All previous random media theories that have been applied to microwave remote sensing applications are only valid for cases of weak fluctuations of dielectric constant. By taking into proper account the singularity of the dyadic Green's function in the renormalization method, the low-frequency limit of vector electromagnetic wave scattering from a random medium with large variance of permittivity function is studied. The strong fluctuation random theory is then applied to a ‘discrete scatterer’ problem in which the permittivity can assume only two values. It is then shown that the results of the strong fluctuation theory are consistent with those derived from discrete scatterer theory for all values of dielectric constants of the scatterers. Numerical results of the effective permittivity are illustrated for random media with isotropic and anisotropic correlation functions. It is shown that the results of the weak fluctuations theory differ significantly from those of the strong fluctuation theory. The second moment of the field in the backscattering direction is calculated using the distorted Born approximation and illustrated using parameters typically encountered in microwave remote sensing of vegetation.
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