*Fundamentals of Earthquake SeismologyDr. Kalyan Kumar, G.

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Wave Motion*

*Elastic Rebound Theory

The elastic rebound model proposed by H.F.Reid after the 1906 San Francisco quake is a useful guide to how an earthquake may occur.

In this model, materials at distances on opposite sides of the fault move relative to each other, but friction on the fault locks it and prevents the sides from slipping.

Eventually the strain accumulated in the rock is more than the rock on the fault can withstand, and the fault slips, resulting an earthquake.

*Elastic Rebound Theory (contd)The model illustrated in Figure by the changes to five parallel lines, drawn normal to the trace of the fault in the unstrained state and intersecting it at the [points A-E ]Suppose they are steadily increasing shear forces on two blocks or rocks separated by existing fault. Because of friction, there is low movement. Unstrained state

*Far from the trace of the fault in the five lines remain straight and parallel, but close to it they are bent.Finally, the strain becomes more than the fault can support, and its weak part of the fault suddenly slips, and this rupture extends rapidly along part of the fault plane, allowing the blocks on either side of it to jerk into a less strained state. The relative displacement that has been taking place preferably between the adjacent plates during years or decades is achieved the fault plane in a few seconds. Elastic Rebound Theory (contd)Accumulation of strain close to the fault due to relative motion of adjacent crustal blocks(Strain growth at 5 cm/yr)

*Elastic Rebound Theory (contd)When the breaking point of the crustal rocks at C is exceeded, rupture occurs and there is a violent displacement on the fault - planeThe strained rocks adjacent to the fault rebound suddenly. The accumulated strain energy is released with the seismic speed of the ruptured rocks which is several km/sec. Strain released at 3.5 km/secRebound of strained segment

*The segments BC and C1D undergo compression, while CD and BC1 experience dilatation. The points A and E do not move, the stored strain energy at these points is not released. The entire length of the fault plane is not displaced, only the region in which the breaking point has been exceeded. The greater length of the fault plane that is activated, the larger is the ensuring earthquake.

Elastic Rebound Theory (contd)Rebound of strained segment

*The elastic rebound was believed by Reid to be the immediate cause of earthquakes, and his explanation has been confirmed over the years. Like a watch spring that is wound tighter and tighter, the more that crystal rocks are elastically strained, the more energy they store. When a fault ruptures, the elastic strain energy stored in the rocks is released, partly as heat and partly as elastic waves. These waves are the earthquakes.The elastic rebound idea was a major conceptual break through, because the faulting seen at the surface had been previously regarded as an incidental side effect of an earthquake, rather than its cause.Elastic Rebound Theory (contd)

Elastic Rebound Theory*

Elastic ReboundThe animated picture shows a road, a fence, and a line of trees crossing a fault. As the rocks adjacent to the fault are deformed, stresses build up in rock, rupture occurs when the shearing stresses induced in the rocks exceed the shear strength of the rock, followed by sudden slip, releasing energy that causes destruction. *

*The occurrence of a large earthquake is not necessarily as abrupt as described earlier, although it can be very suddenExample:1. 1976 Tangshan earthquake of magnitude 7.8 struck a heavily populated area of northen China near the city of Tangshan Although there were known faults in the area, they had long been seismically inactive and the large earthquake struck without warning Completely devastated the industrial region and caused an estimated 2,50,000 6,50,000 fatalities2. However in many instances the accumulating strain is partially released locally as small earthquakes or foreshocks This is an indicator that strain energy is buiding up to the rupture level and is sometimes a premonition that a larger earthquake is imminentElastic Rebound Theory (contd)

*Although in fact the earthquake involves a part of the fault plane measuring several km in area, from the point of view of an observer at a long distance of the earthquake appears to happen at a point. This point is called the focus or hypocenter of the earthquake. It generally occurs at a focal depth many kilometers below the earths surfaceThe point on the earths surface vertically above the focus is called the epicenter of the earthquakeAfter shocks:When an earthquake occurs, most of the stored energy is released in the main shockHowever for weeks or months after a large earthquake there may be numerous lesser shocks known as after shocks, same of which can be comparable in size to the main earthquakeVertical section perpendicular to the plane of normal fault

*Seismic Waves An earthquake source produces two types of waves: body waves and surface waves.

Body waves

travel through the body of the soil or rockP-waves and S-waves. In P-waves the particle motion is in the direction of propagation of the wave; In S-waves the particle motion is transverse to the direction of propagation.

*Surface waves

Occur at the surface of a material or at the interface between materials of different properties.

Typical earthquake accelerogram contains three main groups of waves: P, or primary; S, or secondary; L, or surface waves.

*Seismic Waves

Sensitive seismographs record the passing ground motions of the seismic waves with respect to time, noting the motions of an inertial mass against the moving ground.

*Seismology would be a very different science without instruments.

The real big advances in seismology happened from around 1900 and onwards and was mainly due to the advancement in making more sensitive seismographs and devising timing systems, so that earthquake could be located.

*Instrumentation and Data AcquisitionInput /Physicalquantities Output1. Sensors ---Strain gauges, LVDTs, Accelerometers, etc.2. Signal Conditioning Amplification, Filtration, Isolation Multiplexing3. Data Acquisition PXI Units and MAX software PC4. Data Presentation --Output

*Simple models of pendulum seismographs recording the vertical and horizontal directions of ground motion. The pendulum must be damped in order to separate seismic pulses.

*Photograph of a modern ground motion sensor of a digital seismograph

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*Body WavesP-WavesFastest moving waveParticles move back and forth in compression and extension. In a medium of mass density with shear modulus G and Poissons ratio vp = [2G(1-)/(1-2)]

S-WavesS for secondary. Particle motion is transverse to the direction of propagation, so these waves are also called shear waves. vs = (G/)1/2

*The ratio of vp to vs is

vp/vs = [2(1-)/(1-2)]1/2

Always greater than 1.0 for realistic values of Poissons ratio.

When Poissons ratio is 0.25, this ratio becomes 1.73 -- frequently cited as typical of the ratio of the two velocities.Body Waves (contd)

*S-WavesIn an S-wave the particle motions can be in any direction in a plane perpendicular to the direction of propagation. Convenient to divide this motion into two components: one in which all the particle motion is horizontal, and the other containing the remaining portion of the motion. Because the particles move horizontally, the first is called an SH wave. In addition, the particles may have some vertical motion in the second component, it is called an SV wave.

*Surface wavesIn addition to the body waves, stress waves occur at the surface of an elastic medium. The most important of these are Rayleigh waves. In these waves the particle motion describes an ellipse whose horizontal axis is in the direction of propagation. The motions are retrograde; The amplitude of motion in Rayleigh waves decreases with depth. The velocity of propagation is a function of Poissons ratio, but it is approximately 90 percent of the shear wave velocity.

*

*Modification of Seismic Wave Amplitudes When the body waves move through the layers in the crust they are reflected or refracted at the interfaces between rock typesWhen P and S waves reach the surface of the ground, most of their energy is reflected back into the crust, so that the surface is affected almost simultaneously by upward and downward moving waves. For this reason considerable amplification of shaking typically occurs near the surface, sometimes doubling the amplitude of the upcoming waves.

*Reflection, refraction, and transformation of body waves

*Another reason for the modification of the incoming seismic waves amplitudes near the ground surface is the effect of layers of weakened rock and soil.

When the elastic moduli have a mismatch from one layer to another, the layers act as wave filters amplifying the waves at some frequencies and deamplifying them at others. Resonance effects at certain frequencies occur.

*Definition of Earthquake Terms

The point at which rupture begins and the first seismic waves originate is called the focus, or hypocenter The epicenter is the point on the ground surface that lies directly above the focus. The focal depth is the depth of the focus below the ground surface. The epicentral distance is the distance from the epicenter to the point of interest on the surface of the earth (site or observer) The distance between the site or observer and the focus is focal distance or hypocentral distance.

Notation for description of earthquake location

*Locating EarthquakesOne of the most important tasks in seismology is locating seismic sourcesThe location of earthquake is often initially specified in terms of the determination of hypocentral/epicentral coordinates and the source origin time

*1 Locating an earthquake using the time of the first arrivalsAccording to the times of the wave arrival at different places, the earthquake was closest to station A , furthest from B , and so on , so it is somewhere within the shaded area . This is not very precise, because we dont know how long the signal took to reach the stations and time is not proportional to the distance, because the velocity within the Earth is not uniform.

*2 Location of the epicenter from both P- and S- wave arrivalAs vs < vp , the more distant the earthquake from the receiver the greater the lag of the S after the P-wave arrivalBy matching this delay to standard P and S travel-time curves the distance of the earthquake from a given station can be read offWe can also deduce when the earthquake occurredEpicentral angle =46Earthquake occurred about 8 minutes before P-wave arrival

*Location of an earthquake using P-S arrival-time differences and epicentral distances of three seismic stations

*Since P-waves travel faster than S-waves, they will arrive first at a given seismograph.

The difference in arrival times will depend on the difference between P and S-wave velocities, and the distance of the seismograph and the focus of the earthquake according to

Wheret P-S = The difference in time between the first P and S - wave arrivals.Vp - P-wave velocity (3000 to 8000 m/s in bed rock)Vs S-wave velocity (2000 to 5000 m/s in bed rock)

*Using any single seismograph, it is possible to determine the epicentral distance but not the direction of the epicenter

As we do not know the direction of the earthquake, we can locate the source only on arc centered on the seismogram station, but if the procedure is repeated for other stations then each distance can be drawn as an arc and their location locates the earthquake

More defined estimates of the epicentral distances of the epicentral location is made using multiple seismographs, a 3-D seismic velocity model of the earth and numerical optimization techniques.

*The depth of the hypocenter can be found by measuring the difference in arrival of the P-ray the direct ray -- and the ray that reflects from the surface PpRay paths from a deep earthquakeLocation of Focal Depth

*Quantification of Earthquakes

The intensity of the earthquake is a subjective parameter that is based on assessment of visible effects.

It therefore depends on factors other than the actual size of the earthquake.

The magnitude of an earthquake is determined instrumentally and is more objective measure of its size, but it says little directly about the seriousness of the ensuring effects.

*Earthquake Intensity

Intensity can be defined as a classification of the strength of shaking at any place during an earthquake, in terms of its observed effects.

Intensity is the measure of damage to works of man, to the ground surface, and of human reaction to shaking.

The intensity classification can be usedfor characterizing the rates of reoccurrence of earthquakes of different sizes in various locations, to estimate strong ground motion levels, for comparison of earthquake effects in different geographic regions for earthquake loss estimation.

*The intensity scale commonly used is the Modified Mercalli Intensity Scale (MMI) of 1931 which is reproduced in Table. The description given in Table1 allow the damage to places affected by numerically.

If enough data is collected, contours of equal intensity can be plotted which form an isoseismal map.

Such intensity maps provide crude but valuable information on the distribution of strong ground motion, on the effect of surficial soil and underlying geological strata and the extent of the source.

*Definition of Modified Mercalli Intensity V

Felt by nearly everyone, many awakened. Some dishes, windows, and so on broken; cracked plaster in a few places; unstable objects overturned. Disturbances of trees, poles, and other tall objects sometimes noticed. Pendulum clocks may stop.

*Modified Mercalli Intensity Scale (MMI) of 1931

*Japanese Seismic Intensity Scale

*Comparision of Modified Mercalli (MMI) and Other Intensity scales

*Earthquake Magnitude

The possibility of obtaining a more objective, quantitative measure of the size of an earthquake came about with the development of modern instrumentation for measuring of ground motion during earthquakes.

Seismic instruments allow an objective, quantitative measurement of earthquake size called earthquake magnitude to be made. Magnitude is an experimentally determined measure of the size of an earthquake.

*Approximate classification of earthquakes based on magnitudeEarthquakeMicroSmallModerate LargeGreatMagnitude* Not felt8

* Not specifically defined

*Magnitude scalesThe best way to quantify the size of an earthquake is to determine its seismic moment, M0 and the shape of the overall source spectrum

This can be done by recovering the source time function from either body or surface waves, but this requires relatively complete modelling of waveform in the question

It is desirable to have a measure of earthquake size that is much simpler to make, for example, the amplitude of a single seismic phase such as P-wave

*The concept of earthquake magnitude

A relative size scale based on measurements of seismic Phase amplitudes was developed by Wadati and Richter in the 1930, (over 30 year before the first seismic moment was evaluated in 1964)Magnitude scales are based on two simple assumptionsGiven the same source receiver geometry and two earthquakes of different size, the larger event will on average produce larger amplitude arrivalsThe amplitudes of arrivals below in a predictable fashion. In other words, the effects of geometric spreading and attenuation are known in a statistical fashion

*The general form of all magnitude scales is given byWhere A=The ground displacement of the phase on which the amplitude scale is based T=Period of the signal f=Correction for epicentral distance () and focal depth (h) Cs=Correction for the siting of a station (e.g. variability in amplification due to rock type) Cr=source region correction

----(1)

*The logarithmic scale is used because the seismic wave amplitudes of earthquakes vary enormouslyA unit increase in magnitude corresponds to a 10 fold increase in amplitude of ground displacementMagnitudes are obtained from multiple stations to overcome amplitude laiases caused by radiation pattern, directivity, and anomalous path properties

Four basic magnitude scales are in use today:

Local magnitude (ML)Body wave magnitude (mb)Surface wave magnitude (MS)Moment magnitude (MW)

*Richter Local Magnitude

The magnitude scales used today stem from the one introduced by Richter in 1955. This scale was designed by the network of Wood Anderson seismometers.

Richter designed the magnitude of a local earthquake as the logarithm to base ten of the maximum seismic wave amplitude in microns recorded on a WoodAnderson seismograph located at a distance of 100 Kilometers from the earthquake epicenter.

*As the values have a very large range, he took the logarithm (to base 10) to make the numbers more manageable, so an increase of 1 in magnitude means the amplitude is 10 times as large (the energy is about 30 times as large)

The fundamental period of the Wood-Anderson seismograph is 0.8 second and therefore it selectively amplifies these seismic waves with a period ranging approximately from 0.5 to 1.5 seconds. Because the natural period of many building structures are within this range, the local Richter magnitude remains of value to engineers.

*Definition of local Richter magnitude

*Local magnitude (ML)Richter (1935) developed an earthquake magnitude scale for shallow and local earthquakes in southern CaliforniaHe observed that the logarithm of maximum motion decayed with distance along parallel curves, for many earthquakesThe relative size of events is calculated by comparison to a reference event

*Local magnitude (ML) contWhere ML =local magnitude (also often referred to as Richter magnitude scale)

A = Maximum trace amplitude, mm, as recorded by a standard Wood-Anderson seismograph that has a natural period of 0.8 s, a damping factor of 80%, and a static magnification of 2800. The maximum trace amplitude must be that amplitude that would be recorded if a Wood-Anderson seismograph were located on firm ground at a distance of exactly 100 km (62 mi) from the epicenter of the earthquake. Charts and tables are available to adjust the maximum trace amplitude for the usual case where the seismograph is not located exactly 100 km (62 mi) from the epicenter.

Ao = 0.001 mm. The zero of the local magnitude scale was arbitrarily fixed as an amplitude of 0.001 mm, which corresponded to the smallest earthquakes then being recorded.

*At each seismic station , a value of Ml may be obtained from the measured amplitude of A and the value of log Ao at the appropriate source and receiever distance. From the table of values of Ao for various distance, an appropriate empirical formula has been derived ( Bullen and Bolt, 1985):Where A is the displ. amplitude in microns, and distance in kilometers. This formula is valid for distance between 10 and 600 kilometers.

*

Richter defined a fairly small reference event so that the magnitudes of all but the tiniest earthquakes are positive.

Events below about ml = 3 are generally not felt.

Significant damage to structures in california begins at about magnitude of 5.5

The largest ML recorded is about 7

*Surface Wave MagnitudeAt large epicentral distances (more than 200 km ), body waves have usually been attenuated and scattered sufficiently that the resulting motion is dominated by surface waves.

Gutenberg defined a magnitude scale (Ms) which is based on the measuring amplitude of Rayleigh waves with a period of 20 sec. The surface wave magnitude is obtained fromMS = log A + 1.66 log + 2.0where A = the max. ground displacement in micrometers = the epicentral distance of the seismometer measured in degrees

*The surface wave magnitude is based on the max. ground displacement amplitude therefore it can be determined from any type of seismograph.

The surface wave magnitude is commonly used to describe the size of shallow (less than about 70 km) focal depth, distant (farther than about 1000 km) moderate to large earthquakes.

Body Wave Magnitude

Deep focus earthquakes have only small or insignificant trains of surface waves. But the amplitude of body waves is not sensitive to the focal depth. An equation, proposed by Gutenberg in 1945, can be used to calculate a body - wave magnitude (mb) from the maximum amplitude of the ground motion associated with P - waves having a period of about 1-5 sec.mb= log A log T + 0.01 + 5.9where A is the P - wave amplitude,T is the period of P - wave and is the epicentral distance.*

*Limitations of methods based on wave amplitudeThe different fault dislocation distances with the same seismic moment can produce very different amplitude signalsThe effect of time function will depend on the frequency band of observationThe amplitude of various phases will vary greatly from instrument to instrumentStill very useful because of their simplicity and because high frequency shaking in a narrow frequency band is often responsible for damage from earthquakes

*Moment Magnitude

In the elastic rebound model, a tectonic earthquake arises from abrupt displacement of a segment of a faultThe area F of the fractured segment and the distance S by which it slipped can be inferred. Together with the rigidity modulus of the rocks adjacent to the fault, these quantities define the seismic moment Mo of the earthquake Assuming that the displacement and rigidity are constant over the area of the ruptureMo = F S

*The seismic moment can be used to define as moment magnitude (Mw) using an equation of the form given by Aki and Richards (1980)

Mw = where Mo is the seismic moment in dyne-cm. = Rupture strength of the material along the fault F = Rupture area S = The average amount of slip

Moment Magnitude (contd)

*Moment Magnitude (contd)Moment magnitude has largely replaced Ms in scientific evaluation of earthquake size, although Ms is often quoted in reports in the media.To represent the size of an earthquake as a dislocation phenomenon along a fault, the seismic moment M0 is the most adequate momentThe level of the low frequency and seismic spectrum is controlled by the seismic momentThe seismic moment correlates well with the every released during an earthquakeThe seismic moment can be estimated from geological records for historical earthquakes or obtained from the long-period components of seismogram

*General comments on magnitudesThe magnitude scale is, in principle, open-ended

Negative Richter magnitudes are possible, but the limit of sensitivities of seismographs is around 2

The maximum possible magnitude is limited by the shear strength of the crust and upper mantle, and since the beginning of instrument recording has been obscured with a surface wave magnitude MS as high as 9

*Magnitude Saturation

As the total amount of energy released during an earthquake increases, however, the ground-shaking characteristics do not necessarily increase at the same rate.

For strong earthquakes, the measured ground-shaking characteristics become less than sensitive to the size of earthquake than for smaller earthquakes. This phenomenon is referred to as "saturation", the body wave and Richter local magnitudes saturate at magnitudes of 6 to 7 and the surface wave magnitude saturates at about Ms = 8.

*The moment magnitude scale (Mw) is the only magnitude scale which does not suffer from the above mentioned saturation problem for great earthquakes.

It is due to the fact that it is directly based on the forces that work at the fault rupture to produce the earthquake and the recorded amplitude of specific types of seismic waves.

The relationship between the various magnitudes is shown in Figure Saturation of the instrumental scales is indicated by their flattening at higher magnitude values.

* Saturation of various magnitude scales

*Bolt (2001) suggests the use of different scales for measuring shallow earthquake of various magnitudes:

MD - for magnitudes less than 3

ML or mb - for magnitudes between 3 and 7

MS - for magnitude between 5 and 7.5 Mw - for all magnitude

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*Amplification of seismic waves by various seismographs

*Relationship between Magnitude and Intensity

Karnik (1969) proposed an empirical equation which relates the maximum intensity to the magnitude:

Imax= 1.5MS 1.8log h + 1.7

This type of equation is useful for estimating quickly the probable damage that an earthquake causes.

For example it predicts that in the epicentral region of an earthquake with magnitude 5 and a shallow focal depth of 10 km, the maximum MSK intensity will be VII (moderately serious damage), whereas, if the focal depth is 100 km, a maximum intensity of only IV V (minor damage) can be expected.

*Energy Released during an Earthquake

The definition of an earthquake magnitude relates it to the logarithm of the amplitude of a serious disturbance. Noting that the energy of a wave is proportional to the surface of its amplitude, it should be no surprise that the magnitude is also related to the logarithm of the energy.

The total seismic energy released during an earthquake is often estimated from the following empirical formulae proposed by Gutenberg and Richter (1956) :

log E = 11.8 + 1.5 MS

Where E is expressed in ergs. This relationship is also applicable to moment magnitude as well. It implies that a unit change in magnitude corresponds to a 101.5 or 32 - fold increase in seismic energy.

*A magnitude 5 earthquake would release only 0.001 times the energy of magnitude 7 earthquakeThe largest known value of MW is9.6 (Chile,1960) corresponds to an MS of 8.3

*SUMMARYThe overwhelming majority of earthquakes of engineering significance are generated by strain rebound associated with fault movement caused by tectonic processes.

As the different plates that comprise the earths surface move past or over and under each other, the rocks on opposite sides of the fault do not initially move past each other but instead deform, developing shear strains.

Eventually the shear forces on the fault become too large for the fault to carry, and a sudden slippage occurs, releasing the build-up shear strains. The sudden release of strain energy is perceived as an earthquake.

*There are three different types of plate boundaries and their characteristics influence the amount of strain energy that can build up near them.

As a result, the different types of boundaries have different earthquake capabilities: subduction zone boundaries can produce the largest earthquakes, followed by transform fault boundaries and then spreading ridge boundaries.

Fault movement is divided into dip-slip components (normal and reverse faulting) and strike-slip components (left lateral and rigid lateral faulting).

*Magnitude scales such as Richter local magnitude scale, surface wave magnitude scale, body wave magnitude scale are based on measurement of amplitude of ground motion. Because these amplitudes tend to reach limiting values, these magnitudes scales may not accurately reflect the size of the very large earthquakes.

The moment magnitude, which is not obtained from ground motion characteristics, is able to describe of any earthquake.

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