Using a spherical earth model, we develop a normal mode analysis for the excitation by an azimuthally symmetric source region. We then specialize the general formulation to deal with a vertical antenna with a prescribed current distribution. In particular, we consider the current distribution that would excite a pure Zenneck wave on the corresponding planar earth model. But we also consider excitation by vertical electric dipole and a uniform current distribution. Finally, we examine a horizontal antenna that is excited by a traveling current wave. Our general conclusion is that the Zenneck wave aperture illumination (i.e., current distribution) is a poor choice for enhancing the ground wave over a spherical earth. This point is illustrated for specific calculations at a frequency of 1 and 10 MHz over both land and sea.