similar model formulation:
Ershadi, M. R., Drews, R., Mart´ın, C., Eisen, O., Ritz, C., Corr, H., . . . Mulvaney, R. (2022). Polarimetric radar reveals the spatial distribution of ice fabric at domes and divides in East Antarctica. Cryosphere, 16 (5), 1719–1739. doi: 10.5194/tc-16-1719-2022
Jordan, T. M., Mart´ın, C., Brisbourne, A. M., Schroeder, D. M., & Smith, A. M. (2022). Radar Characterization of Ice Crystal Orientation Fabric and Anisotropic Viscosity Within an Antarctic Ice Stream. Journal of Geophysical Research: Earth Surface, 127 (6), 1–24. doi: 10.1029/2022JF006673
Jordan, T. M., Schroeder, D. M., Castelletti, D., Li, J., & Dall, J. (2019). A Polarimetric Coherence Method to Determine Ice Crystal Orientation Fabric from Radar Sounding: Application to the NEEM Ice Core Region. IEEE Transactions on Geoscience and Remote Sensing, 57 (11), 8641–8657. doi: 10.1109/TGRS.2019.2921980