But I could be all wet. It's not my field. I know enough about RF electromagnetic radiation to get an Extra Class Ham ticket, which means I know I can feed a WHOLE LOT less energy than the dreaded EMP into a small piece of metal in the air and it can reach the other side of the world. Which makes the thought of what could happen in a very high energy pulse just a little bit scary (indeed, a mere lightning bolt causes me some concern).
On the other hand, the usual characteristics of an electromagnetic wave which make atmospheric propagation possible don't exist in a pulse unless and until it approaches the theoretical perfect form. I'm no physicist, but I don't believe the phenomena thought to be possible using known technology can be described as near perfect - so it would be radiation at a somewhat limited (super high frequency) wavelength range roughly defined by it's duration, plus it's harmonics, the strength of those finite components reduced by distance and atmospheric absorption in accordance with the usual earthly conventions. Only a perfect pulse would be universally resonant and become the ultimate destroyer.
In the Afterword to One Second After there is an involved technical description of what happens to the emitted gamma radiation when it interacts with the upper atmosphere. The theory is better described there than anything I could pass on. The footnotes to the Afterword provide additional sources of information.
It is not the radiation itself ... which would obey inverse square ... but a cascade of secondary radiation effects triggered in the ionosphere ... which in turn produces the giant current ... which in turn produces the electromagnetic pulse ... which is what comes down from the sky above. It is line-of-site to the upper atmosphere, from what I gather. there is a large publicly available report by the Congress, recently published I believe, available for download in .pdf format.