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

1

Fast 3D Target-Oriented Reverse Time Datuming

Shuqian Dong

University of Utah2 Oct. 2008

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

3

OutlineOutline


• TheoryTheory






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?

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


6



• 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

7

• 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



8

OutlineOutline


• TheoryTheory






9

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

RRSS

x’x’ x’’x’’

Reverse time datumingReverse time datuming

TheoryTheory


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’’)


RR

TheoryTheory


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”)


RRSS

TheoryTheory


12

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

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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

14

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

15

OutlineOutline


• TheoryTheory







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


2D SEG/EAGE Test2D SEG/EAGE Test

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OutlineOutline


• TheoryTheory






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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


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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


y (km)y (km)00 3.53.5

Tim

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)T

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(s)

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2.52.5

RVSP Green’s function

y (km)y (km)00 3.53.5

Tim

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)T

ime

(s)

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2.52.5

True CSG at datum

y (km)y (km)00 3.53.5

Tim

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(s)

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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

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KM of original data


Z (

km)

Z (

km)

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2.02.0

y (km)y (km)

22

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x (km)x (km) 3.53.5

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KM of RTD data


22x (km)x (km)00 3.53.5

z (k

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2.02.0

Velocity modelx (km)x (km)00 3.53.5

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2.02.0

KM of original data

x (km)x (km)00 3.53.5

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2.02.0


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



23x (km)x (km)00 3.53.5

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Velocity modely (km)y (km)00 2.02.0

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KM of original data

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



25y (km)y (km)00 2.02.0

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Velocity modely (km)y (km)00 2.02.0

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



27x (km)x (km)00 3.53.5

y (k

m)

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m)

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2.02.0


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KM of original data

x (km)x (km)00 3.53.5

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



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OutlineOutline


• TheoryTheory






29

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


30


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

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(s)

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6.06.0

Redatumed CSG


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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)

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88

y (km)y (km)

55

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x (km)x (km) 1212

00




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X (km)X (km)00 1212

Z (

km)

Z (

km)

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8.08.0

KM of original data KM of RTD data


X (km)X (km)00 1212

Z (

km)

Z (

km)

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8.08.0



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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



KM of original data

34


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



KM of original data

35


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



KM of original data

36


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



KM of original data

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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



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



KM of original data

39


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



KM of original data

40


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



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


42

OutlineOutline


• TheoryTheory






43

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

44

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.

45

Thanks!Thanks!


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


z (k

m)

z (k

m)

00

2.02.0

RTM image

x (km)x (km)00 8.08.0

47

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

RRSS

x’x’ x’’x’’

Traditional reverse time datumingTraditional reverse time datuming

TheoryTheory


48

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


49

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


50

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

TheoryTheory


51


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


52


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’’)

53

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


54

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

55

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.

Documents

motivation z

d segeage salt model

time s

velocity model x

s x x dsx

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