Thunderstorm Generated Power

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I've had a question bugging me for a while now.. I work nights offshore and the schedule, and subsequent remodulation of my circadian rhythm has caused my brain to think random things.

I understand that thunderstorms produce an electric potential across the gap between the bottom of the cloud and the ground. This imbalance is brought closer to electrically neutral when dielectric breakdown occurs and a flow of electrons occurs.

In some storms, there is a higher than average rate of lightning strikes per given time interval (average of how long a typical strong thunderstorm lasts before it dissipates).

Could this constitute a AC charge, or pulse DC, at very low frequency? What I mean is, the charges cycle from a strong imbalance, to a "closer-to-zero" balance due to the strikes of lightning.
The frequency would not be constant, as the strikes are random.

I am leading to this:
Could this charge cycling be enough to induce a current in a very large coil (wide and flat covering many square acres) on the ground? Or is the atmospheric potential too small to even register on a voltmeter?
 

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