Communications Project

Document Type:Dissertation
Name:Jakov V. Toporkov
Title:Study of Electromagnetic Scattering from Randomly Rough Ocean-Like Surfaces Using Integral-Equation-Based Numerical Technique
Degree:Doctor of Philosophy
Committee Chair: Royce K. P. Zia
Committee Members:Gary S. Brown, Co-Chairman
Brian K. Dennison
David A. DeWolf
Beate Schmittmann
Keywords:Electromagnetic scattering, numerical analysis, Pierson-Moskowitz spectrum, rough surfaces, Monte Carlo simulations
Date of defense:April 28, 1998
Availability:Release the entire work for Virginia Tech access only.
After one year release worldwide only with written permission of the student and the advisory committee chair.


A numerical study of electromagnetic scattering by one-dimensional perfectly conducting randomly rough surfaces with an ocean-like Pierson-Moskowitz spectrum is presented. Simulations are based on solving the Magnetic Field Integral Equation (MFIE) using the numerical technique called the Method of Ordered Multiple Interactions (MOMI). The study focuses on the application and validation of this integral equation- based technique to scattering at low grazing angles and considers other aspects of numerical simulations crucial to obtaining correct results in the demanding low grazing angle regime. It was found that when the MFIE propagator matrix is used with zeros on its diagonal (as has often been the practice) the results appear to show an unexpected sensitivity to the sampling interval. This sensitivity is especially pronounced in the case of horizontal polarization and at low grazing angles. We show – both numerically and analytically – that the problem lies not with the particular numerical technique used (MOMI) but rather with how the MFIE is discretized. It is demonstrated that the inclusion of so-called “curvature terms” (terms that arise from a correct discretization procedure and are proportional to the second surface derivative) in the diagonal of the propagator matrix eliminates the problem completely. A criterion for the choice of the sampling interval used in discretizing the MFIE based on both electromagnetic wavelength and the surface spectral cutoff is established. The influence of the surface spectral cutoff value on the results of scattering simulations is investigated and a recommendation for the choice of this spectral cutoff for numerical simulation purposes is developed. Also studied is the applicability of the tapered incident field at low grazing incidence angles. It is found that when a Gaussian-like taper with fixed beam waist is used there is a characteristic pattern (anomalous jump) in the calculated average backscattered cross section at incidence angles close to grazing that indicates a failure of this approximate (non-Maxwellian) taper. This effect is very pronounced for the horizontal polarization and is not observed for vertical polarization and the differences are explained. Some distinctive features associated with the taper failure are visible in the surface current (solution to the MFIE) as well. Based on these findings we are able to refine one of the previously proposed criteria that relate the taper waist to the angle of incidence and demonstrate its robustness.

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acknowledgments.pdf dissertation.pdf vita.pdf

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