Ground wave of an idealized lightning return stroke

We model a lightning return stroke by a vertical traveling wave of current with a complex propagation constant. The Sommerfeld-integral analysis is similar to that of a vertical electric dipole over a lossy earth except that the source is distributed in height. When the integration over the source current is performed analytically, an extra term appears in addition to the classical Sommerfeld attenuation function. This term is a result of the height-gain function of the distributed source due to an effective elevated height of the source dipole moment. In most eases of interest, the extra term is small and the height-gain function is not much larger than one. The results have application to remote sensing of lightning from a ground-based observer