Manuel Garcia, Jr.
30 December 2004
The magnitude 9.0 Sumatra-Andaman Islands earthquake of 26 December 2004 generated a tsunami -- one or more large gravity waves -- that ran across the Bay of Bengal devastating the coast and causing an immense loss of life especially in Sri Lanka, India, Bangladesh, Myanmar, Thailand, Malaysia and the Indonesian island of Sumatra. The tsunami even caused deaths across the Indian Ocean along the west coast of Africa between Madagascar and Somalia. On 30 December, the published estimate of lives lost stood at 125,000. (1)
Much has already been written about the poison added to an already horrible natural disaster by separatist disputes, particularly in Sri Lanka but also in Aceh Province in Sumatra. Another disheartening and embarrassing story is that of American parsimony and cold-heartedness, in the person of President Bush's obvious annoyance at having to waste time and money even if only as a gesture on behalf of the Asian victims. The Europeans are seeking to call emergency meetings of the Group of Eight (G8, the rich nations) and the Paris Club (the creditor nations) to gather billions in emergency aid, and to cancel the debt of stricken nations. Clearly, Europe will respond either as a Union or with independent national efforts.
President Bush offered $15M when he was finally compelled to emerge momentarily from his vacation in Crawford, Texas. (2) UN emergency relief coordinator Jan Egeland called this "stingy," to which a New York Times editorial concurred. Later, functionaries in the government found another $20M to toss in the bucket, so the US contribution swelled to $35M. (3) Well, at least you've got to give the man (Bush) credit for honesty -- for a change -- he's not even pretending to care. Americans will no doubt be far more generous in supporting the international relief effort than is reflected by their (sic) government.
However, it is not politics that concerns me now; what I wish to describe is a sense of the physical scale of the tsunami. Why? To help place this event in perspective, and to help motivate thinking about shared global problem solving. Also, to offer some possibly humbling reflections on the power of nature.
Data: Earthquake And Tsunami
The essential facts about the magnitude 9.0 earthquake and its many aftershocks are available from the US Geological Survey. (4) Information about tsunamis generally, and the Indonesian one in particular, is presented by the US National Oceanic and Atmospheric Administration. (5) An animation of the tsunami was produced by the National Institute of Advanced Industrial Science & Technology of Japan. (6)
The earthquake was caused by a rupture -- perhaps 1000 kilometers in length -- along fault lines in the floor of the Andaman Sea, on the eastern side of the Bay of Bengal between Sumatra and Myanmar. The Burma Microplate is a small tectonic plate underlying the seafloor of the Andaman Basin, perhaps 2000 kilometers long and several hundred wide. The India Plate moves northeast at 61 millimeters a year and subducts under the western side of the Burma Microplate along the Sunda Trench. The Australia Plate is south of the India Plate and also moves northeast subducting at the Sunda Trench. To the east of both the Burma Microplate and the Australia Plate is the large Sunda Plate, underlying the Malay Peninsula and southern Indo-China. The epicenter of the 26 December M9.0 earthquake occurred at the southern end of the Burma Microplate, a nearly quadruple junction of four tectonic plates: the India, Australia, Sunda and Burma. The Burma Microplate shifted by an upward thrust of its western edge at the Sunda Trench, and a parallel slip along its north-south fault lines separating it from the Sunda plate to the east. 
The impulsive vertical motion of the seafloor displaced an immense quantity of seawater, launching the tsunami.
Gaging The Tsunami
How much energy went into the tsunami?
Assume a volume of seawater 1000 km long, 32 km wide and 3.6 km deep (typical of the Bay of Bengal) is lifted 2 meters. The energy involved equals the product of the mass of seawater, the acceleration of gravity (9.81 m/s^2) and a vertical displacement of 2 m. The mass of seawater is itself the product of its density, taken to be uniform at 1100 kg/m^3, and the volume of 1.15 x 10^5 km^3, or 1.15 x 10^14 m^3. The energy is E = (1100) * (1.15 x 10^14) * (9.81) * (2) = 2.5 x 10^18 joules.
To make this quantity more easily comprehensible, let us find its equivalent in numbers of Hiroshima atomic bombs. One kiloton (kt) of TNT has an explosive energy of 4.184 x 10^12 joules, the Hiroshima bomb had a yield of about 15 kt or 6.3 x 10^13 joules. The energy E pumped into our hypothetical seafloor upthrust is equivalent to nearly 40,000 Hiroshima bombs (39,683.5, rounded up), that is 600,000 kt or 600 Mt (megatons). One could imagine trying to engineer a comparable seafloor upthrust to that of the 26 December earthquake by planting 40,000 Hiroshima scale bombs spaced at 25 m in a 1000 km line.
The Hiroshima bomb had a yield that is fairly low compared to most bombs produced since 1945. The largest nuclear bomb detonated by the United States was Castle/Bravo at 15 Mt, and the largest bomb ever exploded was a USSR device yielding over 50 Mt. These bombs could be thought of as 1/40 and 1/12 equivalents, respectively, to the hypothetical 600 Mt seafloor uplift.
The Hiroshima bomb destroyed an area 12 km^2, killed up to 80,000 people and resulted in total casualties of up to 150,000. (8) The 26 December tsunami has probably killed 125,000, and displaced millions. It is possible a land area as large 10^4 km^2 has been inundated. This estimate would be equivalent to 3200 km (2000 miles) of coastline affected up to 3 km inland. In a few months, the reports of geophysicists will begin to be published, with refined estimates of inundation based on satellite imagery and ground surveys. While the nature of the destruction from a tsunami and a nuclear blast are very different, it is still useful to reflect that the scale of destruction by the Indonesian tsunami may be hundreds of times that of Hiroshima.
It is also a somber realization that with small numbers of large nuclear bombs a few governments begin to approach the destructive capability of nature itself.
Wave Height And Speed
How does a tsunami propagate?
Imagine once more our column of seawater, with its 32 km wide, 1000 km long "footprint." This is momentarily "lifted," which is to say it is pressurized by the sea floor displacement so that water mounds up above normal sea level. Being liquid, water will not hold a shape, so as it is lifted it will slosh away. The actual mound above normal sea level may only be 10 centimeters (4 inches) in the footprint area.
Under the force of gravity the mound will seek to level out, and the gravitational energy impulsively infused into the column of water by the sea floor motion will seek to equilibrate throughout the mass of the ocean. The tsunami is a wave or series of waves that carries this initial energy from the source volume out to the surrounding ocean.It is energy that flows to great distance, not water. The wave moves because small parcels of water slosh back and forth (in circular vertical paths, for deep water) and this local activity transfers the high pressure of a particular wave forward (think of a sequence of meshed gears). The wave may have a wavelength of many meters, even kilometers, and within that distance the wave will exhibit both a high pressure crest and a low pressure trough. Tsunamis are invisible from the air or satellites because they can have crests of less than a meter in height -- even just inches -- spaced at hundreds to thousands of meters. The water itself moves little and feels "normal," tsunamis pass unnoticed under boats on deep water.
Let L represent the wavelength of a tsunami, and h represent the depth of the sea. Then, a deep water wave will have h > (L/6.3), while a shallow water wave will have (L/6.3) > h. The speed of a deep water wave is given by V = (1.56*L)^(1/2), where V is in m/s and L is in meters. Longer waves travel faster in deep water. The speed of shallow water waves is independent of the wavelength, they all have the same speed set by the depth, V = (9.81*h)^(1/2).
For the Bay of Bengal, deep water waves will be those with wavelength L less than (6.3*h) = 23 km, and shallow water waves will have larger wavelengths. So, tsunamis with L > 23 km will travel at 188 m/s (420 mph), and tsunamis of shorter wavelength will travel at speeds between zero and 188 m/s, for wavelengths L from zero to 23 km, respectively, according to the formula (1.56*L)^(1/2). The Indonesian tsunami crossed 1400 km of the Bay of Bengal to arrive at Sri Lanka in 2 hours.
The sea floor rises as the tsunami approaches land, diminishing the depth of water, which has three effects: the waves slow down (they all become shallow water waves and h is diminishing), they bunch up and their crest heights increase dramatically.
Deep water tsunamis (those with wavelengths under 23 km for the Bay of Bengal) move at a wide range of speeds. Longer waves (under 23 km) will outspeed shorter waves, so they disperse as they move away from the source volume, which can emit a variety of wavelengths, depending on how the earthquake flapped and rattled the sea floor. As tsunamis become shallow water waves their speeds converge, and as they move along a rising sea floor they continually slow and they bunch up. As a sequence of waves bunches up, the individual waves also compress to smaller wavelength with taller crests. The wave tries to preserve the volume of its crest mound. What may have been a 10 cm high, 32 km wide mound in deep water might strike the shore as a 16 m (53 ft) high, 200 m wide wall of water moving at 13 m/s (30 mph).
The limit on cresting is set by the instability of water piled higher than the width of its base -- the wave breaks -- and by the distance from the source volume of the tsunami.
If the cresting of the previous example is doubled to 32 m (106 ft) the base would be 100 m, a still reasonably stable height-to-base ratio of 1/3.
The tsunami is just a gigantic ripple expanding from a point of disturbance. Close to the source, the ripple has more energy per unit volume because it is a small circular arc. As this arc expands, a greater volume of water contains the same amount of energy, so every meter of linear extent along the wave arc has less energy -- or pressure -- with which to rise against the force of gravity as it races up a rising sea floor.
Parting Thoughts: Clinging To Roots Against The Flood
A disaster of this magnitude makes it painfully clear that the most
concentrated forms of power humans have at their disposal are still
dwarfed by natural forces. That this power is in the forms of nuclear
weapons, military power and overbearingly greedy economics only rubs
salt into the wounds of the dispossessed. A disaster of this magnitude
should make it clear to anyone with any degree of human feeling that we
are all simply castaways on this island Earth, and that the sharing of
burdens and the assistance of each other is not really an option but a
necessity for our own survival. It is to that end that our power, and
planning and resources should be aimed. We need some major realignments
of our thinking. Nature is indifferent to us, and its power is such
that with just a twitch any number of us could be wiped away from the
world of the living. The only thing we have that approaches security is
The next article describes the energy of the tsunami waves, see
below (15 December 2005).
[all web sites active 30 December 2004]
 Tomi Soetjipto and Dean Yates, "Tsunami Toll Jumps to over 125,000, Fear Lingers," Reuters, 30 December 2004, http://www.reuters.com/newsArticle.jhtml;jsessionid=N4T0FTC02ODQYCRBAEZSFEY?type=topNews&storyID=7210780, also: http://www.truthout.org/docs_04/123104X.shtml (1 back)
 Patrick Martin, "Bush's response to South Asia disaster: indifference compounded by political incompetence," World Socialist Web Site, 30 December 2004, reference provided by John Steppling, http://www.wsws.org/articles/2004/dec2004/bush-d30.shtml, (2 back)
 "Are We Stingy? Yes," The New York Times, Editorial, 30 December 2004, (http://www.nytimes.com, and obnoxious "registration", or) http://www.truthout.org/docs_04/123104B.shtml (3 back)
 "Magnitude 9.0 - OFF THE WEST COAST OF NORTHERN SUMATRA 2004 December 26 00:58:53 UTC," Preliminary Earthquake Report, U.S. Geological Survey, National Earthquake Information Center World Data Center for Seismology, Denver, http://earthquake.usgs.gov/eqinthenews/2004/usslav/
"M9.0 Sumatra - Andaman Islands Earthquake of 26 December 2004," map of Andaman Islands and Aceh Province in Sumatra, http://earthquake.usgs.gov/eqinthenews/2004/usslav/tect_lg.gif (4 back)
 "NOAA REACTS QUICKLY TO INDONESIAN TSUNAMI," National Oceanic and Atmospheric Administration, US Department of Commerce, 26 December 2004, http://www.noaanews.noaa.gov/stories2004/s2357.htm (5 back)
 "2004 Sumatra Earthquake," Tsunami Animation - National Institute of Advanced Industrial Science & Technology (Japan), http://staff.aist.go.jp/kenji.satake/animation.gif (6 back)
 USGS, see , http://earthquake.usgs.gov/eqinthenews/2004/usslav/tectsetting_lg.gif (7 back)
 Daniel Green, "The Atomic Bomb," World War II Air Power, http://www.ww2guide.com/atombomb.shtml (8 back)
The Energy of the Indian Ocean Tsunami of 2004
Manuel Garcia, Jr.
15 December 2005