1 interferometric interpolation and extrapolation of sparse obs and ssp data shuqian dong and...

1

Interferometric Interpolation and Extrapolation of Sparse

OBS and SSP Data

Shuqian Dong and G.T.Schuster

2

OutlineOutline

• MotivationMotivation

• TheoryTheory

• ConclusionsConclusions

• Numerical TestsNumerical Tests

OBS interpolationOBS interpolation OBS extrapolationOBS extrapolation SSP extrapolationSSP extrapolation

3

OutlineOutline

• MotivationMotivation

• TheoryTheory

• ConclusionsConclusions

• Numerical TestsNumerical Tests

OBS interpolationOBS interpolation OBS extrapolationOBS extrapolation SSP extrapolationSSP extrapolation

4

MotivationMotivation

Answer:Answer:

Interfer. predict. + matching filter Interfer. predict. + matching filter

Questions: Questions:

We have: We have:

Sparse OBS Sparse OBS

Sparse OBS Sparse OBS

?

Narrow aperture OBSNarrow aperture OBS ?Wide aperture OBSWide aperture OBS

Narrow aperture SSPNarrow aperture SSP ?Wide aperture SSPWide aperture SSP

SSP: Interferometric transform SSP: Interferometric transform

VSPVSP

Narrow apertureNarrow aperture wide aperturewide aperture

5

SeabedSeabed

ReflectorsReflectors

SeabedSeabed

ReflectorsReflectors

SeabedSeabed

ReflectorsReflectors

OBS SWP OBS

B

A

x B

A

x B

A

x

TheoryTheory• Sparse OBS interferometric interpolation Sparse OBS interferometric interpolation

NaturalGreen’s Function

Model basedGreen’s Function

Interpolated data

6

Z (

km)

Z (

km)

00

3.03.0X (km)X (km)00 4.54.5

Density model3.03.0

1.01.0Z

(km

)Z

(km

)

00

3.03.0X (km)X (km)00 4.54.5

Velocity model km/s3.63.6

1.51.5

kg/m33

Sparse OBS InterpolationSparse OBS Interpolation

7

Z (

km)

Z (

km)

00

3.03.0X (km)X (km)00 4.54.5

Density model3.03.0

1.01.0Z

(km

)Z

(km

)

00

3.03.0X (km)X (km)00 4.54.5

Velocity model km/s3.63.6

1.51.5

kg/m33

Sparse OBS InterpolationSparse OBS Interpolation

300 shots300 shotsdx = 16 m dx = 16 m

600 receivers600 receiversdx = 8 m dx = 8 m

8

X (km)X (km)00 4.54.5

Tim

e (s

)T

ime

(s)

00

3.03.0

Original CSG

Sparse OBS InterpolationSparse OBS Interpolation

Tim

e (s

)T

ime

(s)

00

3.03.0X (km)X (km)00 4.54.5

Virtual CSG

dx = 80 mdx = 80 mTotal traces: 60Total traces: 60

dx = 8 mdx = 8 m

9

X (km)X (km)00 4.54.5

Tim

e (s

)T

ime

(s)

00

3.03.0

Original CSG

Sparse OBS InterpolationSparse OBS Interpolation

Tim

e (s

)T

ime

(s)

00

3.03.0X (km)X (km)00 4.54.5

Virtual CSG

dx = 80 mdx = 80 mTotal traces: 60Total traces: 60

dx = 8 mdx = 8 m

** ff (t,x )(t,x )dd (t,x )(t,x )realreal

dd (t,x )(t,x )virtualvirtual00 00 00

xx00xx00

** ff (t,x )(t,x )dd (t,x’ )(t,x’ )realreal

dd (t,x’)(t,x’)virtualvirtual 00

10

Sparse OBS InterpolationSparse OBS Interpolation T

ime

(s)

Tim

e (s

)

00

3.03.0X (km)X (km)00 4.54.5

Virtual CSG

Tim

e (s

)T

ime

(s)

00

3.03.0X (km)X (km)00 4.54.5

Real CSG

Tim

e (s

)T

ime

(s)

00

3.03.0X (km)X (km)00 4.54.5

Filtered virtual CSG

11

X (km)X (km)00 4.54.5

Tim

e (s

)T

ime

(s)

00

3.03.0

Original CSG

X (km)X (km)00 4.54.5

Tim

e (s

)T

ime

(s)

00

3.03.0

Virtual CSG

X (km)X (km)00 4.54.5

Tim

e (s

)T

ime

(s)

00

3.03.0

Real CSG

X (km)X (km)00 4.54.5

Tim

e (s

)T

ime

(s)

00

3.03.0

Filtered virtual CSG

dx = 160 mdx = 160 mTotal traces: 30Total traces: 30

dx = 8 mdx = 8 mTotal traces: 600Total traces: 600

dx = 8 mdx = 8 mTotal traces: 600Total traces: 600

dx = 8 mdx = 8 mTotal traces: 600Total traces: 600

Sparse OBS InterpolationSparse OBS Interpolation

12

X (km)X (km)00 4.54.5

Tim

e (s

)T

ime

(s)

00

3.03.0

Original CSG

X (km)X (km)00 4.54.5

Tim

e (s

)T

ime

(s)

00

3.03.0

Virtual CSG

X (km)X (km)00 4.54.5

Tim

e (s

)T

ime

(s)

00

3.03.0

Real CSG

X (km)X (km)00 4.54.5

Tim

e (s

)T

ime

(s)

00

3.03.0

Filtered virtual CSG

dx = 320 mdx = 320 mTotal traces: 30Total traces: 30

dx = 8 mdx = 8 mTotal traces: 600Total traces: 600

dx = 8 mdx = 8 mTotal traces: 600Total traces: 600

dx = 8 mdx = 8 mTotal traces: 600Total traces: 600

Sparse OBS InterpolationSparse OBS Interpolation

13

Migration of interpolated OBS data Migration of interpolated OBS data

Z (

km)

Z (

km)

00

3.03.0

Migration of sparse OBS data

X (km)X (km)00 4.54.5

Z (

km)

Z (

km)

00

3.03.0X (km)X (km)00 4.54.5

300 shots300 shotsdx = 16 m dx = 16 m 6 receivers6 receivers

dx = 800 m dx = 800 m

Sparse OBS InterpolationSparse OBS Interpolation

14

SIGSBEE 2B velocity model

X (km)X (km)

Z (

km)

Z (

km)

00

8.58.5

00 2525

Sparse OBS InterpolationSparse OBS Interpolation

15

Velocity modelZ

(km

)Z

(km

)

00

4.54.5X (km)X (km)00 6.06.0

200 shots200 shotsdx = 30 m dx = 30 m

800 receivers800 receiversdx = 7.62 m dx = 7.62 m

Sparse OBS InterpolationSparse OBS Interpolation

16

X (km)X (km)00 6.06.0

Tim

e (s

)T

ime

(s)

00

3.03.0

Original CSG

X (km)X (km)00 6.06.0

Tim

e (s

)T

ime

(s)

00

3.03.0

Virtual CSG

X (km)X (km)00 6.06.0

Tim

e (s

)T

ime

(s)

00

3.03.0

Real CSG

X (km)X (km)00 6.06.0

Tim

e (s

)T

ime

(s)

00

3.03.0

Filtered virtual CSG

dx = 76.2 mdx = 76.2 mtraces: 80traces: 80

dx = 7.62 mdx = 7.62 mtraces: 800traces: 800

dx = 7.62 mdx = 7.62 mtraces: 800traces: 800

dx = 7.62 mdx = 7.62 mtraces: 800traces: 800

Sparse OBS InterpolationSparse OBS Interpolation

17

X (km)X (km)00 6.06.0

Tim

e (s

)T

ime

(s)

00

3.03.0

Original CSG

X (km)X (km)00 6.06.0

Tim

e (s

)T

ime

(s)

00

3.03.0

Virtual CSG

X (km)X (km)00 6.06.0

Tim

e (s

)T

ime

(s)

00

3.03.0

Real CSG

X (km)X (km)00 6.06.0

Tim

e (s

)T

ime

(s)

00

3.03.0

Filtered virtual CSG

dx = 300 mdx = 300 mtraces: 20traces: 20

dx = 7.62 mdx = 7.62 mtraces: 800traces: 800

dx = 7.62 mdx = 7.62 mtraces: 800traces: 800

dx = 7.62 mdx = 7.62 mtraces: 800traces: 800

Sparse OBS InterpolationSparse OBS Interpolation

18

Z (

km)

Z (

km)

00

4.54.5X (km)X (km)00 6.06.0

Migration of sparse OBS data

20 receivers20 receiversdx =300 m dx =300 m

200 shots200 shotsdx = 30 m dx = 30 m

Sparse OBS InterpolationSparse OBS Interpolation

19

Migration of interpolated OBS data Migration of interpolated OBS data

Z (

km)

Z (

km)

00

4.54.5X (km)X (km)00 6.06.0

20

Z (

km)

Z (

km)

00

4.54.5X (km)X (km)00 6.06.0

Velocity model Velocity model

21

OutlineOutline

• MotivationMotivation

• TheoryTheory

• ConclusionsConclusions

• Numerical TestsNumerical Tests

OBS interpolationOBS interpolation OBS extrapolationOBS extrapolation SSP extrapolationSSP extrapolation

22

SeabedSeabed

ReflectorsReflectors

SeabedSeabed

ReflectorsReflectors

SeabedSeabed

ReflectorsReflectors

OBS SWP OBS

B

A

x B

A

x B

A

x

NaturalGreen’s Function

Model basedGreen’s Function

Etrapolated data

OBS ExtrapolationOBS Extrapolation

23

SIGSBEE 2B velocity model

X (km)X (km)

Z (

km)

Z (

km)

00

4.54.5

00 6.06.0

OBS ExtrapolationOBS Extrapolation

200 shots200 shotsdx = 30 m dx = 30 m

400 receivers400 receiversapertue: 3 kmapertue: 3 kmdx = 7.62 m dx = 7.62 m

24

OBS ExtrapolationOBS Extrapolation T

ime

(s)

Tim

e (s

)

0.80.8

4.04.0X (km)X (km)00 6.06.0

Original CSG

Tim

e (s

)T

ime

(s)

0.80.8

4.04.0X (km)X (km)00 6.06.0

Extrapolated CSG

Tim

e (s

)T

ime

(s)

0.80.8

4.04.0X (km)X (km)00 6.06.0

Real CSG

25

Migration of narrow aperture OBS data Migration of narrow aperture OBS data Z

(km

)Z

(km

)

00

4.54.5X (km)X (km)00 6.06.0

OBS ExtrapolationOBS Extrapolation

200 shots200 shotsdx = 30 m dx = 30 m

400 receivers400 receiversapertue: 3 kmapertue: 3 kmdx = 7.62 m dx = 7.62 m

26

Migration of extrapolated OBS data Migration of extrapolated OBS data Z

(km

)Z

(km

)

00

4.54.5X (km)X (km)00 6.06.0

OBS ExtrapolationOBS Extrapolation

27

Velocity model Velocity model Z

(km

)Z

(km

)

00

4.54.5X (km)X (km)00 6.06.0

OBS ExtrapolationOBS Extrapolation

28

OutlineOutline

• MotivationMotivation

• TheoryTheory

• ConclusionsConclusions

• Numerical TestsNumerical Tests

OBS interpolationOBS interpolation OBS extrapolationOBS extrapolation SSP extrapolationSSP extrapolation

29

SeabedSeabed

ReflectorsReflectors

SSP

BA

xSeabedSeabed

ReflectorsReflectors

SSP

BA

xSeabedSeabed

ReflectorsReflectors

SSP

BA

x

NaturalGreen’s Function

Model based

Green’s Function

Etrapolated data

Natural or

SSP ExtrapolationSSP Extrapolation

30

SIGSBEE 2B velocity modelZ

(km

)Z

(km

)00

4.54.5X (km)X (km)00 6.06.0

SSP ExtrapolationSSP Extrapolation

200 shots200 shotsdx = 30 m dx = 30 m

300 receivers300 receiversapertue: 2.4 kmapertue: 2.4 kmdx = 7.62 m dx = 7.62 m

31

Tim

e (s

)T

ime

(s)

0.80.8

4.04.0X (km)X (km)00 6.06.0

Original CSG

Tim

e (s

)T

ime

(s)

0.80.8

4.04.0X (km)X (km)00 6.06.0

Extrapolated CSG

Tim

e (s

)T

ime

(s)

0.80.8

4.04.0X (km)X (km)00 6.06.0

Real CSG

SSP ExtrapolationSSP Extrapolation

32

Migration of extrapolated SSP data Migration of extrapolated SSP data

Z (

km)

Z (

km)

00

4.54.5X (km)X (km)00 6.06.0

SSP ExtrapolationSSP Extrapolation

200 shots200 shotsdx = 30 m dx = 30 m

300 receivers300 receiversapertue: 2.4 kmapertue: 2.4 kmdx = 7.62 m dx = 7.62 m

33

Migration of extrapolated SSP data Migration of extrapolated SSP data

Z (

km)

Z (

km)

00

4.54.5X (km)X (km)00 6.06.0

SSP ExtrapolationSSP Extrapolation

34

Velocity modelVelocity model

Z (

km)

Z (

km)

00

4.54.5X (km)X (km)00 6.06.0

SSP ExtrapolationSSP Extrapolation

35

Future Work

Field data test.

3D test

Conclusion

Helpful for OBS and SSP survey design

Sparse OBS Sparse OBS

Sparse OBS Sparse OBS

Narrow aperture Narrow aperture Wide apertureWide aperture

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We thank Utah Tomography and We thank Utah Tomography and Modeling/Migration ConsortiumModeling/Migration Consortium

sponsors for their financial supportsponsors for their financial support

AcknowledgementsAcknowledgements

37

ThanksThanks