Seismic critical angle anisotropy analysis in the taup domain

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Seismic critical angle anisotropy analysis in the
tau-p domain

• Samik Sil
• Ph.D. Candidate, Jackson School of Geosciences

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Talk Overview

• What is seismic critical angle?
• How it helps to determine anisotropy?
• Drawbacks of the present method
• New method developed in the tau-p domain
• Synthetic case study
• Conclusions

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Seismic Critical Angle and Anisotropy (Theory)
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Critical Angle in Seismology
For seismic refraction, according to Snells Law
(1)
When ?290, then ?1?c and the formula becomes
?1
V1
?2
V2
(2)
Basic criteria V2 gt V1
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Anisotropy Analysis-Horizontal Velocity
When the underlying layer is anisotropic (VTI,
HTI or ORT) the horizontal velocity of the second
layer becomes
(3)
(4)
(5)
From Landrø and Tsvankin, 2007 and Sil and Sen,
2009
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Critical Angle and Anisotropy
Based on equation 2, 3, 4 and 5
(6) For the VTI
(7) For the HTI
(8) For the ORT
So for the case of azimuthal anisotropy (HTI and
ORT), critical angle ?c is the function of
azimuth f.
Landrø and Tsvankin (2007)
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Present Method of Critical Angle Analysis and
Anisotropic Parameter Estimation
From Landrø and Tsvankin (2007)
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Synthetic Cases
Model ORT layer under isotropic layer
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Amplitude Analysis For Critical Offset
Once Critical offset is determined (Maximum
changes in amplitude) we can convert it into ?c
and determine f and e
Solid line0 Broken line 90
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Result
Exact Critical angle values (solid line) and
values obtained from this analysis (broken line)
as function of azimuth. Maximum mismatch 6 when
velocity of the top layer is known.
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Real Data Example
Model ORT layer under isotropic layer
Raw data
Filtered Data
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Real Data Amplitude Analysis
For amplitude analysis NMO correction is
applied, then amplitudes are picked. Maximum
change in the amplitude corresponds to the
critical offset.
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Drawbacks of The Present Method
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Some Comments
Where is the critical offset?
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Some Comments..

• Process involves filtering of data for avoiding
  noise in the picking process.
• NMO correction is required for removing
  interference in Amplitudes from other layers.
• Determining critical offset from amplitude
  analysis can introduce considerable errors.
• For converting Critical offset to Critical angle
  requires phase velocity of the target layer.
  Phase velocity information can be erroneous in
  the X-t domain.
• Thus the critical angle analysis for anisotropic
  parameter estimation in this form is not robust.

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Proposed New Method
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Tau-p Domain Critical Angle Analysis
Equations 6,7 and 8 can be modified with simple
mathematics and can be written as
(9)
Where Critical slowness, pc sin?c/V1
(10)
(11)
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Identifying Critical slowness in the Tau-p Domain
Diebold and Stoffa, 1981
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Example-Real Data
Red arrow indicates the picked value of the
critical slowness between two layers of interest.
Critical slowness will be function of azimuth f
and e
Stoffa et al., 1981
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Synthetic Example of The New Method
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Synthetic Model
2.4-3 km
ISO
1 km
HTI
1 km
ISO
infinite
1D model used for generating synthetic study.
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Seismogram 0 Azimuth
Seismogram with band limited noise added to it.
Noise does not affect detecting the critical
slowness.
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Seismogram 45 Azimuth
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Seismogram 90 Azimuth
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Picked, Approximated and Exact pc Values
Plot of exact, picked and the approximated
critical slowness values. Mismatch between
approximated and exact is less than 3, mismatch
between picked and exact is almost 0.
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Old Method With This Data
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Conclusions

• X-t domain critical angle reflectometry is not
  robust.
• Conversion of Xc into ?c may be ambiguous in the
  X-t domain.
• Conversion of pc to ?c is not even required for
  anisotropy analysis in the tau-p(f) domain.

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Conclusions

• Velocity analysis for the presented case for the
  top isotropic layer is more accurate in the tau-p
  domain.
• Similar velocity analysis for obtaining ?c can be
  inherently erroneous in the X-t domain.
• Thus tau-p(f) domain critical angle reflectometry
  is a robust method.

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Questions?