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A solution to the inverse problem for a three-layer medium with nonsmooth boundaries, representing a large class of natural subsurface structures, is developed in this paper using simulated radar data. The retrieval of the layered medium parameters is accomplished as a sequential nonlinear optimization starting from the top layer and progressively characterizing the layers below. The optimization process is achieved by an iterative technique built around the solution of the forward scattering problem. The forward scattering process is formulated by using the extended boundary condition method (EBCM) and constructing reflection and transmission matrices for each interface. These matrices are then combined into the generalized scattering matrix for the entire system, from which radar scattering coefficients are then computed. To be efficiently utilized in the inverse problem, the forward scattering model is simulated over a wide range of unknowns to obtain a complete set of subspace-based equivalent closed-form models that relate radar backscattering coefficients to the sought-for parameters including dielectric constants of each layer and separation of the layers. The inversion algorithm is implemented as a modified conjugate-gradient-based nonlinear optimization. It is shown that this technique results in accurate retrieval of surface and subsurface parameters, even in the presence of noise

Retrieval of Parameters for Three-Layer Media with Nonsmooth Interfaces for Subsurface Remote Sensing