Ground Wave Propagation Along an Inhomogeneous Rough Surface in the HF Band: Millington Effect for a Flat Earth

In this paper, for a vertically polarized line source in the high-frequency band (3-30 MHz), a detailed analysis of the ground wave propagation over 1-D highly conducting inhomogeneous (presence of island) smooth and rough surfaces is addressed from two methods: 1) the analytical solution of Bremmer (see also Wait), which assumes that the receiver, emitter, and island heights are zeros and that the surface is composed of three smooth paths of different permittivities, and 2) the efficient rigorous banded matrix iterative approach/canonical grid (BMIA-CAG) method, which is based on the method of moments and is updated to validate the analytical solution of Bremmer. In addition, from the works of Barrick, the sea surface roughness is included in the Bremmer formulation and tested from the BMIA-CAG by considering a surface composed of sea-land-sea mixed paths. The comparisons show a good agreement between the updated BMIA-CAG (reference method) and the Bremmer analytical formulation combined with the works of Barrick. The Earth curvature is neglected.