local reverse time migration with vsp green’s functions

Local Reverse Time Migration with VSP Green’s Functions

Xiang Xiao

UTAM, Univ. of Utah

May 1, 2008

PhD Defense

99 pages

2

Outline

• Introduction and overview• SSP VSP SWP interferometric

transform• Local reverse time migration: horizontal

reflector imaging• Local reverse time migration: salt flank

imaging with transmitted P-to-S waves• Summary

Overview SSPVSP Local RTM Local RTM PS Summary

3

Outline






4

Data

Tim

e

Offset

ModelD

epth

Offset

r(x) D(g|s)Forward modelling

InverseMigration

m(x)

Migration Image

Low subsalt resolution,Defocusing!


10

Outline





imaging by transmitted P-to-S waves• Summary

11

Outline


• SSP VSP SWP interferometric transform

– Motivation– Theory – Numerical Tests

• SEG/EAGE salt model• Double datuming

– Conclusions

12

I. Why we need more VSP?

Surface related statics

SSP VSP

•Twice OnceSeabedSeabed

SaltSalt

TargetTarget

Overburden velocity error

•Twice OnceRaypath

•Longer Shorter Attenuation

•More LessFrequency

Resolution

•Lower Higher

•Lower Higher

SSPVSP Motivation Theory Numerical Tests Conclusions

13

How to get more VSP?

dxG(B|A) ~

RVSP VSP

G(A|x)* G(B|x)

SSP

S2

~

S2

A

Bx

S1

RVSP

S2

A

Bx

S1

VSP

S2

A

Bx

S1

SSP


14

3D Application

3D VSP3D SSP

Naturally datuming !

3D RVSP

SSP + VSP RVSP !

Low fold

High fold !


15

X

SS

SeabedSeabed

TargetTarget

SaltSalt

SSP/RVSP apertureSSP/RVSP aperture

ggVSP apertureVSP aperture

Shot coverageShot coverageReceiver coverageReceiver coverage


16

Use it, or lost it…

3D RVSP

SSP + VSP RVSP !

High folds !

SaltSalt

Better image under the salt !

SSP, VSPWell log

Better Geologic interpretation !


17

What is the benefit ?

– Higher fold virtual RVSP data are obtained;– Sources are closer to the target;

SSP + VSP RVSP

SaltSalt

– No velocity model is needed;– Multi-arrival are considered;


18

How to skip overburden?

dxG(g|g’) ~

SWP VSP

G(g’|s)* G(g|s)

VSP

S~

gg’

s

VSP

gg’

s

VSP

gg’

s

Virtual Source Gather

No velocity model is needed !


19

Application of VSPSWP transform:

gg’

s

Virtual Source Gather

Salt flank imaging

P and S wave checkshot

Sediment imaging

Multiple/teleseismic imaging

4D Reservoir monitoring

Shear wave splitting and crack orientation

Seismic while drilling

……

Application


20

Outline


• SSP VSP SWP interferometric transform


• SEG/EAGE model• Double datuming

– Conclusions

21

P-wave velocity model0

Dep

th (

m)

-7850 7850Offset (m)

Velocity (m/s)4500

15003600

SEG/EAGE Salt Model


22


Dep

th (

m)

-7850 7850Offset (m)

Velocity (m/s)4500

15003600

SSP Data Geometry…SSP


23

Data

Synthetic SSP CSG

Tim

e (s

)

0

6

Offset (m)-2000 2000


24


Dep

th (

m)

-7850 7850Offset (m)

Velocity (m/s)4500

15003600

VSP Geometry…


25

Data

Tim

e (s

)

Synthetic VSP CRG0

6

Offset (m)-7850 7850

Synthetic SSP CSG

Tim

e (s

)

0

6

Offset (m)-7850 7850


26

Traces comparisons

Am

pli

tud

e

Time (s)2 6

Synthetic RVSP CSG

Tim

e (s

)

0

6

Redatumed RVSP

Tim

e (s

)

0

6Offset (m)-7850 7850

1.4 kmComparison

Zoom area

27

Zoom View of TracesN

orm

aliz

ed A

mp

litu

de

Time (s) 5.53

Redatumed RVSP trace

Direct waves are cut

poor data folds


28


Dep

th (

m)

-7850 7850Offset (m)

Velocity (m/s)4500

15003600

Another Datuming Results


29

Synthetic RVSP CSGT

ime

(s)

0

6

Redatumed RVSP

Tim

e (s

)

0

6Offset (m)-2000 2000

Traces comparisons

Am

pli

tud

e

Time (s)2 6

2.4 kmComparison

30

No

rmal

ized

Am

pli

tud

e

Time (s)2.5 6

Zoom viewDirect waves are cut

poor data foldsRedatumed RVSP trace


31


Dep

th (

m)

-7850 7850Offset (m)

Velocity (m/s)4500

15003600

SEG/EAGE Salt Model


32

Shot 320 SSP primary WEM 20 Hz1.5

3.5

Dep

th (

km)

-4 4Offset (km)

Shot 320 RVSP WEM 20 Hz

Dep

th (

km)

1.5

3.5

33

33 shots SSP WEM 20 Hz

33shots VSP WEM 20 Hz

Dep

th (

km)

0

3.6Offset (km)-4 4

33 RVSP+VSP WEM 20 Hz

Offset (km)-4 4

SEG/EAGE salt model0

3.6

Dep

th (

km)

34

ss gg

s’s’

ss

s’s’

gg

s’s’

gg

s’s’ g’g’

gg

g’g’ s’s’ g’g’

SSPVSPSWP Transform


35

1% error in migration model


Dep

th (

km)

0

3.6Offset (km)-8 8


Offset (km)-8 8

645 shots SSP WEM0

3.6

Dep

th (

km)

36



Dep

th (

km)

0

3.6Offset (km)-8 8


Offset (km)-8 8

33 shots VSP WEM0

3.6

Dep

th (

km)

37

645 shots SSP primary WEM 20 Hz0

3.5

Dep

th (

km)

-8 8Offset (km)

Shot 320 BSSP WEM 20 Hz

Dep

th (

km)

1.5

3.5

38

645 shots SSP primary WEM 20 Hz0

3.5

Dep

th (

km)

-8 8Offset (km)

Shot 320 BSSP WEM 20 Hz

Dep

th (

km)

1.5

3.5

40

Conclusions

• Natural datuming, no velocity model is needed !

• Higher fold virtual VSP data are obtained !

• Source are closer to the target, less approximation.• Better resolution.


41

Outline






42

Outline

Motivation Theory Numerical Tests ConclusionsLocal RTM

• Local reverse time migration: horizontal reflector imaging


• Sigsbee VSP Data Set• GOM VSP Data Set

– Conclusions

43

VSP Forward Modeling

s

x

g

D(g|s)

VSP data


44

Reverse Time Migration

s

x

g

D(g|s)

VSP data


46

Reverse Time Migration (RTM)

s

x

G(x|g) g

G(x|s)

BackwardD(g,s)

Forwarddirect

Forward direct:1) Salt velocity model is required, but hard to

build.2) Errors due to imperfect velocity models.

3) Need to estimate statics, anisotropy, etc.


47

s

g

g’

x

VSPSWP Interferometry

Migrate virtual source gather D(g|g’) Limitations

1) s and x are at different sides of the well2) Image near vertical structures


48

Outline





– Conclusions

49

Key Idea of Local RTM

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

Transmission T(g|s)

s

g

Reflection R(g|s)

x


50

(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)s

Local VSP Green’s function

R(g|s)g

x

Key Idea of Local RTM


51

(d1) Crosscorrelation imaging condition


R(g|s)g

x

Deconvolution Imaging Condition


(d2) Deconvolution imaging condition


s

T(x|s)*T(x|s)

52

Benefits

• Target oriented!– Only a local velocity model near the well is

needed.– Salt and overburden is avoided.

– Fast and easy to perform.

• Source statics are automatically accounted for.

• Immune to salt-related interbed cross-talk.

Motivation Theory Numerical Tests SummaryLocal RTM

53

Outline





– Conclusions

54

Sigsbee P-wave Velocity Model0

Dep

th (

km)

9.2

4500

1500

m/s

-12.5 12.5Offset (km)

279 shots

150 receivers


55

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)

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

d = diffractor


56

Outline





– Conclusions

57

Dep

th

(m)

Offset (m)4878

0 1829

0

GOM VSP Well and Source LocationSource @150 m offset

2800 m

3200 m

Salt

82 receivers


@600 m offset @1500 m offset

58

P-to-S ratio = 2.7

Velocity 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)


59

Z-Component VSP DataD

epth

(m

)

Traveltime (s)

2652

3887

1.2 3.0

Salt

Direct P

Reflected P

Reverberations


60

X-Component VSP DataD

epth

(m

)

Traveltime (s)

2652

3887

1.2 3.0

Salt

Direct P

Reflected P

Reverberations Direct S


61

Local 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


62

150 m offset

3.3

3.9

0 100


Dep

th (

km)

Offset (m) 0 100Offset (m)

Without deconvolution

With deconvolution

63

600 m offset

3.3

4.4

0 600


Dep

th (

km)



With deconvolution

64

1500 m offset

3.3

4.4

0 600


Dep

th (

km)



With deconvolution

65

Conclusions• Subsalt reflectors are accurately imaged

near the well with subsalt velocity model only.

• Diffractors are also imaged.

• GOM local RTM image agrees with the well reflectivity.

• Deconvolution imaging condition helps.

• Illuminates horizontal subsalt reflectors around a vertical well.


66

Outline






67

Outline

Local RTM PS Motivation Theory Numerical Tests Summary

• Local reverse time migration: salt flank imaging by transmitted P-to-S waves


• Schlumberger VSP Data Set• GOM VSP Data Set

– Conclusions

68

Standard P-to-S Migration

x

s

m(x) ~ s

~ ds G(x|s)

Forward source P

P

S

g’

G(x|g’)*D(g’|s)dg’

Backward data S

g’

*

Converted wave VSP

D(g|s)


Salt and overburdenvelocity model is needed

69

Interferometric P-to-S Migration

x

s

P

P

S

D(g|g’) ~

s

~ ds*

g’

g

D(g’|s) D(g|s)

m(x) ~ g’

~ dg’dgg

D(g|g’)G(x|g) G(x|g’)* *

Virtual source gather


70

Kirchhoff P-to-S Migration

x

s

m(x) ~ s

~ ds

P

S

g’

e-itxg’ D(g’|s)dg’g’

Converted wave VSP

D(g|s)


e-itsx

Pg

71

Reduce Time Migration

~( ~( tt + + tt )- )- ( ( tt + + tt ) )sxsx xxgg

pickpickpickpick

sxsx xxgg

errorerrortt sxsx xxg’g’=( =( tt + + tt )- )- ( ( tt + + tt ) )pickpickpickpick

sxsx xxg’g’

x

s

P

S

g

Converted wave VSP

D(g|s)

Local RTM PS Motivation Theory Numerical Tests

m(x) ~ s

~ ds e-itxg’ D(g’|s)dg’g’

e-i(tsx+terror)

Summary

Pg

72

Outline





– Conclusions

73

x

s

P

P

S

m(x) ~ s

~ dsg’

G(x|g’)* D(g’,s) dg’

Backward P

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

Backward S

g

g’

g

*

Local Reverse Time Migration Theory


74

Outline





– Conclusions

75

Dep

th

(km

)

Offset (km)

10-12 12

0

Schlumberger 2D Isotropic Elastic Model

0

291 shots

287 receivers


76

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


77

Direct P

PPS

PSS

Dep

th

(km

)

Time (s)

8

0 8

VSP CSG X-component

VSP CSG Z-component4

Dep

th

(km

)

8

4

Two-component VSP Synthetic Data Set


78

4.5

2.0

km/s(a) P-wave submodelD

epth

(k

m)

8.7

6.0 2.5

1.0

km/s(b) S-wave submodel

4.5

2.0

km/s(c) P background model

Dep

th

(km

)

8.7

6.0

Offset (km)0 1.8

2.5

1.0

km/s(d) S background model

Offset (km)0 1.8

79

Dep

th

(km

)

8.7

6

Offset (km)0 1.8

(a) Standard Kirchhoff

(c) Interferometric migration (IM) (d) Local RTM

(b) Reduced-time migration (RM)

Dep

th

(km

)

8.7

6

Offset (km) 1.80

Comparison with Migration Methods


80Offset (km)0 1.8

Local RTM without wavefield separationD

epth

(k

m)

8.7

6

81Offset (km)0 1.8

Local RTM with wavefield separationD

epth

(k

m)

8.7

6

82Offset (km)0 1.8

Local RTM using Z component onlyD

epth

(k

m)

8.7

6

83

Outline

Motivation Theory Numerical Tests

Schlumberger VSP Data Set GOM VSP Data Set

Conclusions


84

Dep

th

(m)

Offset (m)4878

0 1829

0

GOM VSP Well and Source LocationSource @150 m offset

2800 m

3200 m

Salt

82 receivers


@600 m offset @1500 m offset

85

P-to-S ratio = 2.7

Velocity 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)


86

Z-Component VSP DataD

epth

(m

)

Traveltime (s)

2652

3887

1.2 3.0

Salt

Direct P

Reflected P

Reverberations


87

X-Component VSP DataD

epth

(m

)

Traveltime (s)

2652

3887

1.2 3.0

Salt

Direct P

Reflected P

Reverberations Direct S


88

Processing WorkflowOriginal Data

Rotate components

Pick desired events

Median filtering

Migration (KM, RM, IM, RTM)


89

Raypath Coverage

2000

4200

0 200

Dep

th

(m)

Migration of PPS

Salt

Offset (m)

39receivers


90

Migration of PPS

Salt

RM IM

0 200 0 200

KM

2000

4200

0 200

Dep

th

(m)

Offset (m)Offset (m) Offset (m)


91

Migration of PPS

Salt

IM, sediment flood Local RTM

0 200 0 200

RM

2000

4200

0 200

Dep

th

(m)

Offset (m)Offset (m) Offset (m)


92

Dep

th

(km

)

3.9

2.9

Offset (m)0 100

(a) Without deconvolution (b) With deconvolution

Offset (m)0 100

150 m Offset LRM Image

93


Dep

th

(km

)

4.4

2.9

Offset (m)0 600


Offset (m)0 600

94

Dep

th

(km

)

4.4

2.9

Offset (m)0 600


Offset (m)0 600


95

a) Synthetic b) 150 m offsetReduce time migration

c) 600 m offsetReduce time migration

Reduce Time Migration Image

Salt

2800 m

3200 m

Dep

th

(km

)

4.5

2.4

96

Summary

• Target oriented!– Only a local velocity model near the well is

needed.– Salt and overburden is avoided.

– Fast and easy to perform.

• Source statics are automatically accounted for.

• Immune to salt-related interbed cross-talk.


97

Summary






98

Acknowledgements

• Dr. Gerard Schuster and my committee members: Dr. Michael Zhdanov, Dr. Robert smith, Dr. Cari Johnson, Dr. Jianming Sheng for their advice and constructive criticism;

• Scott Leaney and Hornby Brian for their help on modeling;

99

Acknowledgements

• UTAM friends:– Jianhua Yu and Yonghe Sun on the research;– Jianming Sheng and Min Zhou for their experiences

on interferometric imaging;– Zhiyong Jiang and Ruiqing He for their help on

classes;– Travis Crosby and all UTAM students for their

cheerful attitude; All UTAM sponsors for their support;• Family

– My parents, brother and sister;

• Friends– Liyun Ma, Min Zhou, Jun Wang, Shuqian Dong,

Chaoxiong Ma, who encouraged me to continue on with my research.

100

Questions?

local reverse time migration with vsp green’s functions

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