For earth moving, I figure a matter-antimatter reaction would be best.
The earth has about
3 * 10^33 J of kinetic energy, and
2 * 10^29 Ns of momentum
The Kinetic Energy of the earth has a mass of about
3*10^16 kg. That's alot of antimatter. Feh, back to the drawing board.
Hmm. How about a superstring? It is a macroscopic linear singularity predicted by brane theory.
SPOILERS for a book.
Or
Greg Bear's Forge of God method. Which works out to "have really heavy objects hit each other really hard in the middle of the earth". The plan in the book is, actually, more than a little overblown. If the 'bezerkers' are as common as they are in that novel, then we have already sent out sufficiently taunting messages. So, blame Hitler for his overly-loud TV broadcast!