Fast 3d target oriented reverse time datuming
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Fast 3D Target-Oriented Reverse Time Datuming. Shuqian Dong University of Utah. 2 Oct. 2008. Outline. Motivation. Theory. Numerical Tests. 2-D SEG/EAGE salt model. 3-D SEG/EAGE salt model. 3-D field data. Conclusions. Motivation. Numerical Tests. Theory. Conclusions. Motivation.

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Fast 3D Target-Oriented Reverse Time Datuming

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Fast 3D Target-Oriented Reverse Time Datuming

Shuqian Dong

University of Utah

2 Oct. 2008


Outline

  • Motivation

  • Theory

  • Numerical Tests

2-D SEG/EAGE salt model

3-D SEG/EAGE salt model

3-D field data

  • Conclusions

Motivation

Numerical Tests

Theory

Conclusions


Motivation

Numerical Tests

Theory

Conclusions

Outline

  • Motivation

  • Theory

  • Numerical Tests

2-D SEG/EAGE salt model

3-D SEG/EAGE salt model

3-D field data

  • Conclusions


km/s

Velocity model

0

0

0

Common shot gather

4.5

Time (s)

z (km)

z (km)

1.5

2.0

4.0

2.0

x (km)

x (km)

x (km)

8.0

8.0

8.0

0

0

0

KM image

Problem:

Defocusing: lower resolution, distorted image

Multiples: image artifacts.

Reason:

KM: high frequency approximation.

Motivation

Numerical Tests

Theory

Conclusions

Motivation

Solutions?


RTM image

Velocity model

KM image

Motivation

Numerical Tests

Theory

Conclusions

Motivation

Solutions:

  • Reverse time migration: solving two-way wave equation

  • Target-oriented reverse time datuming:

  • solving two-way wave equation to bypass overburden

Luo, 2002: target-oriented RTD

Luo and Schuster, 2004: bottom-up strategy


RTD

  • Complex structures cause defocusing effects

  • RTD can reduce defocusing effects

  • RTM is computationally expensive

  • RTD + Kirchhoff = accurate + cheap

Motivation

Numerical Tests

Theory

Conclusions

Motivation


Motivation

Numerical Tests

Theory

Conclusions

Motivation

  • Reduce defocusing effects for subsalt imaging

  • Closer to the target: better resolution

  • Bottom-up strategy: computational efficiency

  • Redatumed data can be used for least squares

  • migration and migration velocity analysis (MVA)


Motivation

Numerical Tests

Theory

Conclusions

Outline

  • Motivation

  • Theory

  • Numerical Tests

2-D SEG/EAGE salt model

3-D SEG/EAGE salt model

3-D field data

  • Conclusions


Motivation

Numerical Tests

Theory

Conclusions

Theory

Reverse time datuming

d(s|r)

S

R

x’’

x’


d(s|x’’)

g*(r|x”)

d(s|r)

d(s|x”)=

Motivation

Numerical Tests

Theory

Conclusions

Theory

Reverse time datuming

S

R

x’’

x’


g*(r|x”)

d(s|r)

d(s|x”)=

d(x’|x’’)

Motivation

Numerical Tests

Theory

Conclusions

Theory

Reverse time datuming

S

R

d(x’|x”)=g*(s|x’) d(s|x”)

x’’

x’


Real source number on surface: 10

Virtual source number on datum: 3

Motivation

Numerical Tests

Theory

Conclusions

Theory

Calculate Green’s functions

VSP (source on surface) Green’s functions: 10


Real source number on surface: 10

Virtual source number on datum: 3

VSP (source on surface) Green’s functions: 10

Motivation

Numerical Tests

Theory

Conclusions

Theory

Calculate Green’s functions

Reciprocity: RVSP=VSP

RVSP (source on datum) Green’s functions: 3


Reciprocity: RVSP =>VSP

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

Crosscorrelation: Green’s functions with original data

IFFT: frequency domain => time domain

Redatumed data

Motivation

Numerical Tests

Theory

Conclusions

Workflow

FD: Compute RVSP Green’s functions

Original data: FFT: time domain =>frequency domain


Motivation

Numerical Tests

Theory

Conclusions

Outline

  • Motivation

  • Theory

  • Numerical Tests

2-D SEG/EAGE salt model

3-D SEG/EAGE salt model

3-D field data

  • Conclusions


km/s

Velocity model

0

0

0

0

4.5

Time (s)

Time (s)

Time (s)

z (km)

1.5

2.0

4.0

4.0

4.0

x (km)

x (km)

x (km)

x (km)

8.0

8.0

8.0

8.0

0

0

0

0

Motivation

Numerical Tests

Theory

Conclusions

2D SEG/EAGE Test

RVSP Green’s function

True CSG at datum

Redatumed CSG


km/s

Velocity model

0

0

0

0

4.5

z (km)

z (km)

z (km)

z (km)

1.5

2.0

2.0

2.0

2.0

x (km)

x (km)

x (km)

x (km)

8.0

8.0

8.0

8.0

0

0

0

0

KM image

RTM image

Motivation

Numerical Tests

Theory

Conclusions

2D SEG/EAGE Test

KM of redatumed data


Motivation

Numerical Tests

Theory

Conclusions

Outline

  • Motivation

  • Theory

  • Numerical Tests

2-D SEG/EAGE salt model

3-D SEG/EAGE salt model

3-D field data

  • Conclusions


km/s

4.5

0

x (km)

3.5

0

1.5

Z (km)

2.0

0

y (km)

2

Motivation

Numerical Tests

Theory

Conclusions

3D SEG/EAGE test

Velocity model

SSP geometry:

1700 shots

1700 receivers

Datum depth:

1.5 km

RVSP Green’s functions:

850 shots

1700 receivers


Original CSG

RVSP Green’s function

0

0

0

0

Time (s)

Time (s)

Time (s)

Time (s)

2.5

2.5

2.5

2.5

Redatumed CSG

True CSG at datum

y (km)

y (km)

y (km)

y (km)

3.5

3.5

3.5

3.5

0

0

0

0

Motivation

Numerical Tests

Theory

Conclusions

3D SEG/EAGE test


KM of RTD data

x (km)

x (km)

0

0

3.5

3.5

0

0

Z (km)

Z (km)

2.0

2.0

0

0

y (km)

y (km)

2

2

KM of original data

Motivation

Numerical Tests

Theory

Conclusions

3D SEG/EAGE test


KM of original data

KM of redatumed data

0

0

0

z (km)

z (km)

z (km)

2.0

2.0

2.0

3.5

3.5

3.5

x (km)

x (km)

x (km)

0

0

0

Velocity model

Motivation

Numerical Tests

Theory

Conclusions

3D SEG/EAGE test

( Inline No. 41 )


0

0

0

z (km)

z (km)

z (km)

2.0

2.0

2.0

3.5

3.5

3.5

x (km)

x (km)

x (km)

0

0

0

Motivation

Numerical Tests

Theory

Conclusions

3D SEG/EAGE test

KM of original data

KM of redatumed data

Velocity model

( Inline No. 101 )


0

0

0

z (km)

z (km)

z (km)

2.0

2.0

2.0

2.0

2.0

2.0

y (km)

y (km)

y (km)

0

0

0

Motivation

Numerical Tests

Theory

Conclusions

3D SEG/EAGE test

KM of original data

KM of redatumed data

Velocity model

( Crossline No. 161 )


0

0

0

z (km)

z (km)

z (km)

2.0

2.0

2.0

2.0

2.0

2.0

y (km)

y (km)

y (km)

0

0

0

Motivation

Numerical Tests

Theory

Conclusions

3D SEG/EAGE test

KM of original data

KM of redatumed data

Velocity model

( Crossline No. 201 )


0

0

0

y (km)

y (km)

y (km)

2.0

2.0

2.0

3.5

3.5

3.5

x (km)

x (km)

x (km)

0

0

0

Motivation

Numerical Tests

Theory

Conclusions

3D SEG/EAGE test

KM of original data

KM of redatumed data

Velocity model

( depth: z=1.4 km )


0

0

0

y (km)

y (km)

y (km)

2.0

2.0

2.0

3.5

3.5

3.5

x (km)

x (km)

x (km)

0

0

0

Motivation

Numerical Tests

Theory

Conclusions

3D SEG/EAGE test

KM of original data

KM of redatumed data

Velocity model

( depth: z=1.5 km )


Motivation

Numerical Tests

Theory

Conclusions

Outline

  • Motivation

  • Theory

  • Numerical Tests

2-D SEG/EAGE salt model

3-D SEG/EAGE salt model

3-D field data

  • Conclusions


Interval velocity model

km/s

0

5.5

Z (km)

8.0

0

y (km)

12

x (km)

6.0

0

1.5

Motivation

Numerical Tests

Theory

Conclusions

3D 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


Redatumed CSG

Original CSG

0

0

Time (s)

Time (s)

6.0

6.0

y (km)

y (km)

4.5

4.5

0

0

Motivation

Numerical Tests

Theory

Conclusions

3D Field Data Test


x (km)

0

12

KM of original data

0

Z (km)

8

KM of redatumed data

0

0

y (km)

5

Z (km)

8

0

12

y (km)

x (km)

5

0

Motivation

Numerical Tests

Theory

Conclusions

3D Field Data Test

KM of RTD data


0

0

Z (km)

Z (km)

8.0

8.0

0

0

X (km)

X (km)

12

12

Motivation

Numerical Tests

Theory

Conclusions

3D Field Data Test

( Inline No. 21 )

KM of original data

KM of RTD data


0

0

Z (km)

Z (km)

8.0

8.0

0

0

X (km)

X (km)

12

12

Motivation

Numerical Tests

Theory

Conclusions

3D Field Data Test

( Inline No. 41 )

KM of original data

KM of RTD data


0

0

Z (km)

Z (km)

8.0

8.0

0

0

X (km)

X (km)

12

12

Motivation

Numerical Tests

Theory

Conclusions

3D Field Data Test

( Inline No. 61 )

KM of original data

KM of RTD data


0

0

Z (km)

Z (km)

8.0

8.0

0

0

Y (km)

Y (km)

5.0

5.0

Motivation

Numerical Tests

Theory

Conclusions

3D Field Data Test

( Crossline No. 41 )

KM of original data

KM of RTD data


0

0

Z (km)

Z (km)

8.0

8.0

0

0

Y (km)

Y (km)

5.0

5.0

Motivation

Numerical Tests

Theory

Conclusions

3D Field Data Test

( Crossline No. 61 )

KM of original data

KM of RTD data


0

0

Z (km)

Z (km)

8.0

8.0

0

0

Y (km)

Y (km)

5.0

5.0

Motivation

Numerical Tests

Theory

Conclusions

3D Field Data Test

( Crossline No. 81 )

KM of original data

KM of RTD data


0

0

Y (km)

Y (km)

5.0

5.0

0

0

X (km)

X (km)

12

12

Motivation

Numerical Tests

Theory

Conclusions

3D Field Data Test

( Depth 2.0 km )

KM of original data

KM of RTD data


0

0

Y (km)

Y (km)

5.0

5.0

0

0

X (km)

X (km)

12

12

Motivation

Numerical Tests

Theory

Conclusions

3D Field Data Test

( Depth 2.5 km )

KM of original data

KM of RTD data


0

0

Y (km)

Y (km)

5.0

5.0

0

0

X (km)

X (km)

12

12

Motivation

Numerical Tests

Theory

Conclusions

3D Field Data Test

( Depth 4.0 km )

KM of original data

KM of RTD data


Motivation

Numerical Tests

Theory

Conclusions

Computational Costs


Motivation

Numerical Tests

Theory

Conclusions

Outline

  • Motivation

  • Theory

  • Numerical Tests

2-D SEG/EAGE salt model

3-D SEG/EAGE salt model

3-D field data

  • Conclusions


Motivation

Numerical Tests

Theory

Conclusions

Conclusions

  • 2-D numerical test

KM of RTD achieved image quality comparable to RTM at much lower cost.

  • 3-D numerical test

3-D RTD is implemented for synthetic and GOM data at acceptable computational cost;

Apparent improvements in mage quality are achieved compared to KM image of original data.

  • Future application

Subsalt least suqares migration and migration velocity analysis


Acknowledgements

  • 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!


km/s

Velocity model

0

0

0

0

Common shot gather

4.5

Time (s)

z (km)

z (km)

z (km)

1.5

2.0

2.0

2.0

4.0

x (km)

x (km)

x (km)

x (km)

8.0

8.0

8.0

8.0

0

0

0

0

KM image

RTM image

Motivation

Numerical Tests

Theory

Conclusions

Motivation


Motivation

Numerical Tests

Theory

Conclusions

Theory

Traditional reverse time datuming

d(s|r)

S

R

x’’

x’


d(s|x’’)

g*(r|x”)

d(s|r)

d(s|x”)=

Motivation

Numerical Tests

Theory

Conclusions

Theory

Reverse time Datuming

S

R

x’’

x’


g*(r|x”)

d(s|r)

d(s|x”)=

d(x’|x’’)

Motivation

Numerical Tests

Theory

Conclusions

Theory

Reverse time Datuming

S

R

d(x’|x”)=g*(s|x’) d(s|x”)

x’’

x’


Motivation

Numerical Tests

Theory

Conclusions

Theory

Target-oriented RTD

(Luo , 2006)


g(r|x”)

g(s|x’)

d(s|r)

*

= d(x’|x’’)

Motivation

Numerical Tests

Theory

Conclusions

Theory

Target-oriented RTD

(Luo , 2006)


g(r|x")

g(s|x’)

d(s|r)

*

= d(x’|x’’)

Motivation

Numerical Tests

Theory

Conclusions

Theory

Target-oriented RTD

(Luo , 2006)


Green’s functions: Time domain to frequency domain

Reverse time datum for different frequency

Sum over frequency

Redatumed data: frequency domain to time domain

Motivation

Numerical Tests

Theory

Conclusions

Workflow

Compute VSP Green’s functions in time domain

Original data: time domain to frequency domain


Reciprocity: RVSP =>VSP

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

Crosscorrelation: Green’s functions with original data

Sum over frequency

IFFT: frequency domain => time domain

Redatumed data

Motivation

Numerical Tests

Theory

Conclusions

Workflow

FD: Compute RVSP Green’s functions

Original data: FFT: time domain =>frequency domain


Motivation

Numerical Tests

Theory

Conclusions

Conclusions

Benefits:

  • Reduce defocusing effects for subsalt imaging

  • Closer to the target: better resolution

  • Bottom-up strategy: computational efficiency

  • Redatumed data can be used by LSM & MVA

Limitations:

  • Extra I/O for accessing Green’s functions


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