VSP->SWP InterferometryVSP->SWP Interferometry

Redatum sources below overburdenRedatum sources below overburden

Local VSP migrationLocal VSP migration

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

Problem:Problem: Overburden+statics defocus VSP migration Overburden+statics defocus VSP migration

Redatum sources below overburdenRedatum sources below overburden

Local VSP migrationLocal VSP migration

Solution:Solution: VSP -> SWP Transform VSP -> SWP Transform

MotivationMotivation

• MotivationMotivation

• Interferometry TheoryInterferometry Theory

• Numerical ExamplesNumerical Examples

• ConclusionConclusion

OutlineOutline

AA

BB

xx

Reciprocity Correlation EquationReciprocity Correlation Equation

==kG(kG(BB||xx))* * G(G(AA||xx) )

SS00

VSPVSP{

Im G(Im G(BB||AA))

SWPSWP{

Far-field VSP -> SWP TransformFar-field VSP -> SWP Transform

SS 00

SS 0000

SS 0000++

• MotivationMotivation

• Interferometry TheoryInterferometry Theory

• Numerical Examples: 3 Syn. DataNumerical Examples: 3 Syn. Data

• ConclusionConclusion

OutlineOutline

FD ExperimentFD Experiment

Offset (m)Offset (m)00 10001000

DepthDepth (m)(m)

15001500

35003500 Depth (m)Depth (m)15001500 35003500

TimeTime (s)(s)

00

33

Reflection Reflection wavefieldwavefield

Reduced Form GSMReduced Form GSMRay tracing of line sourceRay tracing of line source (picked direct wave)(picked direct wave) Reduce form GSM resultReduce form GSM result

Offset (m)Offset (m)00 10001000

DepthDepth (m)(m)

15001500

35003500Offset (m)Offset (m)00 10001000

??

Reduced Form GSMReduced Form GSMRay tracing of line sourceRay tracing of line source (picked direct wave)(picked direct wave) Reduce form GSM resultReduce form GSM result

Offset (m)Offset (m)00 10001000

DepthDepth (m)(m)

15001500

35003500Offset (m)Offset (m)00 10001000

??

Lesson: Super-resolutionLesson: Super-resolution

Synthetic ExperimentSynthetic Experiment(He, 2006)(He, 2006)

94 geophones

10 shots10 shots

Overburden

0 km0 km 7 km7 kmOffset (m)Offset (m)

DepthDepth (m)(m)

55005500

00

A Shot GatherA Shot Gather

2 km2 km 6.5 km6.5 km

0 s0 s

5 s5 s

WEIM Result (one shot)WEIM Result (one shot)

Offset Offset (m)(m)

00 17001700

Dep

th (

m)

Dep

th (

m)

27002700

55005500

ArtifactsArtifacts

WEIM Result (ten shots)WEIM Result (ten shots)

Offset Offset (m)(m)

00 17001700

Dep

th (

m)

Dep

th (

m)

27002700

55005500

Tricks: Filter down and up going waves: m(x) = U(x)/D(x)Tricks: Filter down and up going waves: m(x) = U(x)/D(x)Lesson: Fltering+extra stacking reduces artifacts Lesson: Fltering+extra stacking reduces artifacts

• MotivationMotivation

• Interferometry TheoryInterferometry Theory

• Numerical Examples: GOM DataNumerical Examples: GOM Data

• ConclusionConclusion

OutlineOutline

VSP Salt Flank Imaging VSP Salt Flank Imaging (BP Hornby et al, 2006)(BP Hornby et al, 2006)

? 98 geophones

120 shots

Overburden

Poor image of flank by standard migrationPoor image of flank by standard migration

0 2000 ft 0 2000 ft

VSP DataVSP Data

3.2 s3.2 s

7.2 s7.2 s

0 2000 ft 0 2000 ft

Interferometric Migration Interferometric Migration ResultResult

VSP->SWP SummaryVSP->SWP Summary

3. Kills Source Statics and no need to know src location or excitation time3. Kills Source Statics and no need to know src location or excitation time

1. Redatum sources below overburden1. Redatum sources below overburden

2. Local VSP migration2. Local VSP migration

4. Super-resolution4. Super-resolution

5. Instead of redatuming receivers to surface, we5. Instead of redatuming receivers to surface, we

redatum sources to depth.redatum sources to depth.

X (m) 14001000

950

1950

Dep

th (

m)

Main Parameters in VSP:

• Source number: 100

• Shot interval: 10 m

• Receiver number: 91

• Receiver interval: 10 m

• Depth of the first receiver: 950 m

• Depth of the last receiver: 1850 m

• Temporal interval: 0.001 s