3-D Vector Electromagnetic Scattering From Arbitrary Random Rough Surfaces Using Stabilized Extended Boundary Condition Method for Remote Sensing of Soil Moisture

Abstract

We develop the stabilized extended boundary condition method (SEBCM) based on the classical EBCM to solve the 3-D vector electromagnetic scattering problem from arbitrary random rough surfaces. Similar to the classical EBCM, we expand the fields in terms of Floquet modes and match the extended boundary conditions at test surfaces away from the actual rough surface to retrieve the surface currents and therefore the scattered fields. However, to solve long-standing stability problems of the classical EBCM, we introduce a z-coordinate transformation to restrict and control the test surface locations explicitly. We also introduce the concepts of moderated test surface locations and balanced k-charts for further stabilization and optimization of the solutions. The computational efficiency is optimized by judicious submatrix decomposition. The resulting bistatic scattering cross sections are validated by comparing with analytical and numerical solutions. Specifically, the solutions are compared with those from the small perturbation method and small-slope approximation within their validity region, and with those from the method of moments outside the validity domains of analytical solutions. It is shown that SEBCM gives accurate, numerically efficient, full-wave solutions over a large range of surface roughnesses and medium losses, which are far beyond the validity range of analytical methods. These properties are expected to make SEBCM a competitive forward solver for soil moisture retrieval from radar measurements.