Bounds on the complex permittivity of sea ice

An analytic method for obtaining bounds on effective properties of composites is applied to the complex permittivity e* of sea ice. The sea ice is assumed to be a two-component random medium consisting of pure ice of permittivity e1, and brine of permittivity e2. The method exploits the properties of e* as an analytic function of the ratio e1/e2. Two types of bounds on e * are obtained. The first bound R1 is a region in the complex e* plane which assumes only that the relative volume fractions pl and p2 = 1 - pl of the ice and brine are known. The region Rl is bounded by circular arcs and e* 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.