When a subduction zone earthquake jolts the seafloor up or down by meters, it lifts or drops the whole column of water above it, from the bottom to the surface. That water spreads out as a tsunami, a series of waves unlike any wind wave.
Why it works
Wind waves stir only the top few meters of the sea and are tens of meters long. A tsunami moves the whole depth and can be hundreds of kilometers long, much longer than the ocean is deep. For such waves the speed depends only on depth: $v = \sqrt{g d}$. In the open ocean, 4,000 m deep, that is about 200 m/s (over 700 km/h), yet the wave may be less than a meter high, unnoticed by ships. Near shore the depth shrinks, the front slows, and the water behind catches up and piles up, so the wave grows tall. Because the waves are so long, each one floods inland for many minutes, like a fast-rising tide, and several arrive in a series.
Key idea
A tsunami is a series of very long waves from a sudden shift of the seafloor. It travels at $v = \sqrt{g d}$: as fast as a jet airliner in the deep ocean, slowing and growing taller near shore.
Worked examples
Worked example: Speed in the open ocean
How fast does a tsunami cross ocean 4,000 m deep?
- $v = \sqrt{9.8 \times 4,000} = \sqrt{39,200} \approx 198\,\text{m/s}$.
- $198 \times 3.6 \approx 713\,\text{km/h}$.
Answer: About $198\,\text{m/s}$, or $713\,\text{km/h}$.
Worked example: Crossing the Pacific
About how long does a tsunami take to cross 8,000 km of ocean averaging 4,000 m deep?
- $t = \dfrac{8,000,000\,\text{m}}{198\,\text{m/s}} \approx 40,400\,\text{s}$.
- About 11 hours. Warning centers use such travel times to alert coasts on the far side of the ocean.
Answer: About 11 hours.
Common mistake
A tsunami is often pictured as one giant breaking wave, like surf in a movie. It is usually a series of long waves that surge far inland, and the first is often not the largest; later waves can arrive many minutes apart. Check with the wavelength: with crests hundreds of kilometers apart, each wave takes many minutes to pass.