Let me say from the outset that I have no firm conclusions on how this works, but work it definitely does.
My theory is that it forms a loop in the ground, so the effective loop area increases as the frequency is lowered. If the spacing between the electrodes is increased the effective loop increases in diameter. This structure has been used (by others) for amateur radiated tests at extremely low frequencies. In my case it has proved effective with QRP up to 60m. On 630m WSPR it has proved very effective with reports from Finland with low mW ERP. It is almost invisible, with the XYL and neighbours not even aware it is there!
If the loop theory is correct a low impedance is needed as the electrodes enter the ground, but a high impedance between the electrodes so the effective loop diameter is large.
At present, I am using a mains earth (please check your mains earth is suitable) at one end, but tests at the old QTH showed that using 2 electrodes in the ground worked just as effectively.
Before anyone says that it is the wire back from the far electrode that is doing all the radiating, I tried putting the return wire on the ground with very little difference in performance.
See https://sites.google.com/view/g3xbm4/home/antennas/earth-electrode-antennas .