The rheology and evolution of the polar ice sheet are deeply influenced by the anisotropy of ice crystals. Studying the anisotropy of ice crystals can help to well understand and predict the behavior of the polar ice sheet and then the sea level rising and global climate change. In this paper, firstly, we deduce the expression of eigenvalues and eigenvectors of anisotropic media, which are determined by permittivity tensor and geometry of media. Then, the analytic formulas of reflection and transmission coefficients are derived directly by matrix transformation. Some models with real ice parameters are tested, and they present some special features at the anisotropic interface. We also discuss the physical meanings of eigenvalues and eigenvectors and the geometry analyzing to polarimetric radar. This analytic solution reveals the functional relationship between the macroradar reflection and the microphysical properties of ice crystals, which provides a feasibility of ice fabric identification by polarimetric radar detection.

中文翻译：

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各向异性冰盖界面反射透射问题的解析解

极地冰盖的流变性和演变受到冰晶各向异性的影响。研究冰晶的各向异性可以帮助您更好地理解和预测极地冰盖的行为，进而了解海平面上升和全球气候变化的情况。在本文中，首先，我们推导了各向异性介质的特征值和特征向量的表达式，它们由介电常数张量和介质的几何形状决定。然后，通过矩阵变换直接导出反射系数和透射系数的解析公式。测试了一些具有真实冰参数的模型，它们在各向异性界面上表现出一些特殊功能。我们还讨论了特征值和特征向量的物理含义，以及对极化雷达进行几何分析。