This study is based on the analysis of detailed measurements of firn dielectric properties performed in Antarctica through coring down to 106 m. Dielectric measurements in the frequency band (0.4–2.5 GHz) have been carried out using an open−resonator probe. Density was also measured for the same samples. The experimental results confirmed the well−known dependence of the real part of permittivity ε′ on depth and density, showing an increase of ε′ with density. The imaginary part also increases with depth with a rather complex dependence on frequency, probably due to the presence of salts or impurities.

The analysis of the experimental data was performed by implementing 3D and 2D full wave numerical models, to simulate a mixture of firn crystals at prescribed densities, corresponding to the measured densities on the ice cores. The numerical analysis of the ensemble of inclusions showed that the usual symmetric formulae used for modeling ice dielectric properties agree with the average results of the simulation, but they are not able to explain the spreading of the measured data at given density.

A dielectric model was then developed allowing for quantification of the dependence of dielectric properties on density, by combining two models: one consisting in firn crystals into an air host, the other assuming the presence of air inclusions into a homogeneous firn host. The weighted equation is based on the volume fraction. A simple geometric shape (ellipsoidal) is assumed for both ice crystals and air inclusions. This kind of shape is reasonable for the purpose of the dielectric study. The result is a mixture, smoothly changing from firn particles in air (low density) to air bubbles in an ice matrix (high density).

A statistical analysis has been accomplished to investigate the dependence of the dielectric properties on the geometrical arrangement of the inclusions. For that purpose, a large number of simulations with different arrangements (micro−states) giving rise to the same average density (macro−states) has been carried out. The permittivity change due to micro−state variability appears to be at least two−three times the model variation due to density alone, and comparable to the measured variability at a given depth, suggesting that firn structure has a significant effect on the dielectric properties.

这项研究基于对南极至低至106 m取芯进行的电介质介电特性的详细测量分析。频带（0.4–2.5 GHz）中的介电测量已使用开放式谐振器探头进行。还测量了相同样品的密度。实验结果证实了介电常数ε'的实部对深度和密度的众所周知的依赖性，表明ε'随着密度的增加而增加。虚部也随着深度的增加而增加，并且对频率的依赖性相当复杂，这可能是由于盐或杂质的存在所致。

通过实施3D和2D全波数值模型对实验数据进行分析，以模拟指定密度下的烧结晶体混合物，该密度与冰芯上的测量密度相对应。对夹杂物整体的数值分析表明，用于模拟冰介电特性的常用对称公式与模拟的平均结果一致，但是它们不能解释在给定密度下测量数据的分布。

然后，通过结合两种模型来开发介电模型，从而可以量化介电性质对密度的依赖性：一种模型将烧结晶体包含在空气主体中，另一种假设将空气夹杂物存在于均匀的烧结主体中。加权方程式基于体积分数。冰晶和空气夹杂物均采用简单的几何形状（椭圆形）。对于介电研究而言，这种形状是合理的。结果是一种混合物，从空气中的烧结颗粒（低密度）平稳地转变为冰基质中的气泡（高密度）。

已经完成统计分析以研究介电性质对夹杂物的几何排列的依赖性。为了这个目的，已经进行了具有不同排列（微观状态）的大量模拟，从而产生了相同的平均密度（宏观状态）。由于微状态变异性引起的介电常数变化至少是由于密度引起的模型变异性的2到3倍，并且与给定深度处的测量变异性相当，这表明烧结结构对介电性能具有显着影响。