gabriel alvarez sep120 pages: 365-376 email:gabriel@sep ...sepmultiples in image space gabriel...
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Multiples in Image Space
Gabriel Alvarez
SEP120 pages: 365-376
Email:[email protected]
[email protected] SEP120 pages 365-376
From Last Year
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Residual Moveout (RMO) Equation
Biondi and Symes (2004) residual moveout equation:
∆nRMO = (ρ− 1) tan2 γ z0 n
where:
n: unit normal to the reflector.
ρ: true slowness/migration slowness.
γ: true half-aperture angle.
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Aproximations of RMO Equation
This equations has several approximations:
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Aproximations of RMO Equation
This equations has several approximations:
• Flat reflectors
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Aproximations of RMO Equation
This equations has several approximations:
• Flat reflectors
• Rays are stationary: apparent angles taken as equal to
true angles.
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Aproximations of RMO Equation
This equations has several approximations:
• Flat reflectors
• Rays are stationary: apparent angles taken as equal to
true angles.
• ρ is small.
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RMO approximation for Multiples
V1
V2
Surface
For water-bottom multiples V2 >> V1 so apparent
aperture angle may be significantly different than true
aperture angle and ρ is not close to one.
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RMO approximation for Multiples
V1
V2
Surface
For water-bottom multiples V2 >> V1 so apparent
aperture angle may be significantly different than true
aperture angle and ρ is not close to one.
What about diffracted multiples?
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Motivation
• Understand the residual moveout of multiples in image
space when migrated with the velocity of the primaries.
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Motivation
• Understand the residual moveout of multiples in image
space when migrated with the velocity of the primaries.
• Use the residual moveout to design the appropriate
Radon transform to attenuate the multiples in the
image space.
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Raypath of Primary
0 500 1000 1500 2000 2500 3000
0
500
1000
1500
2000
Horizontal coordinate (m)
Dep
th (m
)
tp(hD) =
√t2p(0) +
(2hD
VNMO
)2VNMO = V
cos ϕ
hD: half-offset ϕ: reflector dip
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Raypath of Water-bottom Multiple
0 500 1000 1500 2000 2500 3000
0
500
1000
1500
2000
Horizontal coordinate (m)
Dep
th (m
)
tm(hD) =
√t2m(0) +
(2hD
V̂NMO
)2V̂NMO = V
cos(2ϕ)
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Raypath of Diffracted Multiple
0 500 1000 1500 2000 2500 3000
0
500
1000
1500
2000
Horizontal coordinate (m)
Dep
th (m
)
tm(hD) = 2(ZD−hD sinϕ) cos ϕcos(βs+3ϕ) + zd
V cos βr
βs, βr: take-off angles zd: diffractor position
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Moveouts on a CMP Gather
0 500 1000 1500 2000 2500 3000
0.8
1
1.2
1.4
1.6
1.8
2
2.2
Offset (m)
Tim
e (s
)CMP gather
PrimaryMultipleDiff PrimDiff Mul
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Schematic of Moveout of Multiples
Tim
e
OffsetMidpo
int
Data spaceD
epth
Subsurface offsetImag
e point
Image space
Depth
Imag
e point
Aperture angle
Image space
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Example with 2-D Synthetic Dataset
200 cmps
100 traces/cmp
0-2970 m offsets
20 m cmp interval
4 events:
? primary
? wb multiple
? primary diffraction
? diffracted multiple
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Primary. Two Velocities
Zero subsurface-offset section SOCIG (x=6280)
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Diffraction. Two Velocities
Zero subsurface-offset section SOCIG (x=5800)
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Diffracted Multiple. Two Velocities
Zero subsurface-offset section SOCIG (x=4600)
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WB Multiple. Two Velocities
Zero subsurface-offset section SOCIG (x=3600)
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Diffracted Multiple. One Velocity
Angle stack ADCIG (x=4600)
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Primary. No Diffraction. Two Velocities
Angle stack ADCIG (x=6280)
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WB Multiple. No Diffraction. Two Vels
Angle stack ADCIG (x=6280)
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Primary. No Diffraction. One Velocity
Angle stack ADCIG (x=6280)
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Diffracted Multiple Only. Two Velocities
Angle stack ADCIG (x=4600)
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Diffracted Multiple Only. One Velocity
Angle stack ADCIG (x=4600)
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Conclusions
• Water-bottom multiples from a dipping interface
behave kinematically as primaries from an interface
with twice the dip at twice the depth.
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Conclusions
• Water-bottom multiples from a dipping interface
behave kinematically as primaries from an interface
with twice the dip at twice the depth.
• Diffracted multiples do not behave like primaries and
are not properly migrated even if the correct velocity is
used.
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Conclusions
• Water-bottom multiples from a dipping interface
behave kinematically as primaries from an interface
with twice the dip at twice the depth.
• Diffracted multiples do not behave like primaries and
are not properly migrated even if the correct velocity is
used.
• Understanding the correct moveout of the multiples in
the image space (diffracted multiples in particular) is
critical to the design of the proper Radon transform.
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Future Work
• Formalize the residual moveout issue for the multiples
in the image space.
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Future Work
• Formalize the residual moveout issue for the multiples
in the image space.
• Design the Radon transform that best focuses the
multiples in the image space.
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Future Work
• Formalize the residual moveout issue for the multiples
in the image space.
• Design the Radon transform that best focuses the
multiples in the image space.
• Apply to synthetic and real 3D data.
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