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Least Squares Migration of Stacked Supergathers

Least Squares Migration of Stacked Supergathers. Wei Dai and Gerard Schuster KAUST. vs. RTM Problem & Possible Soln. Problem: RTM computationally costly; IO high Solution: Multisource LSM RTM. Preconditioning speeds up by factor 2-3

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Least Squares Migration of Stacked Supergathers

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  1. Least Squares Migration of Stacked Supergathers Wei Dai and Gerard Schuster KAUST vs

  2. RTM Problem & Possible Soln. Problem: RTM computationally costly; IO high Solution: Multisource LSM RTM Preconditioning speeds up by factor 2-3 Encoded LSM reduces crosstalk. Reduced comp. cost+memory

  3. Outline Motivation Multisource LSM theory Signal-to-Noise Ratio (SNR) Numerical results Conclusions

  4. Ld +L d 1 2 2 1 = L d +L d + =[L +L ](d + d ) 1 2 1 2 1 1 2 2 d +d =[L +L ]m 1 2 1 2 mmig=LTd Multisource Migration: Phase Encoded Multisource Migration { { d L Forward Model: mmig T T mmig T T T T Crosstalk noise mmig T T T T = L d +L d + Ld +Ld 1 2 2 1 1 1 2 2 mmig = L d +L d 1 1 2 2 Standard migration

  5. Ld +L d 1 2 2 1 = L d +L d + =[L +L ](d + d ) 1 2 1 2 1 1 2 2 d +d =[L +L ]m 1 2 1 2 mmig=LTd Multisource Migration: Phase Encoded MultisrceLeast Squares Migration { { L d Forward Model: mmig T T T T T T m = m + (k+1) (k) Crosstalk noise Standard migration

  6. Outline Motivation Multisource LSM theory Signal-to-Noise Ratio (SNR) Numerical results Conclusions

  7. ~ ~ 1 GI G GS [S(t) +N(t) ] S S Standard Migration SNR Zero-mean white noise Assume: d(t) = Standard Migration SNR Neglect geometric spreading GS Cost ~ O(S) # CSGs # geophones/CSG + + + Iterative Multisrc. Mig. SNR Cost ~ O(I) Standard Migration SNR SNR= # iterations migrate stack migrate iterate . SNR= . . SNR=

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

  9. Multisource LSM Summary Stnd. MigMultsrc. LSM IO 1 1/100 GS GI S I Cost ~ SNR Resolution dx 1 1/2 Cost vs Quality: Can I<<S?

  10. Outline Motivation Multisource LSM theory Signal-to-Noise Ratio (SNR) Numerical results Conclusions

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

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

  13. 200-source Supergather: Multisrc. KM vs LSM Multisource KM (1 iteration) 0 1 x Z k(m) 200 3 0 X (km) 16 Multisource KLSM (300 iterations) 0 I=1.5S Z (km) 1.5 x 3 0 X (km) 16

  14. What have we empirically learned? Stnd. MigMultsrc. LSM IO 1 1/200 1 1.5 Cost ~ S=200 I=300 SNR~ Resolution dx 1 1/2 Cost vs Quality: Can I<<S?

  15. Z (km) 0 SEG/EAGE Salt Reflectivity Model 1.4 Use constant velocity model with c = 2.67 km/s Center frequency of source wavelet f = 20 Hz 320 shot gathers, Born approximation 0 6 X (km) • Encoding: Dynamic time, polarity statics + wavelet shaping • Center frequency of source wavelet f = 20 Hz • 320 shot gathers, Born approximation

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

  17. Single-source PSLSM (Yunsong Huang) 1.0 Conventional encoding: Polarity+Time Shifts Model Error Unconventional encoding 0.3 0 Iteration Number 50

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

  19. ConclusionsMigvs MLSM 1. SNR: VS GS GI 2. Memory 1 vs1/S 2. Cost: S vsI 3. Caveat: Mig. & Modeling were adjoints of one another. LSM sensitive starting model 4. Unconventional encoding: I << S • Next Step: Sensitivity analysis to starting model

  20. Back to the Future? Evolution of Migration 1960s-1970s 1980s 1980s-2010 2010? Poststack migration Prestack migration Poststack encoded migration DMO

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