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.