7 Magnitude Intensity - UCL · 2006-02-21 · GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND...

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GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Magnitude & Intensity Lecture 7 Seismometer, Magnitude & Intensity

Transcript of 7 Magnitude Intensity - UCL · 2006-02-21 · GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND...

Page 1: 7 Magnitude Intensity - UCL · 2006-02-21 · GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Intensity attenuation Average EMS intensity attenuation relationships

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD

Magnitude & Intensity

Lecture 7Seismometer, Magnitude & Intensity

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GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD

Vibrations: Simple Harmonic Motion

0)()( 22

2

=+∂

∂ xut

xu ωSimplest vibrating system:

ω is the angular frequency, f = ω / πThere are two solutions: u(x)= A sin (ωt) and u(x) = B cos (ωt) A and B are amplitude, or in exponential form:

xDisplacement u

]exp[)()( tiUtu ωω −=

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GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD

Basic principlemass attached to a moveable framewhen frame is shaken by seismic waves the inertia of the mass causes it’s motion to lag behindrelative motion recorded on rotating drum, on magnetic tape or digitally

Mass is damped to prevent continued oscillation

This limits the frequency response of the seismometer

Relative motion amplified up to 100s of thousands of times Schematic of a horizontal motion

mechanical seismometer

The Seismometer

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GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD

Modern seismometers

Earthscope array - 250Güralp Systems Ltd

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GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD

Review: Earthquake magnitudeRichter magnitude scale

M = log A(∆) - log A0(∆)where A is max trace amplitude at distance ∆and A0 is at 100 km

Surface wave magnitude MSMS = log A + α log ∆ + βwhere A is max amp of 20s period surface waves

Magnitude and energylog Es = 11.8 + 1.5 Ms (ergs)

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GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD

The Inertial SeismometerSpring – stiffness k

Damping ηMass m

Fs = - k zz(t)

Displacement of m relative to Earth u(t) Displacement of

Earth

Fd = - η dz/dt

Equating the resistive forces on the mass to the inertial forces:

[ ])()()()( 2

2

tztudtdm

dttdztzk +=−− η

Damping parameter ζ=η/m Resonant undamped angular frequency ω0

2 = k/m

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GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD

Earth noise

Individual acceleration spectra at over 100 stations showing Earth noise. Note the microseism peak at 5 to 8s period and the relatively low noise levels at 20 to 200s period.

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GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD

Response of 4 different seismometers

Velocity response functions for four different vertical-component instruments

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GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD

Strong motion seismometersDesigned to pickup strong, high-amplitude shaking close to quake sourceInsensitive to weak shakingMost common type is the accelerometerDirectly records ground accelerationNot continuously recording -triggered by first wavesDifficult to differentiate different earthquake wavesStandard seismographs go off scale (clipped) by strong ground motionsMost useful for understanding response of buildings to earthquakes

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GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD

Strong motion record

Acceleration

Velocity

Displacement

Remember the acceleration of the Earth is determined by measuring the acceleration, velocity and displacement

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GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD

Response Spectrum

0.1 1 100.01Fundamental period (seconds)

5

0

Spe

ctra

l acc

eler

atio

n (m

/sec

2 )

15

10

5% damping

100,000 year return period

10,000 year

1,000 year

Arup

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GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD

World seismic hazard maps

Accelerations

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GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD

Attenuation of seismic waves: reduction in amplitude / loss of energy

a) Elastic attenuation: geometric spreadingSpherical body waves spread in 3DSurface waves spread in 2D

Elastic attenuation R

f(t,R)

b) Anelastic attenuationPermanent rock deformation: close to earthquake sourceHeat loss due to ‘internal friction’e.g. between pore fluids and rock motion

R.f(t)

R

Elastic

Anelastic

But even after correcting for geometric spreading there is still attenuation:

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GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD

Elastic attenuation: geometric spreading

Body waves (P, S etc.):As a spherical wave front grows the energy

of the source is spread out over a wider and wider area leading to a reduction of amplitude with distance

AmplitudeEnergy: area under the curve ∝ Amp2

solid angle

A1 - areaA2 - area

R1R2

r1r2

Energy is proportional to:

(i) square of amplitude

(ii) area of wavefront

Find A2 / A1 = r22 / r1

2 = R22/ R1

2

So the wave energy of body waves diminishes as 1/R2

and the body wave amplitude diminishes as 1/R

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GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD

Elastic attenuation: geometric spreading

Surface waves (LR, LQ etc.):Surface wave are consigned to the surface

R

Earthquake sourceEnergy of surface waves falls off as 1/R

Energy of body waves falls of as 1/R2

The spreading of surface wave energy does not translate directly into wave amplitudes, because surface waves are strongly dispersive, and the waveform changes shape

But we can see the dominance of surface waves on teleseismic records is due to the geometric spreading of the wavefront has different dependence on R

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GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD

Anelastic attenuation

Anelastic attenuation

Definition: Quality factor Q = 2 π E / δE

Q is dimensionless Q ≥ 2π ~ 6

High quality ⇒ Good transmission ⇒ Low attenuation

Low quality ⇒ Poor transmission ⇒ High attenuation

1 2

∫∝ dttfE )(2 ∫ −= dtffE 221 )(δ

t

E – energy per cycle

δE – energy lost per cycle

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GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD

There is an exponential decay of amplitude with distance due to anelastic attenuation

Anelastic attenuation

Amp/Amp0

Distance R

long wavelength,

low frequency

short wavelength

high frequency

Short wavelength, high frequency waves are attenuated more than long wavelength, low frequency waves

This is why if your upstairs neighbour is playing music, it is the bass which comes through the ceiling

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GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD

Anelastic attenuation

In the frequency domain( )ωωω bFF −= exp)()( 0F

ω

exp -bω

low freq, low energy loss, few cycles high freq, high loss, many cycles

wave distortion as well as amplitude reduction i.e. change in shape of the wavelet

loss of resolution down seismogram

c.f. someone playing a stereo in the next room – get distortion

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GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD

Attenuation of ground acceleration

The range of published average attenuation relationships for acceleration with distance from an earthquake magnitude 6.5 in western North American (after Atkinson and Boore, 1990)

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GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD

Intensity attenuation

Average EMS intensity attenuation relationships from analysis ofisoseismals of 53 earthquakes, southern Italy (after Coburn et al., 1988).