1 fast 3d target-oriented reverse time datuming shuqian dong university of utah 2 oct. 2008
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1
Fast 3D Target-Oriented Reverse Time Datuming
Shuqian Dong
University of Utah2 Oct. 2008
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2
OutlineOutline
• MotivationMotivation
• TheoryTheory
• ConclusionsConclusions
• Numerical TestsNumerical Tests 2-D SEG/EAGE salt model2-D SEG/EAGE salt model
3-D SEG/EAGE salt model3-D SEG/EAGE salt model
3-D field data3-D field data
Motivation Theory Numerical Tests Conclusions
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3
OutlineOutline
• MotivationMotivation
• TheoryTheory
• ConclusionsConclusions
• Numerical TestsNumerical Tests 2-D SEG/EAGE salt model2-D SEG/EAGE salt model
3-D SEG/EAGE salt model3-D SEG/EAGE salt model
3-D field data3-D field data
Motivation Theory Numerical Tests Conclusions
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4Motivation Theory Numerical Tests Conclusions
z (k
m)
z (k
m)
00
2.02.0
KM image
x (km)x (km)00 8.08.0
Tim
e (s
)T
ime
(s)
00
4.04.0
Common shot gather
x (km)x (km)00 8.08.0
MotivationMotivationz
(km
)z
(km
)
00
2.02.0
Velocity model
x (km)x (km)00 8.08.0
km/s
4.54.5
1.51.5
Defocusing: lower resolution, distorted image
Multiples: image artifacts.
Problem:
KM: high frequency approximation.
Reason:
Solutions?
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5
Solutions:Solutions:
MotivationMotivation
• Reverse time migration: solving two-way wave equationReverse time migration: solving two-way wave equation
Velocity modelKM image RTM image
• Target-oriented reverse time datuming:Target-oriented reverse time datuming: solving two-way wave equation to bypass overburdensolving two-way wave equation to bypass overburden
Luo, 2002: target-oriented RTDLuo, 2002: target-oriented RTDLuo and Schuster, 2004: bottom-up strategyLuo and Schuster, 2004: bottom-up strategy
Motivation Theory Numerical Tests Conclusions
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MotivationMotivation
Motivation Theory Numerical Tests Conclusions
• RTD + Kirchhoff = accurate + cheap RTD + Kirchhoff = accurate + cheap
• RTD can reduce defocusing effectsRTD can reduce defocusing effects
RTDRTD
• Complex structures cause defocusing effectsComplex structures cause defocusing effects
• RTM is computationally expensiveRTM is computationally expensive
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• Bottom-up strategy: computational efficiency Bottom-up strategy: computational efficiency
• Redatumed data can be used for least squares Redatumed data can be used for least squares migration and migration velocity analysis (MVA)migration and migration velocity analysis (MVA)
• Reduce defocusing effects for subsalt imagingReduce defocusing effects for subsalt imaging
• Closer to the target: better resolutionCloser to the target: better resolution
Motivation Theory Numerical Tests Conclusions
MotivationMotivation
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8
OutlineOutline
• MotivationMotivation
• TheoryTheory
• ConclusionsConclusions
• Numerical TestsNumerical Tests 2-D SEG/EAGE salt model2-D SEG/EAGE salt model
3-D SEG/EAGE salt model3-D SEG/EAGE salt model
3-D field data3-D field data
Motivation Theory Numerical Tests Conclusions
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d(s|r)d(s|r)
RRSS
x’x’ x’’x’’
Reverse time datumingReverse time datuming
TheoryTheory
Motivation Theory Numerical Tests Conclusions
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10
SS
x’x’ x’’x’’
d(s|x”)=d(s|x”)= g*(r|x”)g*(r|x”) d(s|r)d(s|r)d(s|x’’)d(s|x’’)
Reverse time datumingReverse time datuming
RR
TheoryTheory
Motivation Theory Numerical Tests Conclusions
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11
x’x’ x’’x’’
d(s|x”)=d(s|x”)= g*(r|x”)g*(r|x”) d(s|r)d(s|r)d(x’|x’’)d(x’|x’’)
d(x’|x”)=g*(s|x’) d(s|x”)d(x’|x”)=g*(s|x’) d(s|x”)
Reverse time datumingReverse time datuming
RRSS
TheoryTheory
Motivation Theory Numerical Tests Conclusions
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TheoryTheory
Motivation Theory Numerical Tests Conclusions
Calculate Green’s functionsCalculate Green’s functions
Real source number Real source number on surface: 10on surface: 10
Virtual source number Virtual source number on datum: 3on datum: 3
VSP (source on surface) VSP (source on surface) Green’s functions: 10Green’s functions: 10
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Calculate Green’s functionsCalculate Green’s functions
TheoryTheory
Motivation Theory Numerical Tests Conclusions
Real source number Real source number on surface: 10on surface: 10
Virtual source number Virtual source number on datum: 3on datum: 3
VSP (source on surface) VSP (source on surface) Green’s functions: 10Green’s functions: 10
RVSP (source on datum) RVSP (source on datum) Green’s functions: 3Green’s functions: 3
Reciprocity: RVSP=VSPReciprocity: RVSP=VSP
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FD: Compute RVSP Green’s functions
Original data: FFT: time domain =>frequency domain
Crosscorrelation: Green’s functions with original data
WorkflowWorkflow
Motivation Theory Numerical Tests Conclusions
Reciprocity: RVSP =>VSP
Green’s functions: FFT: time domain => frequency domain
IFFT: frequency domain => time domain
Redatumed data
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15
OutlineOutline
• MotivationMotivation
• TheoryTheory
• ConclusionsConclusions
• Numerical TestsNumerical Tests 2-D SEG/EAGE salt model2-D SEG/EAGE salt model
3-D SEG/EAGE salt model3-D SEG/EAGE salt model
3-D field data3-D field data
Motivation Theory Numerical Tests Conclusions
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16Motivation Theory Numerical Tests Conclusions
z (k
m)
z (k
m)
00
2.02.0
Velocity model
x (km)x (km)00 8.08.0
km/s
4.54.5
1.51.5
Tim
e (s
)T
ime
(s)
00
4.04.0
RVSP Green’s function
x (km)x (km)00 8.08.0
2D SEG/EAGE Test2D SEG/EAGE Test
Tim
e (s
)T
ime
(s)
00
4.04.0
True CSG at datum
x (km)x (km)00 8.08.0
Tim
e (s
)T
ime
(s)
00
4.04.0
Redatumed CSG
x (km)x (km)00 8.08.0
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z (k
m)
z (k
m)
00
2.02.0
Velocity model
x (km)x (km)00 8.08.0
km/s
4.54.5
1.51.5
z (k
m)
z (k
m)
00
2.02.0
KM image
x (km)x (km)00 8.08.0
z (k
m)
z (k
m)
00
2.02.0
RTM image
x (km)x (km)00 8.08.0
z (k
m)
z (k
m)
00
2.02.0
KM of redatumed data
x (km)x (km)00 8.08.0
Motivation Theory Numerical Tests Conclusions
2D SEG/EAGE Test2D SEG/EAGE Test
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18
OutlineOutline
• MotivationMotivation
• TheoryTheory
• ConclusionsConclusions
• Numerical TestsNumerical Tests 2-D SEG/EAGE salt model2-D SEG/EAGE salt model
3-D SEG/EAGE salt model3-D SEG/EAGE salt model
3-D field data3-D field data
Motivation Theory Numerical Tests Conclusions
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3D SEG/EAGE test3D SEG/EAGE test Z
(km
)Z
(km
)
00
2.02.0
y (km)y (km)
22
00
x (km)x (km)
3.53.5
00
km/s
4.54.5
1.51.5
Velocity model
SSP geometry:
1700 shots
1700 receivers
Datum depth:
1.5 km
RVSP Green’s functions:
850 shots
1700 receivers
Motivation Theory Numerical Tests Conclusions
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3D SEG/EAGE test3D SEG/EAGE test
y (km)y (km)00 3.53.5
Tim
e (s
)T
ime
(s)
00
2.52.5
Original CSG
Motivation Theory Numerical Tests Conclusions
y (km)y (km)00 3.53.5
Tim
e (s
)T
ime
(s)
00
2.52.5
RVSP Green’s function
y (km)y (km)00 3.53.5
Tim
e (s
)T
ime
(s)
00
2.52.5
True CSG at datum
y (km)y (km)00 3.53.5
Tim
e (s
)T
ime
(s)
00
2.52.5
Redatumed CSG
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Z (
km)
Z (
km)00
2.02.0
y (km)y (km)
22
00
x (km)x (km) 3.53.5
00
KM of original data
3D SEG/EAGE test3D SEG/EAGE test
Z (
km)
Z (
km)
00
2.02.0
y (km)y (km)
22
00
x (km)x (km) 3.53.5
00
KM of RTD data
Motivation Theory Numerical Tests Conclusions
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22x (km)x (km)00 3.53.5
z (k
m)
z (k
m)
00
2.02.0
Velocity modelx (km)x (km)00 3.53.5
z (k
m)
z (k
m)
00
2.02.0
KM of original data
x (km)x (km)00 3.53.5
z (k
m)
z (k
m)
00
2.02.0
KM of redatumed data
( Inline No. 41 )( Inline No. 41 )
Motivation Theory Numerical Tests Conclusions
3D SEG/EAGE test3D SEG/EAGE test
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23x (km)x (km)00 3.53.5
z (k
m)
z (k
m)
00
2.02.0
Velocity modelx (km)x (km)00 3.53.5
z (k
m)
z (k
m)
00
2.02.0
KM of original data
x (km)x (km)00 3.53.5
z (k
m)
z (k
m)
00
2.02.0
KM of redatumed data
( Inline No. 101 )( Inline No. 101 )
Motivation Theory Numerical Tests Conclusions
3D SEG/EAGE test3D SEG/EAGE test
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24y (km)y (km)00 2.02.0
z (k
m)
z (k
m)
00
2.02.0
Velocity modely (km)y (km)00 2.02.0
z (k
m)
z (k
m)
00
2.02.0
KM of original data
y (km)y (km)00 2.02.0
z (k
m)
z (k
m)
00
2.02.0
KM of redatumed data
( Crossline No. 161 )( Crossline No. 161 )
Motivation Theory Numerical Tests Conclusions
3D SEG/EAGE test3D SEG/EAGE test
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25y (km)y (km)00 2.02.0
z (k
m)
z (k
m)
00
2.02.0
Velocity modely (km)y (km)00 2.02.0
z (k
m)
z (k
m)
00
2.02.0
KM of original data
y (km)y (km)00 2.02.0
z (k
m)
z (k
m)
00
2.02.0
KM of redatumed data
( Crossline No. 201 )( Crossline No. 201 )
Motivation Theory Numerical Tests Conclusions
3D SEG/EAGE test3D SEG/EAGE test
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26x (km)x (km)00 3.53.5
y (k
m)
y (k
m)
00
2.02.0
Velocity modelx (km)x (km)00 3.53.5
y (k
m)
y (k
m)
00
2.02.0
KM of original data
x (km)x (km)00 3.53.5
y (k
m)
y (k
m)
00
2.02.0
KM of redatumed data
( depth: z=1.4 km )( depth: z=1.4 km )
Motivation Theory Numerical Tests Conclusions
3D SEG/EAGE test3D SEG/EAGE test
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27x (km)x (km)00 3.53.5
y (k
m)
y (k
m)
00
2.02.0
Velocity modelx (km)x (km)00 3.53.5
y (k
m)
y (k
m)
00
2.02.0
KM of original data
x (km)x (km)00 3.53.5
y (k
m)
y (k
m)
00
2.02.0
KM of redatumed data
( depth: z=1.5 km )( depth: z=1.5 km )
Motivation Theory Numerical Tests Conclusions
3D SEG/EAGE test3D SEG/EAGE test
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OutlineOutline
• MotivationMotivation
• TheoryTheory
• ConclusionsConclusions
• Numerical TestsNumerical Tests 2-D SEG/EAGE salt model2-D SEG/EAGE salt model
3-D SEG/EAGE salt model3-D SEG/EAGE salt model
3-D field data3-D field data
Motivation Theory Numerical Tests Conclusions
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Z (
km)
Z (
km)
00
8.08.0
y (km)y (km)
6.06.0
00
x (km)x (km)
1212
00
Interval velocity model
3D Field Data Test3D Field Data Test
OBC geometry:
50,000 shots
180 receivers per shot
Datum depth:
1.5 km
RVSP Green’s functions:
5,000 shots
180 receivers per shot
km/s5.55.5
1.51.5
Motivation Theory Numerical Tests Conclusions
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3D Field Data Test3D Field Data Test
y (km)y (km)00 4.54.5
Tim
e (s
)T
ime
(s)
00
6.06.0
Original CSG
y (km)y (km)00 4.54.5
Tim
e (s
)T
ime
(s)
00
6.06.0
Redatumed CSG
Motivation Theory Numerical Tests Conclusions
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KM of RTD data
Z (
km)
Z (
km)00
88
y (km)y (km)
55
00
x (km)x (km) 1212
00
KM of original data
Z (
km)
Z (
km)
00
88
y (km)y (km)
55
00
x (km)x (km) 1212
00
KM of redatumed data
Motivation Theory Numerical Tests Conclusions
3D Field Data Test3D Field Data Test
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X (km)X (km)00 1212
Z (
km)
Z (
km)
00
8.08.0
KM of original data KM of RTD data
( Inline No. 21 )( Inline No. 21 )
X (km)X (km)00 1212
Z (
km)
Z (
km)
00
8.08.0
Motivation Theory Numerical Tests Conclusions
3D Field Data Test3D Field Data Test
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( Inline No. 41 )( Inline No. 41 )
X (km)X (km)00 1212
Z (
km)
Z (
km)
00
8.08.0
KM of RTD data
X (km)X (km)00 1212
Z (
km)
Z (
km)
00
8.08.0
Motivation Theory Numerical Tests Conclusions
3D Field Data Test3D Field Data Test
KM of original data
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( Inline No. 61 )( Inline No. 61 )
X (km)X (km)00 1212
Z (
km)
Z (
km)
00
8.08.0
KM of RTD data
X (km)X (km)00 1212
Z (
km)
Z (
km)
00
8.08.0
Motivation Theory Numerical Tests Conclusions
3D Field Data Test3D Field Data Test
KM of original data
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( Crossline No. 41 )( Crossline No. 41 )
Y (km)Y (km)00 5.05.0
Z (
km)
Z (
km)
00
8.08.0
KM of RTD data
Y (km)Y (km)00 5.05.0
Z (
km)
Z (
km)
00
8.08.0
Motivation Theory Numerical Tests Conclusions
3D Field Data Test3D Field Data Test
KM of original data
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( Crossline No. 61 )( Crossline No. 61 )
Y (km)Y (km)00 5.05.0
Z (
km)
Z (
km)
00
8.08.0
KM of RTD data
Y (km)Y (km)00 5.05.0
Z (
km)
Z (
km)
00
8.08.0
Motivation Theory Numerical Tests Conclusions
3D Field Data Test3D Field Data Test
KM of original data
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( Crossline No. 81 )( Crossline No. 81 )
Y (km)Y (km)00 5.05.0
Z (
km)
Z (
km)
00
8.08.0
KM of RTD data
Y (km)Y (km)00 5.05.0
Z (
km)
Z (
km)
00
8.08.0
Motivation Theory Numerical Tests Conclusions
3D Field Data Test3D Field Data Test
KM of original data
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( Depth 2.0 km )( Depth 2.0 km )
X (km)X (km)00 1212
Y (
km)
Y (
km)
00
5.05.0
KM of RTD data
X (km)X (km)00 1212
Y (
km)
Y (
km)
00
5.05.0
Motivation Theory Numerical Tests Conclusions
3D Field Data Test3D Field Data Test
KM of original data
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( Depth 2.5 km )( Depth 2.5 km )
X (km)X (km)00 1212
Y (
km)
Y (
km)
00
5.05.0
KM of RTD data
X (km)X (km)00 1212
Y (
km)
Y (
km)
00
5.05.0
Motivation Theory Numerical Tests Conclusions
3D Field Data Test3D Field Data Test
KM of original data
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( Depth 4.0 km )( Depth 4.0 km )
X (km)X (km)00 1212
Y (
km)
Y (
km)
00
5.05.0
KM of RTD data
X (km)X (km)00 1212
Y (
km)
Y (
km)
00
5.05.0
Motivation Theory Numerical Tests Conclusions
3D Field Data Test3D Field Data Test
KM of original data
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RTM
(CPU-hours)
RTD
(CPU-hours)
Speed up
2D SEG/EAGE test
21.0 6.5 3
3D SEG/EAGE test
16,000
(estimated)1,866 9
3D filed data test5,000,000
(estimated)52,000 100
Computational CostsComputational Costs
Motivation Theory Numerical Tests Conclusions
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OutlineOutline
• MotivationMotivation
• TheoryTheory
• ConclusionsConclusions
• Numerical TestsNumerical Tests 2-D SEG/EAGE salt model2-D SEG/EAGE salt model
3-D SEG/EAGE salt model3-D SEG/EAGE salt model
3-D field data3-D field data
Motivation Theory Numerical Tests Conclusions
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KM of RTD achieved image quality comparable to RTM KM of RTD achieved image quality comparable to RTM
at much lower cost.at much lower cost.
Motivation Theory Numerical Tests Conclusions
• 2-D numerical test2-D numerical test
3-D RTD is implemented for synthetic and GOM data at 3-D RTD is implemented for synthetic and GOM data at acceptable computational cost;acceptable computational cost;
• 3-D numerical test3-D numerical test
Apparent improvements in mage quality are achieved Apparent improvements in mage quality are achieved compared to KM image of original data.compared to KM image of original data.
• Future applicationFuture application
Subsalt least suqares migration and migration velocity Subsalt least suqares migration and migration velocity analysisanalysis
ConclusionsConclusions
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AcknowledgementsAcknowledgements• Dr. Gerard Schuster and my committee members:
Dr. Michael Zhdanov, Dr. Richard D. Jarrard for their advice and constructive criticism;
• UTAM friends:– Dr. Xiang Xiao, Weiping Cao, and Chaiwoot Boonyasiriwat
for their help on my thesis research;
– Ge Zhang for his experiences on field data processing;
– Dr. Sherif Hanafy, Shengdong Liu, Naoshi Aoki and all other UTAM members for their support in my life and work;
• CHPC for the computation support.
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Thanks!Thanks!
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46Motivation Theory Numerical Tests Conclusions
z (k
m)
z (k
m)
00
2.02.0
Velocity model
x (km)x (km)00 8.08.0
km/s
4.54.5
1.51.5
z (k
m)
z (k
m)
00
2.02.0
KM image
x (km)x (km)00 8.08.0
Tim
e (s
)T
ime
(s)
00
4.04.0
Common shot gather
x (km)x (km)00 8.08.0
MotivationMotivation
z (k
m)
z (k
m)
00
2.02.0
RTM image
x (km)x (km)00 8.08.0
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d(s|r)d(s|r)
RRSS
x’x’ x’’x’’
Traditional reverse time datumingTraditional reverse time datuming
TheoryTheory
Motivation Theory Numerical Tests Conclusions
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SS
x’x’ x’’x’’
d(s|x”)=d(s|x”)= g*(r|x”)g*(r|x”) d(s|r)d(s|r)d(s|x’’)d(s|x’’)
Reverse time DatumingReverse time Datuming
RR
TheoryTheory
Motivation Theory Numerical Tests Conclusions
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x’x’ x’’x’’
d(s|x”)=d(s|x”)= g*(r|x”)g*(r|x”) d(s|r)d(s|r)d(x’|x’’)d(x’|x’’)
d(x’|x”)=g*(s|x’) d(s|x”)d(x’|x”)=g*(s|x’) d(s|x”)
Reverse time DatumingReverse time Datuming
RRSS
TheoryTheory
Motivation Theory Numerical Tests Conclusions
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Target-oriented RTDTarget-oriented RTD(Luo , 2006)(Luo , 2006)
TheoryTheory
Motivation Theory Numerical Tests Conclusions
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Target-oriented RTDTarget-oriented RTD(Luo , 2006)(Luo , 2006)
g(s|x’)g(s|x’) g(r|x”)g(r|x”)** d(s|r)d(s|r)
= d(x’|x’’)= d(x’|x’’)
TheoryTheory
Motivation Theory Numerical Tests Conclusions
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Target-oriented RTDTarget-oriented RTD(Luo , 2006)(Luo , 2006)
TheoryTheory
Motivation Theory Numerical Tests Conclusions
g(s|x’)g(s|x’) g(r|x")g(r|x")** d(s|r)d(s|r)
= d(x’|x’’)= d(x’|x’’)
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Compute VSP Green’s functions in time domain
Original data: time domain to frequency domain
Green’s functions: Time domain to frequency domain
Reverse time datum for different frequency
WorkflowWorkflow
Sum over frequency
Redatumed data: frequency domain to time domain
Motivation Theory Numerical Tests Conclusions
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FD: Compute RVSP Green’s functions
Original data: FFT: time domain =>frequency domain
Crosscorrelation: Green’s functions with original data
WorkflowWorkflow
Motivation Theory Numerical Tests Conclusions
Reciprocity: RVSP =>VSP
Green’s functions: FFT: time domain => frequency domain
Sum over frequency
IFFT: frequency domain => time domain
Redatumed data
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ConclusionsConclusions
• Bottom-up strategy: computational efficiency Bottom-up strategy: computational efficiency
• Redatumed data can be used by LSM & MVARedatumed data can be used by LSM & MVA
• Reduce defocusing effects for subsalt imagingReduce defocusing effects for subsalt imaging
• Closer to the target: better resolutionCloser to the target: better resolution
Benefits:Benefits:
Limitations:Limitations:
•Extra I/O for accessing Green’s functionsExtra I/O for accessing Green’s functions
Motivation Theory Numerical Tests Conclusions