Bounds on the complex permittivity of sea ice

Abstract

An analytic method for obtaining bounds on effective properties of composites is applied to the complex permittivity ∈* of sea ice. The sea ice is assumed to be a two‐component random medium consisting of pure ice of permittivity ∈1 and brine of permittivity ∈2. The method exploits the properties of ∈* as an analytic function of the ratio ∈1/∈2. Two types of bounds on ∈* are obtained. The first bound R1 is a region in the complex ∈* plane which assumes only that the relative volume fractions p1 and p2 = 1 ‐ p1 of the ice and brine are known. The region R1 is bounded by circular arcs and ∈* for any microgeometry with the given volume fractions must lie inside it. In addition to the volume fractions, the second bound R2 assumes that the sea ice is statistically isotropic within the horizontal plane. The region R2 is again bounded by circular arcs and lies inside R1. Built into the method is a systematic way of obtaining tighter bounds on ∈* by incorporating information about the correlation functions of the brine inclusions. The bounding method developed here, which does not assume any specific geometry for the brine inclusions, offers an alternative to the classical mixing formula approach adopted previously in the study of sea ice. In these mixing formulas, specific assumptions are made about the inclusion geometry, which are simply not satisfied by the sea ice under many conditions. The bounds R1 and R2 are compared with experimental data obtained from artificially grown sea ice at the frequencies 4.8 and 9.5 GHz. Excellent agreement with the data is achieved.