Xueyang Duan

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

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.

Coherent Scattering of Electromagnetic Waves From Two-Layer Rough Surfaces Within the Kirchhoff Regime

We present an analytical solution for coherent scattering of electromagnetic waves from a two-layer rough surface structure with uncorrelated random rough interfaces. The Kirchhoff approximation is used to predict the coherent (specular) component of the scattered wave from a layered rough surface that is assumed to have radii of curvature much larger than the wavelength to allow the application of the method. The roughness on both boundaries is assumed small such that the coherent component of the scattered wave is dominant. The derived solution includes all orders of the scattered wave and has a simple algebraic expression that can be readily computed. We validate the solution against a numerical method and present simulation results for various cases.

Bistatic Vector 3-D Scattering From Layered Rough Surfaces Using Stabilized Extended Boundary Condition Method

A model of 3-D electromagnetic scattering from multiple rough surfaces within homogeneous-layered or vertically inhomogeneous media is developed in this work. This model, aimed at radar remote sensing of surface-to-depth profiles of soil moisture, computes total bistatic radar cross sections from the multilayer structure based on the scattering matrix approach, cascading the scattering matrices of individual rough interfaces and the layer propagation matrices. We have recently developed the single-surface scattering matrix obtained using the stabilized extended boundary condition method (SEBCM) providing both large validity range over the surface roughness and higher computational efficiency compared to fully numerical solutions. In the presence of a vertical dielectric profile, the aggregate scattering matrix of the profile is obtained from the model of stratified homogeneous layers. Results of this multilayer SEBCM model are validated with small perturbation method of up to third order and the method of moments. Additionally, the model is used to perform a sensitivity analysis of the scattering cross section with respect to perturbations in ground parameters such as subsurface layer separation, roughness of surface and subsurface layers, and moisture content of subsurface layers. The multilayer SEBCM model developed in this work presents a realistic and computationally feasible method for solving scattering from multilayer rough surfaces of realistic roughness, providing an accurate and efficient tool for future retrievals of soil moisture profiles.

Vector electromagnetic scattering from layered rough surfaces with buried discrete random media for subsurface and root-zone soil moisture sensing

In this work, a 3D scattering model from layered arbitrarily random rough surfaces with embedded discrete random scatterers is constructed based on the scattering matrix approach. Scattering matrix of a single rough surface is found using the stabilized extended boundary condition method (SEBCM). Meanwhile, by finding the T-matrices of discrete scatterers using analytical or numerical methods, the random medium scattering solution is found based on the recursive T-matrix approach and near-to-far field transformed numerical plane wave expansion of the vector spherical harmonics. Solutions provided in this work include multiple scattering effects among the medium scatterers and between subsurfaces and sublayers. The high computational efficiency and accuracy of this method enable it to serve as a powerful tool for studying the role of vegetation roots and other sublayer inhomogeneities in retrieval of subsurface and root-zone soil moisture from radar measurements.

Electromagnetic scattering from arbitrary random rough surfaces using stabilized extended boundary condition method (SEBCM) for remote sensing of soil moisture

In this paper, the stabilized extended boundary condition method (SEBCM) is developed based on the classical EBCM to solve both 2D and 3D electromagnetic scattering from arbitrary random rough surfaces. The SEBCM gives accurate full wave solutions over large range of surface roughnesses and medium losses, which are far beyond the validity range of analytical methods, and perform with much higher efficiency than numerical methods. These properties make SEBCM a competitive forward model in the inverse problem for soil moisture retrieval from radar measurements.

Full-Wave Electromagnetic Scattering From Rough Surfaces With Buried Inhomogeneities

We develop a methodology for modeling coherent electromagnetic scattering from rough surfaces with buried inhomogeneities in three dimensions. The inhomogeneities considered in this paper include random spherical media, random cylindrical media, and root-like cylindrical clusters. They are used to simulate rocks, ice particles, and vegetation roots buried beneath the ground surface that can be seen by the low-frequency radars in Earth remote sensing applications. The approach we develop first calculates volumetric scattering from the media using coherent approaches, including both the conventional recursive transition matrix (T-matrix) method as well as a new generalized iterative extended boundary condition method we developed for tilted finite cylinders, and then transforms the T-matrix to the scattering matrix, which is then used to form the full scattered field of layered structures with rough surface and subsurfaces. We validate the methodology by comparing with other numerical solutions for special cases, and show sensitivity results for scattering from rough surface with buried random spherical media and random cylindrical media of different densities. We also construct a basic root model and calculate the scattering cross sections from single and multiple root clusters with or without a subsurface interface underneath. With the approach developed in this paper, we are able to study the sensitivity of radar signals to subsurface scatterers. For example, our simulations show that, depending on their density and water content, buried roots could enhance the backscatter from a single rough surface by as much as 5 dB in co-pol components, and substantially more in cross-pol components. The results of this model are expected to enable more accurate geophysical retrievals of soil moisture as well as soil organic content.

Experimental Verification of the Recursive T-Matrix Method Solutions at Microwave Frequencies

We present an experimental verification of the recursive T-matrix method (RTM), which is a common method for solving electromagnetic scattering from multiple scatterers. This is done using an antenna and propagation model uniquely suited for T-matrices and network analyzer measurements. In the experiments, we use a multistatic system to measure the scattering from collections of objects consisting of conducting or dielectric spheres, as well as conducting cylinders. In simulation, we calculate the scattering from the objects using the RTM and further predict the transition parameters expected between the receivers and the transmitter in the measurement setup using a propagation model. The predicted and measured values of the transmission parameters are compared, and thereby used to verify the recursive T-matrix algorithm. Good agreement observed in these results provides experimental validation of the RTM.

Airborne Microwave Observatory of Subcanopy and Subsurface radar retrieval of root zone soil moisture: Preliminary results

We present an overview of the radar retrieval processing system for estimation of root zone soil moisture (RZSM) in several major North American biomes as one of the products of the Airborne Microwave Observatory of Subcanopy and Subsurface (AirMOSS) project. The AirMOSS mission is briefly described along with the methodologies implemented to collect field data, to prepare several data layers required for retrievals, and to ultimately retrieve the soil moisture profiles. The retrieved soil moisture maps over several sites will be available when the radar data from AirMOSS flights are fully processed and calibrated, which is anticipated in early 2013.

Stabilized extended boundary condition method for 3D electromagnetic scattering from arbitrary random rough surfaces

The stabilized extended boundary condition method (SEBCM) is developed in this work based on the classical EBCM to solve 3D electromagnetic scattering from arbitrary random rough surfaces. The SEBCM gives accurate full wave solutions over large range of surface roughnesses, which are far beyond the validity range of analytical methods, and perform with much higher efficiency than numerical methods. In developing SEBCM, we explicitly impose test surfaces. We further propose a method for balancing and controlling the k-boundary. We validate the results with small slope approximation (SSA) and method of moments (MoM).

Full wave vector electromagnetic scattering from two-dimensional arbitrary random rough surfaces

A solution to scattering from two-dimensional (2D) surfaces with arbitrary roughness based on the extended boundary condition method (EBCM) is presented. The bistatic scattering cross section (SCS) is obtained from the superposition of the upgoing Floquet modes. This method places no limitation on the roughness scale of the surface, and produces both co-pol and cross-pol components of fields and scattering cross sections. The method is validated for the small roughness regime by comparing the simulation results with an existing solution using the small perturbation method (SPM) for the co-pol components. Comparison of results shows very good agreement between these two methods in the validity domain of SPM. Further validations for rougher surfaces and for cross-pol components are currently under-way.