Validity of Simplified Approaches for the Evaluation of Lightning Electromagnetic Fields above a Horizontally Stratified Ground

We review in this paper 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 horizontally stratified ground. Considerations regarding the use of these formulations as well as their domain of applicability are given. For the case, where the upper ground layer has a lower conductivity than the lower layer, the magnitude of the attenuation function can take values greater than unity. Time-domain waveforms of the vertical electric field along a horizontally stratified ground, obtained using the simplified formulations feature, an oscillatory behavior in their early-time response. The peak value of the field is also found to be larger than that corresponding to the case of a perfect ground. The accuracy of the Wait's formulations is examined taking as reference full-wave simulations obtained using the finite-difference time domain (FDTD) technique. FDTD simulations confirm the oscillatory waveform of the far field above a horizontally stratified ground (with an upper layer characterized by a lower conductivity than that of the lower layer), as well as the enhancement of the field peak compared to the case of a homogeneous, perfectly conducting ground