While I was in high school (about 4 decades+ ago), I operated a pirate AM radio station on 1200 Khz.  We’d always end our transmission with a sign-off then cut the transmitter.  I had a Sony Earth Orbiter radio that I used to monitor our transmission and one night, after I cut the transmitter, I heard the last perhaps 1/2 second of our transmission on the radio as if it had been reflected back from some distant location.  The thing is at 100 watts, our range was quite limited.  With a high quality communications receiver you could hear us maybe 15 miles away, with the average radio maybe 3-4 miles.  Not nearly far enough to account for the delay.

     While there are many instances of echo on YouTube, it’s usually by not even 1/2 second but more on the order of 1/15th of a second, more of a reverb than an echo.

     I have read of accounts of long delayed echos of as much as 30 seconds.

     I have heard theories that it might involve a conversion from an electromagnetic wave into an acoustic wave in the plasma of the ionosphere and because the acoustic wave travels much slower, and then if by the same mechanism translated back into an electromagnetic signal, because the acoustic transmission was much slower in than the speed of light, especially in the tenuous plasma, that a relatively short path could account for the extreme delays.

     I personally find this theory a bit convoluted and can’t help but wonder if perhaps something more direct is involved, something involving the nature of time perhaps not being strictly linear as we commonly think of it.  Perhaps there are loops or vorticies in time.