LECTURE3 INTERPRETATION OF SEISMIC DATA IN TERMS OF ANISOTROPY

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LECTURE-3 INTERPRETATION OF SEISMIC DATA IN
TERMS OF ANISOTROPY
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(Babuska and Cara, 1991)
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(Babuska and Cara, 1991)
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INTERPRETATION OF SEISMIC DATA IN TERMS OF
ANISOTROPY (Babuska and Cara, 1991)

• Teleseismic P-wave arrival times
• Isotropic model gt 50 initial data variance
• Anisotropic model
• What is the cause of misfit to the data ?
• Noise in arrival times
• Inadequate ray tracing or non linear effects in
  the inverse theory
• Anisotropy
• Trade-off between seismic anisotropy and
  heterogeneity
• A stack of isotropic layers (h layer thickness)
• hltlt ? (seismic wave length) gt
• Heterogeneous Isotropic Model or Homogeneous
  Anisotropic Model
• You can not distinguish them !

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• Anisotropy or large scale heterogeneties gt
  Love/Rayleigh wave discrepancy
• Average phase velocity
• Average group velocity

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• Classical linear inversion schemes of
  surface-wave dispersion curves should not be
  applied to regions of too strong lateral
  heterogeneties.
• Correct for the effects of lateral
  heterogeneties to reduce the risk of misleading
  interpretation of an observed Love/Rayleigh wave
  incompatibility.

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A two-block isotropic model A homogeneous
anisotropic model

• Ray path 1 t1w / V1 V(?)Vo? V cos(2??o)
• Ray path 2 t2(L1/V1)(L2/V2) ?o0 gt 2
  unknowns
• Vo(w / t1 L / t2) / 2
• ?V(L / t2 w / t1)/2
• ?o unknown gt 3 unknowns gt more data
  are needed.
• Both models can fit equally well the two data t1
  and t2 !

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• Heterogeneity X Anisotropy
• Resolving local anisotropy from a finite set of
  travel-time data gt ??
• A priori information is necessary.
• Bounds on the local velocity distributions
• Spatial correlation lengths for the physical
  parameters
• Bounds on the local azimuthal variations of
  velocities

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Seismic Anisotropy Inverse Methods

• Problems
• Model parameters in anisotropic case ?
• Differences in the physical units of the model
  parameters
• (elastic parameters, angles and density) ?
• Solutions
• Add appropriate petrological constraints and
  reduce the number of unknowns
• Example Olivine in the upper mantle
• a-axis gt Vmax // Flow direction
• Hexagonal symmetry (5 elastic constants) of
  Olivine ? Special case of Orthorhombic (9 elastic
  constants) of ?-spinel

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• Reduce the number of anisotropic parameters
  based on the physical grounds
• Example
• Randomly oriented fluid filled cracks with the
  normals to their surface statistically oriented
  on one direction gt hexagonal symmetry
• A problem of physical inhomogeneity of the model
• Variation of single physical parameter (Lets say
  P) of oriented cracks
• Specific problems in the inverse theory (the
  consistency problem)
• Solution State the problem by using the
  independent physical parameters.

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• In this case, a coherent setting of the priori
  covariance matrices have been necessary to make
  the inverted models consistent.
• BODY- WAVE DATA
• Causes of the azimuthal variations of refracted
  wave velocity
• Shape of the horizon on which refraction takes
  place
• Anisotropy of the underlying layer
• If no constraint is put on the anisotropic
  velocity model (i.e. hexagonal symmetry with
  horizontal axis of symmetry), more than two
  profiles at right angle are necessary to retrieve
  the anisotropic parameters.

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• See Short Notes for particle motion, polarization
  and shear wave splitting.
• S-wave polarization was strongly distorted only
  if the incidence angle was larger than the
  critical angle
• icarcsin (Vs/Vp)
• Different windows of incidence angle for each
  interface !
• Inner windows The transmission coefficients of
  shear waves are real and very little distortion
  occurs.
• External window The transmitted polarization is
  more and more perturbated by converted
  inhomogeneous waves.
• Problem Sources of the apparent shear-wave
  splitting ?
• Anisotropy
• Wave conversion at a planar interface

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Case studies Shear wave polarizations near NAF
in Turkey (Booth et. al., 1985 Crampin and
Booth 1985)

• Location NW Turkey, NAFZ (Turkish Dilatancy
  Project)
• Methods
• 1) Shear wave Splitting Anisotropy above the
  earthquake foci
• Stress induced cracks gt Crack induced anisotropy
  
• 2)Variation of velocity with direction
• 3) Polarization Anomalies
• 4) Attenuation with directions
• Conclusions
• Shear wave splitting stress induced cracking
• Polarization of faster split shear waves //
  distribution of parallel vertical cracks
• Orientation of the effective crack induced
  anisotropy derived from
• the shear wave polarizations is consistent with
  the common directions of compression and tension
  in fault-plane mechanisms of the earthquakes

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SEISMIC REFRACTION DATA

• UPPER CRUSTAL STRUCTURE
• Study Area Mount Hood , Oregon Region USA
  (Cascade volcanoes and geologically complex area)
• Source Controlled source
• Instruments 100 seismic stations and 6 shot
  points
• Method Time Term Analysis (Berry and West, 1966
  Willmore and Bancroft, 1960)
• Objective of the method Determining local time
  delays under each recording site to refine the
  estimate of P wave velocities

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(Kohler et al., 1982)
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(Kohler et al., 1982)
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(Kohler et al., 1982)
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(Kohle et al., 1982)
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Time Term Method

• Assumptions
• V(z)
• Refractor velocitygtconstant
• Slope and curvature of the refracting surfacegt
  small
• Travel time relation
• tij travel time between shot (i) and recorder (j)
• ?ij shot-recorder distance
• V refractor velocity
• ai,aj time term for site i and site j
• N1 number of shot sites
• N2 Number of recorder sites
• Observed data tij and ?ij
• Unknowns ai and aj

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P-wave anisotropy

• The apparent refractor velocity
• The data points are fitted with a sine curve of
  the form
• V A D cos2? E sin 2?
• ? is the shot to recorder azimuth.

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(Kohler et al., 1982)
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(Kohler et al., 1982)
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(Kohler et al., 1982)
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(Kohler et al., 1982)
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CONCLUSION

• The region around Mount Hood is characterized
  by a time term low (fast rocks at shallow depths)
  Intrusion of batholith
• Velocity gt azimuthal dependency
• Possibilities
• 1) Maximum velocity lies in the direction of
  maximum principal stress gt
• The effect is caused by the action of the stress
  field on fractures in the rocks.
• 2) Unrecognized structural complexity

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UPPER MOST MANTLE

• Profile Length 200-3500 km (long-range
  refraction profiles)
• Source Controlled source or earthquake data
• Observations Sequence of high and low velocity
  layers in the upper most mantle
• (Vp 7.7-8.8 km/s)
• Impossible to explain in terms of isotropic
  models
• Examples S. Germany Pn anisotropy 7-8
• W. USA
• W. Europe 60-100 km depth anisotopic layer
• Siberian plateau 200 km depth anisotropic
  layer
• 70-100 km depth high velocity layer
• 130-170 km high velocity layer
• Anisotropy Several tens of km Olivine
  orientation
• Heterogeneity Dipping Structures
• Anisotropy Heterogeneity

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(Cerveny, 1986)
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(Babuska and Cara, 1991)
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SKS-WAVE DATA

• Isotropic model
• SKS is a pure SV phase, nearly vertical beneath
  the station and radially polarized in the
  horizontal plane
• Anisotropic model
• S wave splitting will occur and yield 2 SKS waves
  polarized at a right angle from each other. Two
  split SKS waves can arrive at the station with a
  noticeable time differences.

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For a spherical Isotropic Earth

• s(t) A radially polarized SKS signal
• s1(t) and s2(t) The projections of the ground
  motion on 2 directions
• s1(t)s(t) cos ? // symmetry axis
• s2(t)s(t-?t) sin ? ? symmetry axis
• R(t) s(t) cos2 ? s(t-?t) sin2 ?
• T(t)s(t)- s(t-?t)/2 sin 2?
• For a weak anisotropy occuring withn the
  lithosphere,
• ?t gt0 T(t) gt 1st derivative of R(t)
• Large heterogeneity in the orientation of
  symmetry axis may destroy overall anisotropy.
• Olivine in the upper mantle gt 10 shear-wave
  splitting

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Observations of transversely polarized SKS
(Silver and Chan, 1988)

• Because SKS has been converted from a P-wave to
  an S-wave at the core mantle boundary, it will be
  polarized in the vertical plane of propagation
  for a sphericallysymmetric isotropic Earth.
  Thus, the transverse component of energy SKST
  will be identically zero.
• Both anisotropy and aspherical structure will
  tend to produce a nonzero SKST through shear-wave
  splitting and perturbations to the ray path,
  respectively.
• Asperical structure gt Rectilinear particle
  motion
• Shear wave splitting gt Elliptical partical
  motion

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• Best distance range for splitting measurements gt
  85o-110o
• gt 85o gt SKS is isolated from S and ScS.
• lt110o gt sufficiently energetic.
• Since SKST should be identically zero in the
  absence of anisotropy,
• the method is based on a search for the pair ?
  and ?t in inrements of
• 1 degree and .05 s to remove the energy on the
  transvese component.
• Depth extent
• L(?t ?o)/?
• L thickness of layer ? the fractional
  difference in velocity between the fast and slow
  directions 4 ?o shear velocity ?t the delay
  time between the fast and slow velocities.

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Jeffreys-Bullen travel time curves for surface
focus (Bullen and Bolt, 1985)http//www-gpi.physi
k.uni-karlsruhe.de/pub/widmer/IASP91/iasp91.html
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(Babuska and Cara, 1991)
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(Babuska and Cara, 1991)
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(Brechner et al., 1998)
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Case Study Tomographic Pn velocities and
anisotropy structure (Al-Lazki et al., 2003) in
the eastern Turkey
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Case study SKS anisotropy in the eastern Turkey
(Sandvol et al., 2003)
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SURFACE-WAVE DATA

• Love/Rayleigh wave discrepancy
• The upper mantle anisotropy could be observable
  on the surface wave dispersion curves. The
  observed phase velocities of the Love-wave
  fundamental mode are too high compared with the
  velocities predicted from a Rayleigh-wave study.
  

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The azimuthal variation of phase velocity

• C(?) Co ? C(?)
• C(?) A2 cos 2? A3 sin 2? A4 cos 4? A5
  sin ?
• Co, An are linear combinations of the partial
  derivatives of a transversely isotropic model
  with the vertical axis of symmetry.
• Once the local phase velocity Co is found
  together with its 2? and 4? azimuthal variations,
  Co, A2-A5 can be inverted in terms of depth
  varying properties.
• The polarization anomalies in surface wave
  particle motion
• Strong anomalies in the particle motion of
  Rayleigh waves have been observed.
• The main problem in interpreting these
  observations is difficulties in the separtion of
  the effects of lateral heterogeneities beneath
  the station from the anisotropy.

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(Babuska and Cara, 1991)
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SHORT NOTES

• PARTICLE MOTION
• POLARIZATION
• SHEAR WAVE SPLITTING

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PARTICLE MOTION

• The particles of the medium involved in the wave
  process leave their equilibrium positions and
  perform oscillatory motion in space describing
  definite trajectories about the equilibrium
  positions. After the elastic wave has passed, the
  particles return their original equilibrium
  positions. The trajectories of particle motion
  are not the same for different types of waves.
  The different waves may have different
  polarizations (linear or elliptical).

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(Scherbaum and Johson, PITSA, 1992)
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POLARIZATION

• Polarization is a preferential direction of wave
  motion. For example, the component of S wave
  whose motion is confined to a horizontal plane is
  called as SH wave.
• The parameters of polarization may generally
  dependent on the type of wave and inhomogeneties
  of the source and the Earth.
• Examples for different polarization types
• 1) Linearly polarized wave
• 2) Elliptically polarized wave

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1) Linearly polarized wave

• The sum of 2 oscillations with identical
  frequencies and
• displacement directions but different phases ?
• A1A01 sin (w?1)
• A2A02 sin (w?2)
• Superposition
• A2A012A0222A01A02 cos (?1- ?2)
• tan?(A01 sin ?1 A02 sin ?2)/(A01 cos ?1 A02
  cos ?2)

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2) Elliptically polarized wave

• The sum of 2 oscillations with the same frequency
  polarized in different directions.
• a) The osciallations are in phase, ?1- ?2 ? 2?n.
  ? The trajectory of motion is
• a straight line.
• The oscillations are in opposite phases, ?1- ?2
  ? (2n1)?. The osciallation is linearly polarized
  but perpendicular to the trajectory considered in
  the first case.
• The phase difference is ?1- ?2 (?/2) ? 2?n. The
  oscillation is elliptically polarized (the
  coordinate axes coincide with the principle axes
  of the ellipse) with the particle moving
  clock-wise.
• d) The phase difference is ?1- ?2 (?/2) ?
  (2n1)?. The trajectory coincides with that of
  preceding case, but the particle moves
  counter-clock wise.

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(Galperin, ??)
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Polarization angles of body-waves

• The polarization angle (?) of a S-wave is
• ?tan-1(uH/uV)
• uH instanteneous particle displacement SH
  component of incident
• S-wave
• uV instanteneous particle displacement SV
  component of incident
• S-wave
• The incidence angle jo
• The critical angle sin-1 (Vs/Vp)

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(Nuttli, 1961)
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• jo lt sin-1 (Vs/Vp) gt For incident S-wave,
  reflected P S waves in phase gt Linear
  particle motion
• jo gt sin-1 (Vs/Vp) gt For incident S-wave, total
  reflection
• 3 waves (SH, horizontal component of SV and
  vertical component of SV) are out of phase gt
• Nonlinear particle motion
• jo gt35 elliptical polarization except for ?0,
  ?90 or jo90, jo45 (Pure
• SV, Pure SH) which show linear polarization.

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SHEAR WAVE SPLITTING

• In anisotropic media, an incident shear wave is
  polarized into orthogonal directions travelling
  with different velocities (Babuska and Cara,
  1991). The delay between the shear waves
  properties along the ray path.

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(Babuska and Cara, 1991)
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(Babuska and Cara, 1991)
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REFERENCES

• Babuska, V. And Cara, M., 1991, Seismic
  Anisotropy in the Earth, Kluwer
• Academic Pub.
• Thomsen, L., 2002, Understanding Seismic
  Anisotropy in Exploration and
• Exploitation, EAGE.
• Galperin, E.I., The polarization method of
  seismic exploration, D.Reidel Pub.
• Company.
• Silver, P.G. And Chan, W. W., 1988, Seismic
  Anisotropy from Shear-Wave
• Splitting Implications for Continental
  Structure and Evolution, Nature.
• Kohler, W.M., Healy, J.H. and Wegener, S.S.,
  1982, Upper crustal structure of
• the Mount Hood, Oregon, Region as revealed by
  Time Term Analysis, Journal of
• Geophysical Research, V 87, No B1, 339-355.

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Seismic Anisotropy Studies in Turkey

• Booth, D.C., Crampin, S., Evans, R. and Roberts,
  G., 1985, Shear-wave polarizations near the North
  Anatolian Fault - I. Evidence for
  anisotropy-induced shear-wave splitting, Geophys.
  J. R. Astr. Soc. , 83, 61-73.
• Crampin, S. and Booth, D.C., 1985, Shear-wave
  polarizations near
• the North Anatolian Fault - II. Interpretation in
  terms of crack-induced anisotropy, Geophys. J. R.
  Astr. Soc. , 83, 75-92.
• Sandvol E., N. Türkelli, E. Zor, R. Gök, T.
  Bekler, C. Gürbüz, D. Seber, M., 2003 Barazangi,
  Shear wave splitting in a young
  continent-continent collision. An example from
  Eastern Turkey, GRL 30, 24, 8041,
  doi10.1029/2003GL017390, TUR 4-1/4-4.
•  
• Al-Lazki, A.I., D. Seber, E. Sandvol, N.
  Türkelli, R. Mohamad, M. Barazangi, 2003
  Tomographic Pn velocity and anisotropy structure
  beneath the Anatolia plateau (eastern Turkey) and
  the surrounding regions, GRL 30, 24, 8043, doi
  10.1029/2003GL017391, TUR 6-1/6-4.

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• Nuttli, O., 1961, The effect of the Earths
  surface on the S wave particle motion, BSSA, V51,
  237-246.