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

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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 vertical-component instruments

  • 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

  • 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).