6 seismic moment
DESCRIPTION
gTRANSCRIPT
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GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD
Earthquake source mechanics
Lecture 6Seismic moment
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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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GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD
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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GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD
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
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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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GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD
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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GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD
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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GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD
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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GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD
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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GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD
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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GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD
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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GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD
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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GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD
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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GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD
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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GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD
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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GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD
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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GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD
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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GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD
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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GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD
Regional tectonics from seismotectonics
Fault plane solutionsType of faultingSlip directionStress field orientation
Quantitative seismotectonicsSeismic momentSlipStress dropSeismic and tectonic slip rate
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GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD
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