Investigating the influence of the grain size and distribution on the macroscopic dielectric properties of Antarctic firn

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.