1

OBS->OBS Extrapolation OBS->OBS Extrapolation InterferometryInterferometry

Shuqian Dong and Sherif HanafyShuqian Dong and Sherif Hanafy

Coarse OBSCoarse OBS Coarse OBSCoarse OBS Virtual SWPVirtual SWP

2

3x3 Classification Matrix3x3 Classification Matrix

SSPSSP VSPVSP SWPSWP

VSPVSP

SSPSSP

SWPSWP

SSPSSP SSPSSP SSPSSP SSPSSPVSPVSP SWPSWP

VSPVSP VSPVSP VSPVSP

SWPSWP SWPSWP SWPSWP

VSPVSP

SWPSWP

SWPSWP

VSPVSP

SSPSSP

SSPSSP

3

SeabedSeabed

ReflectorsReflectors

OBS

B

A

x

NaturalGreen’s Function

SeabedSeabed

ReflectorsReflectors

SWP

B

A

x

Model basedGreen’s Function

SeabedSeabed

ReflectorsReflectors

OBS

B

A

x

Extrapolated Data

OBS ExtrapolationOBS Extrapolation

4

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 receiversapertuaperturre: 3 kme: 3 kmdx = 7.62 m dx = 7.62 m

5

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

We can improve the results by a matching filter but we do not have enough time

6

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 receiversapertuaperturre: 3 kme: 3 kmdx = 7.62 m dx = 7.62 m

7

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

Shows that you only recover Shows that you only recover part of the Green’s functionpart of the Green’s functionShows that you recover Shows that you recover

all of the Green’s function hereall of the Green’s function here

8

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

Shows that you only recover Shows that you only recover part of the Green’s functionpart of the Green’s functionShows that you recover Shows that you recover

all of the Green’s function hereall of the Green’s function here

9

Velocity model Velocity model Z

(km

)Z

(km

)

00

4.54.5X (km)X (km)00 6.06.0

OBS ExtrapolationOBS Extrapolation

10

OutlineOutline

• MotivationMotivation

• TheoryTheory

• ConclusionsConclusions

• Numerical TestsNumerical Tests

OBS interpolationOBS interpolation OBS extrapolationOBS extrapolation SSP extrapolationSSP extrapolation

11

SeabedSeabed

ReflectorsReflectors

SSP

BA

xSeabedSeabed

ReflectorsReflectors

SSP

BA

x

NaturalGreen’s Function

SeabedSeabed

ReflectorsReflectors

SSP

BA

x

Extrapolated DataModel based

Green’s Function

Natural ,

SSP ExtrapolationSSP Extrapolation

12

AA

xx

SSP->SSP Reciprocity Correlation EquationSSP->SSP Reciprocity Correlation Equation

BBSS

Free surface G(A|x)=G(B|x)=0Free surface G(A|x)=G(B|x)=0

Water-layer Green’sWater-layer Green’sfunctionfunction

==G(G(BB||xx))* * G(G(AA||xx) ) S+S0

OBSOBS{

G(G(BB||AA) – G() – G(A|BA|B) )

OBSOBS{

0

SWP dataSWP data

02ik

Sea-floor

13

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 receiversapertuaperturre: 2.4 kme: 2.4 kmdx = 7.62 m dx = 7.62 m

14

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

We can improve the results by a matching filter but we do not have enough time

15

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 receiversapertuaperturre: 2.4 kme: 2.4 kmdx = 7.62 m dx = 7.62 m

16

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

17

Velocity modelVelocity model

Z (

km)

Z (

km)

00

4.54.5X (km)X (km)00 6.06.0

SSP ExtrapolationSSP Extrapolation

18

Field Data TestField Data Test

Mahogony OBS Data

800 Shots beneath free surface

180 receivers on sea floor

Sea floor depth: about 120m

Shots and receivers interval: 25 m

Time sample interval: 4ms

Z (

m)

Z (

m)

00

120120

X (m)X (m)00 2000020000

Acquisition geometry demenstration

180 receivers180 receiversdx =25 m dx =25 m

800 shots800 shotsdx = 25 m dx = 25 m Sea floorSea floor

19

OBS ExtrapolationOBS Extrapolation T

ime

(s)

Tim

e (s

)

00

3.03.0

Original CSG

X (m)X (m)00 12001200250250

Tim

e (s

)T

ime

(s)

00

3.03.0

Virtual CSG

X (m)X (m)00 12001200250250

virtual traces real traces

20

OBS ExtrapolationOBS Extrapolation T

ime

(s)

Tim

e (s

)

00

3.03.0

Virtual CSG by 1 iteration

X (m)X (m)00 12001200250250

Tim

e (s

)T

ime

(s)

00

3.03.0

Virtual CSG by 5 iterations

X (m)X (m)00 12001200250250

21

Tim

e (s

)T

ime

(s)

00

3.03.0

Original CSG

X (m)X (m)00 12001200500500

Tim

e (s

)T

ime

(s)

00

3.03.0

Virtual CSG

X (m)X (m)00 12001200500500

virtual traces real traces

OBS ExtrapolationOBS Extrapolation

22

OBS ExtrapolationOBS Extrapolation

Virtual CSG by 1 iteration Virtual CSG by 5 iterations

X (m)X (m)00 12001200500500

Tim

e (s

)T

ime

(s)

00

3.03.0X (m)X (m)00 12001200500500

Tim

e (s

)T

ime

(s)

00

3.03.0

23

3D Extrapolation3D Extrapolation

Input: sparse OBS data Input: sparse OBS data

• Recording spreadRecording spread

x: 500 m tx: 500 m too 3,000 m 3,000 m

y: 0 to 3,000 my: 0 to 3,000 m

Goal:Goal:

Fill the near-offset gapFill the near-offset gap

500 m500 m 3000 m3000 m00XX

00

3000 m3000 m

YY

24

3D Extrapolation3D Extrapolation

Extrapolated Data for a 2D Line at X =400 mExtrapolated Data for a 2D Line at X =400 m00

3.03.0

Tim

e (s

)T

ime

(s)

00 24002400Y (m)Y (m)

25

3D Extrapolation3D Extrapolation

Real Data for the 2D Line X = 400 mReal Data for the 2D Line X = 400 m00

3.03.0

Tim

e (s

)T

ime

(s)

00 24002400Y (m)Y (m)

26

3D Extrapolation3D Extrapolation

Extrapolated Data for the 2D Line X = 300 mExtrapolated Data for the 2D Line X = 300 m00

3.03.0

Tim

e (s

)T

ime

(s)

00 24002400Y (m)Y (m)

27

3D Extrapolation3D Extrapolation

Real Data for the 2D Line X = 300 mReal Data for the 2D Line X = 300 m00

3.03.0

Tim

e (s

)T

ime

(s)

00 24002400Y (m)Y (m)

28

3D Extrapolation3D Extrapolation

Extrapolation Result for the 2D Line Y=1000 mExtrapolation Result for the 2D Line Y=1000 m00

3.03.0

Tim

e (s

)T

ime

(s)

00 14001400Y (m)Y (m)

ExtraExtrap.p.

Actual dataActual data

200200

30

Future Work

Field data test

3D test

Conclusions

Helpful for OBS and SSP survey design

Sparse OBS Sparse OBS

DenseDense OBS OBS

Narrow aperture Narrow aperture Wide apertureWide aperture

Helpful for survey design in environmentally sensitive areas: receivers in town, sources out of town, e.g., Dhahran, Saudi Arabia

Problems: attenuation ?