Concorde sonic booms
When I was at test pilot school in France we had a very interesting sonic boom lecture. In North America, to avoid complaints from the public, military jets were prohibited from supersonic flight, except in some very specific areas. The French had a very adult approach to sonic booms from military jets - they spent hours teaching you about sonic boom propogation, so you had a chance of predicting which spots on the ground would get hit by a sonic boom if you did certain things, and then they told you "you can fly as fast as you want, where ever you want, but don't bang any populated areas".
The lecturer was a very experienced sonic boom expert, who had participated in the sonic boom studies that were done when Concorde was in development. He explained that as the sonic booms from Concorde were coming down towards the ground, they would be refracted as the speed of sound changed due to the increasing air temperature. If the atmosphere was close to standard conditions, and the ground level was close to sea level, the sonic boom from Concorde in cruise would be refracted such that the angle of descent of the boom decreased at it approached the ground. The angle of descent of the boom would reach zero several thousand feet above the ground, then it would start going upwards, without touching the ground. It would be refracted as it increased in altitude, and its angle of ascent would increase until it hit the tropopause, where the air temperature became constant, and thus the speed of sound was constant. The boom would continue to very high altitude, when the air temperature would start increasing as the altitude increased, which would cause the boom to be refracted again. It's angle of ascent would decrease with altitude, and it would eventually start coming down again. It would be coming down quite steeply on this pass, and it would hit the ground. But it would have travelled such a long distance by the time it hit the ground that it would be quite weak, and at a very acceptable level.
Of course, the atmospheric temperature profile is often quite far from standard, and it was possible for the Concorde sonic boom to hit the ground on the first pass. In this case it would be very strong, and probably not acceptable to the public. The sonic boom would also be very strong when the aircraft was accelerating, or if it was turning in supersonic flight, as these manoeuvres would focus parts of the boom, such that the sonic energy created at different locations along the flight path would be concentrated in a small area.
I was home visiting my parents in south western Nova Scotia many, many years ago. I was helping my father work outside, and I noticed that he kept looking at his watch. I asked him why, and he said that he had noted a very faint boom about the same time each day, which he assumed came from Concorde. Sure enough, at the appointed hour I heard a very, very faint boom - I would not have noticed it unless I had been looking for it. Later, I tracked down the Concorde schedules, and it was plausible that he was hearing the boom as it went by Nova Scotia.