gabriel alvarez sep120 pages: 365-376 email:gabriel@sep ...sepmultiples in image space gabriel...
TRANSCRIPT
![Page 1: Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep ...sepMultiples in Image Space Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep.stanford.edu gabriel@sep.stanford.edu](https://reader034.vdocuments.net/reader034/viewer/2022051807/6006110d3f84e9298f7c7b15/html5/thumbnails/1.jpg)
Multiples in Image Space
Gabriel Alvarez
SEP120 pages: 365-376
Email:[email protected]
[email protected] SEP120 pages 365-376
![Page 3: Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep ...sepMultiples in Image Space Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep.stanford.edu gabriel@sep.stanford.edu](https://reader034.vdocuments.net/reader034/viewer/2022051807/6006110d3f84e9298f7c7b15/html5/thumbnails/3.jpg)
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.
[email protected] SEP120 pages 365-376 2
![Page 4: Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep ...sepMultiples in Image Space Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep.stanford.edu gabriel@sep.stanford.edu](https://reader034.vdocuments.net/reader034/viewer/2022051807/6006110d3f84e9298f7c7b15/html5/thumbnails/4.jpg)
Aproximations of RMO Equation
This equations has several approximations:
[email protected] SEP120 pages 365-376 3
![Page 5: Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep ...sepMultiples in Image Space Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep.stanford.edu gabriel@sep.stanford.edu](https://reader034.vdocuments.net/reader034/viewer/2022051807/6006110d3f84e9298f7c7b15/html5/thumbnails/5.jpg)
Aproximations of RMO Equation
This equations has several approximations:
• Flat reflectors
[email protected] SEP120 pages 365-376 3
![Page 6: Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep ...sepMultiples in Image Space Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep.stanford.edu gabriel@sep.stanford.edu](https://reader034.vdocuments.net/reader034/viewer/2022051807/6006110d3f84e9298f7c7b15/html5/thumbnails/6.jpg)
Aproximations of RMO Equation
This equations has several approximations:
• Flat reflectors
• Rays are stationary: apparent angles taken as equal to
true angles.
[email protected] SEP120 pages 365-376 3
![Page 7: Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep ...sepMultiples in Image Space Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep.stanford.edu gabriel@sep.stanford.edu](https://reader034.vdocuments.net/reader034/viewer/2022051807/6006110d3f84e9298f7c7b15/html5/thumbnails/7.jpg)
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.
[email protected] SEP120 pages 365-376 3
![Page 8: Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep ...sepMultiples in Image Space Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep.stanford.edu gabriel@sep.stanford.edu](https://reader034.vdocuments.net/reader034/viewer/2022051807/6006110d3f84e9298f7c7b15/html5/thumbnails/8.jpg)
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.
[email protected] SEP120 pages 365-376 4
![Page 9: Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep ...sepMultiples in Image Space Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep.stanford.edu gabriel@sep.stanford.edu](https://reader034.vdocuments.net/reader034/viewer/2022051807/6006110d3f84e9298f7c7b15/html5/thumbnails/9.jpg)
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?
[email protected] SEP120 pages 365-376 4
![Page 10: Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep ...sepMultiples in Image Space Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep.stanford.edu gabriel@sep.stanford.edu](https://reader034.vdocuments.net/reader034/viewer/2022051807/6006110d3f84e9298f7c7b15/html5/thumbnails/10.jpg)
Motivation
• Understand the residual moveout of multiples in image
space when migrated with the velocity of the primaries.
[email protected] SEP120 pages 365-376 5
![Page 11: Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep ...sepMultiples in Image Space Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep.stanford.edu gabriel@sep.stanford.edu](https://reader034.vdocuments.net/reader034/viewer/2022051807/6006110d3f84e9298f7c7b15/html5/thumbnails/11.jpg)
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.
[email protected] SEP120 pages 365-376 5
![Page 12: Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep ...sepMultiples in Image Space Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep.stanford.edu gabriel@sep.stanford.edu](https://reader034.vdocuments.net/reader034/viewer/2022051807/6006110d3f84e9298f7c7b15/html5/thumbnails/12.jpg)
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
[email protected] SEP120 pages 365-376 6
![Page 13: Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep ...sepMultiples in Image Space Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep.stanford.edu gabriel@sep.stanford.edu](https://reader034.vdocuments.net/reader034/viewer/2022051807/6006110d3f84e9298f7c7b15/html5/thumbnails/13.jpg)
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)
[email protected] SEP120 pages 365-376 7
![Page 14: Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep ...sepMultiples in Image Space Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep.stanford.edu gabriel@sep.stanford.edu](https://reader034.vdocuments.net/reader034/viewer/2022051807/6006110d3f84e9298f7c7b15/html5/thumbnails/14.jpg)
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
[email protected] SEP120 pages 365-376 8
![Page 15: Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep ...sepMultiples in Image Space Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep.stanford.edu gabriel@sep.stanford.edu](https://reader034.vdocuments.net/reader034/viewer/2022051807/6006110d3f84e9298f7c7b15/html5/thumbnails/15.jpg)
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
[email protected] SEP120 pages 365-376 9
![Page 16: Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep ...sepMultiples in Image Space Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep.stanford.edu gabriel@sep.stanford.edu](https://reader034.vdocuments.net/reader034/viewer/2022051807/6006110d3f84e9298f7c7b15/html5/thumbnails/16.jpg)
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
[email protected] SEP120 pages 365-376 10
![Page 17: Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep ...sepMultiples in Image Space Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep.stanford.edu gabriel@sep.stanford.edu](https://reader034.vdocuments.net/reader034/viewer/2022051807/6006110d3f84e9298f7c7b15/html5/thumbnails/17.jpg)
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
[email protected] SEP120 pages 365-376 11
![Page 18: Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep ...sepMultiples in Image Space Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep.stanford.edu gabriel@sep.stanford.edu](https://reader034.vdocuments.net/reader034/viewer/2022051807/6006110d3f84e9298f7c7b15/html5/thumbnails/18.jpg)
Primary. Two Velocities
Zero subsurface-offset section SOCIG (x=6280)
[email protected] SEP120 pages 365-376 12
![Page 19: Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep ...sepMultiples in Image Space Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep.stanford.edu gabriel@sep.stanford.edu](https://reader034.vdocuments.net/reader034/viewer/2022051807/6006110d3f84e9298f7c7b15/html5/thumbnails/19.jpg)
Diffraction. Two Velocities
Zero subsurface-offset section SOCIG (x=5800)
[email protected] SEP120 pages 365-376 13
![Page 20: Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep ...sepMultiples in Image Space Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep.stanford.edu gabriel@sep.stanford.edu](https://reader034.vdocuments.net/reader034/viewer/2022051807/6006110d3f84e9298f7c7b15/html5/thumbnails/20.jpg)
Diffracted Multiple. Two Velocities
Zero subsurface-offset section SOCIG (x=4600)
[email protected] SEP120 pages 365-376 14
![Page 21: Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep ...sepMultiples in Image Space Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep.stanford.edu gabriel@sep.stanford.edu](https://reader034.vdocuments.net/reader034/viewer/2022051807/6006110d3f84e9298f7c7b15/html5/thumbnails/21.jpg)
WB Multiple. Two Velocities
Zero subsurface-offset section SOCIG (x=3600)
[email protected] SEP120 pages 365-376 15
![Page 28: Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep ...sepMultiples in Image Space Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep.stanford.edu gabriel@sep.stanford.edu](https://reader034.vdocuments.net/reader034/viewer/2022051807/6006110d3f84e9298f7c7b15/html5/thumbnails/28.jpg)
Diffracted Multiple. One Velocity
Angle stack ADCIG (x=4600)
[email protected] SEP120 pages 365-376 22
![Page 30: Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep ...sepMultiples in Image Space Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep.stanford.edu gabriel@sep.stanford.edu](https://reader034.vdocuments.net/reader034/viewer/2022051807/6006110d3f84e9298f7c7b15/html5/thumbnails/30.jpg)
Primary. No Diffraction. Two Velocities
Angle stack ADCIG (x=6280)
[email protected] SEP120 pages 365-376 24
![Page 31: Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep ...sepMultiples in Image Space Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep.stanford.edu gabriel@sep.stanford.edu](https://reader034.vdocuments.net/reader034/viewer/2022051807/6006110d3f84e9298f7c7b15/html5/thumbnails/31.jpg)
WB Multiple. No Diffraction. Two Vels
Angle stack ADCIG (x=6280)
[email protected] SEP120 pages 365-376 25
![Page 32: Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep ...sepMultiples in Image Space Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep.stanford.edu gabriel@sep.stanford.edu](https://reader034.vdocuments.net/reader034/viewer/2022051807/6006110d3f84e9298f7c7b15/html5/thumbnails/32.jpg)
Primary. No Diffraction. One Velocity
Angle stack ADCIG (x=6280)
[email protected] SEP120 pages 365-376 26
![Page 33: Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep ...sepMultiples in Image Space Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep.stanford.edu gabriel@sep.stanford.edu](https://reader034.vdocuments.net/reader034/viewer/2022051807/6006110d3f84e9298f7c7b15/html5/thumbnails/33.jpg)
Diffracted Multiple Only. Two Velocities
Angle stack ADCIG (x=4600)
[email protected] SEP120 pages 365-376 27
![Page 34: Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep ...sepMultiples in Image Space Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep.stanford.edu gabriel@sep.stanford.edu](https://reader034.vdocuments.net/reader034/viewer/2022051807/6006110d3f84e9298f7c7b15/html5/thumbnails/34.jpg)
Diffracted Multiple Only. One Velocity
Angle stack ADCIG (x=4600)
[email protected] SEP120 pages 365-376 28
![Page 35: Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep ...sepMultiples in Image Space Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep.stanford.edu gabriel@sep.stanford.edu](https://reader034.vdocuments.net/reader034/viewer/2022051807/6006110d3f84e9298f7c7b15/html5/thumbnails/35.jpg)
Conclusions
• Water-bottom multiples from a dipping interface
behave kinematically as primaries from an interface
with twice the dip at twice the depth.
[email protected] SEP120 pages 365-376 29
![Page 36: Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep ...sepMultiples in Image Space Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep.stanford.edu gabriel@sep.stanford.edu](https://reader034.vdocuments.net/reader034/viewer/2022051807/6006110d3f84e9298f7c7b15/html5/thumbnails/36.jpg)
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.
[email protected] SEP120 pages 365-376 29
![Page 37: Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep ...sepMultiples in Image Space Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep.stanford.edu gabriel@sep.stanford.edu](https://reader034.vdocuments.net/reader034/viewer/2022051807/6006110d3f84e9298f7c7b15/html5/thumbnails/37.jpg)
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.
[email protected] SEP120 pages 365-376 29
![Page 38: Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep ...sepMultiples in Image Space Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep.stanford.edu gabriel@sep.stanford.edu](https://reader034.vdocuments.net/reader034/viewer/2022051807/6006110d3f84e9298f7c7b15/html5/thumbnails/38.jpg)
Future Work
• Formalize the residual moveout issue for the multiples
in the image space.
[email protected] SEP120 pages 365-376 30
![Page 39: Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep ...sepMultiples in Image Space Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep.stanford.edu gabriel@sep.stanford.edu](https://reader034.vdocuments.net/reader034/viewer/2022051807/6006110d3f84e9298f7c7b15/html5/thumbnails/39.jpg)
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.
[email protected] SEP120 pages 365-376 30
![Page 40: Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep ...sepMultiples in Image Space Gabriel Alvarez SEP120 pages: 365-376 Email:gabriel@sep.stanford.edu gabriel@sep.stanford.edu](https://reader034.vdocuments.net/reader034/viewer/2022051807/6006110d3f84e9298f7c7b15/html5/thumbnails/40.jpg)
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.
[email protected] SEP120 pages 365-376 30