Post on 23-Sep-2020
Multiples in Image Space
Gabriel Alvarez
SEP120 pages: 365-376
Email:gabriel@sep.stanford.edu
gabriel@sep.stanford.edu SEP120 pages 365-376
From Last Year
gabriel@sep.stanford.edu SEP120 pages 365-376 1
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.
gabriel@sep.stanford.edu SEP120 pages 365-376 2
Aproximations of RMO Equation
This equations has several approximations:
gabriel@sep.stanford.edu SEP120 pages 365-376 3
Aproximations of RMO Equation
This equations has several approximations:
• Flat reflectors
gabriel@sep.stanford.edu SEP120 pages 365-376 3
Aproximations of RMO Equation
This equations has several approximations:
• Flat reflectors
• Rays are stationary: apparent angles taken as equal to
true angles.
gabriel@sep.stanford.edu SEP120 pages 365-376 3
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.
gabriel@sep.stanford.edu SEP120 pages 365-376 3
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.
gabriel@sep.stanford.edu SEP120 pages 365-376 4
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?
gabriel@sep.stanford.edu SEP120 pages 365-376 4
Motivation
• Understand the residual moveout of multiples in image
space when migrated with the velocity of the primaries.
gabriel@sep.stanford.edu SEP120 pages 365-376 5
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.
gabriel@sep.stanford.edu SEP120 pages 365-376 5
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
gabriel@sep.stanford.edu SEP120 pages 365-376 6
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)
gabriel@sep.stanford.edu SEP120 pages 365-376 7
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
gabriel@sep.stanford.edu SEP120 pages 365-376 8
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
gabriel@sep.stanford.edu SEP120 pages 365-376 9
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
gabriel@sep.stanford.edu SEP120 pages 365-376 10
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
gabriel@sep.stanford.edu SEP120 pages 365-376 11
Primary. Two Velocities
Zero subsurface-offset section SOCIG (x=6280)
gabriel@sep.stanford.edu SEP120 pages 365-376 12
Diffraction. Two Velocities
Zero subsurface-offset section SOCIG (x=5800)
gabriel@sep.stanford.edu SEP120 pages 365-376 13
Diffracted Multiple. Two Velocities
Zero subsurface-offset section SOCIG (x=4600)
gabriel@sep.stanford.edu SEP120 pages 365-376 14
WB Multiple. Two Velocities
Zero subsurface-offset section SOCIG (x=3600)
gabriel@sep.stanford.edu SEP120 pages 365-376 15
Primary. Two Velocities
Angle stack ADCIG (x=6280)
gabriel@sep.stanford.edu SEP120 pages 365-376 16
Diffraction. Two Velocities
Angle stack ADCIG (x=5800)
gabriel@sep.stanford.edu SEP120 pages 365-376 17
WB Multiple. Two Velocities
Angle stack ADCIG (x=4600)
gabriel@sep.stanford.edu SEP120 pages 365-376 18
WB Multiple. Two Velocities
Angle stack ADCIG (x=3600)
gabriel@sep.stanford.edu SEP120 pages 365-376 19
Primary. One Velocity
Angle stack ADCIG (x=6280)
gabriel@sep.stanford.edu SEP120 pages 365-376 20
Diffraction. One Velocity
Angle stack ADCIG (x=5800)
gabriel@sep.stanford.edu SEP120 pages 365-376 21
Diffracted Multiple. One Velocity
Angle stack ADCIG (x=4600)
gabriel@sep.stanford.edu SEP120 pages 365-376 22
WB Multiple. One Velocity
Angle stack ADCIG (x=3600)
gabriel@sep.stanford.edu SEP120 pages 365-376 23
Primary. No Diffraction. Two Velocities
Angle stack ADCIG (x=6280)
gabriel@sep.stanford.edu SEP120 pages 365-376 24
WB Multiple. No Diffraction. Two Vels
Angle stack ADCIG (x=6280)
gabriel@sep.stanford.edu SEP120 pages 365-376 25
Primary. No Diffraction. One Velocity
Angle stack ADCIG (x=6280)
gabriel@sep.stanford.edu SEP120 pages 365-376 26
Diffracted Multiple Only. Two Velocities
Angle stack ADCIG (x=4600)
gabriel@sep.stanford.edu SEP120 pages 365-376 27
Diffracted Multiple Only. One Velocity
Angle stack ADCIG (x=4600)
gabriel@sep.stanford.edu SEP120 pages 365-376 28
Conclusions
• Water-bottom multiples from a dipping interface
behave kinematically as primaries from an interface
with twice the dip at twice the depth.
gabriel@sep.stanford.edu SEP120 pages 365-376 29
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.
gabriel@sep.stanford.edu SEP120 pages 365-376 29
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.
gabriel@sep.stanford.edu SEP120 pages 365-376 29
Future Work
• Formalize the residual moveout issue for the multiples
in the image space.
gabriel@sep.stanford.edu SEP120 pages 365-376 30
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.
gabriel@sep.stanford.edu SEP120 pages 365-376 30
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.
gabriel@sep.stanford.edu SEP120 pages 365-376 30