Odds of a disaster, predict when tsunami will come next

Odds of a disaster, predict when tsunami will come next

John Gribbin, Guardian News Service, London

The fact that such a disaster happened last month in no way
alters the odds of a similar event occurring next month, or even
tomorrow. Probably not in exactly the same location, as far as
the epicentre is concerned, but quite possibly in the same part
of the world.

The statistics that apply to such events are essentially the
same as the statistics that apply to tossing a perfectly balanced
coin -- if it comes up heads on one toss, the odds are still one
in two that it will come up heads next time as well. The only
good news is that the odds of a disaster on the scale of much
smaller than one in two.

There are lots of ways in which you might guess that
earthquakes (the cause of tsunamis like the recent one) are
distributed in time. At one extreme, most earthquakes might be
very large, releasing lots of energy which then takes a lot of
time to accumulate again.

At the other, most earthquakes might be very small, repeatedly
releasing tiny amounts of energy and never doing much harm. Or
there could be some typical size for an earthquake, with both
larger and smaller events relatively rare.

Clearly, guessing is futile, and we need a proper scientific
assessment of the statistics. Indeed, when the records of
earthquakes are investigated to see how many of each size have
occurred around the world over a long period, they show none of
these patterns.

The first person to analyse the records in this way was
Charles Richter, who introduced the eponymous scale used to
measure the intensity of earthquakes.

This scale is another source of confusion to the uninitiated.
How come a magnitude nine event is so much worse than a magnitude
seven event? The answer is that the scale is logarithmic. A
magnitude two event is not twice as powerful as a magnitude one
event but 30 times as powerful. A magnitude three event is 30
times as powerful as a magnitude two event, and so on. So a
magnitude nine event is 900 times as powerful as a magnitude
seven event.

Almost fifty years ago, Richter and his colleague Beno
Gutenberg used this scale as a basis for investigating the
frequency of earthquakes of different sizes. They combined quakes
into "bins" of half a magnitude on the scale, so all the
earthquakes between five and 5.5 went in to one bin, all those
with magnitudes between 5.5 and six into the next bin, and so on.

Since the Richter scale is logarithmic, they took the
logarithm of the number of earthquakes in each bin, and plotted
the results on a graph known as a "log-log" plot. The results lay
on a straight line. Every subsequent study has shown the same
thing.

This is one of the simplest (and most common) patterns of
behaviour found in nature. It is called a power law, and in this
case it means that for every 1,000 earthquakes of magnitude five
there are roughly 100 earthquakes of magnitude six, 10 of
magnitude seven, and so on. This law applies across a huge range
-- a magnitude one event is about the same as the rumble you feel
when a heavy lorry passes your house, while a magnitude nine
event is some 500bn times more energetic.

The power law tells us that although large earthquakes occur
more rarely than small earthquakes, they are produced by the same
physical process. You do not need to invoke a special cause for
why large earthquakes happen -- they just do. The power law also
tells us that for any magnitude you choose, there is a particular
probability of an earthquake that size occurring during, say, any
one year. Small earthquakes are relatively common, but they occur
in the same random way as the way the numbers come up on a set of
dice.

Large earthquakes are rare, but they also occur at random. An
earthquake of any size could happen at any time in an earthquake
zone, even if one the same size happened last month.

The moral is plain. We should be no less, and no more,
concerned about a tsunami disaster affecting the Indian Ocean
today than we were on Christmas Day. If hindsight suggests that
it would have been a good idea to have a tsunami warning system
then, that need is exactly the same now. All this will have been
obvious to anyone with high school physics; such a pity, then,
that only about 30,000 students in the UK the subject in 2003,
and that so few politicians have any background in science at
all.