I get x-ray effect because my computer is slow when I dig through stone, it lags so much I can see through caves and stuff. I have no mods installed so it's cool. Also have really large custom size places.
If you don't mind the concept of "cheating" you can recreate the world in Creative and use that to find the caves under the swamp. Just write down the coordinates and then switch back to the other world.
Otherwise, make a mine downward until you hit a cave and explore from there.
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if you are playing solo, then if you're willing to X-ray you might as well cheat all the way and use a parallel creative world and maybe spectator mode to ind your caves.
If you play on a multiplayer server, well, caves are way to abundant even after the 1.7 reduction (at least it's not total swiss cheese like in 1.6), so yeah, basically you're just plain too lazy to play fair !
Anyway, with or without XRay, branch mining beats cave mining by a mile.