NEC-LIST: image modeling over lossy earth

I am looking for an article that discusses modeling a dipole over lossy
ground in terms of Z1, Z12 and Z11, such that the image current is less than the
source current above ground. In free space with no losses, two dipoles driven
with equal currents allow us to find Z12 easily as Z1 - Z11. We also assume
that Z12 = Z21.

If we model a single dipole over perfect ground, we can assume that the image
reflection is perfect, although 180 degrees out of phase with the
above-ground source.

However, if our two dipoles consist of a dipole 20 feet above 5 mS/m earth,
and an image 20 feet below ground, does Z12 = Z21? If so, then I1 cannot equal
I2. NEC can tell us what Z1, I1 and Z11 are, but how do we solve for Z12 and
I2?

Grant W. Bingeman, P.E.

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