"Wimpie" wrote
When you would measure the field strength of an AM broadcast
transmitter over seawater, the 1/distance decay holds to about 100km.
Above that you have to correct for earth curvature.

This is approximately, but not precisely true, as the conductivity of sea
water is not perfect. Divergence from the inverse distance field is present
at distances up to 100 km, as well.

You should distinguish between transition region and far field
(Fraunhofer) region. Close to the transmitter the field generated by
the ground current coincide with the field from the vertical radiator
therefore 3 dB gain increase in field strength occurs. Further away
from the antenna, both amplitude and phase of ground current will
change with respect to the field from the radiator, partly destructive
interference occurs.

I did state that BL&E's measurements were made in the far field. The
longest radiator length in their study was 90 feet, and the test frequency
was 3 MHz. Using the equation commonly accepted for the transition to the
far field zone (D = 2*L^2/lambda), D = 49.4 feet for these conditions. BL&E
took their measurements at 0.3 miles (1,584 feet).

Only a surface with infinite conductivity will support the surface
wave up to infinity, hence giving main lobe at zero elevation (for
vertical radiators up to 5/8 lambda).

This is a common belief based on a mathematical analysis for an infinite
distance from the radiator. But the main lobe _as launched_ from a vertical
monopole up to 5/8-wave in height, and with its base on the earth _always_
is directed in the horizontal plane, regardless of the r-f loss in the
ground system used with the vertical, or earth conductivity in the near
vicinity of the site.

The BL&E study was done in the sandy soil of New Jersey (about 4 mS/m), yet
for a 1/4-wave radiator with 113 0.41-wave radials they measured fields at
0.3 miles that were within a few percent of their theoretical maximum for a
perfect 1/4-wave monopole radiator over a perfect ground plane.

A calculation of the elevation field at an infinite distance over other than
a perfect, infinite ground plane shows zero field in the horizontal plane,
and a peak in relative field at some positive elevation angle. That is the
field that survives to infinity, but does not mean that this is the shape of
the field that is radiated by the monopole in the first place, and that
exists at far-field distances closer to the radiator. Closer to the
radiator, the h-plane field is not zero -- which in fact is the basis for
the daytime coverage of all MW broadcast stations.

BTW, they did a good job as the field strength from a 1/2-wave dipole,
free space, 1kW input is about 138mV/m (rms) at 1 mile. Their
measurements show 190mV/m (almost 3 dB gain).

That is due to the fact that radiation from a 1/4-wave monopole with its
base on the earth is restricted to one hemisphere, which for a perfect
ground plane produces 3 dB gain over a 1/2-wave dipole in free space. To
account for this, multiply your 138 mV/m by SQRT(2). This produces the
same 195 mV/m value that I posted earlier as the theoretical, h-plane
maximum for a 1/4-wave monopole for these conditions.

RF