[Steuard]

When I hear "energy dispersed at the edges", I think "lost" (or effectively absorbed), not "reflected back the way it came". I can't think of any obvious mechanism that would lead to significant coherent reflection of sound waves off the upper atmosphere. Similarly, I think a lot of the sound intensity would be absorbed by material on the ground rather than reflected back up. I vote for predominantly 1/r^2 behavior.

[As a physics prof, I probably ought to be doing some sort of calculation to justify that, but I don't have the time. I'm sure it's been analyzed formally somewhere already. Just off the cuff, though, the speed of sound is lower at low temperature, so refraction of a sound wave in the upper atmosphere will tend to bend it outward, away from the Earth. I'm thus imagining that loud sounds may tend to locally push the atmosphere out from the planet a little bit, and I expect that coming back to equilibrium will be a lossy process that doesn't preserve the shape of the wave.]