Journal: News & Comment

How can a tsunami go so far?

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NOTE: I've combined all my various writings about tsunamis from December 2004 and January 2005, including this entry, into a single tsunami article, which might make a good introductory reference.

Bill Copeland of Binnington Copeland & Associates in South Africa wrote to me to ask about why tsunamis travel so far. I feel a bit out of my league trying to explain wave behaviour to an engineer, but hey, being out of my league never stopped me before, so here we go...

Dear Mr Miller,

I am a Professional Engineer and am mystified by the fact that the Engineering principal of the inverse law does not appear to apply to Tsunami waves. Whilst I can understand that a big bang under the water will create a large vertical movement of water above it, I fail to understand why the volume of displaced water does not remain constant, and the amplitude of the wave diminish in proportion to the distance it travels (due to the larger circumference or increasing wave front). From reading the reports of the 26th December 2004 tsunami, one can only gain the impression that the wave front hitting the various countries was many thousands of kilometers long, and the volumes of water huge, which appear to have been much greater than the volume which could have been generated by the original earthquake.

Can you or your advisors help me please?

Energy, not volume

I don't have any advisors (other than Google!), but as far as I understand it (and I'm neither an engineer nor a geophysicist), it's not as though tsunami waves don't dissipate like others, it's just that they contain so much energy that even as they do, they remain powerful enough to destroy and kill. And it does not have to be amplitude that changes; so can period and wavelength, or the number of waves in the train.

Tsunamis are also not so much about volume displacement as about energy transfer. The water shifted above a quake does not move across the ocean, i.e. a log floating at the surface above the epicentre would not have been carried to Thailand or Somalia. So the water that drowned people in Somalia was African water, and that in Thailand was Thai water—just the energy that pushed it came from the Andaman sea floor several hours away.

A tsunami wave train moves as ocean swells do, by raising and lowering the water level as it passes by. In mid-ocean, a tsunami is unnoticeable without a sea-level gauge, since it might take an hour to raise and lower sea level by one metre—and you'd never notice that with all the bigger swells out there. But the energy contained in that slow, slow peak and trough is (as we have all seen) stupendous.

Sound around the world

Think of another, similar event in the same part of the world: the eruption of Krakatoa in 1883. Ignore the tsunamis and earthquake damage and focus only on the sound. At the site of the eruption the bang surely would have been deadly on its own, purely from sound pressure, like the shock wave of an atomic bomb. It dissipated rapidly as it spread outward, but even in South Australia it sounded like nearby dynamite being blasted.

More recently, on a Sunday morning in May, 1980, my father rushed downstairs because he thought our water heater had exploded. It turned out that Mount St. Helens, hundreds of kilometres southwest of us in the United States, had erupted that morning, and when the sound reached Vancouver it was still loud enough to seem like an explosion within the house.

Of course, like sound, energy does dissipate as a tsunami moves. The energy expended at and near the site of the quake is much larger than across the ocean, which is why buildings in northwestern Sumatra collapsed, totally aside from the tsunami, but in India and Africa the quake itself only registered on instruments.

Less powerful, but still powerful enough

Tsunamis are remarkably efficient ways of moving energy, but the waves that reached the coast of Africa were not by a long shot as energetic as those that pounded Sumatra and Thailand. They might have been just as high by the time they ran up beaches—that is determined more by the slope of the sea floor than by the strength of the original source of the waves—but they did not travel as far inland in Tanzania as they would have on some theoretically identical beach in Sri Lanka, or in Indonesia. I suspect that the series of waves in the wave train was smaller at farther shores too, and that there were fewer noticeable waves on African shores than Southeast Asian ones.

The mathematics of quake magnitude are beyond me, but this may help:

www.seismo.unr.edu/ftp/pub/louie/class/100/magnitude.html

Down at the bottom, the chart indicates that this quake released the energy of the explosion of several billion tons of TNT. You could probably strew that several billion tons very thin, along all the coastlines affected by the tsunami, and if you detonated it, you'd still kill a lot of people. You could throw most of it away, and strew what was left along those shores, and maybe kill the same number of people.

By the same logic, even a tsunami that is significantly less energetic than when it started can still be damaging, or deadly. If you live 100 metres from the shoreline on a nearly flat piece of land, a wave that reaches 200 metres inland will drown you just as well as one that reaches a full kilometre. If you're trapped in a hut completely consumed by brown swirling water, whether it's two metres or ten metres to the surface doesn't matter. If a tsunami engulfs the tree you're clinging to for seven minutes, you're just as dead as if it lasted fifteen—even if only half the volume of water passed through.

By the horrible numbers

And, in the end, the numbers tell the story: nearly 100,000 dead in Indonesia, 50,000 in Sri Lanka, 10,000 in India, 5,000 in Thailand—and 300 in Somalia. It's an imperfect measure, and gruesome, but (taking into account the directionality of the tsunami, differing coastal population densities, and energy absorbed by intervening land masses and sea floor features) that looks like a clear inverse distance relationship to me.

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