125 miles? That's a glaring error, I'm afraid. I'd say more like 12.5 miles, even less in some spots. There are places in Yellowstone where the magma is no more that 3 miles from the surface. That's the nature of a caldera -- it is an upward "bubble" of magma, in this case, it is about 30 miles across.
I wonder if a nuke would breach that puppy ?