Numerical studies of rough surface scattering models

The research presented in this dissertation comprises numerical studies of two theoretical models, the phase perturbation technique and the small slope approximation, recently proposed for rough surface scattering. Numerical results for the bistatic scattering cross sections obtained using these models are compared to those of the classical methods, first-order perturbation theory and the Kirchhoff approximation. Cases studied include randomly rough two-dimensional (2-D) Dirichlet surfaces with a Gaussian roughness spectrum and randomly rough 1-D fluid-elastic solid interfaces with either a Gaussian or a modified power-law roughness spectrum. For the 2-D, Dirichlet surface case it is found that both new techniques bridge the classical solutions and both give lower scattering levels than for the equivalent 1-D surfaces. The phase perturbation technique performs better in the backscattering region for correlation lengths greater than approximately one radiation wavelength while both the first- and second-order small slope approximations yield higher accuracy in the forward scattering region at low grazing angles. Results for both new methods agree well with fourth-order (in the intensity) perturbation results for a case when the classical approximations fail. For the case of a 1-D penetrable fluid-elastic solid interface, expressions for the lowest-order, first-order, and second-order bistatic scattering cross sections are derived for the small slope approximation. Numerical results are obtained for the lowest-order scattering cross section for water-granite, water-basalt, or water-sediment interfaces. For the Gaussian spectrum, the small slope results agree with those of the classical methods in the appropriate limits, although both the small slope and perturbation results show complex structure at the critical and Rayleigh angles which is missing in the Kirchhoff approximation results. The same is true for the modified power law spectrum. In addition, for this latter spectrum the theoretical averages agree with Monte Carlo results obtained by Berman.