# Understanding Earthquakes and Tsunamis – part 2

Prof Dhammika A. Tantrigoda
Department of Physics, University of Sri Jayewardenepura
Nugegoda, Sri Lanka

Part 1>
Origin of Earthquakes

Richter Scale Magnitude of Earthquakes

Normally we would like to represent the magnitude or intensity of any process using a numerical value of a certain property related to the process on a suitable scale. For example, intensity of rainfall is expressed using height of the water collected in an open vessel kept in the rain (rain gauge) using a millimetre scale. Similarly the magnitude of an earthquake is expressed in terms of the amplitude of the ground motion. The scale on which this is expressed is called the Richter scale. In the original Richter scale, Richter defined the magnitude in terms of the maximum trace amplitude on a standard seismometer, sensitive equipment capable of monitoring vibrations of the earth, stationed at a distance of 100 km from the epicentre of the earthquake. The amplitude is expressed on a logarithmic scale. According to this scale an earthquake that shows amplitude of one metre on the standard seismometer has a magnitude 6. An earthquake that shows 1 km amplitude is designated to have a magnitude of 9 on this scale. There are practical problems in using this scale especially due to non-availability of seismic stations at an epicentral distance of 100 km of each and every earthquake. Therefore the original concept of Richter has been modified and new formula has been suggested. The new formula is capable of computing the magnitude of an earthquake monitored at any seismic station on the globe.

Energy Release

Methods of estimation of total energy released in an earthquake have been given by Richter, Guternburg and many others. It is somewhat difficult to appreciate the amount of energy released in an earthquake from the numerical magnitude alone. Comparison with other known processes that release energy would be of some help in this regard. A magnitude 1 earthquake is so weak that they can only be observed with sensitive instruments. Kinetic energy associated with such an earthquake is more or less equal to the kinetic energy of a vehicle weighing 15000 kg travelling at a speed of 130 km per hour. One ton of the explosive trinitrotoluene (TNT) releases about 4.2×109 (four thousand two hundred million) of Joules of energy. Energy released in the atomic bomb, which destroyed Hiroshima, is the same as that released by an explosion of eleven kilotons of TNT. This is equivalent to the energy released in a magnitude 5 earthquake. An earthquake of magnitude 9 releases about 1.6 x 1018 Joules. All lesser earthquakes numbering more than 500 000 per year only releases five per cent of the energy released by a magnitude 9 earthquake.

Generation of Tsunamis

When a very large earthquake occurs at a subduction zone, dislocation of the deformed and strained rock units cause the ocean bottom above the focus to rupture and collapse. This may result in either vertical upward or downward movement of the sea floor of an extensive region. Disturbed water mass will soon try to regain the equilibrium under gravity and in the process a train of waves are generated. This is somewhat analogous to a plucked string of a musical instrument trying to regain equilibrium by undergoing vibrations. The manner in which a disturbance caused by collapsing of sea floor generates a train of sea waves and the calculation of properties of the waves so generated can be carried out using classical fluid dynamics. The discussion, which follows, is based on qualitative treatment of the results obtained from such calculations.

Basics of Wave Propagation

We are all familiar with tiny water waves or ripples generated on the surface of a clear and calm pond as a result of dropping a pebble. We see that even though the ripples move outwards from the point at which pebble was dropped, small pieces of leaves floating on the water do not travel with the wave. Instead they oscillate up and down and to and fro around a fixed position. This clearly indicates that the medium (ie. water) does not travel when a wave is propagated through the medium. But the wave gives the capability to a piece of leaf to oscillate and this indicates what is been propagated is only the energy. In a wave we observe the repetition of a certain fundamental shape (figure 3). Length of this fundamental shape is known as the wavelength, speed at which this shape travels through the medium is called the wave speed and the time taken by the fundamental shape to travel its own distance is called the period of the wave. It is interesting to see how water particles (the medium) oscillate when a water wave is propagated. Contrary to what is stated in many elementary physics textbooks including those we use in our own schools, oscillations of water waves are not confined to the vertical direction. If the oscillations are confined to the vertical direction, then water should have stretched vertically at crests and compressed at troughs of the wave. We know very well that water does not have sufficient elastic properties to sustain such deformations. Therefore when a crest is formed water from the neighbouring region will flow in the horizontal direction to compensate for the amount of water that has gone up resulting in a trough in that region. So the oscillations are taking place in the vertical as well as horizontal directions. Very often horizontal component is more pronounced compared to the vertical component.

figure 3

Speed of Tsunami Waves

A sudden vertical disturbance of a water column generates a very large number of waves (pulses to be precise) with different wavelengths and they normally travel with different speeds and have different periods. All the waves that have wavelengths greater than six times the depths of the water layer travels with the same speed. This speed is equal to the square root of the product of acceleration due to gravity and the depth. According to this formula tsunami waves travelling in region of 4 km water depth has a speed of 200 meters per second or 720 km per hour. This value is comparable with the speed of a commercial jet aircraft. When tsunami waves reach the edge of the continental shelf their velocity reduces to about 45 metres per second and further reduces to about 10 metres per second when reaches the show. As a result of progressive reduction of speed when climbing the continental shelf tsunami waves acquire large amplitudes. Lower speed in the front part and higher speed in the rear part of the wave will result in bunching up water over a narrow region forming a tall wall of water near the shore.

Energy Propagation

Tsunamis are quite different to the water waves generated by the wind that we are very much familiar with. Tsunami waves have very long wavelengths, which are generally of the order 100 km to 200 km where as the wavelengths of waves generated by winds rarely exceeds a few tens of metres. In waves generated by winds the surface of the water mostly takes part in oscillations and the energy of the wave is almost limited to the surface. In tsunami waves the whole water column from the surface to the bottom of the sea takes part in oscillations and the energy is distributed in the whole water column. When it is passing through a region of the deep ocean its amplitude becomes very small as the total energy of the wave is now shared by a water column, which may be five to six kilometres deep. This is the reason as to why in the deep ocean tsunamis have amplitudes of less than one metre and are not detected by ships passing by. When a tsunami reaches a region of shallow water its energy is distributed in a small column of water and therefore should have higher amplitude to have the same amount of energy it had when passing through a deep region (tsunami waves loose very little energy when travelling through the deep ocean).

Main Phases of Tsunami Waves

Physicists and mathematicians have extensively studied water waves including tsunamis. It has been shown that a tsunami wave has two main phases in general as shown in figure 4. First phase is part of the wave in-between A and B in Figure 4 and this is known as Jeffery phase, in memory of one of the mathematicians who contributed to the better understanding of propagation of tsunamis. Rest of the wave is known as the oscillatory phase. It is useful to note that the Jeffery phase is only a sort of a crest of a wave and it does not have a trough. Actual size of the Jeffery phase depends on the nature of the initial disturbance of the water caused by the collapse of the sea floor.

It has been reported that mainly two destructive waves struck most coastal towns of Sri Lanka on the last 26th of December. There has been a spectacular recession of the sea exposing the sea floor to a distance of about 1 km from the shore in many places during the time interval between the two waves. It may be interpreted that the Jeffery phase with reduced amplitude may be responsible for the initial wave, which was not very strong. The Jeffery phase will be followed by the first trough of the oscillatory phase, which is responsible for the recession of the sea. As explained earlier a trough of water waves are formed as a result of horizontal movements of the water towards the crests and this further explains complete depletion of water exposing the sea floor. Then the first crest of the oscillatory phase will come with enhanced amplitude and most of the devastation will be caused by this stronger second wave. It is possible for several other waves also to come, but their severity would depend on several other factors.

Alteration of Direction and Penetrating into Shadow Areas

When a wave undergoes change in velocity it normally suffers a change in its direction of propagation. This phenomenon is known as refraction. Tsunami waves also can undergo refraction as a result of change in velocity due to the change in depth of the water column in which they are travelling. Sharp variation of the topography of the sea floor due to the presence of oceanic ridges and massive seamounts are capable of guiding the direction of tsunamis in this manner. Capability of a wave front to bend at an obstacle and reach areas covered by the obstacle is known as diffraction. Any wave type has this capability and the extent to which it can penetrate into the covered area is limited to a distance of the order one wavelength. This phenomenon may responsible for the tsunami waves that originated near Sumatra, which faces the eastern coast of Sri Lanka to reach its western coast. As the wavelength of the tsunami is of the order of 200 km it can easily affect the western coast even upto Negombo due to the diffraction phenomena.
In the recent tsunami we noticed that Maldives, which is an oceanic atoll, is comparatively less affected in spite of its seemingly vulnerable position in the Indian Ocean. The safeguards available to atoll dwellers are twofold. First of all the atoll isles rise steeply from the sea floor like pinnacles and there is no desirable topography of the sea floor for the wave to enhance its amplitude. Further, most of the isles have dimensions less than the wavelength of tsunami waves and therefore the waves will pass the isles almost “unnoticed”.

Tsunami Warning System and Public Awareness Programme

After the tragic events of December 26th many professionals and several others have urged the government to consider the possibility of having an early tsunami warning system in Sri Lanka. There is such a system that covers most countries in the Pacific Basin, Hawaii islands and other US regions bordering the Pacific Ocean. Basically a tsunami warning system is an international network of seismometers (or seismic observatories) and “tide stations” installed in relevant countries and relevant sea areas. These instruments are connected to a central station via satellite. The central station may also have access to other international seismic networks such as the one owned by the United States Geological Survey. Seismometer network will indicate occurrence of earthquakes in the region covered by the network and the geophysicists in the central station will compute the location and the magnitude of the earthquake. If the earthquake has taken place in a vulnerable sea area and if its magnitude is reasonably high (more than 7 on the Richter scale) they can examine readings of the tide gauges in the vicinity of the focus of the earthquake to see any signs of the formation of a tsunami. Warning bulletins will then be issued to the member countries if the necessity arises.

A tsunami warning system cannot be established by a single country. Several countries in a region, which are likely to be threatened by this natural disaster, will have to work together in establishing such a system. Therefore there are practical difficulties in establishing an early tsunami warning system immediately. Until such time we establish a suitable early warning system we may think of having our own improvised warning system. This system may consist of a small group of scientifically oriented dedicated people who work around the clock in a central station. They should examine seismic records at Pallekele and other stations or which we have access and compute the location and magnitude of any earthquake recorded. These computations do not require much advanced knowledge of seismology. Any person with reasonably good background of physics and mathematics and some exposure to computing can be easily trained for this purpose. They can also be on alert for news reports coming from neighbouring countries and warning bulletins issued by already established tsunami early warning centres and any other relevant information appearing on the internet. If a centre of this nature is available any outside agency that would like to warn us regarding an impending disaster can direct such warnings to this centre.

Sri Lanka has been generally considered a safe country with regard to natural disasters. Droughts and floods are the most frequently heard natural disasters. Sometimes heavy rains are reported to have triggered off landslides especially in the upcountry. Earthquakes of magnitude of the order of 5 or less on the Richter scale have been felt occasionally only arousing academic interest. Articles in the press by the experts often appear to reassure the safety of Sri Lanka soon after such events. Popular belief among many of us was that there is no need to worry about earthquakes and tsunamis, as they are not “destined” to occur in Sri Lanka. This false sense security that has been developed over the years has contributed much towards our ignorance with regard to extreme natural disasters. Our failure to realise the possibility of having a tsunami after a submarine earthquake exceeding magnitude eight on the Richter scale off the coast of Sumatra explains the extent of our ignorance regarding these matters. Had the general public being knowledgeable about recession of the sea immediately prior to the arrival of the major tsunami wave they would have gone to safe places resisting the natural tendency to take advantage of once in a life time opportunity of exploring the exposed sea floor. All these are sad and grim reminders of our ignorance about natural disasters. The importance of having a comprehensive long-term programme to educate the general public with regard to such disasters has become an urgent need of the country. Earthquakes and tsunamis should occupy a centre place of this educational programme. Different aspects of natural disasters including scientific as well as sociological aspects should come into our education system at different levels starting from he junior school to postgraduate level in the universities. Scientists will have the arduous task of understanding how these disasters originate and how they affect the different parts of the county and to draw up risk mitigation strategies. Finally through the media and education system of the country this knowledge should steadily permeate down to the general public. Intellectuals, educators and journalists of Sri Lanka have an enormous responsibility giving leadership to the initiation an effective awareness programme.

Part 1>
Origin of Earthquakes