Local Migration with Extrapolated VSP Green’s Functions Xiang Xiao and Gerard Schuster Univ. of...

Local Migration with Extrapolated VSP Local Migration with Extrapolated VSP Green’s FunctionsGreen’s Functions

Xiang Xiao and Gerard SchusterXiang Xiao and Gerard Schuster

Univ. of UtahUniv. of Utah

OutlineOutline

MotivationMotivation

OutlineOutline

MotivationMotivation

Local VSP Migration Theory Local VSP Migration Theory

OutlineOutline

MotivationMotivation

Local VSP Migration Theory Local VSP Migration Theory

Numerical TestsNumerical Tests

Sigsbee VSP Data SetSigsbee VSP Data Set

GOM VSP Data Set GOM VSP Data Set

OutlineOutline

MotivationMotivation

Local VSP Migration Theory Local VSP Migration Theory

Numerical TestsNumerical Tests

Sigsbee VSP Data SetSigsbee VSP Data Set

GOM VSP Data Set GOM VSP Data Set

ConclusionsConclusions

MotivationMotivation

ProblemProblem: VSP Migration image distorted by overburden+statics: VSP Migration image distorted by overburden+statics

SolutionSolution: Local VSP Migration: Local VSP Migration

OutlineOutline

MotivationMotivation

Local VSP Migration Theory Local VSP Migration Theory

Numerical TestsNumerical Tests

Sigsbee VSP Data SetSigsbee VSP Data Set

GOM VSP Data Set GOM VSP Data Set

ConclusionsConclusions

Theory: Theory: StandardStandard VSP Migration VSP Migration

directdirect

reflectionreflection

Reflections: R(g)

reflectionreflection gG(x|g)*R(g)

g

x G(x|s)W()x

Backproject Backproject Forwardproject Forwardproject

Standard VSP migration image: m(x) = G(x|g)*R(g)g

/G(x|s)W()

Backprojected refl. Forwardproject. direct

Src. Wavelet: Src. Wavelet: W(W())

s

~~ G(x|g)*R(g)g

G(x|s)*W()*

Theory: Theory: LocalLocal VSP Migration VSP Migration

directdirect

reflectionreflection

Reflections: R(g)

reflectionreflection gG(x|g)*R(g)

g

x

Backproject Backproject

directdirect

Theory: Theory: LocalLocal VSP Migration VSP Migration

directdirect

reflectionreflection

Backproject Direct waves: Backproject Direct waves: D(D(gg))Reflections: R(g)

reflectionreflection gG(x|g)*R(g)

g

x

Backproject Backproject

directdirect

D(g)G(x|g)*D(g)

g

Backprojected refl. Backproject. direct

Local VSP migration image: m(x) = G(x|g)*D(g)g

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

~~ G(x|g)*R(g)g

G(x|g)D(g)*g

Static killerStatic killerFAST 3D RTMFAST 3D RTM

Local vs Local vs StandardStandard VSP Migration VSP MigrationReflection Illumination ZonesReflection Illumination Zones

~~LocalLocal VSP migration image: m(x) VSP migration image: m(x) G(x|g)*R(g)G(x|g)*R(g)[[g

G(G(xx||gg)*D()*D(gg)]*)]*g

StandardStandard VSP migration image: m(x) VSP migration image: m(x) ~~ G(x|g)*R(g)G(x|g)*R(g)g

[G([G(xx||ss)W()W(

Backprojected refl.Forwardprojected direct.

Backproject. direct

Standard VSP ReflectionStandard VSP ReflectionIllum. ZoneIllum. Zone

Local VSP ReflectionLocal VSP ReflectionIllum. ZoneIllum. Zone

Benefits of Local VSP MigrationBenefits of Local VSP Migration• Target oriented!Target oriented!– Only a local velocity model near the well is needed.Only a local velocity model near the well is needed.

– Salt and overburden are avoided.Salt and overburden are avoided.

– Fast 3D RTM Fast 3D RTM

• Source statics are automatically accounted for.Source statics are automatically accounted for.

Liabilities of Local VSP MigrationLiabilities of Local VSP Migration• Limited illumination ZoneLimited illumination Zone

Standard VSP ReflectionStandard VSP ReflectionIllum. ZoneIllum. Zone

Local VSP ReflectionLocal VSP ReflectionIllum. ZoneIllum. Zone

OutlineOutline

MotivationMotivation

Local VSP Migration Theory Local VSP Migration Theory

Numerical TestsNumerical Tests

Sigsbee & Schlumberger VSP DataSigsbee & Schlumberger VSP Data

GOM VSP Data Set GOM VSP Data Set

ConclusionsConclusions

Sigsbee P-wave Velocity ModelSigsbee P-wave Velocity Model00

Dep

th (

km)

Dep

th (

km)

9.29.2

45004500

15001500

m/sm/s

-12.5-12.5 12.512.5Offset (km)Offset (km)

279 shots279 shots

150 receivers150 receivers

15

Local Reverse Time Migration Results

4.6

9.2

Dep

th (

km)

-3 3Offset (km)

True modelMigration image

f = fault

f

d

d

(1)

(2)

(3)

d = diffractor

Virtual well

OutlineOutline

MotivationMotivation

Local VSP Migration Theory Local VSP Migration Theory

Numerical TestsNumerical Tests

Sigsbee & Schlumberger VSP DataSigsbee & Schlumberger VSP Data

GOM VSP Data Set GOM VSP Data Set

ConclusionsConclusions

17

Dep

th

(km

)

Offset (km)

10-12 12

0

Schlumberger 2D Isotropic Elastic Model

0

291 shots

287 receivers

Direct P

PPS

PSS

Dep

th

Dep

th

(km

)(k

m)

Time (s)Time (s)

88

00 8

VSP CSG X-componentVSP CSG X-component

VSP CSG Z-componentVSP CSG Z-component44

Dep

th

Dep

th

(km

)(k

m)

88

44

Two-component VSP Synthetic Data SetTwo-component VSP Synthetic Data Set

(Acknowledge VSFusion)

4.5

2.0

km/s(a) P-wave submodel

Dep

th

(km

)

8.7

6.0

Dep

th

(km

)

8.7

6.0

Offset (km)0 1.8

(b) P-wave background1D model

4.5

2.0

km/s

Offset (km)0 1.8

Dep

th

Dep

th

(km

)(k

m)

8.78.7

6.06.0

Offset (km)Offset (km)00 1.21.2

Local RTM Image

OutlineOutline

MotivationMotivation

Local VSP Migration Theory Local VSP Migration Theory

Numerical TestsNumerical Tests

Sigsbee & Schlumberger VSP DataSigsbee & Schlumberger VSP Data

GOM VSP Data Set GOM VSP Data Set

ConclusionsConclusions

Dep

th

Dep

th

(m)

(m)

Offset (m)Offset (m)

48784878

0 18291829

00

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

2800 m2800 m

3200 m3200 m

SaltSalt

82 82 receiversreceivers

@600 m offset@600 m offset @1500 m offset@1500 m offset

Z-Component VSP DataZ-Component VSP DataD

epth

D

epth

(m

)(m

)

Traveltime (s)Traveltime (s)

26522652

38873887

1.21.2 3.03.0

SaltSalt

Direct PDirect P

Reflected PReflected P

ReverberationsReverberations

24

150 m offset

(1)

(2)

(3)

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

3.3

Dep

th (

km)

3.9

0 100Offset (m)

39receivers

reflectivity

Local VSP Migration Images Local VSP Migration Images 600m and 1500 m offsets600m and 1500 m offsets

3.33.3

4.44.4

00 600600

Dep

th (

km)

Dep

th (

km)

Offset (m)Offset (m) 00 600600Offset (m)Offset (m)

600 m Image600 m Image 1500 m Image1500 m Image

ConclusionsConclusions

• Synthetic tests show accurate imaging around Synthetic tests show accurate imaging around well by Local VSP. Field data results?well by Local VSP. Field data results?

• Advantages: Advantages:

Only local velocity model neededOnly local velocity model needed

Inexpensive target oriented RTMInexpensive target oriented RTM

Statics removedStatics removed

• Disadvantages: Disadvantages:

Smaller illumination zone: Smaller illumination zone:

Less resolutionLess resolution

vsvs

G(g|x)*G(g|x)*G(x|s)*G(x|s)* vs vs G(g|x)*G(g|x)*G(x|s)G(x|s)

AcknowledgmentAcknowledgment

• We thank the sponsors of the 2007 We thank the sponsors of the 2007 UTAM consortium for their support.UTAM consortium for their support.

• We thank VSFusion for Schlumberger We thank VSFusion for Schlumberger modelmodel

• We thank BP for VSP DataWe thank BP for VSP Data

• Prev. WorkPrev. Work

Yonghe Sun (UTAM report 2004)Yonghe Sun (UTAM report 2004)Jianhua Yu (UTAM report 2005)Jianhua Yu (UTAM report 2005)Xiao Xiang (Geophysics 2006)Xiao Xiang (Geophysics 2006)

28

Subsalt Imaging

s

x

G(x|g) g

G(x|s)

m(x) ~

~ G(x|s)

Forwarddirect

sds

*

D(g|s)

G(x|g)*

Backward reflection

g

D(g|s)dg

Errors in the overburden

and salt body velocity model

Defocusing

Overview SSPVSP Local RTM Local RTM PS Summary

29

Local Reverse Time Migration

s

x

G(x|g) g

G(x|s)

g’

G(x|s)= G(x|g’)* D(g’|s)dg’

Backward Direct wave

g’ Local VSP Green’s function

Overview SSPVSP Local RTM Local RTM PS Summary

30

m(x) ~ s

~ dsg’

G(x|g’)* D(g’|s) dg’

Backward D(g’|s)

G(x|g)* D(g|s)dg

Backward D(g|s)

g

*

x1(1)

(2)

x2

x3

(3)

s

g

g’

Illumination Zones

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

TheoryMotivation Numerical Tests Conclusions

31

Dep

th

(km

)

10

0

Offset (km)-12 120

(a) Ray tracing direct P

(c) PPS events (d) Pp events

(b) PSS events

Dep

th

(km

)

10

0

Offset (km)-12 120

Aperture by Ray Tracing

Introduction Numerical Tests ConclusionsTheory

Theory: Theory: LocalLocal VSP Migration VSP Migration

directdirect

reflectionreflection

Direct waves: Direct waves: D(g)D(g)Reflections: R(g)

reflectionreflection gG(x|g)*R(g)

g

x

Backproject Backproject

Backproject Backproject

Migration image: m(x) = G(x|g)*R(g)g

G(x|g)W()

Backprojected refl. Forwardproject. directG(x|g)W()

directdirect

D(g)

Sigsbee P-wave Velocity ModelSigsbee P-wave Velocity Model00

Dep

th (

km)

Dep

th (

km)

11.011.0

45004500

15001500

m/sm/s

12.512.5Offset (km)Offset (km)

279 shots

150 receivers287 recs

291 recs

35

X-Component VSP DataD

epth

(m

)

Traveltime (s)

2652

3887

1.2 3.0

Salt

Direct P

Reflected P

Reverberations Direct S

Introduction Numerical Tests ConclusionsTheory

36

150 m offset

3.3

3.9

0 100

Dep

th (

km)

Offset (m) 0 100Offset (m)

Without deconvolution

With deconvolution

Introduction Numerical Tests ConclusionsTheory

Dep

th

Dep

th

(km

)(k

m)

1313

00

VSP CSGVSP CSG

00 1313Time Time (s)(s)