In the first Austin Powers movie, Dr. Evil steals a 50 kiloton nuclear weapon, straps it to a drill and is going to fire it into the mantle to trigger volcanic eruptions world wide.
My instinct is that, compared to a lot of nuclear weapons in the megaton range, 50 kilotons is not really a lot, and using it to try to move rock (even molten rock) is not going to accomplish his goal. Would it even cause a measurable change in the pressure that far down?
It’s a comedy movie parodying the stylistic exaggeration that is part of the Bond movies.
It’s going to be a hard math problem to get this bomb to go off near molten lava but not in it. The bomb will probably not be able to generate its full destructive potential if it melts first. Also, there is more atmospheric pressure down there and we didn’t build bombs for that. But even if you accounted for all that, worldwide eruptions sound like a stretch. The shock wave in air of a 50 kiloton explosion would probably be in the 10 mile range. That’s going to be lower in a thick liquid medium and a not insignificant part of that energy would also want to travel back up the drilled shaft. So this will probably affect an area of the world but far from all of it. And there is no guarantee it would work or be instantaneous. Pressure buildups that lead to eruptions can take ages. It’s a bad plan.