Abstract
We determine the statistical distributions for the co- and cross-polarized scattered intensity ratios characterizing three-dimensional layered structures with an arbitrary number of rough interfaces illuminated by a plane wave. Within the framework of the first-order small perturbation method, we show for slightly rough interfaces with infinite surface areas and Gaussian height distributions that the intensity ratio is a random variable, the probability law of which is a function of two parameters. For air/clayey soil/rock structures, we analyze the influence of a snow layer upon the probability laws and we validate the closed-form formulae by comparison with Monte-Carlo simulations.
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