1. Overview of Multisource Phase Encoded Seismic Inversion Wei Dai, Ge Zhan, and Gerard Schuster KAUST

2. Outline 1. Seismic Experiment: L m = d 1 1 2 2... N N 2. Standard vs Phase Encoded Least Squares Soln. L 1 L 2 d 1 d 2 m = vs N L + N L 1 2 1 2 [ m = [N d + N d ] ]m = [N d + N d ] 1 2 1 2 3. Theory Noise Reduction 4. Summmary and Road Ahead

3. Gulf of Mexico Seismic Survey L m = d Time (s) 4 0 d Goal: Solve overdetermined System of equations for m Predicted dataObserved datam(x,y,z) Common Shot Gather Streamer Reel Streamer Cables 4 km

4. Details of Lm = d Time (s) 6 X (km) 4 0 d G(s|x)G(x|g) G(s|x)G(x|g)m(x)dx = d(g|s) Reflectivity or velocity model Predicted data = Born approximation Solve wave eqn. to get G’s m

5. Outline 1. Seismic Experiment: L m = d 1 1 2 2... N N 2. Standard vs Phase Encoded Least Squares Soln. L 1 L 2 d 1 d 2 m = vs N L + N L 1 2 1 2 [ m = [N d + N d ] ]m = [N d + N d ] 1 2 1 2 3. Theory Noise Reduction 4. Summmary and Road Ahead

6. Conventional Least Squares Solution: L= & d = Given: Lm=d Find: m s.t. min||Lm-d|| 2 Solution: m = [L L] L d TT m = m –  L (Lm - d) T(k+1)(k)(k)(k) or if L is too big Problem: L is too big for IO bound hardware L 1 L 2 d 1 d 2 = m –  L (L m - d ) = m –  L (L m - d ) (k) + L (L m - d ) 1 1 2 2 2 1 TT [] In general, huge dimension matrix

7. Conventional Least Squares Solution: L= & d = Given: Lm=d Find: m s.t. min||Lm-d|| 2 Solution: m = [L L] L d TT m = m –  L (Lm - d) T(k+1)(k)(k)(k) or if L is too big Problem: L is too big for IO bound hardware L 1 L 2d1 d 2 = m –  L (L m - d ) = m –  L (L m - d ) (k) + L (L m - d ) 1 1 2 2 2 1 TT [] In general, huge dimension matrix Note: subscripts agree

8. Conventional Least Squares Solution: L= & d = Given: Lm=d Find: m s.t. min||Lm-d|| 2 Solution: m = [L L] L d TT m = m –  L (Lm - d) T(k+1)(k)(k)(k) Problem: L is too big for IO bound hardware L 1 L 2d1 d 2 = m –  L (L m - d ) = m –  L (L m - d ) (k) + L (L m - d ) 1 1 2 2 2 1 TT [] In general, huge dimension matrix Problem: Each prediction is a FD solve Solution: Blend+encode Data

9. Blending+Phase Encoding 2 d = N d + N d + N d d = N d + N d + N d2 1 1 3 3 PhasePhase Blending Encoding Matrix Supergather L = N L + N L + N L 3 3 2 2 1 1 m[ ]m d1 L m=L m=L m=L m=1 Encoded supergather modelerd3 L m=L m=L m=L m=3d2 L m=L m=L m=L m=2 O(1/S) cost! Blending

10. Blended Phase-Encoded Least Squares Solution L = & d = N d + N d Given: L m= d Find: m s.t. min|| L m- d || 2 Solution: m = [ L L ] L d T T m = m –  L ( L m - d ) T (k+1)(k)(k)(k) or if L is too big 1 N L + N L 21 = m –  L (L m - d ) = m –  L (L m - d ) (k) + L (L m - d ) 1 1 2 2 2 1 TT [] 1 2 1 2 2 In general, SMALL dimension matrix + Crosstalk + L (L m - d ) 2 T 1 1 1 T 2 2 Iterations are proxy For ensemble averaging

11. Brief History Multisource Phase Encoded Imaging Romero, Ghiglia, Ober, & Morton, Geophysics, (2000) Krebs, Anderson, Hinkley, Neelamani, Lee, Baumstein, Lacasse, SEG, (2009) Virieux and Operto, EAGE, (2009) Dai, and Schuster, SEG, (2009) Migration Waveform Inversion and Least Squares Migration Biondi, SEG, (2009)

12. Outline 1. Seismic Experiment: L m = d 1 1 2 2... N N 2. Standard vs Phase Encoded Least Squares Soln. L 1 L 2 d 1 d 2 m = vs N L + N L 1 2 1 2 [ m = [N d + N d ] ]m = [N d + N d ] 1 2 1 2 3. Theory + Numerical Results 4. Summmary and Road Ahead

13. SEG/EAGE Salt Reflectivity Model Use constant velocity model with c = 2.67 km/s Center frequency of source wavelet f = 20 Hz 320 shot gathers, Born approximation Z (km) 0 1.40 X (km) 6 Encoding: Dynamic time, polarity statics + wavelet shaping Center frequency of source wavelet f = 20 Hz 320 shot gathers, Born approximation

14. 0X (km)6 0 Z k(m) 1.4 0 Z (km) 1.4 0X (km)6 Standard Phase Shift Migration (320 CSGs) Standard Phase Shift Migration vs MLSM (Yunsong Huang) Multisource PLSM (320 blended CSGs, 7 iterations) 1 x 44

15. Single-source PSLSM (Yunsong Huang) Model Error 1.0 0.3 050Iteration Number Unconventional encoding Conventional encoding: Polarity+Time Shifts

16. Multi-Source Waveform Inversion Strategy (Ge Zhan) Generate multisource field data with known time shift Generate synthetic multisource data with known time shift from estimated velocity model Multisource deblurring filter Using multiscale, multisource CG to update the velocity model with regularization Initial velocity model 144 shot gathers

17. 3D SEG Overthrust Model (1089 CSGs) 15 km 3.5 km 15 km

18. 3.5 km Dynamic QMC Tomogram (99 CSGs/supergather) (99 CSGs/supergather) Static QMC Tomogram (99 CSGs/supergather) 15 km Dynamic Polarity Tomogram (1089 CSGs/supergather) Numerical Results 1000x 300x

19. Outline 1. Seismic Experiment: L m = d 1 1 2 2... N N 2. Standard vs Phase Encoded Least Squares Soln. L 1 L 2 d 1 d 2 m = vs N L + N L 1 2 1 2 [ m = [N d + N d ] ]m = [N d + N d ] 1 2 1 2 3. Theory + Numerical Results 4. Summmary and Road Ahead

20. Multisource Migration: m mig =L T d Forward Model: Multisource Least Squares Migration d +d =[ L +L ]m 1221 L {d { Standard migration Crosstalk term Phase encoding Kirchhoff kernel 34

21. Multisource Least Squares Migration Crosstalk term

22. Crosstalk Prediction Formula L (L m - d ) 2 T 1 1 + L (L m - d ) 1 T 2 2 e -  2 O( ) ~ X = X  

23. Standard Migration SNR GS # geophones/CSG # CSGs SNR=... migrate SNR= d(t) = Zero-mean white noise [S(t) +N(t) ] [S(t) +N(t) ] Neglect geometric spreading Standard Migration SNR Assume: migrate + + + stack S 1 S GS G ~ ~ iterate GI Iterative Multisrc. Mig. SNR # iterations SNR= Cost ~ O(S) Cost ~ O(I)

24. SNR 0 1 Number of Iterations 300 7 The SNR of MLSM image grows as the square root of the number of iterations. SNR = GI

25. IO 1 1/320 Cost ~ Resolution dx 1 1 SNR~ Stnd. Mig Multsrc. LSM Stnd. Mig Multsrc. LSM Less 1 1 <1/44 Cost vs Quality Summary 1 L 1 L 2 d 1 d 2 m = N L + N L 1 2 1 2 [ m = [N d + N d ] ]m = [N d + N d ]1 2 1 2

26. Multisource FWI Summary (We need faster migration algorithms & better velocity models) Future: Multisource MVA, Interpolation, Field Data, Migration Filtering, LSM Issues: Optimal encoding strategies, data compression, loss of information.

27. Summary (We need faster migration algorithms & better velocity models) IO 1 vs 1/20 or better Cost 1 vs 1/20 or better Resolution dx 1 vs 1 Sig/MultsSig ? Stnd. FWI Multsrc. FWI Stnd. FWI Multsrc. FWI

28. Multisource Migration: m mig =L T d Forward Model: Multisource Least Squares Migration d +d =[ L +L ]m 1221 L {d { Standard migration Crosstalk term Phase encoding Kirchhoff kernel 34

29. Multisource Least Squares Migration Crosstalk term

30. Numerical Result of Multi-source Super stacking Reflectivity model 5.9 X (km) 0 Z (km) 1.4 0 KM of 320 Single Source CSG 5.9 X (km) 0 Z (km) 1.4 0 Narrowed Spectrum Wavelet 0.5 time (s)0 Amplitude -0.3 0.4 Signal FT of Wavelet 0.5 Frequency (Hz) 0 0 4.5 50 Dominant frequency (Xin Wang)

31. Numerical Result of Multi-source Super stacking KM of 320 Shots Supergather w/o PE 5.9 X (km) 0 Z (km) 1.4 0 -0.05 0 4000 0.05 KM of 3000 Stacking Supergather 5.9 X (km) 0 Z (km) 1.4 0 320 × 3000 0 KM of 320 Shots Supergather with PE 5.9 X (km) Z (km) 1.4 0 Gaussian Distribution 0.05 -0.05 0 50 320 Signal + Noise Singal + Noise (Xin Wang)

32. Numerical Result of Multi-source Super stacking Noise = Σ Σ Γ(g,x,s) * D 0 (g|s) s g + R Σ Σ Σ Γ (g,x,s) * D 0 (g|s’) s g s≠s’ = Signal + Noise − Signal = if s≠s’ R = e -2ω σ 22 Crosstalk damping coefficient R (σ) / R (σ 0 )= e 2ω (σ 0 - σ ) 222 (Xin Wang)

33. 0 Z k(m) 3 0X (km)16 The Marmousi2 Model (Wei Dai) The area in the white box is used for SNR calculation. 200 CSGs. Born Approximation Conventional Encoding: Static Time Shift & Polarity Statics

34. 0X (km)16 0 Z k(m) 3 0 Z (km) 3 0X (km)16 Conventional Source: KM vs LSM (50 iterations) Conventional KM 50x 1x Conventional KLSM

35. 0X (km)16 0 Z k(m) 3 0 Z (km) 3 0X (km)16 Multisource KM (1 iteration) 200-source Supergather: Multisrc. KM vs LSM Multisource KLSM (300 iterations) 1 x 200

36. Outline 1. Migration Problem and Encoded Migration 2. Standard vs Monte Carlo Least Squares Soln. 3. Numerical Results: Kirchhoff, Phase Shift, RTM 4. Summary L 1 L 2 d 1 d 2 m = vs N L + N L 1 2 1 2 [ m = [N d + N d ] ]m = [N d + N d ] 1 2 1 2

37. SEG/EAGE Salt Reflectivity Model Use constant velocity model with c = 2.67 km/s Center frequency of source wavelet f = 20 Hz 320 shot gathers, Born approximation Z (km) 0 1.40 X (km) 6 Encoding: Dynamic time, polarity statics + wavelet shaping Center frequency of source wavelet f = 20 Hz 320 shot gathers, Born approximation

38. 0X (km)6 0 Z k(m) 1.4 0 Z (km) 1.4 0X (km)6 Standard Phase Shift Migration (320 CSGs) Standard Phase Shift Migration vs MLSM (Yunsong Huang) Multisource PLSM (320 blended CSGs, 7 iterations) 1 x 44

39. Single-source PSLSM (Yunsong Huang) Model Error 1.0 0.3 050Iteration Number Unconventional encoding Conventional encoding: Polarity+Time Shifts

40. Outline 1. Migration Problem and Encoded Migration 2. Standard vs Monte Carlo Least Squares Soln. 3. Numerical Results: Kirchhoff, Phase Shift, RTM 4. Summary L 1 L 2 d 1 d 2 m = vs N L + N L 1 2 1 2 [ m = [N d + N d ] ]m = [N d + N d ] 1 2 1 2

41. 3D SEG Overthrust Model (1089 CSGs, Chaiwoot) 15 km 3.5 km 15 km

42. 3.5 km Dynamic QMC Tomogram (99 CSGs/supergather) (99 CSGs/supergather) Static QMC Tomogram (99 CSGs/supergather) 15 km Dynamic Polarity Tomogram (1089 CSGs/supergather) Numerical Results (Chaiwoot Boonyasiriwat) 1000x 300x

43. IO 1 1/320 Cost ~ Resolution dx 1 1/2 SNR~ Stnd. Mig Multsrc. LSM Stnd. Mig Multsrc. LSM I=7 1 1/44 Cost vs Quality: Can I<<S? Yes. What have we empirically learned? S=320

44. Outline 1. Migration Problem and Encoded Migration 2. Standard vs Monte Carlo Least Squares Soln. 3. Numerical Results 4. S/N Ratio L 1 L 2 d 1 d 2 m = vs N L + N L 1 2 1 2 [ m = [N d + N d ] ]m = [N d + N d ] 1 2 1 2

45. Standard Migration SNR GS # geophones/CSG # CSGs SNR=... migrate SNR= d(t) = Zero-mean white noise [S(t) +N(t) ] [S(t) +N(t) ] Neglect geometric spreading Standard Migration SNR Assume: migrate + + + stack S 1 S GS G ~ ~ iterate GI Iterative Multisrc. Mig. SNR # iterations SNR= Cost ~ O(S) Cost ~ O(I)

46. SNR 0 1 Number of Iterations 300 7 The SNR of MLSM image grows as the square root of the number of iterations. SNR = GI

47. Summary IO 1 1/100 Cost ~ Resolution dx 1 1/2 SNR Stnd. Mig Multsrc. LSM Stnd. Mig Multsrc. LSM GSGI S I Cost vs Quality: Can I<<S? L 1 L 2 d 1 d 2 m = vs N L + N L 1 2 1 2 [ m = [N d + N d ] ]m = [N d + N d ] 1 2 1 2

48. Outline MotivationMotivation Multisource LSM theoryMultisource LSM theory Signal-to-Noise Ratio (SNR)Signal-to-Noise Ratio (SNR) Numerical resultsNumerical results ConclusionsConclusions

49. Conclusions Mig vs MLSM Conclusions Mig vs MLSM 1. 2. Cost: S vs I 3. Caveat: Mig. & Modeling were adjoints of one another. LSM sensitive starting model 5.Next Step: Sensitivity analysis to starting model SNR: VS GSGI 4. Unconventional encoding: I << S 2. Memory 1 vs 1/S

50. Back to the Future? Back to the Future? Poststack encoded migration DMO Prestack migration 1980s1980s-20102010? Evolution of Migration Poststack migration 1960s-1970s

51. 1980 Multisource Seismic Imaging vs copper VLIW Superscalar RISC 197019902010 1 100 100000 10 1000 10000 Aluminum Year 202020001980 CPU Speed vs Year

52. Multisource Migration: m mig =L T d Forward Model: Multisource Phase Encoded Imaging d +d =[ L +L ]m 1221 L {d { =[ L +L ](d + d ) 122 1 TT = L d +L d + 122 1 TT L d +L d L d +L d212 1 Crosstalk noise Standard migration TT m = m + (k+1)(k)

53. FWI Problem & Possible Soln. Problem: FWI computationally costlyProblem: FWI computationally costly Solution: Multisource Encoded FWISolution: Multisource Encoded FWI Preconditioning speeds up by factor 2-3 Iterative encoding reduces crosstalk

54. Outline 1. Migration Problem and Encoded Migration 2. Standard vs Monte Carlo Least Squares Soln. 3. Numerical Results: Kirchhoff, Phase Shift, RTM 4. Summary L 1 L 2 d 1 d 2 m = vs N L + N L 1 2 1 2 [ m = [N d + N d ] ]m = [N d + N d ] 1 2 1 2