The Chilean earthquake could have changed the earth's axis if the quake caused movement of the Earth's mass inward. According to the U.S. Geological Survey, this is influenced if not caused by the interaction of two tectonic plates, separate masses of the earth's crust, that move independently of each other.(1) This shift of the Earth's axis is called 'Precession' and is caused by a change in 'Torque' which is a variable within the physics of precession. Essentially, a chain of events occurred within the variables governed by the rules of physics which had the presumed result of shifting the Earth's axis and later the Earth's angular velocity.(2)
To further illustrate how the Chilean earthquake was able to change the earth's axis can be realized with understanding more about earthquakes, tectonic plates, and how they cause movement of the Earth's mass. For example, take two soft-cover books, place them side by side and push them against each other until something happens. Sometimes the pages smoothly slide underneath each other, but other times they may curve and bend causing the position of the books to change. These books are like tectonic plates except tectonic plates are part of a greater mass, namely the earth. When tectonic plates move they can change the distribution of mass in the earth
The two tectonic plates around Chile are called the Nazca plate and the South American Plate. The Haitian earthquake may have originated from movement along the fault between the North American and Caribbean tectonic plates. When the movement of earth caused by the earthquake changed the distribution of mass in and around the Earth, this may have affected the magnitude of force that affects the earths angular velocity which caused a change in precession. A partial sequence of events is numbered below:
(i) Tectonic plates move: Nazca plate and North American plate
(ii) Earthquake occurs: Chilean earthquake, February 27, 2010
(iii) Earths mass shifts: Seismic waves measured by richter scale
(iv) Earths axis tilts: Shift in mass incorporated into rules of physics
(v) Angular velocity of Earth changes: As defined by physical 'laws'
The physics behind this change in the Earth's rotation is due to a change in the variables that result in the angular momentum of the Earth's rotation. Since the Chilean earthquake was a result of the movement of two tectonic plates, the differential in the variables explained, tested and proven with physics changed. In other words, movement, mass, distance and velocity all interact after the Chilean earthquake possibly causing the Earth's axis to change position. These changes are calculated using mathematical formulas such as angular velocity, linear velocity, and angular momentum.(3)
Essentially, how the Chilean earthquake shifted the Earth's axis is explained by a combination of geological 'theories', and physical 'laws'. Since many events on Earth are related and connected, changes in one thing, can also cause changes in another. Similarly, just as it may be true that the Earth's axis changes every time there is an earthquake strong enough to displace the earth's mass, some think the Earth's axis may also change with changes in atmospheric temperatures i.e. global warming. (4) These kinds of changes may have happened many times in the history of our planet, and may continue to occur on a relatively frequent basis as well.
(1) http://earthquake.usgs.gov/learn/topics/plate_tectonics/rift_man.php (U.S. Geological Survey)
(2) http://farside.ph.utexas.edu (University of Texas)
(3) http://hyperphysics.phy-astr.gsu.edu (Georgia State University)
(4) http://www.newscientist.com (Newscientist.com)