Say you embark on this location:
HFS is on the top row, second column...should be obvious since there are no other features, but just making it perfectly obvious since I'm using a tileset so the graphics aren't standard.
Each of these tiles measures 48x48 tiles when you embark, so if you picture the embark area as a map where the tile at the very top left is (1,1) and the one to the right of that is (2,1) and so on, I know that HFS should be somewhere between (49,1) and (96,48)...here's the local area map, with a white rectangle around the approximate area that the HFS could potentially be
You can see there that it's still the same sort of area as in the first pic, yes?
Now comes the hard part, because it's a bit of guesswork (if you don't cheat), but finding HFS can still be easier than finding a cave river (which is a real pain in the ass without cheating) because it SHOULD be around the centre of the region tile. Dig a shaft right down in the very centre of that area (so, in my example that'd be (72, 24)) to the very bottom z-level.
I've done this in my example...assuming ground level is z0, my miner came along and hit Sylvite at z-2, Mica at z-5, more Mica at z-7, Pitchblende at z-8, yet more Mica at z-9, Microcline at z-10 (right colour but not the right material
), Mica
again at z-12, Orthoclase at z-13, and breached the HFS at z-14 (lowest level was z-17)
Voila, HFS found in under two minutes