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Earthquakes are the most devastating natural events that occur on earth. The Study of these Earthquakes is a part of Seismology. Acceleration time-series or Accelerograms are records of sample seismic data over the entire duration of the Earthquake. They are actually records of the response of the ground motion being measured. However the actual ground motion is convolved with the instrument response and needs to be recovered. The project includes the extraction of the actual data from the convolved data. So we need to de-couple the Noise and base level Signals using the Filters and some other Instruments. The project involves in developing the program which estimates the Co-efficients using the Adaptive filtering techniques like Recursive Least Squares.
When analyzing signals (data), the quantity of the data to process, the doubt related with the data and the different mixture of data are vital factors to bank on. In the oil and gas industry, computing plays an important role in the processing of data. Software is employed for the analysis and interpretation (which gives the physical model of the subsurface of the earth of the crust) of data, from diverse data such as seismic data, production data, geological data etc. Earthquakes are the most devastating natural events that occur on earth. The Study of these Earthquakes is a part of Seismology. The Seismologists evaluate the potential dangers of earthquakes and seek to reduce their impact by improving the constructions standards. Acceleration time-series or Accelerograms are records of sample seismic data over the entire duration of the Earthquake. They are actually records of the response of the ground motion being measured. However the actual ground motion is convolved with the instrument response and needs to be recovered and this is done using adaptive filtering technique, the Recursive Least Squares.
The aim of the project is to extract the actual data from the convolved data by decoupling the noise and base level Signals using Filters and some other Instruments.
The objective of the project is to develop a program that estimates the Co-efficients using adaptive filtering technique, the Recursive Least Squares.
An adaptive filtering technique like Recursive Least Squares is used in the project to achieve the aim and objective of the project.
2.1 Interior of the Earth:
The earth is divided into four different layers. They are
Earth layers diagram
Fig 1: The interior of the earth
The first layer is the Crust. The crust is the thinner layer of all the other layers. It is composed of less denser minerals like Sodium (Na) aluminum-silicate and Calcium (Ca). It also consists of metamorphic, igneous, and sedimentary rocks. It is cold compared to other layers. The crust also consists of rocks and brittle which gets fracture in case of an earthquake.
The second layer is the Mantle. Most of the mass of the Earth mass is in the Mantle. It is a highly viscous layer that lies between the crust and the outer core. It is a rocky shell of thickness of about 2890 kilometers (1,800 miles) and constitutes about eighty four percent (84%) of total volume of the Earth. It is composed of silicate compounds like Magnesium (Mg), Silicon (Si), Iron (Fe), Aluminum (Al), Oxygen (O). At over 1000 degrees Centigrade, the mantle is a solid but can deform slowly like a plastic.
The third layer, i.e. the outer core of the Earth is a liquid layer. It is about 2260 kilometers thick. It is composed of composed of iron (Fe) and nickel (Ni). It is very hot and in molten state with 10% sulphur. The outer core's outer boundary is located at a distance of 2,890 kilometers (i.e. 1,800 miles) under the surface of the earth.
The fourth layer is the Inner Core. It is the hottest part of the earth as detected by seismological studies. Because of the extreme pressure in the inner core the inner core is in solid state. Its radius is about 1220 kilometers (760 miles).
An earthquake (also known as a quake, tremor, or temblor) is the result of sudden release of energy in the Earth's crust that creates seismic waves. Earthquakes are recorded with a seismometer, also known as a seismograph. When energy that is stored in some or the other form in the earth's crust is suddenly released, it results in Seismic Waves. This happens when rock masses that are resting one over the other suddenly slip or moves aside. Mostly earthquakes occur along geological faults and narrow zones where huge masses of rocks slide with one another. The main faults of the earth are located at the edges (or fringes) of the very huge tectonic plates that make up earth's crust. Epicenter is the point on the surface of the earth directly above the focus of an earthquake.
Before the invention of 'Seismology', only a very few information about earthquakes was known to us. It was estimated that about 50,000 earthquakes occurs annually. Out of these 50,000 earthquakes, approximately 100 earthquakes cause substantial damage, and very huge earthquakes occur once in a year can cause much damage to the life and property on earth.
2.2 Causes for Earthquakes:
There are different belts on earth and the major earthquakes occur in these belts where the margins of the tectonic plates coincide. Circum-Pacific Belt is the most important earthquake belt. Earthquakes that origin in this belt affects many populated coastal regions of the Pacific Ocean. Some of the densely populated coastal regions of the Pacific Ocean are Alaska, New Zealand, Japan, New Guinea, The Aleutian Islands, , and the western coasts of South and North America. About eighty percent (80%) of the energy that is released during earthquakes comes from those whose epicenters are in this Circum-Pacific Belt. The earthquake seismic activity will not be uniform throughout the belt. There are a number of branches at various points in this belt. This belt is also popularly known as 'Pacific Ring of Fire', because of the volcanic activities at many places in the Belt.
There is also another belt, known as the Alpide Belt. This belt passes towards eastward of the Mediterranean region through Asia and it joins the Circum Pacific belt in the East Indies. About fifteen percent (15%) of the world total earthquakes energy is released in earthquakes from this belt. There are also other seismic activity belts and they are along the oceanic ridges which include the western Indian Ocean, the Atlantic Ocean, and the Arctic Ocean and also include the rift valleys of the East Africa. This entire global seismic activity distribution can be best understood in the terms of its plate tectonic setting.
2.3 Tectonic Earthquakes:
As said above, earthquakes occur due to sudden release of some energy within a certain limited region of the massive rocks. This release of energy can be in different forms like, gravity, chemical reactions, elastic strain, and also in the movement of the heavy rock bodies. Among all of the above, the release of energy in the form of elastic strain is of major importance during earthquakes as it is the only kind of energy release form that can be stored in ample quantity in the earth to produce many major disturbances. The earthquakes that occur due to this form of energy release are known as 'Tectonic Earthquakes'.
Tectonic earthquakes are explained based on the elastic rebound theory. After the San Andreas Fault rupture, that led to the great San Francisco earthquake in 1906, Harry Fielding Reid, an American geologist formulated this theory. This theory states that a Tectonic Earthquake occurs when the strains in the rock masses of the earth have accumulated to a point at which the resulting stresses exceed the strength of the rocks, and then sudden fracturing occurs. These fractures propagate rapidly through the rocks, generally in the same direction and sometimes extend to many miles.
As these fractures progress in fault direction, the rock masses are thrown in opposite directions and thus moves to a less strain position. This process does not occur at once; rather it occurs in irregular steps. This sudden slowing down and restarting produce vibrations which propagate as seismic waves. Such irregular properties are now-a-days included in modeling of the earthquake sources, both mathematically and physically. Asperities are the roughnesses along the fault and fault barriers are the places where the fault rupture slows or stops. Generally, the fault rupture starts at the focus of the earthquake. The earthquake focus is a point that is about 5 to 15 kilometers under the surface. The rupture continues its propagation over the fault plane till it is slowed or stopped at a fault barrier. Also, sometimes, instead of being stopped at the fault barrier, the rupture will recommence on the farther side; and at some other times the stresses in the rocks are strong enough to break the fault barrier, and once the barrier is broken the rupture continues its propagation.
Depending upon the fault slip type that causes the earthquake, the earthquakes have different properties. Usually the fault model has a "Strike" and a "Dip". The "Strike" is the direction from the north taken by a horizontal line in the fault plane and the "Dip" is the angle from the horizontal shown by the steepest slope in the fault. 'Footwall' is the lower wall of the inclined fault. 'Hanging wall' is the wall that lies over the footwall. "Strike slip faulting" is the movement that is caused when the rocks slip each other parallel to the Strike. "Dip-Slip Faulting" is the movement that is caused when the rocks slip each other parallel to the Dip. Depending upon the movement of the block to the left or right that is on the opposite side of the fault to an observer, the Strike-slip faults are left lateral or right lateral. Similarly, depending upon the movement of the Hanging wall block to the downward or upward relative to the footwall block, the Dip-Slip faults are 'Normal' faulting and 'Reverse' or 'Thrust' faulting.
Displacements of the order of hundreds of kilometers are observed in geological faults whereas only a few centimeters to some tens of meters of seismic waves are produced in sudden slip offsets.
2.4 Volcanic Earthquakes:
Earthquakes also occur due to volcanic activities and such earthquakes are known as 'Volcanic Earthquakes'. Even in these volcanic earthquakes the disturbances are due to the sudden slip of the rocks masses that are adjacent to the volcanoes and due to the release of the energy in the form of elastic strain. However this energy is in partly of hydrodynamic origin because of the heat provided by the magma that is moving below the volcano and also due to the release of the gas pressure.
2.5 Human Activities:
Earthquakes also occur due to some human activities like pouring fluids into deep wells, digging of mines, the detonation of huge under-ground nuclear explosions, and also filling of reservoirs. The digging and removing of the rock masses from the mines causes changes in the strain around the tunnels. In case of injection of fluids, the slip may be due to the premature release of the elastic strains. In case of underground nuclear explosions the slip is produced on existing strained fault ruptures that are near the test devices. In case of filling of the large reservoirs the rock masses that are near the reservoirs are strained already due to local tectonic forces and the faults are ready to slip. When water is stored in the reservoir, there is pressure on the these rocks and may lead to earthquakes. But history says that filling of large reservoirs has not produces any hazardous earthquakes.
2.6 Earthquake Effects:
Earthquakes have many different effects on human and animal life, man made structures like buildings, bridges, and many more, and also affect the geological features. Most of the above mentioned effects happen on the surface of the earth, but actually most of the earthquakes foci are located beneath the water bodies like seas, oceans, and hence they also show a great impact on the water life and life along the ocean margins.
Geographical changes like horizontal or vertical movement of the ground structures that are present along the fault ruptures; also dipping or rising or tilting of the ground surfaces, changes in the direction of the flow of water in rivers and ground water etc. Earthquakes also affect roadways, railways, and waterways transportation. When they earthquakes occur they cause damages to roads and railway tracks due to which the transportation through roads and the transportation through rails have to face many difficulties. They cause delays. Also as most of the earthquakes foci are located beneath seas and oceans they generate tides that have several meters of height. Because of these large tides the movement of boats and ships becomes impossible and also they push the boats and ships away from their actual route. Sometime they may get sunk in the ocean causing loss of men and material. Due to earthquakes the underground pipelines broke and cause contamination of sewerage water with drinking water. If people drink this contaminated water then they may fall ill. Damage due to earthquake also depends on the topography and the nature of the surface materials that are present in the area. Damage due to earthquakes is more on the unconsolidated sediments and soft alluvium surfaces than on hard massive rocks. In case of severe earthquakes, the damage can be observed even at some hundreds of kilometers from the earthquake source, and this damage is mainly caused by the seismic waves that travel along the earth surface.
It is observed that earthquakes are generally associated with distinctive lights and sounds. The lights like streamers, bright balls and different luminous flashes in the night sky are due to the electric induction in the atmospheric air that is along the source of the earthquake. The sounds are due to the travelling of the high frequency seismic waves through the ground. These sounds are generally low pitched.
Also as most of the earthquakes foci are located beneath seas and oceans they generate tides that have several meters of height. These tides with such large height are also called as Tsunamis or Seismic Sea Waves and commonly known as tidal waves, although the attractions of the Sun and the Moon play no role in the formation of these tidal waves. These waves at times come onshore to very great heights of about some tens of meters that are above the mean tidal level and may lead to huge damage.
Tsunamis are the results of sudden displacements in the seabeds that cause sudden movement (lowering or rising) of a large amount of water. Also, large eruptions of volcanoes along the shoreline produce tsunamis. The Tsunami that occurred on 26th December, 2004 was recorded as the most destructive tsunami. It occurred as a result of the displacement of the seabed off the coast of Sumatra, Indonesia, due to an earthquake. More than two lakh (200000) people were killed in that drastic incident. The effect of the tidal waves that are generated due to the tsunami have caused a massive destruction in Indonesia, India, SriLanka and even hit the Horn of Africa. These waves speeded in all directions. Their speed in deep water is given by the formula (gh), where 'g' is the acceleration of gravity and 'h' is the depth of the sea. For example, if h=1000 meters (i.e. 3300 feet) then the speed is 100 meters per second. However, in deep water, the amplitude of these waves (i.e., height of the disturbance) at the surface of the water does not exceed beyond a few meters, and principal wavelength might vary in hundreds of kilometers; correspondingly, the time gap between the arrival of successive crests i.e. the principal wave time period may vary in the order of some tens of minutes.
The amplitude of the waves increases when tsunamis approach shallow waters. The height of the waves may sometimes reach to a height of 20 to 30 meters above the mean sea level in harbors that are in the shapes of V and U and in inlets and these waves do a great damage in the low lying areas such as inlets. In some cases, the time interval between the successive waves may be in the order of several minutes or more or even about half an hour. As a result of the great tsunami that occurred on 26th December, 2004 many countries like India, Siberia, Hawaii, Japan, Alaska have set up tsunami early warning seismographic stations.
Earthquakes cause seismic shaking that varies over area to area. One cannot simply quantitatively define the effects by observing only certain destructions. To define the effects in qualitative terms, 'intensity scales' are used to estimate the strength of seismic shaking. Intensity scales existed before the advent of the seismographs. The Intensity not only depends on the accelerations of the ground but also on the local geologic structure, the distance between the source and the measuring point, the periods and some other features of the seismic waves. One must note the difference between the earthquake magnitude and earthquake strength or intensity. Earthquake magnitude is the measure of size or amplitude of the seismic waves that are specified in a seismograph.
Different intensity scales were setup during the past century to measure the intensity of the earthquakes. In 1878, Michele Stefano de Rossi and Francois-Alphonse Forel devised a 10 point scale and it was most widely used for many years. Mercalli scale, which was modified by Harry O. Wood and Frank Neumann in 1931, having suitable grades is now used in North America. Modified form of the Mercalli scale is known as 12-point abridged form. Countries like Japan, Europe developed some other alternative scales for local conditions. The European scale (MSK) of 12 grades is similar to the modified form of the Mercalli, i.e. abridged version.
The measure of the amplitude or size of the seismic waves that are generated by the source of an earthquake is known as 'Earthquake magnitude'. This earthquake magnitude is recorded by seismometers. In 1935, Charles F Richter, an American seismologist set up earthquakes magnitude scale as the logarithm to base 10 of the maximum amplitude (in thousandths of a millimeter) of a seismic wave that is recorded on a standard seismograph (the Wood-Anderson torsion pendulum seismograph) that is located at a distance of about 100 km (i.e. 60 miles) from the epicenter of the earthquake. This measurement is based on empirical tables. The Richter magnitudes i.e M L are calculated based on the assumption of that the ratio of the maximum wave amplitudes at two given distances is same for all of the earthquakes and is independent of the azimuth.
Richter first applied his magnitude scale to the shallow focus earthquakes that were recorded in the range of 600 km of the epicenter in Southern California area. Later on, extra empirical tables were setup, where the observations made on different on seismographs other than standard type and at different distant stations are used.
Presently, there are many different magnitude scales that are being used by engineers and scientists to measure the relative size of an earthquake. A P wave magnitude (M b) defined in terms of amplitude of the P wave that is recorded on a standard seismograph. In a similar manner, Surface wave magnitude (M s) is defined in terms of logarithm of the maximum amplitude (size) of ground motion of the surface waves with 20 seconds wave period.
There is no upper or lower limit for an earthquake magnitude. Highly sensitive seismometers can record magnitudes of negative values also. The highest earthquake magnitude recorded till now is about 9.0. A magnitude of about 8.25 is recorded in San Francisco in 1906.
The magnitude scale is an empirical parameter that is similar to the stellar magnitude used by astronomers. Now days, Seismic Moment (M 0) type parameter that is related to angular leverage of forces that produce the slip on the causative fault is used to measure the earthquakes. This parameter provides a more uniform scale and allows a more scientific magnitude, called moment magnitude (M w) to use. It is directional proportional to the logarithm of the M 0 (i.e. the seismic moment). From the above definitions, it was found that the values of M 0=820 10 27 dyne centimeters and M w =9.2 and M s=8.4 for the great Alaska earthquake that occurred in the year 1964, which had a Richter magnitude (M L) 8.3.
The energy that is released by an earthquake can be found by knowing the seismic ground motion like the ground velocity. For a moderate earthquake and energy of around 10 5 watt/m2 (i.e. 9300 watts/foot2) will be released by the earthquake source. In case of shallow earthquakes the total output power will be in the order of 10 14 watts, which is higher when compared to that of the total output power 10 5 that is generated by rocket motors.
There exist a relation between the Surface Energy (E s) of an earthquake and the Surface wave magnitude (M s) based on some empirical formulas. For an earthquake with the surface wave magnitude M s of 0 and 8.9 there will be an E s of 6.3*1011 and 1.4*1025 ergs, respectively. Also if the M s is increased by a unit then the E s will increase approximately 32 times. Based on the Surface wave magnitude values one one can say how destructive an earthquake can be. An earthquake with 5.0 as the magnitude can cause a little damage and an earthquake with 6.0 can cause a destruction confined to a certain region and an earthquake with greater than 7.0 can cause major tremendous destructions.
About 1025 ergs of the total annual energy is released in all the earthquakes. This corresponds to a rate of work that is between ten million and hundred million kilo watts. It is estimated that about 90% of the total seismic energy comes from earthquakes with 7.0 or higher magnitudes. These magnitudes corresponds to the energies greater thatn 1023 ergs.
There also exist some empirical relationships between the magnitudes of the earthquakes and their frequencies. Let N be the average no: of shocks/year and M s be the magnitude range, then the empirical formula log 10 N = a bM s fits the data properly for both global and particular areas. It was found that a=6.7 and b=0.9 for M s > 6.0 for shallow earthquakes across the globe. This implies that for a unit decrease in magnitude there will be 10 times increase of frequency in case of large earthquakes. Also as frequency increases with decrease in magnitude the energy also decreases. About 50000 earthquakes occur annually whose magnitude M b > 4.0.
2.7 Earthquake Occurrences
There was no perfect theoretical explanation of the seismic patterns until 1960s. In 1960, dynamic model called 'Plate Tectonics' was developed. According to this theory, the Lithosphere, the earth's upper shell has dozens of large unstable slabs called 'Plates'. These plates has a thickness of approximately 80 kilometers (i.e. 50 miles) and move horizontally relative to other neighboring slabs or plates with rates of about 0.4 to 4 inches (i.e. 1 to 10 centimeters) annually over Asthenosphere, a less strength shell. At the edges of the adjoining plates, different tectonic forces operate on the rock masses. Due to these forces there occur chemical and physical changes in the rocks. Earth's mantle consists of magma and due to the upwelling and cooling of this magma, new lithosphere will be created at the ridges of the oceans. At the ocean trenches these horizontally moving plates believed to be absorbed. At these trenches a process called subduction, occur and it carries the lithosphere still down into the interior of the earth. The total amount of lithosphere material that is generated at the ridges is equal to the total amount of the lithosphere material that is destroyed at the subduction areas.
Fig. Plate Tectonics
Some of the earthquakes that are associated with ridges of the oceans are confined to faults, called 'Transform Faults', which offset the crests of the ridges. Most of the earthquakes that occur along the horizontal shear faults are of slip motions.
In the plate tectonic description the seismicity of low values within the plates is consistent. Within the boundary of plates, and within limited areas, small to large earthquakes occur; and this type of intra plate seismic activities are explained by tectonic mechanism.
At least occasional shallow earthquakes occur in most parts of the world. These shallow earthquakes occur within 60 kilometers (i.e. 40 miles) of the outer surface of the Earth. It is well known that majority of the great earthquakes foci are shallow in nature. The geographical distribution of small earthquakes is not completely determined when compared to that of great and severe earthquakes. It is because; the relevant data that is available depends on the distribution of the observatories.
About twelve percent (12%) of the total energy that is released from earthquakes comes only from earthquakes of intermediate type. The focal depth of these intermediate earthquakes range from 60 to 300 kilometers. And about three percent (3%) of the total energy that is released from earthquakes comes from earthquakes of deeper type. In the intermediate range, as the focal depth increases, the frequency of occurrence of the earthquake falls down rapidly. The frequency of occurrence is uniform below intermediate range to great focal depths that are about 700 kilometers (430 miles).
Earthquakes with deep focus generally occur in some patterns called Benioff zones. These benioff zones dip into Earth, which indicates the presence of subducting slabs. The Dip angles of some shallow slabs will be about 45Â° and someother may be 90Â°. Some tectonically active island arcs like the Aleutians, Tonga, Vanuatu, and Japan coincide with Benioff zones. These zones are sometimes associated with deep ocean trenches like Andes in South America.
Generally some less size earthquakes will occur after the occurrence of moderate or major size earthquakes of shallow focus near the earthquake source regions. This happens because if the fault rupture that is responsible for the occurrence of a moderate or major earthquake does not release all of the accumulated strain energy at a time, instead in irregular steps. Because of this there will be an increase in the strain and the stress in much number of places near the focal region. It was found that after a major earthquake about 1000 small size earthquakes will occur and this phenomenon is referred to as aftershocks.
In some cases a major earthquake will be followed by another major earthquake within half an hour or within a day. And this occurrence will be referred as multiple earthquakes in which the principle earthquake will be more effective and destructive. The number of aftershocks decreases with increase in time per day. i.e the frequency of occurrence of aftershocks roughly inversely proportional to time.
In contrast to aftershocks there also exist foreshocks. Occurrences of small earthquakes before a principle earthquake are referred to as foreshocks. These foreshocks may occur for months in a region. Sometimes these foreshocks may last without any major earthquakes. For example, between Aug, 1965 and Aug, 1967, in Matsushiro, Japan, there occurred a series of some thousands of earthquakes. Some of them are sufficiently strong enough to cause damages to properties like buildings, bridges etc., but does not cause any deaths. A maximum number of about 6,780 foreshocks were observed on 17th April, 1966. Such large number of foreshocks is referred to as 'earthquake swarms'. Some of the volcanic earthquakes occur in swarms. Swarms are also observed in many non volcanic areas.
2.8 Earthquakes list:
Occurred in Sparta, Greece in 464 BC with 7.2 as the magnitude.
Occurred in Palmyra, Baalbek, Syria on August 12, 1042, with 7.2 as the magnitude.
Occurred in Eastern Mediterranean on June 29, 1170 with 7.5 as the magnitude.
Occurred in Cilicia, Anatolia (Armenian Kingdom of Cilicia) in the year 1268 with 7 as the magnitude.
Occurred in Chihli (Hopeh), China on September 27, 1290 with 6.7 as magnitude.
Occurred in Friuli, Venice, Rome on January 25, 1348 with 6.9 as magnitude.
Occurred in Canterbury, UK, on May 21, 1382 with 5.8 as magnitude.
Occurred in Istanbul, Turkey, on September 10, 1509, with 7.2 as magnitude.
Occurred in Port Royal, Jamaica on June 7, 1692, with 7 as magnitude.
Occurred in San Diego, California, USA, on November 22, 1800 with 6.5 as magnitude.
Occurred in Kodiak Island, Alaska, USA, on October 9, 1900, with 7.7 as magnitude.
Occurred in Parkfield, California, United States, on March 3, 1901, with 6.4 as magnitude.
Occurred in Kamchatka, Russia, on November 4, 1952 with 9 as magnitude.
Occurred in New Ireland, Papua New Guinea, on November 16, 2000 with 8 as magnitude.
Occurred in El Salvador, on January 13, 2001, with 7.7 as magnitude.
Occurred in Gujarat, India, on January 26, 2001, with 7.7 as magnitude.
Occurred in Afyon, Turkey, on February 3, 2002, with 6.5 as magnitude.
Occurred in southeastern Iran, on December 26, 2003, with 6.6 as magnitude.
Occurred in Papua, Indonesia, on November 26, 2004, with 7.1 as magnitude.
Occurred in Tarapacá, Chile, on June 13, 2005, with 7.8 as magnitude.
Occurred in Java, Indonesia, on August 8, 2007, with 7.5 as magnitude.
Occurred in Sea of Okhotsk, on November 24, 2008, with 7.3 as magnitude.
Occurred in Samoa Islands, on September 29, 2009, with 8.1as magnitude.
Occurred in Sumatra, Indonesia, on April 6, 2010, with 7.8 as magnitude.
The study of the earthquakes and the movement of Seismic waves around the earth is known as Seismology and the person who studies about these earthquakes and the seismic waves is known as a Seismologist.
3.2 Seismic Waves:
The energy waves that are caused by the sudden breaking of rocks inside the earth are called as Seismic waves.
3.3 Types of Seismic Waves:
There are many types of seismic waves, moving in different ways. Body waves and Surface waves are two main types of seismic waves. The Body waves can travel through the inner layers of the earth, whereas the surface waves can only travel along the surface of the earth, just like water ripples. When earthquake occurs, it radiates the seismic energy as both body and surface waves.
Body waves have higher frequency than surface waves and hence they travel faster than the surface waves. There are mainly two types of Body waves. They are (a) P(Pressure or Primary) -Waves (b) S(shear or secondary waves) -Waves.
The P-Waves are longitudinal waves and travel at high velocity and therefore these waves arrive first at a seismic station or on a seismogram. They can travel through solid rock and fluids of the earth. They push and pull the material or matter they move through like sound waves which push and pull the air. Some animals like, dogs can hear the P-Waves and they bark before an earthquake occur. Because of the pushing and pulling action of the P-Waves they are sometimes called as Compressional Waves.
Figure 1 - Illustration of a P wave different times T.
The S-Waves are transverse waves and travel slowly compared to P-Waves, so they appear later at a seismic station or on a seismogram. They can travel only through solid rock and not through liquids. These waves move the rock particles side-to-side and up and down, perpendicular to the direction of propagation of the S-Wave.
Figure 2 - Illustration of a S wave at different times T
Surface waves have lower frequency than Body waves and hence they travel slower than Body waves. Surface waves have larger amplitude than body waves, and are almost entirely responsible for the damages and destructions that occur during earthquakes. There are mainly two types of Surface waves. They are: (a) Love Waves, (b) Rayleigh Waves.
Love Waves are named after a British mathematician, called A.E.H. Love, who worked out the mathematical model for this kind of waves. Love waves are the fastest surface waves and moves the ground side-to-side (i.e. they produce horizontal motion).
Figure 3 - Illustration of a LOVE wave at different times T
Rayleigh Waves are named for John William Strutt, Lord Rayleigh, who worked out the mathematical model for this kind of waves. These type of waves rolls along the ground just like a ocean waves and moves the ground up and down, and side-to-side in the same direction in which the waves are moving. Rayleigh waves are responsible for the shaking that is felt during an earthquake and these are the larger than other types of waves.
Figure 4 - Illustration of a RAYLEIGH wave at different times T
3.4 Seismograph (or Seismometer):
The strength of the earthquake is measured (studied) using an instrument called Seismograph (also known as Seismometer). A seismograph records the shaking of the earth's surface that is caused by seismic waves during an earthquake.
Around 132 A.D, a Chinese astronomer and mathematician, called Chang Heng invented the first Seismograph. He called it as an "earthquake weathercock." Later in 136 A.D., another Chinese scientist, named Choke, updated this instrument and he called it as a "Seismoscope."
Most of the seismographs that are used today are electronic. A basic seismograph construction is as below: It consists of a paper on a drum, a spring or a bar with a hinge at one or both the ends, a pen and also a weight. To a pole one end of the bar (spring) is bolted to a metal box or a pole which is also bolted to the ground. To the other end of the bar, the weight is connected and the pen is stuck to the weight. The pen is pressed by the drum with paper on it and turns constantly. This whole arrangement is known as Seismograph or Seismometer. During an earthquake, everything that is present in the seismograph moves except the weight with pen on it. So, because of the movement (shake) of the drum and paper, the pen makes some wiggly lines on the paper, which looks like a graph. This graph recording of the earthquake made by the seismograph is called Seismogram. This seismograph gives the information about the strength of the earthquake.
Fig 1: TWO ILLUSTRATIONS OF A MODERN SEISMOGRAPH IN ACTION
3.5 Understanding a Seismogram:
A typical seismogram looks like the one that is shown in figure 2 below. It consists of wiggly lines all across it. These lines represent the seismic waves that the seismograph has recorded. There are also some marks or little dots evenly spaced along the paper for every minute that the drum has been turning.
Fig 2: SEISMOGRAM
From the above figure we can observe that the P wave will be the first wiggle and as stated above that the P-waves are the fastest seismic waves, they appear first on the seismogram. The next set of seismic waves on the seismogram will be the S waves and as stated above they are slower than P-waves and has higher amplitudes they appear after P-waves with higher amplitudes on the seismogram. If there are no S-waves on the seismogram, then it implies that the earthquake has occurred on the other side of the earth, because S-waves cannot travel through liquid layers on the earth.
Then after, the surface waves (Love waves and Rayleigh waves) which are larger waves are recorded on the seismogram. Because they have a lower frequency, they are more spread out and hence they appear after the P-waves and S-waves on the seismogram.
3.6 Noise in Seismogram:
Due to many factors like waves hitting the beach, the winds, and many other ordinary things cause some shaking of the seismograph due to which the originally plotted seismogram may also contain noise. Because of this noise, we cannot get the actual (or perfect) seismic data. So, to get the perfect seismic data, we need to eliminate (or at least reduce) the amount of noise in the original seismogram. There are different techniques to eliminate the effect of noise in the original seismogram and Recursive Least Squares technique is one of them. This project uses this adaptive filtering technique, called Recursive Least Squares to filter the original seismogram which contains noise. The filtered seismogram may contain less noise than the original seismogram and, consequently, we get a less noise seismic data.