New image representation for dipoles near a dissipative earth 2. Discrete plus continuous images

Abstract

A modified image theory for vertical magnetic and electric dipoles above a dissipative earth is presented. Namely, the Fresnel reflection coefficient for horizontally polarized waves is approximated by an exponential term plus a new term which extends the validity of the approximation to high values of the horizontal wave number. While the exponential term represents a single image inside the earth, the new added term represents a set of continuous distribution of images. A similar approximation is applied to the Fresnel reflection coefficient of the vertically polarized waves. These image representations are applied for the determination of input impedances of vertical magnetic and electric dipoles and horizontal large loops at a very low height above the earth. Excellent agreement with previous exact results is reported in all cases.