7 Magnitude Intensity  UCL · 20060221 · GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND...
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GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD
Magnitude & Intensity
Lecture 7Seismometer, Magnitude & Intensity

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD
Vibrations: Simple Harmonic Motion
0)()( 222
=+∂
∂ 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 −=

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

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD
Modern seismometers
Earthscope array  250Güralp Systems Ltd

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)

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:
[ ])()()()( 22
tztudtdm
dttdztzk +=−− η
Damping parameter ζ=η/m Resonant undamped angular frequency ω02 = k/m

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.

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD
Response of 4 different seismometers
Velocity response functions for four different verticalcomponent instruments

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD
Strong motion seismometersDesigned to pickup strong, highamplitude 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

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

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

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD
World seismic hazard maps
Accelerations

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:

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 / r12 = R22/ R12
So the wave energy of body waves diminishes as 1/R2
and the body wave amplitude diminishes as 1/R

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/R2The 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

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 )(δt
E – energy per cycle
δE – energy lost per cycle

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

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

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)

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).