I decided to change my comment into an answer.
Scientifically, no, there is no series of human-geneated events using technology available to us today that could achieve what you're looking for.
In my answer to Can a planet's axial tilt be changed by carefully planned and set high-energy explosions? I compare the Magnitude 9 Sumatra Earthquake to the RDS-220 Tsar Bomba explosion. It points out pretty clearly that the energy humanity needed to tilt the earth a few centimeters would destroy more than half the planet.
Humanity simply doesn't have the ability to change much of anything on a planetary basis without a considerable period of time.
But this isn't important!
However, scientifically accurate is irrelevant, isn't it? The movie The Core uses a fictional how-to-make-an-earthquake experiment to cause the core to stop spinning, thereby setting up the premise for the story.
This is important. Stopping the core from spinning was simply backstory. It's not really that important and not particularly explained in the movie. This is because how the core was stopped isn't actually the story the writers wanted to tell. It was simply the premise to set up the story they really wanted to tell.
So, what you're really looking for are explanations that allow readers to suspend their disbelief just long enough to get to the story you really want to tell.
The tiny middle-eastern country of Bahrain has had it up to here with all the nuclear super powers! They want to be a nuclear super power, too! So they steal nuclear bomb tech from Iran, Pakistan, and India, and resolve to set off the biggest underground nuclear test in history! They're not fools! Nosiree! They're going to set off their 1,000 megaton nuke an astonishing 1,500 miles below the surface! That's almost the bottom of the mantle! After all, they don't actually want to hurt anybody. They just want respect! And on the day they decided to push the button — the Earth reacted with what can only be called indigestion.
Greenland is tired of waiting for the world to solve global warming. It wants its glaciers back! Exhausted of patience, they contracted with the Chinese to send a series of boosters into space ostensibly to set some high-orbit satellites. But they hijacked the boosters! They found this rogue asteroid that looks like it's all ice and they're determined to land that sucker right on top of Greenland. Glaciers forever! Unfortunately, they didn't realize the reflective surface of the asteroid was actually mercury, and the much more massive than expected asteroid slammed into the Earth taking Greenland and most of Northern America, Europe, and northern Asia with it. On the other side of the Earth, landmasses connecting South America, Africa, and Australia popped up due to the concussion wave of the impact.
Nobody paid much attention to the Atlantis Arrives! blog until intelligence agencies world-wide started tracking explosive shipments arriving all around the Pacific's Rim of Fire. I mean, it's Atlantis, right? What could those nut jobs possiblly do? Unbeknownst to the world's intelligence agencies (something that's apparently much easier to do than anybody thought), several mega corps have been convinced that Atlantis really is in the middle of the Atlantic ocean (Atlantis... Atlantic... can't be a coincidence... right?) As usual, the intelligence agencies received confirmation via CNN when the explosives blew, raising the Atlantic sea floor and sinking Australia and most of the land surrounding the Indian Ocean....
Have some fun with this. People will swallow almost any ridiculous premise if the story you really want to tell is worth telling. Every "Young Adult" book on earth lives by this axiom.