When a large earthquake occurs under the ocean, the vertical motion of the seafloor displaces the water column, causing gravitational instability; the potential energy change of the water column converts to kinetic energy, forming a tsunami, or seismic sea wave. (Although this tectonic mechanism is the most common cause of tsunamis, they can also be generated by submarine landslides or mass debris entering the sea from volcanic eruptions.) Tsunamis have wavelengths of tens to hundreds of kilometers, depending on the horizontal dimensions of the source, and travel over long distances with little attenuation. Their speed depends on ocean depth, increasing from 500 kilometers per hour in a 2-kilometer-deep ocean to about 900 kilometers per hour in a 6-kilometer-deep ocean (24). The waves are refracted away from regions of deep water and scattered from local bathymetric highs. Accurate bathymetric maps can be used to simulate tsunami propagation (Figure 3.7) and predict the arrival time and, if the details of the source are known, the amplitude. As the tsunami enters shallower water, the propagation speed and wavelength decrease, and the amplitude increases. Transgression of the shoreline by large tsunamis causes runup (measured as the water rise above the shoreline level, in meters), often as a very fast-rising tidal wave that floods well past the normal high-water level, sometimes as a turbulent bore. Considerable structural damage can occur to ports and other coastal installations from the exceptional currents generated during runup and withdrawal and the impact of debris entrained by these currents.

Tsunamis claimed more than 100,000 lives in the twentieth century. In some cases, the destruction occurred far from the earthquake epicenter, as on April 1, 1946, when an M 7.1 earthquake in the Aleutian Islands triggered a Pacific-wide tsunami. A runup of 8.1 meters occurred 4.9 hours later at Hilo, Hawaii, causing $26 million in damage and 159 deaths (Figure 3.8). This disaster led to the first Seismic Sea Wave Warning System, established in Hawaii on August 12, 1948. Additional systems have since been deployed, including those designed to provide rapid warnings of tsunami hazards from local earthquakes, when the runups occur soon after ground shaking (see below).

Although these warning systems can estimate tsunami arrival time accurately, their prediction of wave amplitude and coastal runup is much less precise. Major uncertainties are associated with the tsunami excitation process. Although tsunami amplitude depends on the total deformation of the seafloor (and should therefore be proportional to low-frequency seismic moment), it correlates poorly with standard earthquake magnitude determined at high frequencies (25). Moreover, seafloor deformation in the epicentral region depends on the depth and orientation of the fault-

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