An integral equation approach for the analysis of a horizontal wire antenna(s) located in free space near a lossy half-space is described. Two methods, a rigorous one based upon the Sommerfeld formulation and an approximation technique involving the Fresnel plane-wave reflection coefficients, are used to account for the influence of the interface-reflected field upon the antenna current distribution. A moment method (subsectional collocation) solution procedure is used to obtain numerical results for antenna impedance and radiation patterns. The reflection coefficient approach is found to agree well (generally within 10%) with those due to the rigorous method at a fraction (approximately 1%) of the computer cost.
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Miller et al. (1972) studied this question.