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Theoretical formulas without a clear comprehension of their intrinsic meaning are of difficult use in the context of practical applications. In this paper, we investigate on the physical meaning of existing first-order solutions for the field scattered by layered structures with rough interfaces, which were derived by Imperatore in the framework of perturbation theory. To capture the intrinsic significance of the closed-form scattering solutions, suitable expansions are rigorously performed by leveraging on local scattering descriptors. The obtained series expansions, which can be seen as ray series, can be then accurately analyzed showing that each term has a direct physical explanation. The analysis is carried out for both from- and through-layered-structure scattering configurations. As a result, analytical perturbative solutions turn out to be completely interpretable by simple physical concepts, so that the global scattering response can be interpreted as the superposition of single-scattering interaction mechanisms taking place locally, which are filtered by the layered structure. The meaning of the first-order approximation is also discussed in the layered structure context. Finally, we give a complete explanation for the scattering enhancement phenomenon contemplated in the first-order limit.