Type of Document Dissertation Author Awadallah, Ra'id S. M.S. Author's Email Address firstname.lastname@example.org URN etd-4598-0751 Title Rough Surface Scattering and Propagation over Rough Terrain in Ducting Environments Degree PhD Department Electrical Engineering Advisory Committee
Advisor Name Title Brown, Gary S. Committee Chair Besieris, Ioannis M. Committee Member Kohler, Werner E. Committee Member Mili, Lamine M. Committee Member Nayfeh, Ali H. Committee Member Keywords
- ducting environments
- rough surfaces
- Electromagnetic propagation
- numerical methods
- Asymptotic techniques
Date of Defense 1998-04-30 Availability unrestricted AbstractThe problem of rough surface scattering and propagation over rough terrain in
ducting environments has been receiving considerable attention in the literature. One
popular method of modeling this problem is the parabolic wave equation (PWE) method.
In this method, the Helmholtz wave equation is replaced by a PWE under the assumption
of predominant forward propagation and scattering. The resulting PWE subjected to the
appropriate boundary condition(s) is then solved, given an initial field distribution, using
marching techniques such as the split-step Fourier algorithm. As is obvious from the
assumption on which it is based, the accuracy of the PWE approximation deteriorates in
situations involving appreciable scattering away from the near-forward direction, i.e.
when the terrain under consideration is considerably rough. The backscattered field is
neglected in all PWE-based models.
An alternative and more rigorous method for modeling the problem under
consideration is the boundary integral equation (BIE) method, which is formulated in two
steps. The first step involves setting up an integral equation (the magnetic field integral
equation, MFIE, or the electric field integral equation EFIE) governing currents induced
on the rough surface by the incident field and solving for these currents numerically. The
resulting currents are then used in the appropriate radiation integrals to calculate the field
scattered by the surface everywhere in space. The BIE method accounts for all orders of
multiple scattering on the rough surface and predicts the scattered field in all directions in
space (including the backscattering direction) in an exact manner.
In homogeneous media, the implementation of the BIE approach is
straightforward since the kernel (Green's function or its normal derivative) which appears
in the integral equation and the radiation integrals is well known. This is not the case,
however, in inhomogeneous media (ducting environments) where the Green's function is
not readily known. Due to this fact, there has been no attempt, up to our knowledge, at
using the BIE (except under the parabolic approximation) to model the problem under
consideration prior to the work presented in this thesis.
In this thesis, a closed-form approximation of the Green's function for a two-
dimensional ducting environment formed by the presence of a linear-square refractivity
profile is derived
using the asymptotic methods of stationary phase and steepest descents. This Green's
function is then modified to more closely model the one associated with a physical
ducting medium, in which the refractivity profile decreases up to a certain height,
beyond which it becomes constant. This modified Green's function is then used in the
BIE approach to study low grazing angle (LGA) propagation over rough surfaces in the
aforementioned ducting environment. The numerical method used to solve the MFIE
governing the surface currents is MOMI, which is a very robust and efficient method that
does not require matrix storage or inversion.
The proposed method is meant as a benchmark for people studying forward
propagation over rough surfaces using the parabolic wave equation (PWE). Rough
surface scattering results obtained via the PWE/split-step approach are compared to those
obtained via the BIE/MOMI approach in ducting environments. These comparisons
clearly show the shortcomings of the PWE/split-step approach.
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