1. Super-virtual Refraction Interferometry: Theory
Pawan Bharadwaj, Gerard Schuster, Ian Mallinson
KAUST
Standard OBS Receiver Gather
Super-virtual OBS Receiver Gather
110 km
110 km

2. Motivation Problem: Short Streamer=Missing Low-Wavenumber Components
Solution: Streamer+OBS+Refraction Interferometry+Tomography?
Key Idea: Stack Refractions to get SNR= N for Wide-Offset
Refractions
source

3. Outline Supervirtual Refraction Theory Synthetic OBS Results
Taiwan OBS Results
Summary

4. Outline Supervirtual Refraction Theory Synthetic OBS Results
Taiwan OBS Results
Summary

5. Refl., Refrac., Inteferometry Background
Reflection Stacking: Harry Mayne (1950’s-60’s)
Refraction Conv. & Correl: Palmer (1980’s)
Daylight Imaging: Claerbout/Rickett (1990s)
Virtual Sources: Calvert & Bakulin (2004)
Recip. Eqn. Correlation: Wapenaar (2004)
Stationary Phase & Src Points: Snieder (2004)
Refraction Interferometry: Dong et al. (2006)
Applications Refraction Interferometry: BSU (2008- current)
Super-virtual Refraction Interferometry: KAUST (2010- )
datum
dedatum

6. Stacked Reflections: NMO + Stacking
Benefit: SNR = N
Liability: Horizontal Reflectors

7. 1.Stacked Refractions: + Stacking
t - t = t - t
A B’C A B’B B’C B’B
1.Stacked Refractions: Stacking
d d AB AC
~ d BC A d d dt
B C e dt A1
B C

8. { e e e wt wt w(t t ) = What does mean? i -i i - d d ~ d B C A1 B C
Interpretation: Virtual source at B’
excited at advanced time -tB’B
Time it takes to go A->C
A B’C e i wt
A B’B e -i wt
Time it takes to go A->B
d d AB AC
~ d BC A = e
B’C i
w(t - t
B’B ) dt { e A1
B C
Dashed arrow=neg. time
Solid arrow=pos. time B’

9. 1.Stacked Refractions: + Stacking
d d AB AC
~ d BC A
virtual
Wapenaar (2004); Snieder (2004) ~
d d AB AC
~ d BC
Asrc
virtual
Common Pair Gather (Dong et al., 2006) dt dt
B C A
B C e dt
Benefit: SNR = N dt A3 A2 A1
B C
Problem: Unknown Time & Shorter Src-Rec. Offset

10. 2. Dedatum Virtual Refraction to Known Surface Point
Datuming
Dedatuming
real
super-virtual
d d AB BC
~ d AC
Brec
supervirtual *
virtual
d d AB AC
~ d BC
Asrc
virtual
Asrc
Brec A
B C
B C A
B C * =
Raw trace
Virtual trace
(Calvert+Bakulin, 2004)
Super-virtual trace +
The solution is the convolve the redatumed shot record with a real trace recorded at y from a new source position. The unknown time advance is cancelled out and result of the convolution is a virtual trace located at z. * =
Liability: ? Time & Shorter Offset
Benefit: SNR = N

11. Super-virtual Refraction Summary
d d AB AC
~ d BC
Asrc
virtual
1. Datum Refractions: ( Recip. Thm. Correl.)
Asrc
A B C
A B C
B C =
Asrc =
B C
A B C *
2. Dedatum Virtual Traces: (Recip. Thm. Conv.)
Brec
d d AB BC
~ d AC
supervirtual
virtual
In summary these are the three steps to generate a super virtual trace.
3. Assumption: Head Waves. Benefit: SNR = sqrt(N). Liability: No Diving Wave
4. Datum+Dedatum = 1st iteration iterative least squares datuming (Xue+GTS, 2009) 11

12. Outline Supervirtual Refraction Theory Synthetic OBS Results
Taiwan OBS Results
Summary

13. Synthetic Results Marine Model Synthetic CSG Time (s)12 12
Time (s)
12 km km
72 km 12 66
X (km) km
Super-virtual CSG
Noisy CSG 12 12 11 11
Time (s)
Time (s)
Time (s)
Time (s) 16 16 km 30 66
X (km) 30 66
X (km) km

14. Outline Supervirtual Refraction Theory Synthetic OBS Results
Taiwan OBS Results
Summary

15. Deconvolved Taiwan OBS Data (Kirk MicIntosh, UT Austin)8 13
Time (s)
Time (s) 26
128 km km
112 km

16. Summary * 1. Super-virtual Interferometry: Datum & Dedatum
2. Main Benefit: SNR = N vs
3. Key Assumption: Refractions = Head Waves
4. NMO for Reflections (Mayne, 1960s) for Refractions
5. Refraction Applications: FWI, AVO, Anisot., Time Lapse?

17. Acknowledgments
Thank sponsors of CSIM Consortium: Aramco, BP, Chevron, Total, Pemex, Petrobras, Schlumberger-Western-Geco, Tullowoil
Prof. Kirk McIntosh (UT Austin)
Indian School Mines