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?
Absolutely nothing.
For reference, here’s footage of a 5 Megaton nuclear device being detonated underground. No global eruptions, and hard for humans to even feel further from the epicenter - although, seismic monitoring by precision instruments is a known way of monitoring for secret underground nuclear tests.
For further reference, the 2011 Tohoku earthquake off the coast of Japan - the one that unleashed powerful tsunamis - released a staggering 3.9x10^22 Joules, or around 9.3 million megatons of TNT. While this did cause local devastation, it also failed to meet Project Vulcan’s goal.
That’s a different kind of thing. Yes, they would have buried the bombs, but not that deep. Just deep enough to form a nice, deep and just slightly radioactive crater.
It would have been interesting to behold. There were plans to actually bomb a new Panama channel, several miles wide and without any locks. This would have resulted in a steady stream of water from the Pacific side to the Atlantic side, with basically unpredictable results.
Tectonic plates slip and release millions of times as much energy as a 50Kt nuclear bomb and those only sometimes cause localized volcanic activity.
While a lot of posts have touched on the size of the explosion, the real impossible part is getting to the mantle. It was only fairly recently done by digging in the ocean where the mantle was pushed up more than normal.
