1 Fast 3D Target-Oriented Reverse Time Datuming Shuqian Dong University of Utah 2 Oct. 2008

Fast 3D Target-Oriented Reverse Time Datuming

Shuqian Dong

University of Utah2 Oct. 2008

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

OutlineOutline

• TheoryTheory

4Motivation Theory Numerical Tests Conclusions

2.02.0

KM image

x (km)x (km)00 8.08.0

4.04.0

Common shot gather

x (km)x (km)00 8.08.0

MotivationMotivationz

2.02.0

Velocity model

x (km)x (km)00 8.08.0

4.54.5

1.51.5

Defocusing: lower resolution, distorted image

Multiples: image artifacts.

Problem:

KM: high frequency approximation.

Reason:

Solutions?

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

• 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

• 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

OutlineOutline

• TheoryTheory

d(s|r)d(s|r)

x’x’ x’’x’’

Reverse time datumingReverse time datuming

TheoryTheory

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’’)

TheoryTheory

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”)

TheoryTheory

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

Calculate Green’s functionsCalculate Green’s functions

TheoryTheory

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

FD: Compute RVSP Green’s functions

Original data: FFT: time domain =>frequency domain

Crosscorrelation: Green’s functions with original data

WorkflowWorkflow

Reciprocity: RVSP =>VSP

Green’s functions: FFT: time domain => frequency domain

IFFT: frequency domain => time domain

Redatumed data

OutlineOutline

• TheoryTheory

2.02.0

Velocity model

x (km)x (km)00 8.08.0

4.54.5

1.51.5

4.04.0

RVSP Green’s function

x (km)x (km)00 8.08.0

2D SEG/EAGE Test2D SEG/EAGE Test

4.04.0

True CSG at datum

x (km)x (km)00 8.08.0

4.04.0

Redatumed CSG

x (km)x (km)00 8.08.0

2.02.0

Velocity model

x (km)x (km)00 8.08.0

4.54.5

1.51.5

2.02.0

KM image

x (km)x (km)00 8.08.0

2.02.0

RTM image

x (km)x (km)00 8.08.0

2.02.0

KM of redatumed data

x (km)x (km)00 8.08.0

2D SEG/EAGE Test2D SEG/EAGE Test

OutlineOutline

• TheoryTheory

3D SEG/EAGE test3D SEG/EAGE test Z

2.02.0

y (km)y (km)

x (km)x (km)

3.53.5

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

3D SEG/EAGE test3D SEG/EAGE test

y (km)y (km)00 3.53.5

2.52.5

Original CSG

y (km)y (km)00 3.53.5

2.52.5

RVSP Green’s function

y (km)y (km)00 3.53.5

2.52.5

True CSG at datum

y (km)y (km)00 3.53.5

2.52.5

Redatumed CSG

2.02.0

y (km)y (km)

x (km)x (km) 3.53.5

KM of original data

2.02.0

y (km)y (km)

x (km)x (km) 3.53.5

KM of RTD data

22x (km)x (km)00 3.53.5

2.02.0

Velocity modelx (km)x (km)00 3.53.5

2.02.0

KM of original data

x (km)x (km)00 3.53.5

2.02.0

( Inline No. 41 )( Inline No. 41 )

23x (km)x (km)00 3.53.5

2.02.0

KM of original data

x (km)x (km)00 3.53.5

2.02.0

24y (km)y (km)00 2.02.0

2.02.0

Velocity modely (km)y (km)00 2.02.0

2.02.0

KM of original data

y (km)y (km)00 2.02.0

2.02.0

( Crossline No. 161 )( Crossline No. 161 )

25y (km)y (km)00 2.02.0

2.02.0

Velocity modely (km)y (km)00 2.02.0

2.02.0

KM of original data

y (km)y (km)00 2.02.0

2.02.0

26x (km)x (km)00 3.53.5

2.02.0

KM of original data

x (km)x (km)00 3.53.5

2.02.0

( depth: z=1.4 km )( depth: z=1.4 km )

27x (km)x (km)00 3.53.5

2.02.0

KM of original data

x (km)x (km)00 3.53.5

2.02.0

( depth: z=1.5 km )( depth: z=1.5 km )

OutlineOutline

• TheoryTheory

8.08.0

y (km)y (km)

6.06.0

x (km)x (km)

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

y (km)y (km)00 4.54.5

6.06.0

Original CSG

y (km)y (km)00 4.54.5

6.06.0

Redatumed CSG

KM of RTD data

y (km)y (km)

x (km)x (km) 1212

KM of original data

y (km)y (km)

x (km)x (km) 1212

X (km)X (km)00 1212

8.08.0

KM of original data KM of RTD data

X (km)X (km)00 1212

8.08.0

X (km)X (km)00 1212

8.08.0

KM of RTD data

X (km)X (km)00 1212

8.08.0

KM of original data

X (km)X (km)00 1212

8.08.0

KM of RTD data

X (km)X (km)00 1212

8.08.0

KM of original data

Y (km)Y (km)00 5.05.0

8.08.0

KM of RTD data

Y (km)Y (km)00 5.05.0

8.08.0

KM of original data

Y (km)Y (km)00 5.05.0

8.08.0

KM of RTD data

Y (km)Y (km)00 5.05.0

8.08.0

KM of original data

Y (km)Y (km)00 5.05.0

8.08.0

KM of RTD data

Y (km)Y (km)00 5.05.0

8.08.0

KM of original data

( Depth 2.0 km )( Depth 2.0 km )

X (km)X (km)00 1212

5.05.0

KM of RTD data

X (km)X (km)00 1212

5.05.0

KM of original data

X (km)X (km)00 1212

5.05.0

KM of RTD data

X (km)X (km)00 1212

5.05.0

KM of original data

X (km)X (km)00 1212

5.05.0

KM of RTD data

X (km)X (km)00 1212

5.05.0

KM of original data

(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

OutlineOutline

• TheoryTheory

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.

• 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

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.

Thanks!Thanks!

2.02.0

Velocity model

x (km)x (km)00 8.08.0

4.54.5

1.51.5

2.02.0

KM image

x (km)x (km)00 8.08.0

4.04.0

Common shot gather

x (km)x (km)00 8.08.0

2.02.0

RTM image

x (km)x (km)00 8.08.0

d(s|r)d(s|r)

x’x’ x’’x’’

Traditional reverse time datumingTraditional reverse time datuming

TheoryTheory

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

TheoryTheory

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

TheoryTheory

Target-oriented RTDTarget-oriented RTD(Luo , 2006)(Luo , 2006)

TheoryTheory

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

g(s|x’)g(s|x’) g(r|x")g(r|x")** d(s|r)d(s|r)

= d(x’|x’’)= d(x’|x’’)

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

FD: Compute RVSP Green’s functions

Original data: FFT: time domain =>frequency domain

Crosscorrelation: Green’s functions with original data

WorkflowWorkflow

Reciprocity: RVSP =>VSP

Green’s functions: FFT: time domain => frequency domain

Sum over frequency

IFFT: frequency domain => time domain

Redatumed data

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

1 Fast 3D Target-Oriented Reverse Time Datuming Shuqian Dong University of Utah 2 Oct. 2008

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