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Wei Dai, Ge Zhan, Xin Wang, and G. Schuster KAUST and University of Utah

Multi-source Least Squares Migration and Waveform Inversion . Wei Dai, Ge Zhan, Xin Wang, and G. Schuster KAUST and University of Utah. Outline. Fast Multisource+Precond . Theory. Multisource Least Squares Migration. Multisource Waveform Inversion. Conclusion.

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Wei Dai, Ge Zhan, Xin Wang, and G. Schuster KAUST and University of Utah

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  1. Multi-source Least Squares Migration and Waveform Inversion Wei Dai, Ge Zhan, Xin Wang, and G. Schuster KAUST and University of Utah

  2. Outline • Fast Multisource+Precond. Theory • Multisource Least Squares Migration • Multisource Waveform Inversion • Conclusion

  3. RTM Problem & Possible Soln. Problem: RTM computationally costly Partial Solution: Multisource LSM RTM Preconditioning speeds convergence by factor 2-3 LSM reduces crosstalk 3

  4. d +d =[L +L ]m 1 2 1 2 mmig=LTd Multisource Migration: m =[LTL]-1LTd Multisrc-Least Sq. Migration : multisource modeler+adjoint m’ = m - LT[Lm - d] f Preconditioned Steepest Descent f ~ [LTL]-1 multisource preconditioner Multisource Least Squares Migration { { L d Forward Model:

  5. Outline • Fast Multisource+Precond. Theory • Multisource Least Squares Migration • Multisource Waveform Inversion • Conclusion

  6. SEG/EAGE Salt Model 4500 0 Velocity (m/s) Depth (km) 4 0 X (km) 16 1500 Multisource CSG CSG Time (s) 9 X (km) X (km)

  7. d =d + d d and d 2 2 1 1 -1 [LTL] Compute Preconditioner : f = *f = Multisource Least Squares Migration Workflow Generate ~200 CSGs, Born approx: Random Time Shifted CSG and Add : Iterate Preconditioned Regularized CG: f m’ = m - LT[Lm - d] + reg.

  8. Model, KM, and LSM Images Model LS M (30 its) Kirchhoff Migration 0 1x 90x Z (km) Z (km) 3 1.5 0 3km LSM 10 srcs (5 its) LSM 10 srcs (30 its) KM 10 Srcs 9x 0.1x 1.5x 8

  9. Model, KM, and LSM Images Model LS M (30 its) Kirchhoff Migration 0 1x 90x Z (km) Z (km) 3 1.5 0 3km LSM 10 srcs (5 its) LSM 40 srcs(30 its) KM 40Srcs 2.5x 0.02x 1.5x 9

  10. Did Deblurring Help? 1.4 Standard precond. CG ||Data Residual|| CG deblurring 0 0 Iteration # 30

  11. Conclusions 1. Empirical Results: Multisrc. LSM effective in suppressing crosstalk for up to 40 source supergather, but at loss of subtle detail. Did not achieve breakeven 2.5x > 1x. 2. Deblurringprecond. >> Standard 1/r precond. 2 3. Blending Limitation: Overdetermined>Undetermined 4. Future: Better deblurring [L L] and regularizer -1 T

  12. Outline • Fast Multisource+Precond. Theory • Multisource Least Squares Migration • Multisource Waveform Inversion • Conclusion

  13. syn. 2. Generate synthetic data d(x,t) by FD method syn. 2 3. Adjust v(x,z) until ||d(x,t)-d(x,t) || minimized by CG. mute b). Use multiscale: low freq. high freq. Multiscale Waveform Tomography 1. Collect data d(x,t) 4. To prevent getting stuck in local minima: a). Invert early arrivals initially 7

  14. Multi-Source Waveform Inversion Strategy (Ge Zhan) 144 shot gathers Generate multisource field data with known time shift Initial velocity model 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

  15. Acoustic MarmousiModel and Multiscale Waveform Inversion Marmousi Model Single-Source Waveform Tomogram m/s 0 5000 Z (m) 2000 595 0 X(m) 1910 Smooth Starting Model 12-Source Waveform Tomogram m/s 0 12x 5000 50 iterations Z (m) 2000 595 0 X(m) 1910

  16. 12-Source Misfit Gradient vsDeblurred Gradient Standard 12-Src Gradient 19.5% Error 2000 Deblurred 12-Src Gradient 7.1% Error 2000

  17. Residual Gradient vs # of Shots

  18. Summary • Multisource+Precond. +CG Reduces Crosstalk • Multisource Waveform Inversion: reduces • computation by 12x for Marmousi • Multisource LSM: Reduces LSM computation $$ • but still costs > standard mig. • Problem: Need Formulas for S/N vsdx • Potential O(10) speedup with 3D

  19. Outline • Fast Multisource+Precond. Theory • Multisource Least Squares Migration • Multisource Waveform Inversion • Multisource MVA • Conclusion

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