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Selective stacking in the reflection-
angle and azimuth domain
Yaxun Tang
SEP-129, p157
[email protected] SEP-129 2
Sub-salt zero-offset image
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Angle-domain selective stack
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• Wave-equation ADCIGs
• Artifacts in the angle gathers
• SEG/EAGE salt model
Outline
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• ADCIGs before imaging condition Step 1: Decompose source and receiver wavefield into
local plane-waves
Step 2: Local plane-wave imaging for each opening angle
• ADCIGs after imaging condition Step 1: Compute subsurface-offset domain common-image
gathers (SODCIGs)
Step 2: Transform the SODCIGs into ADCIGs
ADCIGs for shot-profile migration
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• ADCIGs before imaging condition Step 1: Decompose source and receiver wavefield into
local plane-waves
Step 2: Local plane-wave imaging for each opening angle
• ADCIGs after imaging condition Step 1: Compute subsurface-offset domain common-image
gathers (SODCIGs)
Step 2: Transform the SODCIGs into ADCIGs
ADCIGs for shot-profile migration
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Downward continuation
Downward continue source wavefield Downward continue receiver wavefield
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Downward continuation
Downward continue source wavefield Downward continue receiver wavefield
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Downward continuation
Downward continue source wavefield Downward continue receiver wavefield
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Multi-offset imaging
Downward continue source wavefield Downward continue receiver wavefield
Multi-offset imaging condition
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Extracting ADCIGs in 2-D
tanx
h
z x
k z
k h= =
: opening angle
: dip angleSava and Fomel (2003)
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3-D Common-azimuth extension
tan cosx
h
z
k
k=
tanym
z
k
k=
: opening angle
: crossline dip angleTisserant and Biondi (2003)
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3-D full prestack extension
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3-D full prestack extension
: opening angle
: reflection azimuth
2
1tan
1 sin cosyx
zmm
z z
k kk
k k
=
+ +
hk
Tisserant and Biondi (2003)
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• Wave-equation ADCIGs
• Artifacts in the angle gathers
• SEG/EAGE salt model
Outline
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A simple example
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Migrated images
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Migrated images
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A space and time domain perspective
Source wavefront
Receiver wavefront
Well sampled
receiver wavefield
Locally constant media
( ) [ ]
[ ] [ ] [ ]
22 2
2 2 2
( ) sin( )
cos( 2 ) sin( 2 ) ( ) sin( )
m
m
x h s z x s
x h s z s x s
+ = +
+ + = +
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A space and time domain perspective
Source wavefront
Receiver wavefront
Well sampled
receiver wavefield
Locally constant media
( ) [ ]
[ ] [ ] [ ]
22 2
2 2 2
( ) sin( )
cos( 2 ) sin( 2 ) ( ) sin( )
m
m
x h s z x s
x h s z s x s
+ = +
+ + = +
tan tanx
z x h=
Linear
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A space and time domain perspective
Source wavefront
Receiver wavefront
Poorly sampled
receiver wavefield
Locally constant media
[ ]
[ ]
22 2
22 2
( ) ( ) sin( )
( ) ( ) sin( )
m
m
x h s z x s
x h r z x r
+ = +
+ + =
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A space and time domain perspective
Source wavefront
Receiver wavefront
Poorly sampled
receiver wavefield
Locally constant media
[ ]
[ ]
22 2
22 2
( ) ( ) sin( )
( ) ( ) sin( )
m
m
x h s z x s
x h r z x r
+ = +
+ + =
[ ]22 2 2( ) ( ) tan( ) tan( )
x xz h r s h r s= + + + +
Non-linear
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• Wave-equation ADCIGs
• Artifacts in the angle gathers
• SEG/EAGE salt model
Outline
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Azimuth vs. offset
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Migrated image
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Angular images
Angle=0 Azimuth=0 Angle=25 Azimuth=30 Angle=55 Azimuth=60
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Model-space weighting function
Half length of
moving window
Determines the shape
of window
Envelope of the ADCIG for a CMP location
The weighting function
1( , , ) ( ) ( , , )
2 1
L
j L
W z s j E z j z j jL =
= + + ++
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Suppressing the artifacts
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Suppressing the artifacts
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Sub-salt zero-offset image
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Angle stacking without weighting function
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Angle stacking with weighting function
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• ADCIGs are prone to illumination and
sampling related artifacts
• Even with wide-azimuth data
• Artifacts are identifiable in the ADCIGs
• Model-space weighting function can
attenuate them effectively
• Selective stacking results in better image
with higher S/N
Conclusions
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• Signal processing based
• If artifacts are strong, it may not work well
• Better model-space weighting function
needed
Problems with current method
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• Hessian can be a measure of subsurface
illumination (Valenciano and Biondi, 2004)
• Angle-domain Hessian can give a range of
angle and azimuth that are well illuminated
• So is angle-domain Hessian the answer?
Future work
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Thanks