ieq 05 earthquake lecture notes 3

8/2/2019 IEQ 05 Earthquake Lecture Notes 3

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Course Title

IEQ-05 : Earthquake Geology and Geoinformatics

(Dept. of Earthquake Engineering, IIT Roorkee)

What is an earthquake?

An earthquake is the vibration of the earth produced by the quick release

Most often, earthquakes are caused by movement along large

of energy.

fractures in the earthscrust. Such fractures are called faults

The energy that is released

.

radiates

These waves are similar to the waves that occur when you drop a stone into water.

in all directions from its origin in the form of waves.

Just as the stone sets the water in motion, the energy released in an earthquake pro-

duces seismic

Frequency range of seismic waves is large, from as high as the audible range (greaterthan 20 hertz) to as low as the frequencies of the free oscillations of the whole Earth (2and 7 millihertz).

waves that move through the earth.

Attenuation of the waves in rock imposes high-frequency limits, and in small to mod-erate earthquakes the dominant frequencies extend in surface waves from about 1 to0.1 hertz.

The amplitude range of seismic waves is also great in most earthquakes. In the great-

est earthquakes the ground amplitude of the predominant Pwaves may be severalcentimeters at periods of two to five seconds. Very close to the seismic sources ofgreat earthquakes, investigators have measured large wave amplitudes with accelera-tions of the ground exceeding that of gravity (9.8 meters, or 32.2 feet, per secondsquared) at high frequencies and ground displacements of 1 meter at low frequencies.


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Earthquake Magnitude and Energy Release Equivalence

What is the mechanism that produces earthquakes?

Earth is not a static planet: in the earths crust, tectonic

In this process, the material is

forces are constantly at work push-

ing rocks on both sides of a fault in different directions.

deformed. As rocks dont slide past each other very easily,

strain is built up, just as if you bend a stick. At a certain level, the rocks can no longer re-

sist the strain and slip

This springing back of the rock is called

past each other into their original shape.

elastic rebound. It is this quick movement that

we feel as an earthquake. The elastic rebound usually happens a few kilometres deep in

the crust. This location is called the focus of the earthquake. The place on the surface

directly over the focus is called the epicentre

.

Reid's Elastic Rebound Theory

From an examination of the displacement of the ground surface which accompanied the

1906 earthquake, Henry Fielding Reid, Professor of Geology at Johns Hopkins University,

concluded that the earthquake must have involved an "elastic rebound" of previously

stored elastic stress.

If a stretched rubber band is broken or cut, elastic energy stored in the rubber band during

the stretching will suddenly be released. Similarly, the crust of the earth can gradually

store elastic stress that is released suddenly during an earthquake.


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This gradual accumulation and release of stress and strain is now referred to as the

"elastic rebound theory" of earthquakes. Most earthquakes are the result of the sudden

elastic rebound of previously stored energy.

The following diagram illustrates the process. Start at the bottom. A straight fence is built

across the San Andreas fault. As the Pacific plate moves northwest, it gradually distorts

the fence. Just before an earthquake, the fence has an "S" shape. When the earthquakeoccurs the distortion is released and the two parts of the fence are again straight; but now

there is an offset.


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Slow, Quiet and Silent Earthquakes

When we think of an earthquake source, we think of a crack that propagates throughthe crust close to the shear-wave speed, which is generally several kilometers per

second.

Fault rupture is sudden, accompanied by violent shaking of the ground.

But, creep events (on the San Andreas fault) during which propagation along a faultoccurs at rates of millimeters per year.

Earth deformation occurs at rates that differ widely.

From fast ruptures that suddenly release stored elastic-strain energy

Ordinary earthquakes to

Slow earthquakes (speed of hundreds of meters per second).

Silent earthquakes (speed of tens of meters per sec.)

Creep events, and finally strain migration episodes with speeds incentimeters or millimeters per second.

Slow earthquakes include episodes of rupture propagation that produce an ordinaryseismogram of high-frequency body waves.

However, slow earthquakes take an unusually long time to rupture in comparison toordinary earthquakes of similar moment magnitude.

Oceanic transform faults have produced several slow earthquakes, such as the 1960Chilean transform fault earthquake that ruptured for about an hour as a series of

small events.

Silent earthquakes are not accompanied by high-speed rupture propagation events. Thus they do not generate high-frequency waves that are recorded teleseismically.

Conventional seismographs do not record these events.

Strain metes document creep events on the San Andreas fault system (10mm/sec).

Silent earthquakes may offer promise as precursors to ordinary earthquakes.

How can the energy of an earthquake be felt?

The energy that is released

Two types of waves can be

in an earthquake travels in waves through the materials of the

earth.

distinguished

1. Some travel along the earths outer layer and are called

.

surface waves

2. Others travel through the earths interior and are called

.

body waves

Body waves are further divided into

.

Primary waves (P waves)

Secondary waves (S waves).


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P waves (primary waves)

P waves are push-pull wavesthey push (compress) and pull (expand) rocks in the di-rection the wave is travelling. Imagine holding someone by their shoulders and shakingthem. This push-pull movement is how P waves move through the earth. Solids, liquidsand gases resist a change in volume when compressed and will elastically spring backonce the force is removed. Therefore, P waves can travel through all these materials.

Highest velocity (6 km/sec in the crust).

S waves (secondary waves)

S waves, on the other hand, shake the particles at right angles to their direction of travel.This can be illustrated by holding one end of a rope steady and shaking the other end (seeillustration below). In contrast to P waves, which for a moment change the volumeof thematerial, S waves change the shapeof the material they travel through. Because liquidsand gases do not respond elastically to changes in shape, they will not transmit Swaves. An S wave is slower than a P wave and can only move through solid rock. (3.6km/sec in the crust)


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Damage nature due to body waves

Surface Waves

Travel just below or along the grounds surface

Slower than body waves; rolling (Rayleigh) and side-to-side (Love) movement

Especially damaging to buildings


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Love Waves

After A.E.H. Love and suggested in early twentieth century. L-wave can be thoughtof as the constructive interference of multiple reflected S-waves whose particlemotion is horizontal.

Travel just below or along the grounds surface with side-to-side particle velocity.

Speed is slower than body waves. This wave is especially damaging to buildings.

Typical velocity: Depends on earth structure (dispersive), but less than velocity ofS waves.

Typical velocity: Depends on earth structure (dispersive), but less than velocityof S waves.

Behavior: Causes shearing motion (horizontal) similar to S waves.

Arrival: They usually arrive after the S wave and before the Rayleigh wave.

Love waves are dispersive, that is, different periods travel at different velocities,generally with low frequencies propagating at higher velocity. Depth of penetrationof the Love waves is also dependent on frequency, with lower frequencies pene-trating to greater depth. VL ~ 2.0 - 4.5 km/s in the Earth depending on frequency ofthe propagating wave

Rayleigh Waves

After Lord Rayleigh who predicted existence in 1887.

These waves are analogous to waves travelling across the ocean. A floatingobject is not only pitched up and down, but also to and fro as wave passes.The actual movement of the object describes an ellipse. The motion of


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waves dies out quickly with depth, and this is also the case with Rayleighwaves.

Rayleigh wave can be thought of as arising from the constructive interfe-rence of multiple reflected P and S waves travelling in vertical plane.

Typical velocity: ~ 0.9 that of the S wave

Behavior: Causes vertical (rolling anticlockwise) together with back-and-forthhorizontal motion. Motion is similar to that of being in a boat in the ocean whena swell moves past.

Most of the shaking felt from an earthquake is due to theRayleigh wave, which can be

much larger than the other waves.ch can be much larger than theArrival: They usually arrive last on a seismogram.

Rayleigh waves are also dispersive and the amplitudes generally decrease with depth in

the Earth. Appearance and particle motion are similar to water waves. Depth of penetra-

tion of the Rayleigh waves is also dependent on frequency, with lower frequencies pene-

trating to greater depth. Generally, Rayleigh waves travel slightly slower than Love waves.

VR ~ 2.0 - 4.5 km/s in the Earth depending on frequency of the propagating wave

Damage pattern due to surface waves


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What is a seismograph and how does it work?

A seismograph is an instrument that records earthquake waves (also called seismic

waves). The principle : A weight is freely suspended from a support that is attached to

bedrock. When waves from an earthquake reach the instrument, the inertia of the weightkeeps it stationary, while the earth and the support vibrate. The movement of the earth in

relation to the stationary weight is recorded on a rotating drum. What is recorded on the

rotating drum is called a seismogram.

Seismograms show t hat t here are t wot ypes of seismic waves generat ed bythe movement of a mass of rock.

Example of an eart hquake record.


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Locating an Earthquakes Epicenter

P waves arrive first, then S waves, then L and R

After an earthquake, the difference in arrival times at a seismograph station can be used tocalculate the distance from the seismograph to the earthquake source (D).

If average speeds for all these waves are known, use the S-P (S minus P) time formula: amethod to compute the distance (D) between a recording station and an event.

Time =Velocity

Distance

P wave has a velocity VP and S wave has a velocity VS; VS is less than VP

Both originate at the same place the hypocenter

They travel same distance, but the S wave takes more time than the P wave.

Time for the S wave to travel a distance DTS =sV

D

Time for the P wave to travel a distance DTP =pV

D

The time difference

(TS TP) =sV

D-

pV

D= D

Vp

1-

Vs

1= D

VsVp

Vs-Vp

Now solve for the Distance D D =

Vs-Vp

VsVp* ( TS TP)

Epicenter of an earthquake can be obtained by surface projection of earthquake source.

Travel-t imes for locat ion

Measure t ime bet ween P and S wave on seismogram Use t ravel- t ime graph to get dist ance to epicenter


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The epi cent er i s locat ed using t hree or moreseismograph

Earthquake depths

Earthquakes originate at depths ranging from 5 to nearly 700 kilometers

Earthquake foci classified as

Shallow (surface to 70 kilometers)

Intermediate (70 to 300 kilometers)

Deep (over 300 kilometers)

Seismic Wave Speeds and Rock Properties

Variations in the speed at which seismic waves propagate through the Earth can cause

variations in seismic waves recorded at the Earth's surface

+

=

k3

4

pV

sV =


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It can be shown that in homogeneous, isotropic media the velocities of P and S wavesthrough the media are given by the expressions as above. Where Vpand Vsare the P and

S wave velocities of the medium, is the density of the medium, and and kare referredto as the shearand bulkmoduli of the media. Taken together, and kare also known aselasticparameters. The elastic parameters quantitatively describe the following physicalcharacteristics of the medium.

Bulk Modulus- Is also known as the incompressibilityof the medium. The bulkmodulus describes the ratio of the pressure applied to the cube to the amount ofvolume change that the cube undergoes. If kis very large, then the material is verystiff, meaning that it doesn't compress very much even under large pressures. If kissmall, then a small pressure can compress the material by large amounts. Forexample, gases have very small incompressibilities. Solids and liquids have largeincompressibilities.

Shear Modulus- The shear modulus describes how difficult it is to deform a cube ofthe material under an applied shearing force. For example, imagine you have acube of material firmly cemented to a table top. Now, push on one of the top edges

of the material parallel to the table top. If the material has a small shear modulus,you will be able to deform the cube in the direction you are pushing it so that thecube will take on the shape of a parallelogram. If the material has a large shearmodulus, it will take a large force applied in this direction to deform the cube. Gasesand fluids can not support shear forces. That is, they have shear moduli of zero.From the equations given above, notice that this implies that fluids and gases donot allow the propagation of S waves.

Any change in rock or soil property that causes , , or k to change will cause seismic wave speedto change. For example, going from an unsaturated soil to a saturated soil will cause both the densi-

ty and the bulk modulus to change. The bulk modulus changes because air-filled pores become

filled with water. Water is much more difficult to compress than air. In fact, bulk modulus changesdominate this example. Thus, the P wave velocity changes a lot across water table while S wave

velocities change very little.

Wave Propagation Through Earth Media

Any change in rock or soil property that causes , , or k to change will cause seis-mic wave speed to change.

For example, going from an unsaturated soil to a saturated soil will cause both thedensity and the bulk modulus to change.

When seismic waves travel from one layer to another, ray gets bent away from ortoward the normal depending on layer density.

Propagation of seismic waves in media is governed by Snells Law

Snell's Law describes the relationship between the angles and the velocities of the waves.

Snell's law equates the ratio of material velocities V1 and V2 to the ratio of the sine's of

incident and refracted angles, as shown in the following equation.


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21L

2

L

1

V

sin

V

sin =

Where:

VL1 is the longitudinal wave velocity in material 1.

VL2 is the longitudinal wave velocity in material 2.


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Shows P and S wave shadow zones that forms on other side of the earth due to the occur-rence of an earthquake in opposite side.

P P wave only in the mantle PP, PPP, SS, SSS P or S wave reflected once or twice off earths surface so

there are two or more P or S wave segments in the mantle. PKP P wave that has two segments in the mantle separated by a segment in the

core. PcP P wave reflected from outer core & mantle boundary. PKiKP P wave reflected from outer core & inner core boundary. PKIKP P wave that traverse inner core is denoted by I.

PKJKP Phases with an S leg in the inner core is denoted by J. PPS, PSP, PSS P wave twice reflected from the Earths surface. S denotes con-

verted wave.


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ScP S wave reflected from outer core-mantle boundary and converted into P typewave.

ScS S wave reflected from outer core & mantle boundary. SKS S wave traversing the outer core as P and converted back into S when again

entering the mantle.


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Earths Major Boundaries

The crust

Continental

Less dense

20-70 km thick

Oceanic

more dense

5-10 km thick

The (Moho) Mohorovicic discontinuity

Discovered in 1909 by Andriaja Mohorovicic

Separates crustal materials from underlying mantle

Identified by a change in the velocity of P waves

The core-mantle boundary

Discovered in 1914 by Beno Gutenberg

Based on the observation that P waves die out at 105 degrees from

the earthquake and reappear at about 140 degrees

35 degree wide belt is named the P-wave shadow zone

Discovery of the inner core

Predicted by Inge Lehmann in 1936

P-wave shadow zone is not a perfect shadow there are weak P-

waves arriving, and Lehmann suggested that these P-waves were

bounced from a solid inner core.


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Foreshocks and Aftershocks

Faults are believed to consist of stronger and weaker parts whose ability to rupture

during an earthquake varies. These stronger parts are called barriers or asperities. These

two terms assign different roles to the stronger patches in the earthquake rupture process.

The left side of the above figure shows the condition of a fault just before an earth-

quake while the right side shows its condition after an earthquake. The upper part of the

figure is based on the barrier hypothesis, while the lower part is based on the asperity hy-

pothesis. The shaded portion indicates a stressed portion of the fault while the unshadedis the slipped or unstressed portion.

According to the barrier hypothesis, the fault is in a state of uniform stress (upper

left) before the earthquake. During the earthquake the rupture propagates leaving unbro-

ken stronger patches (upper right). These patches or barriers are the location of numerous

aftershocks which represent the release of stress through static fatigue.

According to the asperity hypothesis, just prior to the earthquake (main shock) the

fault is not in a state of uniform stress but rather there has been some release of stress

over part of the fault through foreshocks leaving behind strong patches or asperities which

are broken resulting in a smoothly slipped fault (lower right). The existence of both after-

shocks and foreshocks indicate that some strong patches behave as barriers while others

behave as asperities. Barriers and asperities are significant to earthquake ground motion

because they represent locations of concentrated stress release and localized stopping

and starting of the rupturing fault.


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Measuring the size of earthquakes

Two measurements that describe the size of an earthquake are

Intensity a measure of the degree of earthquake shaking at a given localebased on the amount of damage

Magnitude estimates the amount of energy released at the source of the

earthquake The drawback of intensity scales is that destruction may not be a truemeasure of the earthquakes actual severity

The Modified Mercalli (MM) Scale of Earthquake Intensity(Developed in 1931 by the American seismologists Harry Wood and Frank Neuman)

Intensity Felt / DamageI People do not feel any Earth movement.

II A few people might notice movement if they are at rest and/or on theupper floors of tall buildings.

III Many people indoors feel movement. Hanging objects swing back andforth. People outdoors might not realize that an earthquake is occurring.

IV Most people indoors feel movement. Hanging objects swing. Dishes,windows, and doors rattle. The earthquake feels like a heavy truck hit-ting the walls. A few people outdoors may feel movement. Parked carsrock.

V Almost everyone feels movement. Sleeping people are awakened.Doors swing open or close. Dishes are broken. Pictures on the wallmove. Small objects move or are turned over. Trees might shake. Liq-uids might spill out of open containers.

VI Everyone feels movement. People have trouble walking. Objects fallfrom shelves. Pictures fall off walls. Furniture moves. Plaster in walls

might crack. Trees and bushes shake. Damage is slight in poorly builtbuildings. No structural damage.

VII People have difficulty standing. Drivers feel their cars shaking. Somefurniture breaks. Loose bricks fall from buildings. Damage is slight tomoderate in well-built buildings; considerable in poorly built buildings.

VIII Drivers have trouble steering. Houses that are not bolted down mightshift on their foundations. Tall structures such as towers and chimneysmight twist and fall. Well-built buildings suffer slight damage. Poorly builtstructures suffer severe damage. Tree branches break. Hillsides mightcrack if the ground is wet. Water levels in wells might change.

IX Well-built buildings suffer considerable damage. Houses that are not

bolted down move off their foundations. Some underground pipes arebroken. The ground cracks. Reservoirs suffer serious damage.

X Most buildings and their foundations are destroyed. Some bridges aredestroyed. Dams are seriously damaged. Large landslides occur. Wateris thrown on the banks of canals, rivers, lakes. The ground cracks inlarge areas. Railroad tracks are bent slightly.

XI Most buildings collapse. Some bridges are destroyed. Large cracks ap-pear in the ground. Underground pipelines are destroyed. Railroadtracks are badly bent.

XII Almost everything is destroyed. Objects are thrown into the air. Theground moves in waves or ripples. Large amounts of rock may move.


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Magnitude

Magnitude of earthquake is a measure of energy and based on the amplitude of the waves

recorded on a seismogram.

Concept: the wave amplitude reflects the earthquake size once the amplitudes are

corrected for the decrease with distance due to geometric spreading and attenuation.

Magnitude scales have the general form:

whereA: amplitude of the signalT: its dominant periodf: correction for the variation of amplitude with the earthquakes depth h

and distance from the seismometerC: regional scale factor

Richter Magnitude

Charles Richter developed the first magnitude scale in 1935. Richters magnitude isthe logarithm to the base 10 of the maximum seismic wave amplitude, in thousandths of amillimeter, recorded on a special type of seismograph (Wood-Anderson seismograph) at adistance of 100 km from the earthquake epicenter. Wood-Anderson seismograph has anatural oscillation period of about 0.8 seconds, and waves of longer period are increasing-ly diminished on the records even if they are present in the ground.

ML = log10A(mm)+ (Distance correction factor)

Here A is the amplitude, in millimeters, measured directly from the photographic paperrecord of the Wood-Anderson seismometer, a special type of instrument.

He proposed zero magnitude for an earthquake that would produce a record withamplitude of 1.0 micro meter at a distance of 100 km from the epicenter on Wood-

Anderson seismograph with time period 0.8 sec (1.25 Hz natural frequency), damping h0.8 and 2800 magnification factor. He calibrated his scale of magnitudes using measuredmaximum amplitudes of shear waves recorded in southern California. The logarithmic formof Richter magnitude scale (ML) for 100 km epicentral distance is as given below.

ML = log10A -log10A0

Where, A0 is the amplitude for zero magnitude earthquakes. Thus, an earthquake trace

with amplitude 10 micro meter of seismograph at an epicentral distance of 100 km has

magnitude 1.0


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The distance factorby Richter

The diagram below demonstrates how to use Richter's original method to measure a

seismogram for a magnitude estimate in Southern California:

The scales in the diagram above form a

nomogram that allows you to do the ma-

thematical computation quickly by eye.


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Body-wave magnitude is

Mb = log(A/T) + Q(D,h)

where A is the ground motion (in microns), Tis the wave's period (in seconds), and Q(D,h)

is a correction factor that depends on distance to the quake's epicenter D(in degrees) and

focal depth h(in kilometers). Mb uses relatively short seismic waves with a 1-second pe-

riod, so to it every quake source that is larger than a few wavelengths looks the same. Mb

saturates around magnitude above 6.

Surface-wave magnitude is

Ms = log(A/T) + 1.66 logD+ 3.30

Ms uses 20-second waves and can handle larger sources, but it too saturates around

magnitude 8. That's OK for most purposes because magnitude-8 or greatevents happen

only about once a year on average for the whole planet. But within their limits, these two

scales are a reliable gauge of the actual energy that earthquakes release.

Limitations:

Magnitude saturation Its a general phenomenon for Mb above about 6.2 and Ms above

about 8.3.


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A simple solution that has been found by Kanamori: defining a magnitude scale based onthe seismic moment.

Moment Magnitude, Mw, is not based on seismometer readings at all but on the total

energy released in a quake, the seismic moment Mo(in dyne-centimeters):

Mw = 2/3 log(Mo) - 10.7

This scale therefore does not saturate. Moment magnitude can match anything the Earth

can throw at us.

Still, Kanamori inserted an adjustment in his formula such that below magnitude 8 Mw

matches Ms and below magnitude 6 matches Mb, which is close enough to Richter's old

ML. So keep calling it the Richter scale if you likeit's the scale Richter would have made

if he could.

Seismic Moment (Mo) =The seismic moment is a measure of the size of an earthquakebased on the area of fault rupture, the average amount of slip, and the force that was

required to overcome the friction sticking the rocks together that were offset by faulting.

Moment = A D

= shear modulus; A = LW = areaD = average displacement during rupture

Ground Motion Acceleration Measurement

Peak ground acceleration (PGA) is a measure of earthquake acceleration. Unlike the

Richter magnitude scale, it is not a measure of the total size of the earthquake, but ratherhow hard the earth shakes in a given geographic area. It is measured by instruments, notfrom personal reports, although it generally correlates well with the Mercalli scale.


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Peak ground acceleration can be measured in g(the acceleration due to gravity) or m/s.The peak horizontal acceleration (PHA) is the most commonly used type of groundacceleration in engineering applications. Other ground motion parameters used tocharacterize earthquake motion include peak velocity and peak displacement.

Strong Motion Sensors

Most strong motion sensors are designed to measure the large amplitude, high frequencyseismic waves typical of large local earthquakes. These seismic waves result in the strongground motion we feel during a large earthquake. Strong ground motion is often to blamefor the structural damage that occurs during an earthquake. The data seismologists recordwith strong motion sensors is used to improve the design of earthquake resistant buildingsand to understand earthquake-induced geologic hazards like liquefaction and landslides.The range of motions of interest for strong motion applications includes accelerations from0.001 to 2 g and frequencies from 0 to 100 Hz.

Why We Need Strong Motion Sensors

Before the wide use of strong motion instruments, scientists attempted to estimate theshaking from strong earthquakes by extrapolating (scaling up) the observed effects ofsmaller earthquakes (magnitude 2.5-5.0). This method works well for many applicationsand has improved with the use of data from strong motion instruments. However, this ap-proach is not applicable in every situation. Some geologic materials and structures do notrespond to strong shaking in a simple, predictable manner that can be accurately scaledupward. In these situations, scientists need actual data generated by strong ground motionto better understand the processes at work. Strong motion sensors have been installed indifferent areas of geologic interest throughout the Pacific Northwest to provide this type ofdata.

Using strong motion data, earth scientists hope to gain a better understanding of:

1) ground response near fault ruptures of large earthquakes2) effects of severe shaking on different subsurface structures and geologic materials.3) ground response in areas that undergo liquefaction.

ieq 05 earthquake lecture notes 3

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