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This question s titled according to of one of the Nikola Tesla's patents. There he stated that lightning generates electric waves in Earth.

"In the course of certain investigations which I carried on for the purpose of studying the effects of lightning discharges upon the electrical condition of the earth I observed that sensitive receiving instruments arranged so as to be capable of responding to electrical disturbances created by the discharges at times failed to respond when they should have done so, and upon inquiring into the causes of this unexpected behavior I discovered it to be due to the character of the electrical waves which were produced in the earth by the lightning discharges and which had nodal regions following at definite distances the shifting source of the disturbances. From data obtained in a large number of observations of the maxima and minima of these waves I found their length to vary approximately from twenty-live to seventy kilometers, and these results and certain theoretical,deductions led me to the conclusion that waves of this kind may be propagated in all directions over the globe and that they may be of still more widely differing lengths,the extreme limits being imposed by the physical dimensions and properties of the earth. Recognizing in the existence of these waves an unmistakable evidence that the disturbances created had been conducted from their origin to the most remote portions of the globe and had been thence reflected, I conceived the idea of producing such waves in the earth by artificial means with the object of utilizing them for many useful purposes for which they are or might be found applicable. -- U.S. Patent 787,412"

Does Earth shows such properties? How does the Earth responds to lightning discharges?

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    $\begingroup$ This is a really cool question! I remember (a long time ago) reading about electromagnetic waves inside conductive soil that travelled near but below the surface, and remember seeing a circuit for such a receiver in a book about ham radio circuits. So I've just asked Looking for a book that contained a circuit for receiving (literally) underground amateur radio transmissions. $\endgroup$
    – uhoh
    Commented Mar 1, 2020 at 1:56
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    $\begingroup$ Look up "telluric currents". It is a consideration when designing pipeline cathodic protection . $\endgroup$
    – blacksmith37
    Commented Mar 1, 2020 at 17:01
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    $\begingroup$ From Wikipedia "Telluric current": "In industrial prospecting activity that uses the telluric current method, electrodes are properly located on the ground to sense the voltage difference between locations caused by the oscillatory telluric currents. It is recognized that a low frequency window (LFW) exists when telluric currents pass through the earth's substrata. In the frequencies of the LFW, the earth acts as a conductor." $\endgroup$
    – Mike Waters
    Commented Mar 2, 2020 at 0:26
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    $\begingroup$ update: there's now an excellent answer! $\endgroup$
    – uhoh
    Commented Mar 2, 2020 at 2:01
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    $\begingroup$ This will interest you, a magazine from that time: archive.org/details/SI192806/mode/2up $\endgroup$
    – bandybabboon
    Commented Mar 2, 2020 at 9:04

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