Because they rely on radio signals, GPS units generally do not work underground or underwater, but what about a plain ol' magnetic compass? Are the magnetic fields of earth present at all depths? Does water do anything to attenuate them?
Can I go spelunking with a compass to help me keep my bearings or even go through a train tunnel in a mountain (contrived example)? Do divers use compasses regularly?
Compasses are good equipment both spelunking and diving. Even the deepest cave you could go to is still near the earth's surface, geologically speaking. The earth's magnetic field is also essentially the same under water as above.
If you are using a compass, what you need to be aware of is nearby magnets and large sources of iron. So if you were exploring an underwater metal shipwreck, it could throw off a compass, the same as if you are testing a compass in your house standing next to a metal stove or refrigerator. The same is probably true if you explored a cave with a very concentrated source of iron ore. If you store your compass with a strong magnet, you risk demagnetizing it so it won't work at all. But if you treat it properly, a good magnetic compass is going to be more reliable than any electronic ones I've tried.
Magnetic compasses work well in caves (both dry and submerged), with the usual caveat that iron-rich minerals can cause deflections. In mines, consider using regular back-bearings for confirmation.
Compass bearings are the main source of data for cave surveys (along with distance and inclination or altitude measurements, of course). Cave surveyors use either a mechanical (needle) compass or an electronic one for data gathering, regularly achieving closures of better than 1%. I think the electronic ones use Hall Effect to measure the magnetic field direction.
In Britain, a wrist compass is considered standard equipment for diving.
