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# How does mathematics help scientists understand tsunamis?

Depending on where it occurs, a powerful earthquake in the oceans can shift rock, displacing the water above and generating seismic oceanic waves called tsunamis. Erroneously called “tidal waves” (they do not form by tidal action), tsunamis are long surface waves—often expressed as “like dropping a pebble in a pond”—that can attain tens of feet in height once they reach a shoreline. They happen mostly in the Pacific and Indian Oceans, and more rarely in the Atlantic. Because of the Pacific’s propensity toward tsunamis, there are several warning systems in effect; once an earthquake is detected, a network of early warning stations (with automatic sensors) send out signals that a tsunami may be imminent. If the warning is in time, coastal residents in the tsunami’s path may be able to escape to higher ground.

Mathematicians are also trying to help understand the physics and processes of tsunamis, mainly because the landforms, coastlines, and depth of the ocean basins differ. For example, in one study to try and understand the mathematics of the deadly waves that occurred in the 2004 Indian Ocean tsunami, mathematical models have show that the waves were a “classic wave packet,” or the wave behaved in a way that is close to that predicted by mathematical theory—waves traveling together as well as evolving in form as they cross the ocean. Mathematics also showed that, contrary to popular belief, the first tsunami to strike a shoreline is often not the largest; for example, in the Indian tsunami, the third and fourth waves were the larger than the first and second.

Another mathematical model developed in 2010 finds the best spots to install tsunami detection buoys and sea-level monitors in the Indian Ocean, and it can also be used for the less-tsunami-prone areas of the Atlantic Ocean, Mediterranean, Caribbean, and Black Seas. Yet another study used a mathematical model to show that the number and height of the waves hitting the shore depends on the shape of the initial surface wave in deep water.

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