BOUNDS ON THE COMPLEX PERMITTIVITY OF SEA-ICE

An analytic method for obtaining bounds on effective properties of com posites is applied to the complex permittivity epsilon of sea ice. Th e sea ice is assumed to be a two-component random medium consisting of pure ice of permittivity epsilon(1) and brine of permittivity a,. The method exploits the properties of epsilon as an analytic function of the ratio epsilon(1)/epsilon(2). Two types of bounds on epsilon are obtained. The first bound R(1) is a region in the complex epsilon pla ne which assumes only that the relative volume fractions p(1) and p(2) = 1 - p(1) of the ice and brine are known. The region R(1) is bounded by circular arcs and epsilon for any microgeometry with the given vo lume fractions must lie inside it. In addition to the volume fractions , the second bound R(2) assumes that the sea ice is statistically isot ropic within the horizontal plane. The region R(2) is again bounded by circular arcs and lies inside R(1). Built into the method is a system atic way of obtaining tighter bounds on epsilon by incorporating info rmation about the correlation functions of the brine inclusions. The b ounding method developed here, which does not assume any specific geom etry 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 inclusi on geometry, which are simply not satisfied by the sea ice under many conditions. The bounds R(1) and R(2) are compared with experimental da ta obtained from artificially grown sea ice at the frequencies 4.8 and 9.5 GHz. Excellent agreement with the data is achieved.