Sounding the Alarm - Part 2

Nothing can prevent a tsunami from happening they are enormously
powerful events of nature. But in many cases networks of seismic
detectors, sea-level monitors and deep ocean buoys can allow
authorities to provide adequate warning to those at risk.
Mathematical models constructed from partial differential equations
use the generated data to determine estimates of the speed and
magnitude of a tsunami and its arrival time on coastlines. These
models may predict whether a trough or a crest will be the first to
arrive on shore. In only about half the cases (not all) does the
trough arrive first, making the water level recede dramatically
before the onslaught of the crest. Mathematics also helps in the
placement of detectors and monitors. Researchers use geometry and
population data to find the best locations for the sensors that
will alert the maximum number of people. Once equipment is in
place, warning centers collect and process data from many seismic
stations to determine if an earthquake is the type that will
generate a dangerous tsunami. All that work must wait until an
event occurs because it is currently very hard to predict
earthquakes. People on coasts far from an earthquake-generated
tsunami may have hours to take action, but for those closer it.s a
matter of minutes. The crest of a tsunami wave can travel at 450
miles per hour in open water, so fast algorithms for solving
partial differential equations are essential. For More Information:
Surface Water Waves and Tsunamis, Walter Craig, Journal of Dynamics
and Differential Equations, Vol. 18, no. 3 (2006), pp. 525-549.