The influence of frequency dependent soil electrical parameters on the evaluation of lightning electromagnetic fields in air and underground

This paper is aimed at analyzing the influence of the frequency-dependent behavior of the ground electrical parameters ( conductivity and ground permittivity) on the electromagnetic field radiated by a cloud-to-ground lightning return stroke. Both radiation in air ( over the conducting ground plane) and underground are considered in the analysis. The adopted method is based on the classical Sommerfeld's theory and takes advantage of an efficient ad hoc numerical procedure to face with the slow converging Sommerfeld's integrals. This feature allows the electromagnetic field to be computed without any sort of mathematical approximation and, since it is carried out in the frequency domain, can be used either if the ground permittivity and conductivity are considered constant or if they vary with the working frequency with any functional law. Simulations have been performed to identify the cases in which the approximation of constant ground permittivity and conductivity leads to satisfactory results. It is shown that for soils with water contents of 2% to 10% ( ground conductivities in the order of 0.001 to 0.01 S/m), the assumption of constant electrical parameters appears to be reasonable. However, for either very poorly conducting soils (10(-4) S/m or so) or highly conducting soils (10(-1) S/m), the electromagnetic field components appear to be significantly affected by the frequency dependence of the ground electrical parameters.