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Least-squares Migration and Full Waveform Inversion with Multisource Frequency Selection

Least-squares Migration and Full Waveform Inversion with Multisource Frequency Selection. Yunsong Huang. Sept . 5, 2013. Introduction Multisource Frequency Selection Least-squares migration (LSM) test on 2D and 3D synthetic data Full Waveform Inversion (FWI)

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Least-squares Migration and Full Waveform Inversion with Multisource Frequency Selection

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  1. Least-squares Migration and Full Waveform Inversion with Multisource Frequency Selection YunsongHuang Sept. 5, 2013

  2. Introduction Multisource Frequency Selection Least-squares migration (LSM) test on 2D and 3D synthetic data Full Waveform Inversion (FWI) test on 2D synthetic and field GOM data Resolutions for Wave Equation Imaging Summary Outline

  3. Gulf of Mexico Seismic Survey 4 d Predicted data Observed data 1 Time (s) Goal: Solve overdetermined System of equations for m Lm = d 1 1 0 Lm = d 6 X (km) 2 2 Lm = d . . N N . m

  4. Details of Lm = d 4 d 1 Time (s) 0 6 X (km) Reflectivity or velocity model G(s|x)G(x|g)m(x)dx = d(g|s) Predicted data = Born approximation Solve wave eqn. to get G’s m

  5. Standard Migration vs Multisource Migration Romero, Ghiglia, Ober, & Morton, Geophysics, (2000) Given: d1 and d2 Given: d1+ d2 Find: m Find: m Soln: m = (L1 + L2)(d1+d2) T T T Soln: m=L1 d1 + L2 d2 T T = L1 d1 + L2 d2 Benefit: Reduced computation and memory Liability: Crosstalk noise … T T + L1 d2 + L2 d1 Src. imaging cond. xtalk

  6. Multisource LSM & FWI Inverse problem: 1 ~ ~ m || d – L m ||2 arg min J = 2 Dd misfit Iterative update: ~T m(k+1) = m(k) + aLDd K=1 T T L1Dd1 + L2Dd2 K=10 T T + L1 Dd2 + L2 Dd1

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

  8. Goal of the Study Multisource optimization for marine LSM/FWI Standard optimization for LSM/FWI Speed and quality comparison

  9. Introduction Multisource Frequency Selection Least-squares migration (LSM) test on 2D and 3D synthetic data Full Waveform Inversion (FWI) test on 2D synthetic and field GOM data Resolutions for Wave Equation Imaging Summary Outline

  10. Land Multisource FWI Fixed spread Simulation geometry must be consistent with the acquisition geometry

  11. Marine Multisource FWI Mismatch solution with marine data Observed marine data purify Freq. encoding Decode & mute Simulated land data 4 Hz 4 Hz 4 Hz 8 Hz 8 Hz 8 Hz F.T., freq. selec. wrong misfit Blend 4 Hz 8 Hz

  12. Introduction Multisource Frequency Selection Least-squares migration (LSM) test on 2D and 3D synthetic data Full Waveform Inversion (FWI) test on 2D synthetic and field GOM data Resolutions for Wave Equation Imaging Summary Outline

  13. Phase-shift Migration  Multisource freq. sel. initially implemented here. domain decomposition w kx DZ ky Z Y X Embarrassingly parallel

  14. Migration Images (input SNR = 10dB) SNR=30dB 304 shots in total an example shot and its aperture 0 0 b) Standard Migration a) Original Z (km) Z (km) Computational gain 1.48 1.48 9.4 8.0 6.6 5.4 6.75 X (km) 0 • d) 304 shots/gather • 26 iterations c) Standard Migration with 1/8 subsampled shots Conventional migration: 1 Comp. Gain Shots per supergather 76 152 304 38 6.75 6.75 X (km) X (km) 0 0

  15. 3D Migration Volume True reflectivities Conventional migration 6.7 km 3.7 km 256shots/super-gather,16iterations 3.7 km 13.4 km 40x gain in computational efficiency of OBS data

  16. Introduction Multisource Frequency Selection Least-squares migration (LSM) test on 2D and 3D synthetic data Full Waveform Inversion (FWI) test on 2D synthetic and field GOM data Resolutions for Wave Equation Imaging Summary Outline

  17. Transients Reduction FDTD steady transient nt 2nt 2nt causal t t periodic periodic 4 Hz 8 Hz

  18. Computing FWI’s Gradient periodic t nt 2nt 1 forward-propagated source wavefield steady transient 0-lag correlate back-propagated residual wavefield steady transient

  19. Multisource FWI Freq. Sel. Workflow Select unique frequency for each src dd For k=1:K Filter and blend observed data: dd  dpreddpred Purify predicted data: dpreddpred  Data residual: Dd=dpred-d ~T m(k+1) = m(k) + aLDd end

  20. Quasi-Monte Carlo Mapping Q.M. w/ repelling Coulomb force Standard Random permutation 1 1 Source index Source index w index w index 60 60 1 1 60 60

  21. Quasi-Monte Carlo Mapping 3 iterations 31 iterations

  22. Introduction Multisource Frequency Selection Least-squares migration (LSM) test on 2D and 3D synthetic data Full Waveform Inversion (FWI) test on 2D synthetic and field GOM data Resolutions for Wave Equation Imaging Summary Outline

  23. Frequency-selection FWI of 2D Marine Data 0 • Shots: 60 • Source freq: 8 Hz • Receivers/shot: 84 Z (km) • Cable length: 2.3 km 4.5 (km/s) 1.5 1.5 6.8 X (km) 0

  24. FWI images 0 0 • Actual model • Starting model Z (km) Z (km) 1.5 1.5 • Standard FWI • (69 iterations) • Multisource FWI • (262 iterations) 6.8 6.8 X (km) X (km) 0 0

  25. Convergence Rates Waveform error Faster initial convergence rate of the white curve 1 1 supergather, standard encoding Same asymptotic convergence rate of the red and white curves Log normalized by individual sources 3.8x 1 supergather, Quasi-Monte Carlo encoding 0.025 69 1 262 Log iterationnumber

  26. Convergence Rates Speedup 60 / 2 / 2 / 3.8 = 4 Velocity error 1 • Gain • 60: sources • Overhead factors: • 2 x FDTD steps • 2 xdomain size • 3.8 x iterations 1 supergather, standard encoding Log normalized by individual sources 3.8x 1 supergather, Quasi-Monte Carlo encoding 0.35 69 1 262 Log iterationnumber

  27. Introduction Multisource Frequency Selection Least-squares migration (LSM) test on 2D and 3D synthetic data Full Waveform Inversion (FWI) test on 2D synthetic and field GOM data Resolutions for Wave Equation Imaging Summary Outline

  28. Workflow: FWI on GOM dataset Source wavelet estimation 3D to 2D conversion of the data initial velocity model estimation Run FWI in multiscales Generate RTM, CIG & CSG images

  29. -1 water surface delay: Dt s r Received direct wave combined with ghost Source wavelet

  30. Estimated w(t) 0.8 s Bandpass filtered to [0, 25] Hz Power spectrum of (b)

  31. Workflow: FWI on GOM dataset Source wavelet estimation 3D to 2D conversion of the data initial velocity model estimation Run FWI in multiscales Generate RTM, CIG & CSG images

  32. Workflow: FWI on GOM dataset Source wavelet estimation 3D to 2D conversion of the data initial velocity model estimation Run FWI in multiscales traveltime+ semblance Generate RTM, CIG & CSG images

  33. Workflow: FWI on GOM dataset freq. band: grid size: 0—6 Hz, 51 x 376 0—15 Hz, 101x 752 0—25 Hz, 201x 1504 Source wavelet estimation 3D to 2D conversion of the data initial velocity model estimation Multisource Freq. Sel.: # steps: method: Run FWI in multiscales 15 60 Gradient descent w/ line search. Stochastic gradient descent. Step size Generate RTM, CIG & CSG images Mini-batch size: 2 496 shots  8 supergathers

  34. Velocity models obtained from: Traveltime Z (km) FWI cost: 1 Z (km) FWIwMFS cost: 1/8 Z (km) X(km)

  35. Baldplate GOM Dataset • Model size: 18.8 x 2.5 km • Source freq: 0--25 Hz • Shots: 496 • Cable length: 6km • Receivers/shot: 480 FWIwMFS: VQ.M. – Vrandom permutation Velocity difference due to encoding schemes: Q.M. vs standard Z (km) The freq. sel. scheme is resilient to specifics of encoding methods X(km)

  36. Workflow: FWI on GOM dataset Source wavelet estimation 3D to 2D conversion of the data initial velocity model estimation Run FWI in multiscales Generate RTM, CIG & CSG images

  37. RTM image using traveltime tomogram Z (km) X(km)

  38. RTM image using FWI tomogram Z (km) X(km)

  39. RTM image using FWIwMFS tomogram Z (km) X(km)

  40. Zoomed views of the RTM images

  41. Zoomed views of the RTM images

  42. Zoomed views of the RTM images

  43. CIGs for traveltime tomogram

  44. CIGs for FWI tomogram

  45. CIGs for FWIwMFS tomogram

  46. Observed CSG Time (s) 7

  47. FWI predicted CSG Time (s) 7

  48. FWIwMFS predicted CSG Time (s) 7

  49. TRT predicted CSG Time (s) 7

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