Science of Natural Phenomena : Earthquakes
In this review on natural phenomena, basic science and maths of earthquakes are discussed.
Earthquakes
Most earthquakes tragically demonstrate the suddenness with which they occur and the devastations they cause. Earthquakes occur because of sudden movement of Earth’s surface. A basic knowledge of earth’s structure would be, therefore, useful to appreciate the mechanics of earthquakes.
Earth’s structure
In the early part of the 20th century, geologists studied the earthquake-generated vibrations (seismic waves) to learn the structure of Earth’s interior which basically consists of several distinct layers : crust, lithosphere, asthenosphere, mantle and core.
Crust
Crust is defined as Earth’s outermost, thinnest, hard, rigid layer of only a few miles (5km) thick under the oceans and averaging 20 miles (30km) thick under the continents.
Lithosphere/Tectonic plate
The layer underneath the crust known as lithosphere or tectonic plate, is made up of massive, irregular slab of solid rock. It covers the entire surface of the Earth from the top of Mount Everest to the bottom of the deepest part of the world’s oceans (Mariana Trench). It comprises of some crust and uppermost part of the mantle.
Asthenosphere
This is a hot, malleable, semi liquid zone (~ 180km thick) over which the plates of lithosphere move or float.
Mantle
Mantle is a vast ocean of hot, dense, semisolid (pasty) rock, and forms the largest part of earth’s volume. It is subdivided into upper and lower regions and extends down to a depth of about 1800 miles (2900km). Thus although the ground under our feet might seem solid, we are actually standing on a relatively thin crust of rock below which is the mantle. Although the mantle is largely hidden from our view, ii becomes visible in places where crack opens up, allowing the molten rock to escape in the form of volcanoes. The liquid rock pouring out of a volcano is the same as in the mantle.
Mantle convection
When the mantle rocks near the radioactive core are heated, they become less dense than the cooler , uppermost mantle. As a result, these warmer rocks rise while the cooler rocks sink, called subduction process, creates slow, vertical currents within the mantle. This continuous movement of warmer and cooler mantle rocks produces convection cells within the mantle. These convection currents act like giant conveyor belts, propelling tectonic plates slowly but surely by up to 10 cm per year, about as fast as our fingernails grow. Thus the Earth, instead of appearing a solid, motionless body, is a living mobile planet.
Core
Core is subdivided into outer and inner regions. The outer core constitutes the only liquid layer of the earth, while the inner core is an extremely hot, solid sphere. Both layers consist of iron and nickel, and are situated 1800-32000 miles (upper core) and 3200-3900 miles (inner core) below the surface.
Physics
Mechanics of earthquake
Background
The modern theory of earthquake occurrence based on plate tectonics, is widely accepted framework since the 1960s. A tectonic plate is a massive, irregularly shaped slab of solid rock, generally composed of continental and oceanic lithosphere. Powered by forces originating in Earth’s radioactive inner core, the tectonic plates move ponderously about at varying speeds and in different directions atop a layer of malleable asthenosphere.
Despite their tremendous weights, the massive slabs of tectonic plates manage to float about due to compositional variation of the rocks. Continental crust is composed of granitic rocks of lightweight minerals (quartz and feldspar) compared to the denser and heavier basaltic oceanic rocks.
Also, the circulation of convection cells in the mantle is a driving force behind the movement of tectonic plates over the asthenosphere.
Occurrence
The tectonic plates may be colliding, separating or moving laterally past each other. However, sometimes two tectonic plates on grinding passed each other, can get stuck as their rough edges catch due to friction. When this happens, pressure builds up, until eventually, the rock gives way and the plates suddenly slip alongside each other with a jolt. When the stress at a point in the underground exceeds a critical value, a sudden failure occurs along a “fault” plane. Typically, there is a sudden displacement of the crust at the fault plane following the failure. The stored elastic energy is consequently released abruptly causing vibrations to travel in shockwaves (seismic waves) through Earth’s crust.
These elastic waves radiating from the underground source (focus), release energy in all directions. Directly above the focus is the point called epicentre on Earth’s surface from where the earthquake will be experienced most strongly. The result can be anything from a weak tremor to a full blown earthquake, depending on the amount of elastic energy released.
Earthquake and volcano
Earthquakes usually tend to spark volcanic eruptions, just like thunder preceding lightning. The close relationship between earthquakes and volcanic outbursts is evident from the matching of locations prone to both phenomena. The geological connection between them arises due to the shifting of Earth’s tectonic plates against each other which can jostle magma beneath volcanoes, urging it upward. In order for earthquakes to set off a volcano, the magma reservoir beneath the fiery mountain must be already primed to blow.
The seismic activity of a volcano similar to that for an earthquake, is a sign that magma is moving and shifting, increasing the possibility of eruption. Any tectonic movement for an earthquake with large amounts of rock moving together is the same as magma movement that is really hot rock but fluid enough to move causing volcanic eruption.
Earthquake and tsunami
A tsunami is series of ocean waves with very long wavelengths ( typically hundreds of kilometres) generated by large-scale disturbances of the ocean with vertical displacement of the overlying water. An earthquake can give rise to this kind of destructive ocean waves. Creation of tsunami is dependent upon the depth of the earthquake. Subduction earthquakes with giant flat slabs (tectonic plates) sliding under one another are particularly effective in generating tsunamis.
The collision of tectonic plates for an earthquake can sometimes shoot the plates upwards, and if that happens underwater, it pushes the water up with it. As the wail of water falls back down to sea level, it creates a monstrous wave (tsunami) that radiates outwards. The wave travels across the ocean, and becomes weaker with dissipation of energy as it travels out. If the earthquake occurs more than 100 km below the Earth’s surface, a tsunami may not, however, occur because there is not enough vertical displacement of the water.
Forecasting earthquakes
It is obvious that a huge responsibility comes with assessing the likelihood of earthquakes occurring. Although earquakes have been studied extensively and their causes are well understood, predicting such events over short time scales remains difficult.
There are two potential methods of forecasting an earthquake. In the early days, deterministic prediction was adopted to work out when, where and with what magnitude a particular earthquake would strike.
An uncertainty of the above technique led to the development probabilistic forecasting. It involved a change in strategy by calculating the odds that an earthquake above a certain size would occur within a given area and short time period. However, reliability of such prediction is not beyond any doubt.
In the wake of the L’Aquila earthquake in Italy in April 2009 after the specialists a month earlier predicted no such devastation forthcoming, one would realize just how complex earthquakes are and how difficult it is to predict them.
Maths
The cause of an earthquake can be better understood if the epicentre could be traced. Experts use maths to find the epicentre and the magnitude of an earthquake to determine its ultimate the severity. The usefulness of maths is discussed to evaluate the magnitude and strength (seismic energy) of an earthquake.
Monitoring earthquakes : Seismometers
Seismometers are devices that monitor the arrival times of seismic waves from an earthquake on a seismograph. The bigger the earthquake, the greater is the shaking of earth’s surface. A zigzag pattern on a seismograph would correspond to varying amplitude of ground oscillations beneath the instrument. The time, locations and magnitude of an earthquake can be determined from the seismograph data.
There are two phases of the recording pattern. There is an initial pulse of small amplitudes (primary or P-waves) which reduces down slowly. This is followed by a second wave of greater amplitudes (secondary or S-waves). Based on these two waves, the location and magnitude of earthquakes can be ascertained.
Seismologists measure the interval time of S-P to find the distance from the seismometer to the epicentre. Based on the results of three different seismometers at the three different distances, specialists can find the epicentre using the method of triangulation. Thus by drawing three different circles, each around a seismometer, the point where the circles interact is taken as the epicentre of the earthquake.
Magnitude of an earthquake and Richter scale
The magnitude scale of an earthquake is a number that compares amplitudes of waves recorded on seismograms. The most commonly used scale is Richter’s magnitude scale (R) developed by Charles F.Richter in 1935 which is based on the logarithm of amplitude of waves recorded on seismographs. As a result, a tenfold increase in wave amplitude would correspond to a jump in whole number of R. For example, a wave amplitude of an earthquake at R = 7 is ten times greater than an earthquake at scale 6, and would be hundred times greater than that at R= 5.
Richter’s scale can accurately reflect the amount of seismic energy released by an earthquake up to about R= 6.5. This is due to “saturation” of the scale from a combination of instrument characteristics and reliance on measuring only a single, short- period peak height. Development of a concept of magnitude scale based on surface and body waves seem to solve the “saturation” problem by extending the peak period. By definition, surface waves pass through earth’s uppermost layers, while body waves travel into and through the earth.
Strength (seismic energy) of an earthquake
Richter’s scale is related to the amplitudes of waves. However, it is the seismic energy (E) of the quake which is responsible for knocking down buildings. An evaluation of E-values is thus more important rather than the magnitude/amplitude of seismic waves to assess the destructive power of an earthquake.
Historically, calculation of E defined using the logarithm base 10 relies on Gutenberg-Richter (G-R) energy-magnitude relation :
log E (ergs) = 1.5*R + 11.8
where 10^11.8 is the energy (ergs) released by a small reference earthquake based on mathematical averaging techniques. Since detonation of 1 ton of TNT releases 4.184 gigajoules or 4.184*10^16 ergs, energy from an earthquake can be converted to equivalent tons of TNT. For example, an earthquake at R=9.0 would release energy equivalent to about 31 billion tons of TNT, or 2 million Hiroshima bombs.
Let us compare two earthquakes at R=8.5 and 5.5. The magnitude ratio is 1000, while the corresponding estimated seismic energy ratio based on the G-R relation is 31,622. It is obvious that that although the magnitude/amplitude (“size”) ratio is big, the ratio of seismic energy (“strength”) responsible for structural damages is very high for R=8.5 compared to R= 5.5. This explains why big quakes are so much devastating than small ones.
Final comments
Our fragile existence in this planet is made painfully clear by the latest terrible earthquake (9.0 scale) in Japan (11 March,2011) with an indication of a shift of Japan’s main island by over 200 cm. It is apparent that despite our impressive control of power, even for planetary destruction, we are still humbled by (when confronted with) the real power of planetary dynamics. Our achievement of harnessing the power of energy and the capability to describe regular, periodic natural phenomena may be impressive, but confident prediction of sudden planetary changes is still in its infancy.
In this review on natural phenomena, basic science and maths of earthquakes are discussed.
Earthquakes
Most earthquakes tragically demonstrate the suddenness with which they occur and the devastations they cause. Earthquakes occur because of sudden movement of Earth’s surface. A basic knowledge of earth’s structure would be, therefore, useful to appreciate the mechanics of earthquakes.
Earth’s structure
In the early part of the 20th century, geologists studied the earthquake-generated vibrations (seismic waves) to learn the structure of Earth’s interior which basically consists of several distinct layers : crust, lithosphere, asthenosphere, mantle and core.
Crust
Crust is defined as Earth’s outermost, thinnest, hard, rigid layer of only a few miles (5km) thick under the oceans and averaging 20 miles (30km) thick under the continents.
Lithosphere/Tectonic plate
The layer underneath the crust known as lithosphere or tectonic plate, is made up of massive, irregular slab of solid rock. It covers the entire surface of the Earth from the top of Mount Everest to the bottom of the deepest part of the world’s oceans (Mariana Trench). It comprises of some crust and uppermost part of the mantle.
Asthenosphere
This is a hot, malleable, semi liquid zone (~ 180km thick) over which the plates of lithosphere move or float.
Mantle
Mantle is a vast ocean of hot, dense, semisolid (pasty) rock, and forms the largest part of earth’s volume. It is subdivided into upper and lower regions and extends down to a depth of about 1800 miles (2900km). Thus although the ground under our feet might seem solid, we are actually standing on a relatively thin crust of rock below which is the mantle. Although the mantle is largely hidden from our view, ii becomes visible in places where crack opens up, allowing the molten rock to escape in the form of volcanoes. The liquid rock pouring out of a volcano is the same as in the mantle.
Mantle convection
When the mantle rocks near the radioactive core are heated, they become less dense than the cooler , uppermost mantle. As a result, these warmer rocks rise while the cooler rocks sink, called subduction process, creates slow, vertical currents within the mantle. This continuous movement of warmer and cooler mantle rocks produces convection cells within the mantle. These convection currents act like giant conveyor belts, propelling tectonic plates slowly but surely by up to 10 cm per year, about as fast as our fingernails grow. Thus the Earth, instead of appearing a solid, motionless body, is a living mobile planet.
Core
Core is subdivided into outer and inner regions. The outer core constitutes the only liquid layer of the earth, while the inner core is an extremely hot, solid sphere. Both layers consist of iron and nickel, and are situated 1800-32000 miles (upper core) and 3200-3900 miles (inner core) below the surface.
Physics
Mechanics of earthquake
Background
The modern theory of earthquake occurrence based on plate tectonics, is widely accepted framework since the 1960s. A tectonic plate is a massive, irregularly shaped slab of solid rock, generally composed of continental and oceanic lithosphere. Powered by forces originating in Earth’s radioactive inner core, the tectonic plates move ponderously about at varying speeds and in different directions atop a layer of malleable asthenosphere.
Despite their tremendous weights, the massive slabs of tectonic plates manage to float about due to compositional variation of the rocks. Continental crust is composed of granitic rocks of lightweight minerals (quartz and feldspar) compared to the denser and heavier basaltic oceanic rocks.
Also, the circulation of convection cells in the mantle is a driving force behind the movement of tectonic plates over the asthenosphere.
Occurrence
The tectonic plates may be colliding, separating or moving laterally past each other. However, sometimes two tectonic plates on grinding passed each other, can get stuck as their rough edges catch due to friction. When this happens, pressure builds up, until eventually, the rock gives way and the plates suddenly slip alongside each other with a jolt. When the stress at a point in the underground exceeds a critical value, a sudden failure occurs along a “fault” plane. Typically, there is a sudden displacement of the crust at the fault plane following the failure. The stored elastic energy is consequently released abruptly causing vibrations to travel in shockwaves (seismic waves) through Earth’s crust.
These elastic waves radiating from the underground source (focus), release energy in all directions. Directly above the focus is the point called epicentre on Earth’s surface from where the earthquake will be experienced most strongly. The result can be anything from a weak tremor to a full blown earthquake, depending on the amount of elastic energy released.
Earthquake and volcano
Earthquakes usually tend to spark volcanic eruptions, just like thunder preceding lightning. The close relationship between earthquakes and volcanic outbursts is evident from the matching of locations prone to both phenomena. The geological connection between them arises due to the shifting of Earth’s tectonic plates against each other which can jostle magma beneath volcanoes, urging it upward. In order for earthquakes to set off a volcano, the magma reservoir beneath the fiery mountain must be already primed to blow.
The seismic activity of a volcano similar to that for an earthquake, is a sign that magma is moving and shifting, increasing the possibility of eruption. Any tectonic movement for an earthquake with large amounts of rock moving together is the same as magma movement that is really hot rock but fluid enough to move causing volcanic eruption.
Earthquake and tsunami
A tsunami is series of ocean waves with very long wavelengths ( typically hundreds of kilometres) generated by large-scale disturbances of the ocean with vertical displacement of the overlying water. An earthquake can give rise to this kind of destructive ocean waves. Creation of tsunami is dependent upon the depth of the earthquake. Subduction earthquakes with giant flat slabs (tectonic plates) sliding under one another are particularly effective in generating tsunamis.
The collision of tectonic plates for an earthquake can sometimes shoot the plates upwards, and if that happens underwater, it pushes the water up with it. As the wail of water falls back down to sea level, it creates a monstrous wave (tsunami) that radiates outwards. The wave travels across the ocean, and becomes weaker with dissipation of energy as it travels out. If the earthquake occurs more than 100 km below the Earth’s surface, a tsunami may not, however, occur because there is not enough vertical displacement of the water.
Forecasting earthquakes
It is obvious that a huge responsibility comes with assessing the likelihood of earthquakes occurring. Although earquakes have been studied extensively and their causes are well understood, predicting such events over short time scales remains difficult.
There are two potential methods of forecasting an earthquake. In the early days, deterministic prediction was adopted to work out when, where and with what magnitude a particular earthquake would strike.
An uncertainty of the above technique led to the development probabilistic forecasting. It involved a change in strategy by calculating the odds that an earthquake above a certain size would occur within a given area and short time period. However, reliability of such prediction is not beyond any doubt.
In the wake of the L’Aquila earthquake in Italy in April 2009 after the specialists a month earlier predicted no such devastation forthcoming, one would realize just how complex earthquakes are and how difficult it is to predict them.
Maths
The cause of an earthquake can be better understood if the epicentre could be traced. Experts use maths to find the epicentre and the magnitude of an earthquake to determine its ultimate the severity. The usefulness of maths is discussed to evaluate the magnitude and strength (seismic energy) of an earthquake.
Monitoring earthquakes : Seismometers
Seismometers are devices that monitor the arrival times of seismic waves from an earthquake on a seismograph. The bigger the earthquake, the greater is the shaking of earth’s surface. A zigzag pattern on a seismograph would correspond to varying amplitude of ground oscillations beneath the instrument. The time, locations and magnitude of an earthquake can be determined from the seismograph data.
There are two phases of the recording pattern. There is an initial pulse of small amplitudes (primary or P-waves) which reduces down slowly. This is followed by a second wave of greater amplitudes (secondary or S-waves). Based on these two waves, the location and magnitude of earthquakes can be ascertained.
Seismologists measure the interval time of S-P to find the distance from the seismometer to the epicentre. Based on the results of three different seismometers at the three different distances, specialists can find the epicentre using the method of triangulation. Thus by drawing three different circles, each around a seismometer, the point where the circles interact is taken as the epicentre of the earthquake.
Magnitude of an earthquake and Richter scale
The magnitude scale of an earthquake is a number that compares amplitudes of waves recorded on seismograms. The most commonly used scale is Richter’s magnitude scale (R) developed by Charles F.Richter in 1935 which is based on the logarithm of amplitude of waves recorded on seismographs. As a result, a tenfold increase in wave amplitude would correspond to a jump in whole number of R. For example, a wave amplitude of an earthquake at R = 7 is ten times greater than an earthquake at scale 6, and would be hundred times greater than that at R= 5.
Richter’s scale can accurately reflect the amount of seismic energy released by an earthquake up to about R= 6.5. This is due to “saturation” of the scale from a combination of instrument characteristics and reliance on measuring only a single, short- period peak height. Development of a concept of magnitude scale based on surface and body waves seem to solve the “saturation” problem by extending the peak period. By definition, surface waves pass through earth’s uppermost layers, while body waves travel into and through the earth.
Strength (seismic energy) of an earthquake
Richter’s scale is related to the amplitudes of waves. However, it is the seismic energy (E) of the quake which is responsible for knocking down buildings. An evaluation of E-values is thus more important rather than the magnitude/amplitude of seismic waves to assess the destructive power of an earthquake.
Historically, calculation of E defined using the logarithm base 10 relies on Gutenberg-Richter (G-R) energy-magnitude relation :
log E (ergs) = 1.5*R + 11.8
where 10^11.8 is the energy (ergs) released by a small reference earthquake based on mathematical averaging techniques. Since detonation of 1 ton of TNT releases 4.184 gigajoules or 4.184*10^16 ergs, energy from an earthquake can be converted to equivalent tons of TNT. For example, an earthquake at R=9.0 would release energy equivalent to about 31 billion tons of TNT, or 2 million Hiroshima bombs.
Let us compare two earthquakes at R=8.5 and 5.5. The magnitude ratio is 1000, while the corresponding estimated seismic energy ratio based on the G-R relation is 31,622. It is obvious that that although the magnitude/amplitude (“size”) ratio is big, the ratio of seismic energy (“strength”) responsible for structural damages is very high for R=8.5 compared to R= 5.5. This explains why big quakes are so much devastating than small ones.
Final comments
Our fragile existence in this planet is made painfully clear by the latest terrible earthquake (9.0 scale) in Japan (11 March,2011) with an indication of a shift of Japan’s main island by over 200 cm. It is apparent that despite our impressive control of power, even for planetary destruction, we are still humbled by (when confronted with) the real power of planetary dynamics. Our achievement of harnessing the power of energy and the capability to describe regular, periodic natural phenomena may be impressive, but confident prediction of sudden planetary changes is still in its infancy.