Ground flashes with positive polarity associated with both sprites and elves excite the Earth's Schumann resonances to amplitudes several times greater than the background resonances. Theoretical predictions for dielectric breakdown in the mesosphere are tested using ELF methods to evaluate vertical charge moments of positive ground flashes. Comparisons of the measured time constants for lightning charge transfer with the electrostatic relaxation time at altitudes of nighttime sprite initiation (50-70 km) generally validate the electrostatic assumption in predictions made initially by Wilson [1925]. The measured charge moments (Q dS = 200-2000 C-km) are large in comparison with ordinary negative lightning but are generally insufficient to account for conventional air breakdown at sprite altitudes. The measured charge moments, however, are sufficient to account for electron runaway breakdown, and the long avalanche length in this mechanism also accounts for the exclusive association of sprites with ground flashes of positive polarity. The association of elves with large peak currents (50-200 kA) measured by the National Lightning Detection Network in a band pass beyond the Schumann resonance range is consistent with an electromagnetic pulse mechanism for these events.