Your calculations might be wrong. If the distance is 1000 km (1M meters), and inverse square law is correct, then the sound would become 1M*1M = 1T times more silent. 1M times smaller is 120 dB less, and 1T times smaller is 240 db less, so the amplitude of sound should be at 210 - 240 = -30dB less than threshold of hearing.

Also, I wonder, if sound of explosions propagate that well, can one install multiple sensors to detect and map source of gunfire and artillery positions in realtime? (I hope I haven't disclosed NATO military secrets here).