Download - Elementary Seismology

Physics of the Solid Earth (1)Physics of the Solid Earth (1)

Dr. William K. Mohanty

Associate Professor

Department of Geology and Geophysics

IIT, Kharagpur

Seismology Group IIT Kharagpur

“Seismology is the study of the generation, propagation, and recording of elastic waves in the

Earth (and other celestial bodies) and of the sources that produce them”

Sumatra Earthquake Recorded at IIT, Kharagpur Seismic Observatory

“The joy of being a seismologist comes to you, when you find something new about the earth’s interior from the observation of seismic waves

obtained on the surface, and realize that you did it without penetrating the earth or touching or

examining it directly”

KeiitiKeiiti Aki, Presidential address to the Aki, Presidential address to the Seismological Society of America, 1980Seismological Society of America, 1980

Schematic geometry of seismic experiment


Introduction to SeismologyBasic Concepts:

Generates Seismic Waves

Propagate away from source and samples the Earth structure

Recorded ground motion is SEISMOGRAM

Earthquakes (Passive Source)

Free Surface ground motions caused by these propagating waves recorded at surface detectors(SEISMOMETERS)

SEISMIC SOURCES

Natural Events Man-Made Events

Tectonic Earthquakes Controlled Sources (Explosions, vibrators…)

Volcanic Tremors and Earthquakes

Reservoir Induced Earthquakes

Rock Falls/Collapse ofKarst cavities

Mining InducedRock Bursts/Collapses

Strom Microseisms Cultural Noise(Industry, Traffic etc.)

Various Kinds of Seismic Sources


“Earthquakes to the progressive accumulation of strain energy in the rock mass surrounding a pre-existing fault and the sudden release of this energy by faulting when the fracture strength is exceeded”

ElasticElastic-- Rebound TheoryRebound Theory

Earthquake Zones


Interior of Earth

Major Tectonic Plates of the Earth


Frequency of Occurrence of Earthquakes(based on observation since 1900)

Earthquake focus

Seismology (Class 2)Seismology (Class 2)

Dr. William K. Mohanty

Associate Professor

Department of Geology and Geophysics

IIT, Kharagpur


Body wavesP- Waves

S-waves

Rayleigh Wave

Love Wave

Surface waves

P-wave velocity (α ) =ρ

μ34

+K

S-wave velocity (β) = ρμ

Where, K is the bulk modulus or incompressibility, μ the shear modulus or rigidity and ρ the density.

Seismic wave propagation

Long-period vertical component seismogram showing various seismic phases

Ray paths for the seismic phases labeled on the seismogram

Travel-time curves for surface focus

Notation of various phases through Mantle and Core

Earth’s P velocity, S velocity, and density as a function of depth

Earth’s Interior

EARTHQUAKE HAZARDS AND ITS MITIGATION

Dr. William K MohantyAssistant Professor

Department of Geology and GeophysicsIndian Institute of Technology, Kharagpur

EARTHQUAKE HAZARDS

• Ground shaking• Structural Hazards• Liquefaction• Landslides• Retaining structures failures• Lifeline Hazards• Tsunami and Seiche Hazards

GROUND SHAKING

• Most important of all seismic hazards • When the earthquake occurs, seismic waves radiate

away from the source and travel rapidly through the earth’s crust. Produce shaking at the ground surface, which may last from few seconds to minutes

• Strength and duration of shaking at a particular site depends on

a. Sizeb. Location of earthquakec. Characteristics of the site

• Final portion of the trip of seismic waves form source to the ground surface often through soil

• Soil deposits act as “filters”.

GROUND MOTION PARAMETERS

• Strong ground motion data are essential to understand the high-frequency nature of crustal seismogenic failure processes, the nature of seismic radiation from the source, and the nature of crustal wave-propagation phenomena near the source

a) The Amplitudeb) Frequency contentc) Duration of the motion

THE AMPLITUDE

wwawv /)()( =

wwvwu /)()( =where , and are the transformed displacement, velocity and acceleration respectively.

u v a

PEAK HORIZONTAL ACCELERATION (PHA)

PEAK HORIZONTAL VELOCITY (PHV)

• PHV characterize ground motion amplitude accurately at intermediate frequencies.

• Structures or facilities (tall or flexible buildings, bridges etc.), PHV provide accurate indication of the potential damage.

PEAK DISPLACEMENT

• Associate with low frequency.• Difficult to determine accurately.• Less commonly used as a measure of ground

motion.

EFFECTIVE ACCELERATION

FREQUENCY CONTENT PARAMETERS• Frequency content describes how the amplitude of a ground motion is

distributed among different frequencies

GROUND MOTION SPECTRA∑=

++=α

φ1

0 )sin()(n

nnn twCCtx

where Cn and Φn are the amplitude and phase angle respectively of the nth harmonic of the Fourier series

RESPONSE SPECTRA• The response spectra describes the maximum response of a

single-degree-of-freedom (SDOF)

PREDOMINANT PERIOD

• The predominant period is defined as the period of vibration corresponding to the maximum value of the Fourier amplitude spectrum

Vmax/amax

• Vmax/amax should be related to the frequency content of the motion

• For a simple harmonic motion of period T, Vmax/amax =T/2π• For earthquake motion that include many frequencies, the

quantity 2π (Vmax/amax) provides, which periods of the ground motions are most significant

Site Condition Vmax/amax

Rock 5.5 cm/sec/g = 0.056 sec

Stiff soils (<200 ft) 110 cm/sec/g =0.112 sec

Deep stiff Soils (7200 ft) 135 cm/sec/g = 0.138 secSeed and Idris (1982) (less than 50 km from source)

• The corresponding periods of equivalent harmonic waves for the rock, stiff soil and deep stiff soil site conditions are 0.35 sec, 0.70 sec and 0.87 sec respectively, which indicates a shift towards longer period (lower frequency) motion on softer soil deposits

DURATIONDuration (sec)

Magnitude Rock Sites Soil Sites

5.0 4 8

5.5 6 12

6.0 8 16

6.5 11 23

7.0 16 32

7.5 22 45

8.0 31 62

8.5 43 86

Typical earthquake durations at epicentral distances less than 10 km

EFFECTS OF LOCAL SITE CONDITIONS ON GROUND MOTION

• At most sites the density and S wave velocity of material near the surface are smaller than at greater depths

• If the effects of scattering and material damping are neglected, the conservation of elastic energy requires that the flow of energy (energy flux, ρνs u2) from depth to the ground surface be constant

• Since ρ and νs decrease as waves approach the ground surface, the particle velocity u must increase

EFFECTS OF TOPOGRAPHY

EFFECTS OF BASIN

• The effects of basin geometry on ground motion is of great interest in geotechnical earthquake engineering

• The curvature of a basin in which softer alluvial soils have been deposited can trap body waves and cause some incident body waves to propagate through the alluvium as surface waves

• These waves can produce stronger shaking and larger duration

PEAK GROUND ACCELERATION AS A FUNCTION OF MAGNITUDE AND DISTANCE FROM THE FAULT, AS GIVEN

BY THE GROUND-MOTION PREDICTION EQUATION OF ABRAHAMSON AND SILVA (1997)

PROCEDURE FOR MODIFYING GROUND MOTION PARAMETERS FROM A SEISMIC HAZARD ANALYSIS TO

ACCOUNT FOR THE EFFECTS OF LOCAL SITE CONDITIONS

)()()()( kikijkjkij fSfPfEfO ⋅⋅=

Suppose a network has recorded J events by I stations (each event may not be recorded by all I stations). Then the amplitude spectrum of the jth event recorded at the ith station for the kth frequency, Oij(fk) can be written in the frequency domain as a product of a source term Ej(fk), a path term, Pij(fk), and a site effect term, Si(fk),

(1)

Taking the natural logarithm, equation (1) becomes:

(2)

This linear expression often forms the basis of separating the source, path, and site effects

)(ln)(ln)(ln)(ln kikijkjkij fSfPfEfO ++=

METHODOLOGIES FOR SITE RESPONSE ESTIMATION:

1. Reference Station Spectral Ratio (SSR) EstimateThe traditional spectral ratio is estimated with respect to a ‘reference site’. Suppose, at a reference site (i=R) there is negligible site response (lnSR=0) and if the interstation spacing is too small compared to the epicentral distances, so that Pij~PRj, then the site response at each site can be estimated from,

(3)

Equation (3) constitutes the geometric average spectral ratio. If the reference site has a non-negligible site response, then the spectral ratios become relative site-response estimates

∑∑==

−=⎟⎟⎠

⎞⎜⎜⎝

⎛=

J

jkijkij

J

jkRj

kijk

SR

i fOfOJfO

fOJ

fS11

))(ln)((ln1)()(

ln1)(ln

2. Site Response by Horizontal-to-Vertical-Spectral Ratio or Receiver Function TechniqueThus the receiver function SRij (fk) can be computed at each i site for the jthevent at the central frequency fk as,

(4)

where, Hij(fk)|NS , Hij(fk)|EW and Vij(fk) are the Fourier spectra of the NS, EW and vertical components respectively. A pictorial representation of site response computation is depicted in the Figure .The standard deviation represents the scatter of individual spectral ratios and hence the statistical uncertainty of the estimated site response can be calculated as

(5)

( )( ) ( )

( )kij

EWkijNSkij

kij fabsV

fabsHfabsHfSR

22 ||2

1 +=

( ){ } 5.0

1

21

1 ∑=

− −=J

j

aveiijJi SRSRσ

FFT of Signal (S) and Background Noise (B)

100 101

10-5

10-4

10-3

10-2

10-1

FFT(

cm/s

ec/H

z)

Time(sec)100 101

10-5

10-4

10-3

10-2

FFT

(cm

/sec

/Hz)

Time(sec)100 101

10-5

10-4

10-3

10-2

10-1

FFT(

cm/s

ec/H

z)

Time(sec)(f)(d) (e)

Spectra of (S-B) with Smoothening

(g) (h) (i)100 10110-5

10-4

10-3

10-2

FFT(

cm/s

ec/H

z)

Time(sec)100 101

10-4

10-3

10-2

10-1

FFT(

cm/s

ec/H

z)

Time(sec)100 101

10-4

10-3

10-2

10-1

FFT(

cm/s

ec/H

z)

Time(sec)

(b)(a) (c)Time (sec)

Velocity (cm/sec)

Time (sec)

Time (sec)

Vertical Component

NS Component EW ComponentVelocity (cm/sec)

Velocity (cm/sec)

Vel

ocity

(cm

/sec

)

Vel

ocity

(cm

/sec

)

Vel

ocity

(cm

/sec

)

DEVELOPMENT OF PREDICTIVE RELATIONSHIP

• Predictive relationships usually express ground motion parameters as functions of magnitude, distance and in some cases, other variable

Y = f (M, R, Pi)Y: Ground Motion ParameterM: MagnitudeR: Distance from source to sitePi:other parameter

• A typical predictive relationship may have the form[ ] )()()exp(lnln 8765321

4 sitefsourcefRCMCCRCMCMCCY C +++++++=

ESTIMATION OF PEAK ACCELERATION (Campbell and Bozorgnia, 1994)

where R is the closest distance to seismic rupture in km. The source term F, takes on value of 0 for strike-slip and normal faulting and 1 for reverse, reverse-oblique and thrust fault

SSR = 1 for soft-rock site (sedimentary deposit of Tertiary age and crystalline rock)

SHR = 1 for hard-rock (older sedimentary, metamorphic and crystalline rock)

SSR = SHR = 0 for alluvium site

[ ]22 )647.0exp(149.0ln328.1904.0512.3)(ln ww MRMgalsPHA +−+−=

HRSRw SRSRFMR )ln222.0405.0()ln171.0440.0()0957.0ln112.0125.1( −+−+−−+

⎩⎨⎧ −

=38.0

0691.0889.0ln

MPHAσ

M≤7.4

M>7.4

LOCATION OF CHAMOLI EARTHQUAKE

STATIONS WHICH RECORDED THE MAINSHOCK AND THE AFTERSHOCKS OF CHAMOLI

EARTHQUAKE

OBSERVED PEAK GROUND MOTION (TRIANGLES) VS. HYPOCENTRAL DISTANCE ‘R’ DURING THE

CHAMOLI EARTHQUAKE

EAST-WEST COMPONENT OF ACCELERATION AND VELOCITY TRACES AT SITES IN DELHI

DURING THE CHAMOLI EARTHQUAKE

SPECTRAL RATIOS OF SOFT SITES TO RIDGE OBSERVATORY

OBSERVED AND PREDICTED HORIZONTAL AmaxAND Vmax AS FUNCTION OF Mw AT DELHI SITES

Predicted Peak Ground Motion at Sites in Delhi

Simulated Horizontal Ground Motion at CPCB and RO

Hypocentral location in 3-Dimension

Distance = = ts-tp

Azimuth =

Where

Three Component Single Station

Z

NS

EW

AA1tan 090

Direction of first motion

Angle

Vertical

E-W

N-S

up

W

S

00

down

E

N

00

up

W

N

900

down

E

S

900

up

E

N

1800

down

W

S

1800

up

E

S

2700

down

W

N

2700

can be determined from this table

Locating an epicenter

LOCATING EARTHQUAKES

• Forward-Modeling

Ti predicted = f(xi,v)=tiobserved

F(M) = d

• Inverse Modeling

d= Gm

Magnitude

Magnitude is a measure of the strength of an earthquake or strain

energy released by it, as determined by seismographic observations.

It is a function of amount of energy released at focus and is

independent of the place of observation.

General form of all magnitude scales

M = log (A/T)max + f (, h) + Cs + Cr

Where

A = max. amplitude in thousandths of mm,

T = period of the seismic wave in seconds,

f = correction factor for epicentral distance () and focal depth (h),

Cs = correction factor for the seismological station, and

Cr = regional correction factor.

Magnitude Scales

Magnitude scales are based on a few simple assumptions -

• For a given source-receiver geometry “larger events” will produce wave arrivals of larger amplitudes at the seismic station

• The decay of ground displacement amplitudes with epicentral distance ∆ and their dependence on source depth h, i.e. the effects of geometric spreading and attenuation of the considered seismic waves, is known at least empirically in a statistical sense. It can be compensated by a so-called calibration function σ (∆, h). The latter is the log of the inverse of the reference amplitude Ao(∆, h) of an event of zero magnitude, i.e. σ (V,h)= –log Ao(∆, h). The logarithm is used because of the enormous variability of earthquake displacement amplitudes

• Magnitudes should be a measure of seismic energy released and thus be proportional to the velocity of ground motion, i.e. to A/T with T as the period of the considered wave

• The the maximum value (A/T)max in a wave group for which σ (∆, h) is known should provide the best and most stable estimate of the event magnitude

• The effects of prevailing azimuth dependent source directivity can be corrected by a regional source correction term Cr and the influence of local site effects or amplitudes depending on local crustal structure, near-surface rock type, soft soil cover and/or topography may be accounted for by a station correction Cs

Local Magnitude, ML

ML = log Amax - log A o

ML = log A - 2.48 + 2.76 log

MD = a o + a 1 log D+ a 2

Duration Magnitude,

MD

Body Wave Magnitudes (MB)

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

A = actual ground motion amplitude in micrometer, and

T = corresponding period in second.

Surface-Wave Magnitude (Ms )

Ms = Log (A/T) + 1.66 log + 2.0 Where

A = Spectral amplitude, the horizontal component of the Rayleigh wave, with a

period of 20 s, measured on the ground surface in micron,

T = Period of seismic wave in second, and

= Epicentral distance in degree.

Moment Magnitude, Mw

Where M0 is in Nm.

0.6log3

2010 MMW

A = fault area (length x depth) m2

d = longitudinal displacement of the fault , m and

= modulus of rigidity (app. 3 x 1010 Nm-2 for the crust

and 7 x 1010 Nm-2 for the mantle

Relationship between different magnitude

scale (Gutenberg and Richter, 1956)

• MB = 0.63MS + 2.5

• MS = 1.27 (ML – 1) – 0.016M2L

• Log Mo = 1.5 MS + 16.1

Modified Mercalli Intensity (MMI) Scale

Intensity is a measure of the effect that an

earthquake produces at a given location.

Intensity

Isoseismal map for the Arkansas

earthquake of December 16,1811

Isoseismal map of Kutch (Bhuj) earthquake of 26 January 2001.

log amax = Io/3-1/2

M = 1+ 2/3 Io

Energy-Magnitude Relations

•Log Es=2.4m-1.2 (Es in joule)

•Log Es = 1.5Ms+4.8

•Log Es=1.96Ml+2.05

Magnitude Vs Ground motion and Energy

Magnitude of Earthquake and their effects

Aftershocks and Fault Area

Omori’s Law:

ptK

Cn

Where , n = frequency of aftershocks at time t after the main shock.K, C,

and P are constants that depend on the size of the earthquake, and P

value is usually close to 1.0 – 1.4

0.602.1log SMA

Where , A is measured in sq-cm

Attenuation Relation

• LnY =c1+c2M-c3lnR-c4R+c5F+c6S+

2

87

2

87

exp

)(exp

Mccr

MccrR

Log a = -1.02 + 0.249M – log R – 0.00255 R

R2 =D2 + H2 ; H=7.3 km, D=closest distance to surface

projection of the source in km

M=Moment magnitude

(Joyner and Boore, 1981)

Earthquake Prediction

Long Term – Years in advance

Intermediate- Weeks in advance

Short Term- Hours or days in advance

Long Term Recurrence Interval (Seismic Gap)

Fault Characteristics

Time of last earthquakeIntermediate

and

Short Term

Precursory phenomena

• Change in /

• Increase in seismic activity

• Emission of the radioactive gas

• Ground water fluctuation

• Changes in taste and temperature in wells and springs

• Teleseismic P-wave travel time delays

• Variation of geomagnetic, geoelectric fields, resistivity

• Geodetic, leveling measurement

• Animal behavior

Precursory phenomena