Intro to Seismology

8/2/2019 Intro to Seismology

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INS - Technical Courses for IndustrySeismic Design of Industrial Structures,

Equipment and Piping Systems

Chapter-1

An Introduction to Seismology

by

Falguni Roy, B. Gangrade

Seismology Division

Bhabha Atomic Research Centre

Mumbai 400 085

email : [email protected]

Chapter 1 - An Introduction to Seismology 1 of 14
mailto:[email protected]:[email protected]


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An Introduction to Seismology

1.0 Introduction

Seismology deals with the study of the earth and earth vibrations mainly caused byearthquakes. We study the seismic waves from earthquakes because they provide us

information about the seismic source and about the interior of the Earth. Major results from

the study of seismic waves include:

1. Locating the earthquake sources.

2. Measuring the relative sizes and energy release of earthquakes

3. Telling what is the fault geometry and how it slipped

4. Determining internal layering and structure of the Earth

5. Determining seismicity of a region

In structural engineering, some of these results are of significant value particularly for the

designing of earthquake resistant structures.

. The sources of seismic vibrations can be classified into two categories viz. natural sources and

man-made sources. The details of different types of seismic events are given below in the flow

chart.

1.1 Earths Interior, Plate tectonics and faults

Five billion years ago the Earth was formed by a massive conglomeration of space materials

and by releasing the heat energy, it has attained the present form. Dense materials sank to

form core of the Earth, while lighter silicates, oxygen compounds and water formed the outershell of the earth surface. The earth is divided into four main layers: the inner core, outer core,


Seismic

vibrations

Natural events Man-made events

Earthquakes Tectonic forces ExplosionsNuclear. mining

Rock burst Collapse of mines

Cultural noiseTraffic, machines

Volcanic esq. Magma movement

Reservoir seismicityDams, lakes

Microseisms Pressure variations on

ocean surface & cyclones

Tsunamis Undersea earthquakes

Induced seismicityOil field, wells etc


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mantle, and crust (Figure 1.1). The outer core is liquid, while the inner core is solid. The

mantle is solid but can deform slowly in a plastic manner. The crust is thin and is composed of

the calcium and sodium aluminum-silicate minerals and is rocky and brittle in nature, so that

when it fractures under stress earthquakes are produced.

Figure 1.1 Internal structure of earth.

The crust together with the solid outer parts of the mantle down to a depth of about 100 km

forms the lithosphere. Below the lithosphere is the asthenosphere, a region of relatively low

strength. The theory of plate tectonics propounds that the earths lithospheric layer is broken

into mainly a dozen or so large and small fragments called plates (Figure 1.2), which move

relative to each other with an average speed of a few cm per year due to convection processes

at depth. About 225 million years ago these fragments were together to form a super continent

called PANGAEA. According to theory of continental drift put forward by Wegner. Pangaea

broke up into continents we know of now. The differential motion between various plates is

the cause of earthquake activity, which is mostly confined along the plate boundaries.

Figure 1.2 Present day tectonic plates

When an earthquake occurs a near planar surface where material discontinuity occurs iscreated within the earth called fault. This fault becomes nucleating surface for further seismic



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activity. The stresses accumulated due to plate movement produces strain in the plate mostly

along the boundary of the plates, which causes rupture of rocks along fault plane. The fracture,

which originates at a point spreads all around, terminates and produces radiation of different

modes of seismic waves. The faults are classified into three categories based on the way the

rock blocks move on either side of the fault as depicted in Figure 1.3. These include normal,

reverse and strike slip faults.

Strike-slip Normal Reverse

Figure 1.3 Different types of faults

Strike slip faulting is one, which involves purely horizontal shearing motions of the two sides

of the fault. If one looks across the fault and the other side moves to the right during an

earthquake, it is called right-lateral strike-slip faulting. If it moves to the left, one has left-

lateral strike-slip faulting. The San Andreas fault is a right-lateral strike-slip fault.

For faulting, which involves vertical motions; there are a few important conventions. If the

fault is a vertical plane, with purely vertical motions we call it dip-slip motion. If the fault plane

is dipping (not vertical), there will be some rock above the fault and some below the fault. The

rock above the fault is called the hanging wall, while the rock below the fault is called the

footwall.

If the faulting causes the upper block to move downward relative to the lower block, the fault is

a normal fault. This is the type of fault usually found in regions of extension, where the crust

is being pulled apart. This includes mid-ocean ridges where sea floor spreading is taking place

as well as continental rifts, like in Eastern Africa, where the crust is breaking apart. If the

hanging wall moves upward relative to the footwall, we have reverse faulting, and if the dip

(angle from the horizontal) of the fault is less than 30 degrees we call it thrust faulting.

Reverse and thrust faulting occur in regions of compression, where the surface is converging.

This is common in subduction zones and in places where continents are colliding. The biggest

thrust faults are those on the contact between underthrusting oceanic lithosphere and the

overriding plate. The largest earthquakes tend to be thrust faulting events in subduction zones.

On the largest scale, the plate boundaries of the Earth are all faults, across which the relative

motions of the steadily moving plates are taking place. Since we have a pretty clear idea of how

fast plates are moving and from fault geometries, and active measurements of motions using

lasers and satellite methods we know the current directions of relative plate motions, we have

good constraints on how fast various faults are accumulating deformation that will be released

in earthquakes.

1.2 P Wave Radiation Pattern

The amplitudes of elastic waves vary with distance from their source because of attenuation and



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geometric spreading. The amplitudes also depend on the angle at which the seismic ray leaves the

source. For P-waves we observe that the maximum amplitude for compression and dilatation occur

for direction oriented at 45 to the fault plane. The fault and auxiliary planes are nodal planes of zero

amplitude. The sketches (Figure 1.4, on the left) show the radiation pattern of the P-wave amplitude

(F is the fault plane). The radiation pattern of P wave leads to an earthquake source model

represented by a pair of orthogonal couple perpendicular and parallel to the fault plane. The coupleof force acting perpendicular to the fault plane is the result of the elastic reaction of the media

surrounding the fault.

Figure 1.4 Radiation pattern of P waves and orthogonal couple

1.3 Seismographs

When a strong earthquake occurs it gives rise to seismic waves which causes the shaking we

feel. Seismic waves lose much of their energy while traveling over large distances. However,

sensitive detectors such as seismometers can record these waves even if their amplitudes happento be as small as few nanometers. When these detectors are connected to a system that produces

a permanent recording, they are called seismographs. There are various types of seismometers,

but they are all based on the fundamental principle that the differential motion between a free

mass (which tends to remain at rest) and a supporting structure fixed to the ground (which

moves with the vibrating earth) can be used to record seismic waves (Figure 1.5). A single

seismograph pendulum works in only one direction, and cannot give a complete picture of wave

motions from other directions. To overcome this problem, modern seismograph stations have

three separate instruments to record seismic waves, one to record vertical ground motion and

other two to record East-West and North-South components. Besides three component

instruments, clocks are an important part of a seismograph system. Modern seismographs use

broadband seismometers with bandwidths 300s/30s to 0.02s and using a high dynamic rangedigital system with 24-bit resolution acquire the data by computers and computer networks. The

transmission of the data from field to local data center and communication between data centers

are done through digital telemetry using wireless links, dialup lines and VSAT links.



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Horizontal Vertical Vertical Electromagnetic

Figure 1.5 Basic principles of seismometry

1.4 Seismic waves

Most of the energy released from the volume of strained rock around the fault goes into heat, as

the sliding of rock heats up the fault surface. Some of the energy is released as seismic waves,

which spread out through the rock, shaking the ground.

An earthquake generates three major kinds of seismic waves viz. compressional (P), shear (S)

and surface waves. P and S waves together are called body waves because they can travel

through the body of the earth unlike the surface waves, which propagate along the surface of

the earth. The particle motion for the P waves coincide with the direction of wave propagation

as is the case with ordinary sound waves (Figure 1.6). The particles oscillate back and forth in

the same direction as the wave is propagating, returning to their original position due to therestoring forces of the surrounding rock.

Figure-1.6 Particle motion of P waves Figure-1.7 Particle motion of S waves

S waves (Figure 1.7) involve shearing motions perpendicular to the direction in which the wave

disturbance is propagating. In a rock, the adjacent material has a restoring force that causes the

shearing particles to return elastically to their original position. If we try to shear a fluid, there

is no effective restoring force; so S waves cannot propagate in fluid or air.



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It is important to remember that waves spread in all directions away from the source,

surrounding the source in the rock. So, at an instant of time after an earthquake fault slides, the

source will be surrounded by an outward propagating P wave and an outward propagating S

wave. The velocity of P wave, or the velocity of sound in a rock, is faster than the velocity of

S wave so the P wavefront spreads through the rock faster. The P and S velocities are both

controlled by material properties of the rock; in particular the P velocity is controlled by thebulk modulus or compressibility of the rock, its rigidity (resistance to shear), and its density.

The shear velocity is controlled by rigidity and density.

The outward propagating P and S waves spread through the Earth, with the amplitude of the

wave decreasing as the wave travels further. This is because the energy is spread over a larger

and larger surface as a function of increasing time. Eventually, the wave is too small to detect.

The larger the initial input of energy (i.e. the larger the earthquake), the more distant the

perceptible shaking will be.

Because the Earth has layers, as well as a free surface, the P and S waves can bounce around

inside the earth, analogous to echoing sound in a canyon. This gives rise to many paths bywhich P and S wave energy can travel from the source to each point on the Earth's surface.

Thus, the ground motion recordings from earthquakes tend to be rather complex, with a

sequence of arrivals that are mainly controlled by the Earth structure, not by the source (Figure

-1.8).

Figure-1.8 Different ray paths inside the earth

The earthquake faulting may last only a few seconds, while the ground shaking will be more

prolonged because the P and S waves travel with different velocities and there are many paths

with different total travel times for the energy to get to the recording station.

The surface of the Earth causes P and S waves to interact with each other and with the layering

of the crust and mantle to produce patterns of vibrations that we call surface waves. There are

two main types of surface waves: Love waves and Rayleigh waves (Figure-1.9). Love waves

travel faster than Rayleigh waves, but slower than S waves. Love waves involve only

horizontal motions of the Earth, perpendicular to the direction in which the wave is

propagating. They are trapped, reverberating S waves near the surface of the Earth. Rayleigh

waves involve shaking in the vertical direction (up and down), as well as back and forth in the

direction of propagation of the wave characterized by a retrograde, elliptical particle motion in



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a vertical plane. They are a mixture of P and S wave energy reverberating near the surface.

These waves propagate along the surface, rather than through the body of the planet, thus, their

energy is spread out on an expanding ring on the surface rather than over a spherical shell. This

makes surface wave amplitudes larger than body wave amplitudes, and thus most damage from

earthquake shaking is caused by Love or Rayleigh waves. The surface waves also play

significant role in the identification of nuclear or chemical explosions from earthquakes.

Another kind of seismic wave that propagates in a crustal wave-guide in the continental

lithosphere is known as Lg or the surface shear wave whose energy departing downwards is

wholly reflected back into the crust. The type of reflection occurring here is the total internal

reflection. For a fixed source and receiver there may be many reflection paths, all totally

reflected and thus trapped within the crust. The radiation pattern of Lg waves is more isotropic

than that of P and S waves. This feature adds to the usefulness of Lg waves as a magnitude

estimator for small events due to the fact that full azimuthal coverage is not essential and reliable

magnitude estimation can be made from the data of only a few stations.

Figure-1.9 Particle motion of Rayleigh and Love waves

1.5 Locating earthquakes

Whenever an earthquake occurs and seismic signals are recorded at different seismic stations,the first question comes to our mind is "where was its epicenter (i.e. the point on the earths

surface vertically above the focus or hypocenter where a seismic rupture begins)". An

earthquake location tells us what fault it was on and where damage, if any, likely to have

occurred. When an earthquake occurs, it generates an expanding wavefront from the

earthquake focus at a speed of several kilometers per second. Various signals are recorded,

with a network of seismographs on the earth's surface. The times at which P waves arrive at

each recording station are noted. One of the procedures to locate the earthquake source based

on P-arrival times is as follows:

A guess is made about the epicenter, source depth and origin time of the earthquake. Arrival

time of P waves at each station is computed from the prior knowledge of seismic wave

velocities inside the earth. These calculated arrival times are compared with the actual



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observed times at each station. The location is now changed a little so that difference between

observed and calculated time reduces. This process is repeated till the time difference attains an

absolute minimum. Mathematically, the problem is solved by setting up a system of linear

equations, one for each station. The system of linear equations is solved by the method of least

squares, which minimizes the sum of the squares of the differences between the observed, and

the calculated arrival times. The process begins with an initial guessed hypocenter, performsseveral hypocentral adjustments and finally converges to a hypocenter that best fits the

observed set of P wave arrival times at the seismic stations of the network.

As the P waves travel faster than S waves the time difference between the arrivals of the P

wave and the S wave depends on the distance the waves traveled from the source to the

recording station. Over the time, many such measurements have been made and travel-time

curves (i.e. time vs distance curves) for P, S and many other waves have been developed for the

earth. Therefore, the knowledge of S-P time difference on a seismogram will provide the

information about the distance of the source from the station. However, the source could have

been anywhere on a circle whose radius is that distance centered on the station. If source

distances from two stations are known, two locations are possible; the two intersecting pointsof two circles. If distances from three stations are known, the earthquake can be unambiguously

located. This is known as principle of triangulation. This is another method of locating

earthquakes, which may be used to get a quick estimate of the earthquake location, as it

requires data from only three stations. However, the former method is more accurate and

adopted by various international data centers.

Recording of a three component seismograph can also be used to obtain a crude estimate of the

earthquake location. If the vertical motion of the P wave is upward, the radial component of the

P wave is directed away from the epicenter and if the vertical motion of the P wave is

downward, the radial component of the P wave is directed back towards the epicenter. The

amplitudes on the two horizontal components can then be used to obtain the vector projection

of the P wave along the azimuth and to the seismic source. The distance of the seismic source

is obtained from S-P time difference. Thus the knowledge of azimuth and distance from the

recording station will help in identifying the event location.

1.6 Intensity and Magnitude

We saw that the arrival times of waves at the recording stations are used to locate the event,

and once it is known where the event was, we can use the amplitudes at different distances to

determine how big the event was. The basic fact that helps in this effort is that the amplitudes

of the waves get progressively smaller with distance, and knowing the distance, we can correct

for that effect to tell how big the motions were right at the fault. This gives an estimate of thetotal energy put into the ground, which is proportional to how big the area of fault slip is and

how much slip occurred.

There are several measures of earthquake size that reflect the ground shaking amplitudes. The

first is a qualitative measure called Intensity. This is actually a damage scale, in which the level

of shaking felt or damage caused is categorized into ten or twelve categories (see Table I).

Intensities tend to give higher damage for higher intensity values near the source. This does not

use seismograms at all, but is very useful for historical events for which there are no seismic

recordings available. Intensities are also practical, in the sense of reflecting human effects

rather than scientific measures of the source.



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Seismograms, on the other hand, give seismic wave amplitudes that are used to determine

earthquake magnitudes. These are based on the distance corrected amplitudes of seismic waves,

but often have a mix of quantitative and empirical procedures. Magnitude scales are all

logarithmic, meaning that they are based on powers of ten. For each increase in the magnitude

value by one unit, the ground motions are 10 times larger. The energy required to produce 10

times larger motions is about 30 times larger. Before describing various magnitude scales weshall now see how energy and magnitude can be related.

Let the ground displacement at the recording station is given by

Y =A cos (2. t/T) ,where A is the amplitude and T is the period of the wave.

Ground velocity , v, will be v= -(2.A/T) sin(2. t/T)

Kinetic energy of a unit mass at recording station is (v2) , where

is the density.Averaging over one cycle,(0 T), we get kinetic energy density as

T

e=1/2. /T v2 dt = 2A2/T2

0

Mean potential and kinetic energies are equal so the energy, E, becomes

E=2e

Integrating over spherical wavefront to correct for geometrical sreading, we obtain an equationof the form

E = f(r, , c)(A/T) 2

Where r is the distance traveled and c is the velocity of the wave.

log10(E) = log10( f(r, , c)) + 2log10 (A/T)

We know that most of the magnitude scales are expressed as

M= log10(A/T) + F(D,h) + Cs +Cr

Where F is a correction term for distance(D) and depth (h) of the source , Cs is the source

region correction and Cr is the receiver site correction. The correction terms Cs and Cr are

specific to source and receiver sites therefore these terms are usually not included in the

general relations for magnitudes. From the last two equations we see that it is possible to relate

energy to magnitude if f(r, , c ) is known.

The earthquake magnitude that is determined depends on which seismic wave is measured, and

there are different magnitude scales for P waves, for Rayleigh waves, and for different periods

of motion.



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The magnitude of an earthquake describes its energy release on a logarithmic scale. The

Richter Scale is the earliest known scale for measuring the magnitude of earthquakes and was

introduced in the 1930's, based on earthquakes in California only. Basically, this scale

measures the maximum signal amplitude recorded on a standard seismograph, which is then

corrected for distance and instrument gain to obtain the magnitude. To find the magnitude, one

measures the maximum amplitude A from a photographic record of a seismometer using ametric ruler. The formula for determining the Richter magnitude is

ML=log10(A) - log10(Ao)

where Ao is the distance correction term for distances less than 600 km.

The Richter scale concept evolved to include world-wide earthquakes of any distance and

depth, and later evolved into two scales used in global earthquake catalogs: the Ms (surface

wave) and mb (body wave) scales. For most shallow earthquakes, surface waves, or waves that

propagate along the surface of the Earth, are the greatest amplitude waves recorded on a

seismogram. Therefore, a scale based on the amplitude of the surface wave is natural and

convenient. After measuring the maximum surface wave amplitude A (in microns), the surface

wavemagnitude is obtained as

Ms=log10(A/T)+1.66log10(D)+3.30

where T is the measured wave period and D is the distance in degrees.

Earthquakes occurring deep in the Earth do not generate large surface waves. Therefore, we

also need a scale based on body waves, the seismic waves that travel through the Earth's

interior or body. To determine body wave magnitude, we measure the maximum amplitude A

from first 5 seconds of P wave data and then calculate

mb=log10(A/T)+Q(D,h)

where T is the measured wave period and Q is an empirical function of focal depth h and

epicentral distance D. Currently the mb scale uses compressional body waves with a period of

about 1 second, and the Ms scale uses Rayleigh surface waves with 18 to 22 second periods. In

general, all these scales may yield different magnitudes for any particular earthquake.

The most quantitative measure of earthquake size determined using seismograms is called the

Seismic Moment. This is an energy based measure that accounts for the actual geometry of the

faulting. The seismic moment M0 is given by the product of the rigidity, the fault area that

ruptured and the amount of slip. That is

M0 = A D (1)where D is Average displacement and A is Fault area.

Radiated seismic energy, E, is related to the stress drop, (Difference between the initialstress and the final stress) , as

E .D.A/2 (2)or E = M0/2 (3)or log( E)= log( /2) + log (M0) (4)

Gutenberg and Richter found empirical relationships for Ms and mb with E as:



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Log E=11.8 + 1.5 Ms (5)

Log E= 5.8 + 2.4 mb (6)

One can use equation 3 to relate M0 to magnitude through equation 5 (assuming that Ms andmoment magnitude, Mw, are equivalent). If we assume that the stress drop is constant and

equal to ~ 30 bars then equation 3 reduces to

E = 5*10-5

M0Substituting E in equation 5 and replacing Ms by Mw we get,

Mw= (logM0 /1.5) 10.73

This scale is tied to Ms but will not saturate because M0 does not saturate.

M0can be estimated from :1. Amplitudes of the long period surface waves,

2. Amplitudes of seismic body waves.

3. Spectra of seismic waves.

Generally seismic moment is determined by making a computer model of the faulting that

matches the observed amplitudes of the complete seismogram, accounting for any differences

in excitation (strength of radiation) of the P, S, and surface waves caused by fault depth,

geometry, and slip process.. While all other magnitude scales only work for a limited range of

events, the Moment Magnitude scale is good for all events.

Each magnitude scale was initially designed for a particular class of seismograph, and forspecific types of seismic waves. For example, surface waves create the strongest disturbance

only when the earthquake is shallow, perhaps upto around hundred kilometers of depth.

Shallow earthquakes excite especially large surface waves whereas deep earthquakes do not

generate nearly as much surface wave energy. Therefore, Ms generally underestimates the size

of deep earthquakes. In constrast, body waves are well developed for both shallow and deep

earthquakes, so mb can be used to compare them. However, we know that earthquakes do not

radiate equal energy in all directions. For example, a magnitude estimated using a seismograph

located directly North of an earthquake may not be the same as a magnitude estimated using a

seismograph located North-East of the earthquake. While magnitude is a useful, simple, and

widely understood concept, problems exist with assigning and interpreting magnitudes. Since

seismologists define magnitude in terms of the response of a specific instrument at a specific

distance and period, magnitude contains little information about the physics of the earthquake

source. Lastly, all the magnitude scales, except Mw, do not measure the size of large

earthquakes correctly because amplitudes of the seismic waves tend to become constant with

increasing magnitudes at the measuring frequencies (1.2 Hz for ML, 1 Hz for mb and 0.05 Hz

for Ms). This scale "saturation" occurs around magnitude 8 for the Ms scale, and around

magnitude 6.5 for the mb scale. This means that a magnitude Mw=9.0 event will have a Ms

estimate of ~ 8.0 and mb estimate of ~ 6.5 only. Various magnitude definitions are summarized

in Table II.

Table - I



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Relation between epicentral intensity and magnitude for an

earthquake at 20km depth

Magnitude Intensity

mm scale

Description of effect and

damage1.5 I I. Not felt3

3.9

II

III

II. Felt by very few in the upper

floors

III. Felt noticeably in upper floors

Vibrations like passing truck

4

4.9

IV

V

IV. During day felt by many indoor.

Windows, doors, dishes disturbed.

Standing automobile rocked

V. Some windows and doors

broken. Many are awakened.

Disturbance to tall objects like tree,

pole

5

5.9

VI

VII

VI. Heavy furniture moves. Damageto chimneys. People run outdoor

VII. Considerable damage to poorly

built buildings. Slight damage to

good buildings

6

6.9

VIII

IX

VIII. Partial collapse of ordinary

buildings and damage in specially

designed buildings. Changes in well

water. Fall of tall structures like

stacks, columns

IX. Considerable damage / partial

collapse of well built structures.

Ground cracked.

>7 >X X. Most of masonry and framestructures destroyed. Land slides.

Rail bent.

XI. Few structures remain. Broad

fissures in the ground. Earth slumps

XII. Damage total. Waves seen on

the ground. Objects thrown into air.

Table-II

Magnitude definitions used by National Earthquake Information Centre,

Denever,USA



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Designator Name Magnitude formula

Mw Moment magnitude Mw=(2/3) log Mo -10.7

Where Mo is the scalar moment for the best

double couple in dyne-cm

Me Energy magnitude Me = (2/3) log( Es ) 2.9

Where Es is the radiated energy in Newton-meters. Me , computed from the high

frequency seismic data is a measure of seismic

potential for damage

Ms Surface wave

magnitude

Ms= log(A/T) + 1,66 log D + 3.3

Where A is the maximum ground amplitude in

micrometers of the vertical component of the

surface wave within the period range18

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