Backscattering of electromagnetic waves from layered rough surfaces and its application in estimating deep soil moisture

An analytical method to calculate the scattering coefficients of a three-layer 3D rough surface is introduced. The two rough interfaces are assumed to be distinct. The waves in each region are represented as a superposition of an infinite number of up- and down-going spectral wave components, whose amplitudes are found by applying the boundary conditions. A small-perturbation formulation is used in the process and the scattering coefficients are derived to the first order. The formulation is validated against known solutions for special cases of flat interfaces as well as the single rough surfaces. Results are then generated for several cases of the three-layer rough interface medium, to be used for modeling of the backscattered signals from a tower-based radar system and subsequent estimation of multilayered soil properties such as moisture content and subsurface layer height