Mathematical Modeling of Electromagnetic Wave Interference During Oblique Irradiation of Plane-Layered Dielectrics of Natural Origin

Abstract

The paper presents a mathematical description of the interference wave formation process when the Earth’s surface is obliquely irradiated by a radar signal. The current mathematical apparatus primarily focuses on describing interference in relation to communication issues and overlooks subsurface waves. Oblique irradiation at an incidence angle close to the Brewster angle is used to create conditions for the penetration of electromagnetic waves through the “air-surface” interface with minimal reflection coefficient. The proposed mathematical model is based on the solutions of the Helmholtz wave equation and Fresnel formulas for three isotropic media and two boundaries between them. So, it takes into account the maximum possible number of factors involved in the formation of the interference wave. This mathematical model has several peculiarities. The interference wave is represented as a superposition of direct, reflected, and the sum of subsurface waves. The reflection of the radar signal has a diffuse-specular nature, which is determined by the root mean square deviation of the irregularities’ sizes. Additive amplitude noises are considered separately for the direct, reflected, and subsurface waves. The size of the receiving antenna aperture and its directional pattern, which determine the conditions for summing individual partial waves during the formation of a subsurface wave, are taken into account. Based on the obtained mathematical expressions, a simulation model has been developed in MatLab. The adequacy of the simulation results was verified experimentally. The good convergence between the calculated and experimental data allowed us to recommend the developed mathematical model for the study of planar-layered dielectrics.