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Kinematics of 2D specularly-reflected and diffracted multiples in data space and image space. Gabriel Alvarez. Stanford University. Goal. Understand how specularly-reflected and diffracted 2D multiples map to subsurface image gathers when migrated with wave equation migration. The Problem. - PowerPoint PPT Presentation
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Kinematics of 2D specularly-reflected
and diffracted multiples in data
space and image spaceGabriel Alvarez
Stanford University
2
Goal
Understand how specularly-reflected and diffracted2D multiples map to subsurface image gatherswhen migrated with wave equation migration.
3
The Problem
Moveout-based multiple attenuation algorithms inimage space benefit from the power of migration to handle the complex wave propagation of the primaries.
The question remains: What is the moveout of the multiples in image space?
4
Outline• Moveout of 2D diffracted and specularly-reflected multiples in data space
• Mapping of multiples from CMPs to Subsurface Offset Domain Common Image Gathers (SODCIGs)
• Mapping of multiples from SODCIGs to Angle Domain Common Image Gathers (ADCIGs)
• Discussion and conclusions
5
Surface vs. Subsurface OffsetmD hDhD
2
6
Data Space vs. Image SpaceTi
me
m D
hD
Data Space
CMPsD
epth
m ξhξ
Image Space
SODCIGs
Dep
th
m ξ
Image Space
ADCIGs
7
Moveout of speculary-reflected multiplesFlat water-bottom:
ts1 tr1V
mD hDhD
ZDts2 tr2
ZDts2 tr2
8
Moveout of speculary-reflected multiplesDipping water-bottom:
V
mD hD
φ
hD
2φ
ZD
9
Moveout of Diffracted MultiplesFlat water-bottom:
ts1 tr1V
mD hDhD
ZDts2 tr2
ZDts2 tr2
Xd
10
Moveout of Diffracted MultipleDipping water-bottom:
V
mD hD
φ
2φ
hD
Xd
ZD
αs: takeoff angle of the source ray
11
Moveout Comparison
Dipping water-bottom
12
Moveout of Multiples inSubsurface Offset DomainCommon Image Gathers
(SODCIGs)
13
Image Coordinates of Non-diffracted MultipleFlat water-bottom:
V1
mD hD
αs αr
hD
V2=ρV1 βrβs
hξmξ hξ
212
ρξ Dhh
222 412 DDD ZhZz ρρ
ξ
Dmm ξ
14
SODCIG
Specularly-reflected multiple. Flat water-bottom
Half-subsurface offset (m)0-200-400 400200
Depth (m
)
1000
1200
1400
15
SODCIG
Specularly-reflected multiple. Flat water-bottom
Half-subsurface offset (m)0-200-400 400200
Depth (m
)
1000
1200
1400
16
Image Coordinates of Non-diffracted Multiple
ts1 tr1
V1
mD
αr-φ
αs+φ
αr
φ
V2
βr-φ
βs+φts2~
~tr2
hD hD
mξhξ hξ
rsss sinsin4sinsin2 2211
ββρφααξ rsrsD ttttVhh ~ ~
ss coscos21
βραξ sst ttVz ~
rsss sinsin4sinsin2 2211
ββρφααξ rsrsD ttttVmm ~ ~
17
Constant subsurface-offset section
Specularly-reflected multiple from a dipping water-bottom
Horizontal position (m)160014001200 2000
Depth (m
)
800
1200
1600
1800
18
SODCIG
Specularly-reflected multiple from a dipping water-bottom
Half-subsurface offset (m)0-400-800 800400
Depth (m
)
600
1000
1400
19
Image Coordinates of Diffracted Multiple
rsrs sinsinsinsin2 2211
ααρααξ rsrsD ttttVhh ~ ~
rcos2
βρξ rD VtZz ~
rs2
rs sinsinsinsin2 2211
ααρααξ rsrsD ttttVmm ~ ~
ts1
ts2
tr1
tr2
V1
V2
mD hD
hξ
βr
αs
βs
αr
mξ
Zdiff
Xdiff
hD
~~
hξ
20
Constant subsurface-offset sections
Diffracted multiple from a flat water-bottom
Horizontal position (m)260024002000 3000
Depth (m
)
800
1200
1600
2800Horizontal position (m)
260024002000 3000
Depth (m
)
800
1200
1600
2800
Half-subsurface offset 0 m Half-subsurface offset -200 m
21
SODCIGs
Diffracted multiple from a flat water-bottom
Half-subsurface offset (m)0-400 400
Depth (m
)
1000
1600
1400
1200
Half-subsurface offset (m)0-400 400
Depth (m
)
1000
1600
1400
1200
Half-subsurface offset (m)0-400 400
Depth (m
)1000
1600
1400
1200
22
Image Coordinates of Diffracted Multiple
rsrs sinsinsinsin2 2211
ββρααξ rsrsD ttttVhh ~ ~
ss coscos21
βραξ st ttVz ~
rsrs sinsinsinsin2 2211
ββρααξ rsrsD ttttVmm ~ ~
ts1
tr1
V1
V2
mD
hξ
αr-φ
βr-φ
αs+φ
βs+φ
αr
φ
ts2~
~tr2
mξ
hD
Zdiff
hξ
hD
23
Constant subsurface offset sections
Diffracted multiple from a flat water-bottom
Half-subsurface offset 0 m Half-subsurface offset -200 m
Horizontal position (m)200018001600 2400
Depth (m
)
1200
1400
1800
2200
1600
Horizontal position (m)200018001600 2400
Depth (m
)
1200
1400
1800
2200
1600
24
SODCIGs
Diffracted multiple from a dipping water-bottom
Half-subsurface offset (m)0-800 800
Depth (m
)1000
1800
1400
1200
1600
Half-subsurface offset (m)0-800 800
Depth (m
)
1000
1600
1400
1200
1800
Half-subsurface offset (m)0-800 800
Depth (m
)
1000
1600
1400
1200
1800
25
Moveout of Multiples inAngle-Domain
Common-Image-Gathers(ADCIGs)
26
ADCIG for specularly-reflected multiple
γρ
ργργρ
γ
γ
ξξ 22
222
sin
1tancos11
0zz
ts2tr2
(xrξ,zrξ) (xsξ,zsξ)hξ
βrβs
(xγξ,zγξ)
2γ
mξ
~ ~
hξ
2sr ββ
γ
γξξξ γtanhzz
ξξ γmm
27
ADCIG
Specularly-reflected multiple from a flat water-bottom
Half-aperture angle (degrees)20100 4030
Depth (m
)
1200
1400
1600
28
ADDCIG
Specularly-reflected multiple from a dipping water-bottom
Half-aperture angle (degrees)0-20-40 4020
Depth (m
)
1000
1400
1800
29
ADCIGs
Diffracted multiple from a flat water-bottom
Half-aperture angle (degrees)0-40 40
Depth (m
)
1200
1600
1400
Half-aperture angle (degrees)0-40 40
Depth (m
)
1200
1600
1400
0-40 40D
epth (m)
1200
1600
1400
Half-aperture angle (degrees)
30
ADCIGs
Diffracted multiple from a dipping water-bottom
0-40 40D
epth (m)
1400
2000
1600
Half-aperture angle (degrees)
Half-aperture angle (degrees)0-40 40
Depth (m
)
1400
2000
1600
Half-aperture angle (degrees)0-40 40
Depth (m
)
1400
2000
1600
31
Discussion and Conclusions
32
Discussion
Water-bottom, specularly-reflected multiples, migrated with sediment velocity migrate to negative subsurface offsets.
V
mD hDhD
ZD
ZD
2hξ<0
33
Discussion
On the other hand, primaries, migrated with slower velocitiesmap to positive subsurface offsets.
V
mD hDhD
ZD
ZD2hξ>0
34
Discussion
Diffracted multiples may map to positive subsurfaceoffsets in SODCIGs even if migrated with faster velocities.
V
mD hDhD
ZD
2hξ<0
V
mD hDhD
ZD
ZD
2hξ>0
35
ConclusionsSpecularly-reflected water-bottom multiples migrate as primaries at twice the water depthand with twice the dip.
Diffracted multiples do not migrate like primariesbut their moveout in both SODCIGs and ADCIGs can be computed if the location of thediffractor is known.
36
ConclusionsBetter understanding of the moveout of the multiples in SODCIGs and ADCIGs will help in designing more accurate Radon transforms to attenuate the multiples in image space.
37
Thank you for your attention.
I will be happy to entertain your questions.
38
From SODCIGs to ADCIGs
(xrξ,zrξ) (xsξ,zsξ)
βr
βs
mξhξ
2γ
A C
(mξγ,zξγ)D
BF
Ehξ
2sr ββ
γ
γξξξ γtanhzz
ξξ γmm