6 Seismic Moment

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GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Earthquake source mechanics Lecture 6 Seismic moment

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Transcript of 6 Seismic Moment

  • GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD

    Earthquake source mechanics

    Lecture 6Seismic moment

  • GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD

    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 + log + where A is max amp of 20s period surface waves

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

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    Seismic moment

    Seismic intensity measures relative strength of shaking locallyInstrumental earthquake magnitude provides measure of size on basis of wave motionPeak values used in magnitude determination do not reveal overall power of the sourceSeismic Moment: measure of quake rupture size related to leverage of forces (couples) across area of fault slip

    F

    F

    L

    Moment = FL

    - two equal & opposite forces= force couple

    - size of couple = moment- numerical value = product ofvalue of one force times distance between

    Applying couple to fault

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    Seismic Moment II

    Can be applied to seismogenic faultsElastic rebound along a rupturing fault can be considered in terms of resulting from force couples along and across itSeismic moment can be determined from

    fault slip dimensions measured in field or from aftershock distributionsanalysis of seismic wave properties (frequency spectrum analysis)

    F

    F

    Stress &strainaccumulation

    Fault ruptureand rebound

    Applying couple to fault

  • GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD

    Seismic moment

    Empirical relation between moment and magnitude islog10 M0 = c M + d

    or Mw = 2/3 log10 M0 6(Moment-magnitude scale (Kanamori)

    Seismic moment = Area of fault plane x stress drop of earthquake x coseismic slip

    [NB: Area x stress = forceforce x distance = moment]]

    provides estimate of overall size of the seismic sourceUnits: units of moment = newton-metres = Nm =

    = joule = J = unit of energySo seismic moment is also a measure of the energy of the earthquake

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    A few great fracturing events totally dominate the earthquake seismic moment released (moments more realistic than comparing magnitudes)The moment release, even at the major plate boundaries is distributed very unevenlyAbout of the seismic moment released between 1904-86 was by the great Chilean earthquake of 1960 that ruptured 100km of the subduction zone interface at the Peru-Chile trenchSan Francisco 1906 doesnt even get a mention!

    Seismic moment

    Seismic moment does not saturate

    e.g. Alaskan earthquake: Ms=8.4; Mw=9.2

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    Seismic moment tensor

    =

    333231

    232221

    131211

    MMMMMMMMM

    M jk

    The nine different force couples that make up the components of the moment tensor:

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    Seismic moment tensor

    =

    0000000

    0

    0

    MM

    M

    where Mo is defined as the scalar seismic moment:

    M0 = A s

    where is the rigidity modulus, A is the area of the fault and s is the slip or displacement of the fault

    Example of right lateral movement on a strike-slip fault in the x1direction corresponds to:

    Note Mij = Mji

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    Scalar seismic moment

    Define the scalar seismic moment (Aki)M0 = A s - rigidityA - fault areas - slip (vector)

    Units: force x length (Nm or J)

    l

    ws

    Aspect ratio:

    usually l/w 2,

    except for long strike-slip faults

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    Far-field radiation pattern for double couple source

    The orientation of the small arrows shows the direction of first motion; their length is proportional to the wave amplitude. The P-wave first motions are outward in the compressional quadrant and inward in the dilatational quadrant, with nodal lines in between. S-wave first motions are generally away from the pressure axis and toward the tension axis; there are 6 nodal points and no nodal lines in S

    P-waves

    S-waves

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    Example of focal spheres

    Example of focal spheres and their corresponding fault geometries. The lower half of the focal sphere is plotted to the left, with compressional quadrants shaded. The block diagrams show th two fault geometries (the primary and auxillary fault planes) that could have produced the observed radiation pattern.

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    Far-field pulse shapesThe near-field displacements caused by an earthquake will be permanent. M(t) would look like this

    In the far field there is a displacement pulse. dM/dt is proportional to the far-field dynamic response, such as observed with P-wave arrivals.

    Note most seismometers measure velocity or acceleration rather than displacement.

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    Seismic moment from seismograms

    Define seismic momentM0 area under pulseRupture length duration of pulse : l

    Time domain - instrument corrected pulse

    Pulse duration

    0

    30

    Time

    Am

    plitu

    dedM

    /dt

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    Seismic moment from seismograms

    Define seismic momentM0 A0Rupture length 1/ frequency: l 1 / f0

    Frequency domain

    Frequency

    Am

    plitu

    de

    f0

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    Earthquake characteristics

    M0 = A s 2 l sby dimensional analysis slip is:

    s = 2 M0 / l2

    stress drop with earthquake: = 2 M0 / 2 w2 l

    Note can get from seismogram as rupture length,l , pulse duration and M0 is proportional to

    amplitudeStress drops in range 1-30 MPa (Kanamori)

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    Stress drop in earthquakes

    Stress drop is typically a small fraction of total stresses in double couple earthquakes

    Varies according to crustal properties, fault maturity

    Single-force earthquakes (landslides) have much larger stress drops

    Fault length versus moment for large earthquakes (Scholz et al. 1986): larger stress drop produces more seismic moment for a given rupture area

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    Tectonics

    Infer seismic and tectonic slip rateslip rate = (sum of M0) / ( l.w T)

    M0 - summing and earthquake cataloguel.w - overall tectonic settingT - duration of earthquake catalogueFind active slip rate (SAF) is 3 cm/yrAseismic (creep) rate is 3 cm/yrCompare with satellite data, GPS

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    Seismic moment - from fault area

    Scalar seismic moment (Aki)M0 = A s

    l

    ws

    Get area of fault plane from aftershocks

    Measure slip in the field

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    Regional tectonics from seismotectonics

    Fault plane solutionsType of faultingSlip directionStress field orientation

    Quantitative seismotectonicsSeismic momentSlipStress dropSeismic and tectonic slip rate

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    Moment tensor inversions

    1. NEIC fast moment tensors - from teleseismic P waveformshttp://gldss7.cr.usgs.gov/neis/FM/fast_moment.html

    2. Harvard CMT solutions - Centroid momen-tensor (from long perdiod body waves)

    http://www.seismology.harvard.edu/projects/CMT/

    3. EMSC rapid source parameter determination - European-Mediterranean Seismological Centre - uses P & S waves results in 24 hours

    http://www.emsc-csem.org/

    4. NEIC broadband depths and fault-plane solutionshttp://neic.usgs.gov/neis/nrg/bb_processing.html