VSP->Xwell InterferometryVSP->Xwell Interferometry

xx

BB

xx

BB

xxxx

? ??

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

XwellXwell XwellXwell XwellXwell XwellXwellSSPSSP VSPVSP XwellXwell

VSP->Xwell TransformVSP->Xwell Transform

xx

BB

G(B|x)G(B|x)

AA

G(A|x)G(A|x)

xx

BB

AA

G(A|x)*G(A|x)*oo

xx

BB

AA

Model basedModel basedNeeds V(x) around wellNeeds V(x) around well

xx

BB

VSP ExperimentVSP Experiment

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 -> Xwell Transform VSP -> Xwell Transform

MotivationMotivation

xx

BB

VSP ExperimentVSP Experiment

(a) VSP data: P(g|s)=T(g|s)+R(g|s)

T(g|s)

s

gR(g|s)

x

s

(b) Backward reflection

R(g|s)g

x

R(x|s)= G(x|g)*R(g|s)g

(c) Backward transmission

T(g|s)

s

g

x

T(x|s)= G(x|g)*T(g|s)

g

(d) Crosscorrelation

m(x)= R(x|s) T(x|s)*g

Theory

Local VSP Green’s function

R(g|s)g

x

Key Idea of Local RTMKey Idea of Local RTM

Numerical ResultsNumerical Results

1. Synthetic VSP (Jinahua Yu) 1. Synthetic VSP (Jinahua Yu)

3. GOM VSP3. GOM VSP

2. Synthetic VSP (Xiang Xu) 2. Synthetic VSP (Xiang Xu)

0 km0 km

2 km2 km0 km0 km 3 km3 km

Walkaway VSPWalkaway VSP

Source number: Source number: 100100Shot interval: Shot interval: 10 m10 mReceiver number: Receiver number: 9191Receiver interval: Receiver interval: 10 m10 mDepth of the first receiver: Depth of the first receiver: 950 m950 mDepth of the last receiver: Depth of the last receiver: 1850 m1850 mTemporal interval: Temporal interval: 0.001 s0.001 s

Local VSP Migration ImageLocal VSP Migration Image

No Overburden velocity neededNo Overburden velocity needed

No need to know source location or excitation timeNo need to know source location or excitation time

X (m)X (m) 1400140010001000

950

1950

Dep

th (

m)

X (m)X (m) 1400140010001000

LimitationsLimitations

Rotated Pyramid vs PyramidRotated Pyramid vs PyramidLocal VSPLocal VSP Traditional VSPTraditional VSP

LL

DD

Numerical ResultsNumerical Results

1. Synthetic VSP (Jinahua Yu) 1. Synthetic VSP (Jinahua Yu)

3. GOM VSP3. GOM VSP

2. Synthetic VSP (Xiang Xu) 2. Synthetic VSP (Xiang Xu)

Sigsbee P-wave Velocity ModelSigsbee P-wave Velocity Model0

Dep

th (

km)

9.2

4500

1500

m/s

-12.5 12.5Offset (km)

279 shots

150 receivers150 receivers

Local Reverse Time Migration ResultsLocal Reverse Time Migration Results

4.6

9.2

Dep

th (

km)

-3 3Offset (km)

True modelMigration image

f

Numerical ResultsNumerical Results

1. Synthetic VSP (Jinahua Yu) 1. Synthetic VSP (Jinahua Yu)

3. GOM VSP3. GOM VSP

2. Synthetic VSP (Xiang Xu) 2. Synthetic VSP (Xiang Xu)

Dep

th

(m)

Offset (m)4878

0 1829

0

GOM VSP Well and Source LocationGOM VSP Well and Source LocationSource @150 m offset

2800 m

3200 m

Salt

82 receivers

P-to-S ratio = 2.7

Velocity ProfileVelocity ProfileS WaveP Wave

Dep

th

(m)

0

45000 5000 0 5000

2800 m

3200 m

Salt

Incorrect velocity model

P-to-S ratio = 1.6

Velocity (m/s) Velocity (m/s)

Z-Component VSP DataZ-Component VSP DataD

epth

(m

)

Traveltime (s)

2652

3887

1.2 3.0

Salt

Direct P

Reflected P

Reverberations

X-Component VSP DataX-Component VSP DataD

epth

(m

)

Traveltime (s)

2652

3887

1.2 3.0

Salt

Direct P

Reflected P

Reverberations Direct S

Local Reverse Time Migration ResultLocal Reverse Time Migration Result

(1)

(2)

(3)

(1) specular zone, (2) diffraction zone, (3) unreliable zone

3.3

Dep

th (

km)

3.9

0 100Offset (m)

39receivers

reflectivity

ConclusionsConclusions

• VSP->XWell transform alternative to VSP_>SWPVSP->XWell transform alternative to VSP_>SWP

and VSP->SSP transformsand VSP->SSP transforms

• Source statics eliminated, no need to know src. Source statics eliminated, no need to know src. Location or excitation timeLocation or excitation time

• Local v(x) needed, overcomes defocusing due to Local v(x) needed, overcomes defocusing due to overburdenoverburden

• Not battle-field tested, needs decon probably, weird Not battle-field tested, needs decon probably, weird resolution characteristicsresolution characteristics