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

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

Outline Supervirtual Refraction Theory Synthetic OBS Results Taiwan OBS Results Summary

Outline Supervirtual Refraction Theory Synthetic OBS Results Taiwan OBS Results Summary

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

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

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

{ 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’

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

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

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

Outline Supervirtual Refraction Theory Synthetic OBS Results Taiwan OBS Results Summary

Synthetic Results Marine Model Synthetic CSG Time (s) 12 12 Time (s) 12 km 0 72 km 72 km 12 66 X (km) 0 72 km Super-virtual CSG Noisy CSG 12 12 11 11 Time (s) Time (s) Time (s) Time (s) 16 16 0 72 km 30 66 X (km) 30 66 X (km) 0 72 km

Outline Supervirtual Refraction Theory Synthetic OBS Results Taiwan OBS Results Summary

Deconvolved Taiwan OBS Data (Kirk MicIntosh, UT Austin) 8 13 Time (s) Time (s) 26 128 km 16 km 112 km

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?

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