1. Kirchhoff vs Crosscorrelation
Migration
Kirchhoff Mig.
Crosscorr. Mig.
X (m)
1000
0.5 km
2.5 km
0.5 km
2.5 km
950
Depth (m)
1950
0.5 km km
0.5 km km

2. Kirchhoff vs Crosscorrelation
Migration
Kirchhoff Mig.
Crosscorr. Mig.
X (m)
1000
0.5 km
2.5 km
0.5 km
2.5 km
950
Depth (m)
1950
0.5 km km
0.5 km km

3. VSP Images with Static Errors
Kirchhoff Mig.
Crosscorr. Mig.
X (m)
1000
0.5 km
2.5 km
0.5 km
2.5 km
950
Depth (m)
1950
0.5 km km
0.5 km km

4. VSP Images with Static Errors
Kirchhoff Mig.
Crosscorr. Mig.
X (m)
1000
0.5 km
2.5 km
0.5 km
2.5 km
950
Depth (m)
1950
0.5 km km
0.5 km km

5. Field RVSP Images with Static Errors
Kirchhoff Mig.
Crosscorr. Mig.
1000
0.0 km
.9 km
950
Depth (m)
1950
0.0 km km
0.0 km km

6. Enhancing Illumination Coverage of VSP by Crosscorrelation Migration
Interferometric Imaging
Jianhua Yu
Gerard T. Schuster
In this talk, we would like to give our investigation on enhancing illumination coverage of VSP by xcorrmig.
University of Utah

7. Outline Motivation Crosscorrelation Migration SEG/EAGE Model
2-D RVSP Field Data
The talk includes five parts. First is motivation, In the second part, I give a brief introduction to xcorrmig method; then I shown some examples including SEG mode, and field data example. Finally it is conclusion.
Conclusions

8. Outline Motivation Crosscorrelation Migration SEG/EAGE Model
2-D RVSP Field Data
motivation
Conclusions

9. Problems with VSP Imaging Quality?
Limited recording aperture
Narrow illumination coverage
Static errors at VSP well caused by location errors
First we will see what factors affect VSP image quality

10. Solution: Xcorr Migration of Ghost Reflections
Widens illumination coverage VSP CDP
Another question may ask:
Why use crosscorrelation migration method?
(1) It increases the illumination coverage. Look this cartton. Ghost xcorrmig provides wider illimunation

11. Solution: Xcorr Migration of Ghost Reflections
Widens illumination coverage VSP CDP
Eliminates Rec. Statics: No Need to Know Rec. Location
Eliminates ~ ½ of the Raypath
Another question may ask:
Why use crosscorrelation migration method?
(1) It increases the illumination coverage. Look this cartton. Ghost xcorrmig provides wider illimunation

12. Outline Motivation Crosscorrelation Migration SEG/EAGE Model
2-D RVSP Field Data
Conclusions

13. Crosscorrelation Migration
Kirchhoff Migration of Crosscorelograms
m(x) = (g, s, t + t ) gx sx s g s g s
Another question may ask:
Why use crosscorrelation migration method?
(1) It increases the illumination coverage. Look this cartton. Ghost xcorrmig provides wider illimunation g

14. How do you remove kinematic effects of propagating
through unintersting parts of medium?
Uninteresting Part of Medium

15. Pick Direct Arrival Time T and shift all Uninteresting Part of Medium{ M T
Pick Direct Arrival Time T and shift all
Traces by T M
Uninteresting Part of Medium

16. Pick Direct Arrival Time T and shift all
Traces by T M M M
Uninteresting Part of Medium

17. Shifting Traces Removes Kinematic Effects
Of Propagating through Uninteresting Parts of Medium M
Uninteresting Part of Medium

18. Shifting Traces Removes Kinematic Effects
Of Propagating through Uninteresting Parts of Medium M
Uninteresting Part of Medium

19. m(x) = (g, t + t ) Kirchhoff Migrate psuedo-shot gathers
Shifting Traces Removes Kinematic Effects
Of Propagating through Uninteresting Parts of Medium. .
Source Moved to Surface g M M
m(x) = (g, t + t ) gx g Mx
Kirchhoff Migrate psuedo-shot gathers
Can replace time-shifted traces by crosscorrelograms

20. Interferometric Summary
Wider, taller coverage. Eliminates well statics and uninteresting parts of the medium. 
VSP
Above Source
Imaging {
Wider Coverage ?

21. Interferometric Summary
Wider, taller coverage. Eliminates well statics and uninteresting parts of the medium. 
VSP
Above Source
Imaging {
Wider Coverage M
m(x) = (g, t + t ) gx g Mx
Kirchhoff Migrate psuedo-shot gathers

22. Outline Motivation Crosscorrelation Migration SEG/EAGE Model
2-D RVSP Field Data
Let me show one example.
Conclusions

23. SEG/EAGE Model V = 1.5 - 3.0 km/s Well 256 Sources Depth (km) 2 X (km)
V = km/s
Depth (km)
This is SEG geology model. And its velocity model. Velocity ranges from 1.5 km.s to 3.0 km.s
SEG/EAGE Model 2
X (km) 3

24. Acquisition Parameters:
Well location: (1.5 km, 0 km)
Source interval: 10 m
Source number: 256
Acquisition Parameters:
Well
1 km
Depth (km)
Receiver interval: 10 m
Receiver depth range: km
Receiver number: 91
Here I show the main parameters.
Sample interval: 1 ms
Recording length: 3 s 2
X (km) 3

25. Depth (km)
0.2
0.9
CSG 160
Time (s)
This is one common source gather (#160) 3

26. Depth (km) 0.2 0.9 Ghosts (CSG 160) Time (s) 3
Ghosts (CSG 160)
Time (s)
Same shot gather but after separating primaries from ghosts 3

27. CRG 60 Xcross 60 X (km) 1.4 2.4 X (km) 2.4 Time (s) 3
2.4
Time (s)
Left panel is common receiver gather (#60). Green line indicates the master trace. And the right shows the crosscorrelograms.
CRG 60 3

28. Kirchh Mig (45) Xcorr Mig (45) Xcorr. Mig(15’) 0.5 Depth (km) 2.0 0.5
The comparison of standard migration and xcorr migration results.
2.0
0.5
2.5
0.5
2.5
0.5
2.5
X (km)

29. Static Errors at Well Well Depth (m) 900 50 Raw Data
Well Depth (m)
900 50
Raw Data
Static errors (ms)
To investigate the robust of xcorr migration, I add static errors at the receiver location in the well.
-50
Static Errors at Well

30. Kirchhoff Migration Static Error: 0 X (km) Static Error: 25 ms 2.5
0.5
Depth (km)
Here are the standard migration result with different static erorrs
2.0
0.5
2.5
0.5
2.5
0.5

31. Crosscorrelation Migration
Static Error: 0
X (km)
Static Error: 25ms
2.5
Static Error: 50 ms
0.5
Depth (km)
Here the xcorr migration with different static variance level. It is clear that static erorr has little influence to the new migratioon method.
2.0
0.5
2.5
0.5
2.5
0.5

32. Primary vs Multiple Image
Velocity Model
Primary vs Multiple Image
Depth (km) 11 16 16
X (km)
X (km)

33. Contents Motivation Crosscorrelation Imaging Condition SEG/EAGE Model
2-D RVSP Field Data
Another exanple is from 2-D field RVSP data
Conclusions

34. Depth (ft) 30 900 Raw Data(CRG15) Time (s) 0.3
Raw Data(CRG15)
Time (s)
Common receiver gather before separation
0.3

35. Depth (ft) 30
900
Ghosts
Time (s)
Ghost reflections
0.3

36. Field Data (CSG 25) Trace No. 5 24 Trace No. Time (s) 1.2 0.2 5 24 0.5
xcorr data (muted) 5 24
0.5
Master trace
Raw data (muted)
Time (s)
Common source gather and its crosscorrelograms. Master trace is at the left trace.
1.4

37. X (ft) X (ft) 400 400 200 Standard mig Xcorr. mig Depth (ft) 1300
400
400
200
Standard mig
Xcorr. mig
Depth (ft)
Comparison of standard (left) and xcorr migration (right). Note the difference in the deeper part.
1300

38. Exxon Data Standard Well data Xcorr. Depth (ft) 1100
Depth (ft)
The comparison of well log data (center), stabndard migration (left 4 traces) and xcorr migration result (right 4 traces)
1100

39. Outline Motivation Crosscorrelation Migration SEG/EAGE Model
2-D RVSP Field Data
conclusions
Conclusions

40. Crosscorrelogram Migration Conclusions
Increased illumination coverage in the VSP image. VSP ->CDP
Eliminate the static errors in the well
No need to know source (RVSP) or receiver location (VSP)
Half sensitivity to velocity migration errors than mult. migration by “mirrors”.

41. Conclusions Loss of some lateral resolution?
Xcorr
Narrow Angle
Kirchhoff
Wide Angle vs
Be careful about virtual multiple
Ghost is weaker than primary
Extra summation compared to KM

42. Acknowledgments UTAM sponsors Exxon for 2-D field data
J. Claerbout + J. Rickett
II evolved from daylight imaging

43. X (ft) X (ft) 400 400 200 Standard mig Xcorr. mig Depth (ft) 1300
400
400
200
Standard mig
Xcorr. mig
Depth (ft)
Comparison of standard (left) and xcorr migration (right). Note the difference in the deeper part.
1300

44. Geological Model (2001) X(km) 0 4 Depth(km) 3
Depth(km)
In 2001, we proposed a crosscorrelation migration method and tested using a flat-layered model to test 3
(2001)

45. Too simple? Widen illumination? If there are static errors in well?
Migration Result Using Crosscorrelation Imaging
X (km)
1.6
2.1
Too simple?
Widen illumination?
Time (s)
If there are static errors in well?
Here is the crosscorrelation migration result using ghost reflections.
It matches well with true geologic model. But there are severasl questions that may arise?
This model is too simple? How does crosscorrelation migration result work for realistic model?
VSP imaging has narrow limited coverage. Does this method help to address this problem?
Is this method sensitive to the statics errors in the drilling hole?
2.2

46. Why Use Crosscorrelation Migration?
Widen the illumination coverage in the VSP image
VSP geometry
Equivalent surface geometry
Xcorr
The second benefit we can get is by using xcorr. Imaging condition, the VSP geometry is transformed into CDP geometry.
That will has contribution to increase the illumination coverage.

47. Find R(x,z) but not know source location
Seismic Ghost Reflection
Ghost
Direct
Find R(x,z) but not know source location ?

48. t } m(x) = (g, t + t ) Seismic Interferogram: Correlate Traces
Seismic Ghost Reflection
Master
Ghost
Direct has kinematics of primary reflection x
Ghost
Direct x
Direct x
Direct t } 1 2 M
m(x) = (g, t + t ) gx g Mx M
Kirchhoff Migrate psuedo-shot gathers M

49. RVSP Well Receiver Source Ghost Direct Wave Primary
This is RVSP geometry. There are three knids of waves:
Primary, ghost reflection, and direct waves.
Source
RVSP

50. Ghost Reflection Imaging Condition:
There are two geophones. At the geophone G, the ghost reflection travel time is ???, and we also observe the direct waves s x

51. After Crosscorrelation of Two Traces at Locations g & g’
After crosscorrelation of two traces at g’ and g, director traveltime at g is become like this; the ghost reflection traveltime
is becoming s x

52. After Crosscorrelation of Two Traces at Locations g & g’
The new ghost imaging equation imply that after crosscorrelation of two traces, the imaging condition is equivalent to a reflection imaging conditon where source is at g’ position and geophone at g. s x

53. After Crosscorrelation of Two Traces at Locations g & g’
This equation is our xcorrmigration imaging condition. s x

54. Recall Green’s Theorem
Every Surface Point = Source Point

55. Why is there insensitivity to static errors in the well?g’ g x
Static errors
Another question we mak ask? Why is this new crosscorrelation migration insensitive to static errors in the well ? First equation is ghost reflection travetime. There is static error at the well delta tao s. substitute equation 2 into 1, we get the equation 3. after some slightly arrangement, the crosscorrelation imaging condition is the bottom equation. It is free of sttic errors.

56. Crosscorrelogram Migration
Migrated Image
Crosscorrelograms
Crosscorrelation Imaging Condition
This is the basic crosscorrelation migration equation. Input data are the crosscorrelograms.. Using new imaging condition, we can got the final result.

57. Field Data
Well data
Xcorr. Migration
Depth (ft)
1100

58. Exxon Data
Well data
Standard Migration
Depth (ft)
1100