This is probably more than you want to know but this probably explains what I meant.
http://www.sengpielaudio.com/calculator-squarelaw.htm
You start with a certain amount of acoustical energy that radiates equally in all directions. The sphere of energy at one foot radius could be measured at a certain level. Twice as far away, the energy would fall to 1 / (2 squared) or 1/4th the level. Three times the distance away, would be 1 / (3 squared) or 1/9th the power level.
RADAR behaves the same way except it suffers the same degradation during its reflection, so the receiver gets the echo back at 1 (r ^ 4) so doubling a distance would have a 1 / ( 2 ^ 4) or 1/16 reduction. Tripling would have a 1 / (3 ^ 4) of 1 / 81.
> You start with a certain amount of acoustical energy that radiates equally in all directions.
Given that the caps were detonated on a cement floor the acoustic energy would radiate in a hemisphere, along with the reflected energy from the floor. The time delay between the two wave-fronts would probably create cancellation and reinforcement in the acoustic wave, so what the observer hears might well be louder than what would be assumed by the inverse square law, and, given the probability of comb-filtering at various frequencies might have a non-linear output, but I’m not a math person so I’m not even going to try.
Is that the same as the Inverse Square law?