WMG: The Core

How they got 200 megaton bombs
As You Know, the most powerful nuclear weapon ever detonated, Tsar Bomba, let off only around 50 megatons and was larger than an entire Virgil compartment. How, then did they get 200 megaton bombs that were small enough to move? Simple: the movie is set in the Stargate Verse and the nukes were naquadah-enhanced.

Project DESTINI caused other disasters before the events of the film
As suggested on the League Of Extraordinary Gentlemen WMG page, most 90s disaster movies could have occurred in the same world. It's conceivable that the disruption of the Earth's core would cause geological disasters like earthquakes and volcanic eruptions, and it's possible that the corresponding disruption of the magnetic field might also affect the weather. Of course, this doesn't explain asteroid or comet impacts or disasters that were purely caused by human negligence or malice— those were just bad luck.