On the accuracy of approximate techniques for the evaluation of lightning electromagnetic fields along a mixed propagation path

In this paper we review simplified analytical expressions derived by Wait using the concept of attenuation function for the analysis of the propagation of lightning-radiated electromagnetic fields over a mixed propagation path (vertically stratified ground). Two different formulations proposed by Wait that depend on the relative values of ground surface impedances are discussed. It is shown that both formulations give nearly the same results for the time domain electric field. However, depending on the values of the normalized surface impedance for each ground section, the use of one of the two formulations is computationally more efficient. The accuracy of the Wait formulations was examined taking as reference full-wave simulations obtained using the finite difference time domain technique. It is shown that Wait's simplified formulas are able to reproduce the distant field peak and waveshape with a good accuracy.