VLF comms are really interesting. One of the US Navy's big transmitters is not far from me here in Seattle:
https://en.wikipedia.org/wiki/Jim_Creek_Naval_Radio_StationWhen you're only dealing with the groundwave you can really push the Shannon limit by going low/slow, because the phase coherence of the channel is much greater than at shortwave frequencies. Here's a fun write-up of an amateur transatlantic communications experiment at 8971 Hz:
http://www.w4dex.com/vlf/8971Hz/index.htmFor a test of the web SDR receiver, see if you can pick up the nearest VLF time-standards stations in the UK (MSF, 60 kHz) or Germany (DCF77, 77.5 kHz).