Although most readers understand aspects of the behaviour of earthquakes, some context may be useful to those who do not specialize in apocalyptic disasters like the Boxing Day 2004 event in the Indian Ocean. Context is also useful in considering how technical information was brought to bear on public policy in this case. Here follows a more or less nontechnical view, with contributions from Vladimir Kossobokov of the Russian Academy of Sciences’ International Institute for the Theory of Earthquake Prediction and Mathematical Geophysics (MITPAN), of last December’s events.

The earthquake occurred on Boxing Day morning 2004 (Sumatra time) and the tsunami hit Bandah Aceh, the capital of Northern Sumatra, not more than 15 minutes after the strong shaking in that city. This was about the time many Canadians were finishing their Christmas Dinners on Christmas Day. There was absolutely no way the people of Sumatra could have been warned. There simply wasn’t enough time and there will be a like situation when the Cascadia subduction produces a similar mega-thrust; there will not be enough time to warn the west coast of Vancouver Island.

The situation on the west coast of North America is as brutally simple as it was in Sumatra. If you are caught there, as soon as prolonged shaking is evident, head for the highest point you can find. This is the folk wisdom that saved numerous islanders. Oral history is strong among some tribes of the Indian Ocean and it no doubt deals with the last tsunami their people experienced. They knew when to run.

Even if you are too far from the epicentre to sense the seismic vibrations, some basic common sense is helpful. If you’re on the shore and the sea suddenly pulls back unusually far, run for your life; the tsunami will be on you in minutes. Chris Chapman is now a Senior Research Scientist for Schlumberger, but some of you will remember him from many years ago as a junior professor of seismology at the University of Alberta. He experienced the tsunami first hand (EOS, Vol. 86, No. 2, 11 January 2005, p.13-14, and the photos and theory were put in their web pages and as appendices) in Sri Lanka last December.

More sophisticated tsunami predictions are currently done in Hawaii and they require in the first instance an estimate of the magnitude of the earthquake. Magnitude increases in proportion to the logarithm of the energy released by the earthquake, but the proportionality constant is not 1. A good rule of thumb is that with each step in magnitude the energy released by the earthquake goes up by a factor of 30 (definitely not 10).

The initial estimate of magnitude is made from the amplitude of vibration observed for a standard seismic phase on a standard seismograph at a standard distance from the epicentre. For any given earthquake there is never a standard seismograph in the right spot so in practice the first estimates of magnitude come from seismic stations that have been “calibrated” for events in the general area of the earthquake being considered.

Determination of location and magnitude are thus connected and for large events location and magnitude are determined automatically, usually by computers run by the United States Geological Survey. This preliminary determination of epicentre is not instantaneous; it takes time for the seismic waves to reach the seismographs that provide the required data. Roughly speaking the fastest vibrations take an hour to travel to the earthquake’s antipodes. Before magnitude and location calculations kick in, the programs need at least some of these data and I would guess that the preliminary determination of epicentre for the Sumatra event occurred between 15 and 30 minutes after the earthquake.

An hour after the Boxing Day Earthquake occurred in Sumatra every seismograph on the planet was vibrating. The earth was resonating and seismic stations around the globe were acquiring the vast amounts of data that will eventually give a clearer picture of the distribution of elastic, density, and viscous attenuation properties of the planet. The preliminary estimate of the magnitude derived from the amplitudes recorded by seismographs was 8.2, but it was raised as more data became available.

The actual mechanism of the earthquake can be extracted from the frequency spectrum of the waves, and this is done routinely at Harvard University. Harvard’s CMT (Centroid Moment Tensor) project had done a preliminary calculation and identified the event as probably larger than 8.2 and probably a mega-thrust on the Sumatran subduction zone. Later, using nine hours of seismic wave records, they confirmed that the magnitude was 9 and that the earthquake was a movement of between 10 and 30 meters out of the Earth on a fracture extending 900 to 1300 kilometers on the Sumatra trench.

An earthquake of magnitude 8.2 may be a threat to raise a tsunami but a 9.0 makes a tsunami a very definite possibility. It doesn’t make a tsunami a certainty, for the generation of a tsunami relies on how the earthquake changed the boundary conditions in the ocean basin in which it occurred. After the Sumatra earthquake locally raised a column of essentially incompressible water, the surface of the sea deviated from the gravitational equipotential and a wave evolved to restore equilibrium.

This propagating disturbance is a surface wave and the initial disturbance can be thought of as the Fourier sum of a large number of ripples of different wavelengths, each of which have a phase velocity defined by the square root of the water depth multiplied by the acceleration of gravity. Since the wave propagates on a surface, conservation of energy requires that the amplitude of the wave (proportional to the square root of the energy density on the wave front) falls off as the square root of distance from the source (not as the distance from the source as it would for a wave propagating within a medium).

In the deep ocean where the wavelengths are small compared to the ocean depth and in any case the ocean bottom is flat, little dispersion occurs and all phases travel more or less at the pulse’s group velocity. This group velocity is typically something like the velocity of a jet liner. Near the shore, dispersion caused by a sloping ocean bottom can cause the profile of the wave to change (long wavelength ripples interact with the ocean bottom before short wavelength ones do) and the wave may, but doesn’t usually, become a breaking wave.

A more precise calculation of the effect of a tsunami requires a fluid mechanics simulation using initial conditions (the effect of the earthquake) and boundary conditions (details of the ocean basin’s bathymetry). The first is deduced from the location, magnitude and central moment tensor. The second exists as a data base. It takes time to compute the moment tensor and results may not be available soon enough for the tsunami prediction; in this event telemetering sea level buoys are very helpful in defining the way the earthquake interacted with the water (the definition of initial conditions). Neither ocean bottom pressure sensors, floaters, or stilt mounted wave measurers existed in the Indian Ocean. In any case no-one was ready to run the required simulation to compute the probable effect on the populated shorelines. Even if they had been ready, the infrastructure to transmit a warning didn’t exist.

About 30 minutes before the tsunami hit the Thai beaches, the Thai meteorological service knew a great earthquake had happened and knew that a tsunami was probable. The director of that technical branch of the Thai Government didn’t issue a warning because his people had no certainty. Did he deserve to lose his job? I don’t know. I imagine the man considered the economic and political impact of a false alarm.

At least in Kenya the warning system worked. The Kenyan emergency response group monitored CNN, realized big trouble was on the way, had a few hours warning, and cleared the beaches. In Sri Lanka Chris Chapman’s wife, Lillian, apparently insisted that the management of the beach hotel at which she and Chris were holidaying take action. The staff cleared the beach of people who were curious about the way the water had retreated from the shore and one suspects Lillian’s insistence saved a number of lives.

The kind of dithering that occurred in Thailand cannot be blamed solely on the problems of organization in the developing world. It seems to have taken at least three days (some suggest a week) for the magnitude of this historic event to penetrate in Ottawa. The disaster evolved on Christmas Day night in Ottawa, but technical details of what had happened in the Indian Ocean were very clear by noon on Boxing Day. It wasn’t difficult to deduce the human tragedy these facts implied, but administrative obstacles seem to have kept that information from our political decision makers. If they needed confirmation of what their geophysicists could have told them they had only to ask the Canada Centre for Remote Sensing for high resolution satellite imagery.

Dealing with the consequences after the fact would have been easier though if the earthquake had been predicted in some fashion, for it is large earthquakes (or volcanic explosions such as the one that blew away the island of Krakatoa in the latter part of the 19th century) that cause tsunamis. Earthquake prediction, or forecasting, is a dangerous business; the consequences to scientists of a false alarm, or a failure to predict, are huge. One example of this is the reaction of land speculators in Los Angeles to comments from SeismoLab in Caltech some years ago. They sued because an earthquake prediction had dramatically lowered land values. Even so, a number of researchers are quietly trying to find reliable precursors to large seismic events, but for most there has been notably little success. Retrospective prediction has suggested some possibilities, but it’s not convincing. As in all things, hindsight is 20/20.

Measuring the way the surface of the earth deforms in a part of the world with potential for earthquakes is an obvious way to study what is going on. To do that you need to measure distances repeatedly to sub centimeter precision and that’s hard to do if the earthquake generating zone is covered by deep ocean and the nearest land is in a state of insurrection. Such was the case in northern Sumatra. Herb Dragert and his colleagues at Pacific Geoscience Centre are apparently having some success using GPS equipment to measure the way Vancouver Island is deforming but they have no way of telling whether the process they observe is approaching a point of instability. Instrumental records in the area have never covered a magnitude 9 earthquake; the last one occurred in 1700.

Another group, organised some years ago by Academician VI Keilis-Borok of the Russian Academy of Sciences and currently led by Vladimir Kossobokov, has abandoned the mechanistic view of this problem and is exploring the consequence of treating the earthquake generating system as a chaotic phenomenon resulting from heterogeneous non-linear processes. They comb the records of properties of small earthquakes for patterns that precede large earthquakes. Recognizing these patterns and evaluating their significance involves non-trivial mathematics and sophisticated computing, but one principle that appears to have merit is to identify anomalous clustering in space and time.

Since 1992 this MITPAN group has been running an algorithm they call M8 in an attempt to predict Times of Increased Probability (TIPs) for largest (about magnitude 8) earthquakes. They’ve had enough successes to prove the statistical significance of the M8 predictions and to justify monitoring aimed at smaller magnitude earthquakes.

However, the numerous alarms and a number of failures to predict suggest their tool is not yet useful to public policy. The parameters of the algorithm and the rules that constrain these parameters control not only the lower, but also the upper limit of the magnitude of predictable earthquakes. With an investigation of Italian earthquakes they gained confidence at lower magnitude levels, but until Boxing Day 2004 they had no way to test their algorithm in the range of magnitude 9.

Since 1992 the M8 algorithm has been applied to earthquakes occurring within “Circles of Investigation” (CI) with typical diameters of 1300 km and centred on seismic zones known to be active. This relatively small diameter means the algorithm is sensitive to earthquakes with rupture lengths of the order of 200 km or less and that puts them in the lower part of the magnitude range from 8 to 9.

Volodya Kossobokov tells me that, had the MITPAN group had the nerve to run a 3000-km CI on the northern part of the Sumatra Trench in the middle of 2004, they would have seen a TIP for a rupture with length ~ 1000 km. At that time there was no evidence that M8 would work for larger magnitudes, so they didn’t do the calculation. Therefore, Boxing Day 2004 was not really a failure to predict; they weren’t looking for a shock this big. It was a case of not being able to see the forest for the trees. Still, their retrospective success suggests M8 might well work over a significant magnitude range.

Great earthquakes of the Boxing Day type are not very common so the chance to test M8 further at large magnitudes might not appear soon. Still, there is a chance. Kossobokov pointed out to me that 4 mega thrust earthquakes of this size occurred within a few years of each other in 1952-1964. The odds of that happening with uniformly distributed events are miniscule and one wonders if the Sumatra event is the first in another such cluster. There are known candidates for 9+ seismic events and the Cascadia zone on the west coast of Canada and the USA is one such. Another may well be the seismic zone off Lisbon and others are, I’m told, off the Outer Antilles and in the southern part of the Sumatra Trench.

If M8 produces an identifiable alarm in any of these cases, the conundrum for seismologists will be a classic one. How should one present such a low probability, high impact event to the world at large? I have no answer.



The following article is reprinted by the kind permission of the Institute of Geophysical Research, University of Alberta. It originally ran in the February 2005 issue of their magazine “inuksuk”.


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