The field of a vertical antenna above inhomogeneous ground

Inhomogeneous ground can cause significant scattering of incident electromagnetic fields. For example, the introduction of a metallic ground mat can have a significant effect on the radiation pattern of an antenna. Several approaches to the problem have been developed and most are based on integral electromagnetic formulations such as the extinction and compensation theorems. The extinction theorem approach derives the leading order behaviour of the scattered field from the leading order behaviour of the incident field. For most practical situations, however, the field becomes extremely weak close to the ground, and higher order terms are required. The paper extends earlier work (Coleman, C.J., 1996, 1997, 1998, 2003) on the extinction theorem approach to these higher order terms. The procedure for calculating the leading order scattered field is described and it is shown how this process can be extended to the calculation of higher order terms. Finally, the procedure is used to derive an expression for the field of a general antenna in the vicinity of inhomogeneous ground. In the case of large inhomogeneous features, the theory predicts behaviour that is expected from the results of other approaches.