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Each region of the Earth’s crust can be morphologically modeled as a suitable layered structure, in which some amount of roughness is presented by every interface. Actually, propagation in stratified soil, sand cover of arid regions, forest canopies, urban buildings, snow blanket, snow cover ice, sea ice and glaciers, oil flood on sea surface, and other natural scenes can be modeled referring to most likely discrete (piecewise-constant) systems, rather than continuous, with some amount of roughness presented by every interface. Moreover, a key issue in remote sensing of other Planets is to reveal the content under the surface illuminated by the sensors: also in this case a layered model is usually employed. The aim of this chapter is to provide a structured presentation of the main theoretical and conceptual foundations for the problem of the electromagnetic wave interaction with layered rough media. In the first part, special emphasis is on the analytical models obtainable in powerful framework of the perturbation approach. The comprehensive scattering model based on the Boundary Perturbation Theory (BPT), which permits to systematically analyze the bi-static scattering patterns of 3D multilayered rough media, is then presented highlighting the formal connections with all the previously existing simplified perturbative models, as well as its wide relevance in the remote sensing applications scenario. The polarimetric Scattering Matrix of a multilayered medium with an arbitrary number of rough interfaces is also provided. The second part is devoted to a mathematical description which connects the concepts of local scattering and global scattering. Consequently, a functional decomposition of the BPT global scattering solution in terms of basic single-scattering local processes is rigorously established. The scattering decomposition gives insight into the BPT analytical results, so enabling a relevant physicalrevealing interpretation involving ray-series representation. Accordingly, in first-order limit, the way in which the character of the local scattering processes emerges is dictated by the nature of the structural filter action, which is inherently governed by the series of coherent interactions with the medium boundaries. As a result, the phenomenologically successful BPT model opens the way toward new techniques for solving the inverse problem, for designing SAR processing algorithms, and for modelling the time-domain response of layered structures. 11

Electromagnetic Models for Remote Sensing of Layered Rough Media