A proper "magma sea"? That exists below the caverns (which are possibly to accidentally dig past, so you might have got three, but are just (un)lucky in the spot(s) you dug down through.
If you find a magma-pipe (circular-ish in plan, fairly constant plan down as far as you can see, until your visibility[1] runs out), that might be an intrusion into an upper cavern. No matter, it's magma. It's all good. But at the bottom of the pipe[2] is a magma sea (you should get an announcement to that effect), and unless you get a buggy embark point you're not going to find open areas below that, except for... spoilerstuff.
"You have found a magma sea" should be the announcement, not just "You have found magma". (May be paraphrasing, it's from memory.)
40D magma pipes, BTW, were quite 'rough' in the vertical direction, much more so than the ones in .31/DF2010. You could usually find spots in their sides that (once you had peered into them, and new their layout) you could mine sideways to and then channel down to release lava sideways on the level below. You can't really do that with the pipes, these days, although you can with the expansive sea. Not that I care, since I tend to use a fortification behind a prepared floodgate to access magma from the side on the level of digging (my magmaducts).
Sorry, bit of a history lesson, and not entirely accurate, but it'll do.
[1] Through molten
rock, no less...
[2] Originally typoed as 'pope'. Darn this keyboard, I'm having to tap extra-hard on some keys and sometimes catching others in the process.