rotational ground motions: a new observable for...
TRANSCRIPT
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Rotational Ground Motions:A New Observable for Seismology?H. Igel1, A. Cochard1,4, A. Flaws1,2, W. Suryanto1, B. Schuberth1, U. Schreiber3 , Pham Dinh Nguyen1, A. Velikoseltsev3
1Department of Earth and Environmental Sciences, LMU Munich2Department of Physics and Astronomy, Christchurch, New Zealand3Fundamentalstation Wettzell, Kötzting4EOST Strasbourg
• What is rotation in seismology? (Why bother?)
• The ring laser instrument
• Broadband observations of rotations• Peak rotation rates• Waveform comparison with translations• Horizontal phase velocities• Love wave dispersion• P-coda
• Array-derived vs. directly measured rotations
• Conclusions and future
ringlaser.geophysik.uni-muenchen.de
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Rotation is the curl of the wavefield… it separates P- and S-wave in isotropic media
∂−∂∂−∂∂−∂
=×∇=
xyyx
zxxz
yzzy
z
y
x
vvvvvv
21
21 v
ωωω
vz
vy
vx
ωz
ωy
ωx
Ground velocity Seismometer
Rotation rateRotation sensor
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Rotation from seismic arrays?... by finite differencing ...
xyyxz vv ∂−∂≈ω
vy
vx
ωz
vy
vx
vy
vx
vy
vx
Rotational motion estimated from
seismometer recordings
seismometers
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Radiation from a double-couple point source
Geometry we use to express the seismic wavefield radiated by point double-couple source with area A and slip ∆u
Here the fault plane is the x1x2-plane and the slip is in x1-direction.
Aki and Richards (2002)
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Radiation from a point source
Near field term contains the static deformation
Intermediate terms
Far field terms: the main ingredient for source inversion, ray theory, etc.
Ground displacement
Aki and Richards (2002)
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Radiation pattern
Far field P – blueFar field S - red
Aki and Richards (2002)
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The rotational part
• Rotations are zero before S arrival
• This includes the near field!
• Far-field P-rotation is not zero! Only the sum of all contributions cancel!
Cochard et al. (2006)
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Basic seismograms, full space
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Acceleration vs. Rotation rate
... in the far field ...
sF
FS
ss
F
ss
FS
vu
vrtMrv
vrtMrv
u
2
)/(8
1
)/(4
1
04
03
−=
−−=
−=
ϖ
πρϖ
πρ
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Rotations – why bother?
• Standard seismological observations are polluted by rotations
• Tiltmeters (rotation around horizontal axes) are polluted by translations
• Rotations may contribute to co-seismic structural damage
• Rotational measurements my provide additional wavefield information (phase velocities, etc)
• ... and may allow further constraints on rupture processes ...
Instruments
Earthquake engineering
Waves and
rupture
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A+R‘s view ...
„The state-of-the-art sensitivity of the general rotation-sensor is not yet enough for a useful geophysical application“ (Aki and Richards, Quantitative Seismology, 1980)
„... note the utility of measuring rotation near a rupturing fault plane (...), but as of this writing seismology still awaits a suitable instrument for making such measurements“ (Aki and Richards, Quantitative Seismology, 2nd edition 2002)
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Previous studies
Schreiber, Stedman, and co-workersRing laser technology New Zealand and Germany
Takeo and co-workersGyroscopic rotation sensor, theoretical work
Nigbor and co-workersrotational sensor and observation of rotational motion of nuclear blast
Teisseyre and co-workersmechanical rotational sensor and observation of local events
it seems that only optical technology provides the required high resolution for (tele-)seismic measurements
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The ring laser at Wettzell
ring laser
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How can we observe rotations?-> ring laser
Ring laser technology developed by the groups at the Technical University Munich and the University of Christchurch, NZ
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The Sagnac Frequency(schematically)
Tiny changes in the Sagnac
frequencies are extracted to
obtain the time series with
rotation rate∆f -> Θ
Sagnac frequency sampled with 800Hz
Rotation rate sampled with 4Hz
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Ring laser – the principle
PfSagnac λ
AΩ ⋅=∆ 4
A surface of the ring laser (vector)Ω imposed rotation rate (Earth‘s rotation +
earthquake +...)λ laser wavelength (e.g. 633 nm)Pperimeter (e.g. 4-16m)∆f Sagnac frequency (e.g. 287,3 Hz sampled at
800Hz)
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Ring laser – resolution
PfSagnac λ
A⋅Ω=∆ 4
4.8 10-10
9.1 10-11
7.3 10-12
79.4348.61512.8
116366
Resolutionrad/s
fSagnac (Hz)Area m2
After Schreiber et al., 2002
... ring lasers are used in any commercial airplanes for stabilizing ...
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Effects of tilt on rotational measurements
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... before presenting observations ...
• ... the ring laser should be sensitive to SH type motion only (S waves, Love waves) ...
• ... P-waves (or Rayleigh waves) should not lead to a signal (except via tilt coupling) ...
• ... Rotation rate and transverse acceleration should be in phase ...
• ... their amplitude ratio should be twice the local phase velocity – assuming plane non-dispersive transversely polarized wave propagation ...
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Theoretical relation rotation rate and transverse acceleration
plane-wave propagation
Plane transversely polarized wave propagating in x-direction with phase velocity
kctkxftxu y /)(),( ωω =−=
)(),(),( 2 tkxftxutxa yy ωω −′′== Acceleration
]0),(21,0[]0,,0[
21),( tkxfkutx y ωω −′′−=×∇=Ω Rotation rate
ctxtxa 2),(/),( −=Ω
Rotation rate and acceleration should be in phase and the amplitudes scaled by two times the horizontal phase velocity
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Data base 2003 + 2004
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4C recordings – raw dataMw = 8.3 Tokachi-oki earthquake25.09.2003 19:50:38.2 GMTLat= 42.21 Lon= 143.84
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Compatibility with MS (surface wave magnitude)T=30s, c=4300m/s
3.3log66.1log 1010 ++= DTAM S
3.9log66.12
2
210102),(2 −−==Ω DM
SzS
cTDMA
cTππ
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Rotational data baseevents with varying distance
transverse acceleration – rotation rate
incr
easi
ng e
pice
ntra
l dis
tanc
e400kmM5.0
10000kmM8.3
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Mw = 8.3 Tokachi-oki 25.09.2003transverse acceleration – rotation rate
From Igel et al., GRL, 2005
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Max. cross-corr. coefficient in sliding time window transverse acceleration – rotation rate
Small tele-seismic event
P-onset
S-waveLove waves Aftershock
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Spectral element modeling of 3D global wave propagation
Cubed Sphere Chunk Partitioning
100GByte Memory60 hours on theBundeshöchstleistungsrechner
Tromp and Komatitsch, 2003
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M8.3 Tokachi-oki, 25 September 2003phase velocities ( + observations, o theory)
From Igel et al. (GRL, 2005)
Horizontal phase velocity in sliding time window
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Real vs. Synthetics : Papua event
Cochard et al., 2006
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incr
easi
ng d
omin
ant
peri
od (s
)
Mw = 8.3 Tokachi-oki 25.09.2003transverse acceleration – rotation rate
narrow band-pass filtering
100
150
50
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Mw = 6.3 Greece 14.08.2003transverse acceleration – rotation rate
narrow band-pass filtering
100
150
50
incr
easi
ng d
omin
ant
peri
od (s
)
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Rotational seismogramsSynthetics and Observations
M8.3 Hokkaido, 25 September 2003(recorded in Wettzell, Germany)
Absolute amplitudes
SeismometerTransverse acceleration
Ring laserRotation rate
Absolute amplitudes
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Phase velocity determination... by dividing accelerations by rotation rates in a sliding window ...
... point measurement!
Note the decreasing velocities with time (and increasing frequency)
Love wave phase velocities
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Phase velocity determination... by dividing accelerations by rotation rates in a sliding window ...
... point measurement!
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Restitute your broadband seismograms!transverse acceleration – rotation rate
Time (s)
Before restitution
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Restitute your broadband seismograms!transverse acceleration – rotation rate
After restitution
Time (s)
... an independent confirmation of the quality of the restitution processing ...
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Phase velocity determination... by calculating spectral ratios ...
Phase velocities obtained by dividing Spectra of transverse acceleration by Rotation rate: Al Hoceima event M6.4Feb 24, 2004.
Theoretical Love wave dispersion (ak135)
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Stacked spectral ratios ...... accurate enough for structural inversion ...?
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Direction of propagation of transversely polarized energy
rotation rate
acceleration
Back azimuth
Max. cross-corr. coeff. as a function of time and propagation direction
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Direction of propagation of transversely polarized energy
rotation rate
acceleration
Back azimuth
Max. cross-corr. coeff. as a function of time and propagation direction
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Rotational signals in the P-coda???
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Array measurementsDec 2003-Mar 2004
xyyxz vv ∂−∂≈ω
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A quick-and-dirty experiment
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Synthetics
Uniformity of rotation rate across array
Real data
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Effects of noise on array-derived rotation:Phase uncertainty
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First comparison of array-derived rotations (black) and direct ring laser measurements (red)
From Suryanto et al (2005, BSSA, submitted)
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Summaryseismic ground rotations
• Yes, we do have a new observable for broadband seismology, that is consistent in phase and amplitude with collocated recordings of translations
• The joint observations allow seismic array-type processing steps (but array-free!)
• A prototype sensor designed for seismology has been installed at Pinon Flat, CA
• A less sensitive (portable) sensor for near source studies and applications in earthquake engineering is planned.
Next steps:• Further comparison with array observations (phase
velocities)• Love-wave dispersion, how accurate? -> Tomography?• Understanding observations in data base in terms of
structure, anisotropy, source, etc.
![Page 50: Rotational Ground Motions: A New Observable for Seismology?eost.u-strasbg.fr/semipgs/pres_Heiner_Igel.pdf · Quantitative Seismology, 1980) „... note the utility of measuring rotation](https://reader033.vdocument.in/reader033/viewer/2022042221/5ec77e767b4ff16c3d0c813a/html5/thumbnails/50.jpg)
ringlaser.geophysik.uni-muenchen.de
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