Watch NOAA's Animation of the Tsunami Spreading Across the Pacific
NOAA is the government agency that oversees tsunami warnings and measurement. They use data collected by so-called DART buoys to trace the movement of wave energy in the ocean, and using the history of that data, to make predictions. Approximately 25 minutes after the earthquake, the tsunami was first recorded at DART buoy 21418 off the east coast of Japan.
Immediately, NOAA generated forecast models of the tsunami, taking into account "tsunami wave interaction with ocean floor bathymetric features, and neighboring coastlines." The video above is a "tsunami propagation animation" that shows how the wave energy should travel across the Pacific Ocean. (All of the forecasts are generated with the NOAA forecast method using the MOST model.) It wound up taking just about half an hour for the tsunami to travel the 80 miles to the coast of Japan, sweeping away cars, trucks and whole houses.
The colored image below is a model prediction of anticipated wave heights for the tsunami. You can see that the model predicted potentially 40 foot waves to hit the Japanese coast, and that the tsunami would reach as far as Chile a full day later.
Islands and even underwater peaks can alter the direction of the wave energy. As you watch the video above, compare the ripples sent off in various directions with this image below, which shows the height of the ocean floor. (Hawaii looks like a little chain of dots peaking out over vast canyons of deep blue.) The few pacific floor peaks and islands speckled around the open ocean cause reverse ripples on the tsunami's course towards the Americas in the animation.
Images and video: NOAA.