Transmission of electromagnetic fields through an air-ground interface in the presence of statistical roughness

The transmission coefficient for a vacuum-dielectric interface with small (compared to the wavelength) statistically homogeneous roughness is analyzed. The analytical expressions for the transmission coefficients for both vertically and horizontally polarised plane waves are derived. For simplicity only terms quadratic in the roughness height are taken into account. For typical GPR scenarios the energy transmitted into the ground for both vertically and horizontally polarised plane waves is calculated as functions of dielectric permittivity, operating frequency, incident angle and corrugation´s parameters