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Multisource Least-squares Reverse Time Migration

Multisource Least-squares Reverse Time Migration. Wei Dai. Outline. Introduction and Overview Chapter 2: Multisource least-squares reverse time migration Chapter 3: Frequency-selection encoding LSRTM Chapter 4: Super-virtual inteferometric diffractions Summary.

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Multisource Least-squares Reverse Time Migration

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  1. Multisource Least-squares Reverse Time Migration Wei Dai

  2. Outline Introduction and Overview Chapter 2: Multisource least-squares reverse time migration Chapter 3: Frequency-selection encoding LSRTM Chapter 4: Super-virtual inteferometric diffractions Summary

  3. Introduction: Least-squares Migration • Seismic migration: Given: Observed data •  modelling operator Migration velocity Goal: find a reflectivity model to explain by solving the equation •  expensive Direct solution: Conventional migration: •  Iterative solution:

  4. Introduction: Motivation for LSM • Problems in conventional migration image 0 Z (km) migration artifacts 3 0 X (km) 6 0 X (km) 6 imbalanced amplitude

  5. Problem of LSM • Least-squares migration has been shown to produce high quality images, but it is considered too expensive for practical imaging. • Solution: combine multisource technique and least-squares migration (MLSM).

  6. Multisource Migration Image Motivation for Multisource • Problem: LSM is too slow Many (i.e. 20) times slower than standard migration • Solution: multisource phase-encoding technique Multisource  Crosstalk • Multisource LSM • To: • Increase efficiency • Remove artifacts • Suppress crosstalk

  7. Overview • Chapter 2 : Multisource least-squares reverse time migration is implemented with random time-shift and source-polarity encoding functions. • Chapter 3: Multisource LSRTM is implemented with frequency-selection encoding for marine data. • Chapter 4: An interferometric method is proposed to extract diffractions from seismic data and enhance its signal-to-noise ratio.

  8. Outline Introduction and Overview Chapter 2: Multisource least-squares reverse time migration Chapter 3: Frequency-selection encoding LSRTM Chapter 4: Super-virtual inteferometric diffractions Summary

  9. Random Time Shift Random source time shifts O(1/S) cost! Encoding Matrix Supergather Encoded supergather modeler

  10. Random Time Shift ×(-1)× (+1) Encoding Matrix Supergather Encoded supergather modeler

  11. Conventional Least-squares Given: & In general, huge dimension matrix Find: an s.t. min Direct solution: If is too big Iterative solution: Note: subscripts agree

  12. Conventional Least-squares Problem: Each prediction is a FD solve Solution: Multisource technique

  13. Multisource Least-squares Given: & In general, small dimension matrix Find: an s.t. min Direct solution: If is too big Iterative solution: + crosstalk

  14. HESS VTI Model Size: 1800 x 750 Grid interval: 10 m Source number: 1800 Receiver number: 1800 FD kernel: 2-4 staggered grid Source: 15 Hz km/s 0 4.5 Z (km) 7.5 1.5 0 X (km) 18

  15. HESS VTI Model Delta and Epsilon Models Delta 0 1.5 Z (km) 7.5 0 Epsilon 0 2.5 Z (km) 7.5 0 0 X (km) 18

  16. Migration Velocity and Reflectivity km/s Migration Velocity 0 4.5 Z (km) 7.5 1.5 Reflectivity 0 0.2 Z (km) -0.4 7.5 0 X (km) 18

  17. Artifacts removed RTM VS Multisource LSRTM Multisource LSRTM, 4 Supergather Multisource LSRTM, 8 Supergather Standard RTM 0 Z (km) Resolution Enhanced 7.5 0 X (km) 18 Multisource LSRTM, 1 Supergather 0 Z (km) 8 supergather 30 iterations Speedup: 3.75 7.5 0 X (km) 18

  18. Signal-to-noise Ratio SNR ∞

  19. 3D SEG/EAGE Model 400 Shots Evenly Distributed Size: 676 x 676 x 201 Grid interval: 20 m Receiver: 114244 Source: 5.0 hz 13.5 km 4.0 km 13.5 km

  20. Smooth Migration Velocity Obtained by 3D boxcar smoothing 13.5 km 4.0 km 13.5 km 20

  21. Conventional RTM 400 Shots, Migrated One by One 13.5 km 4.0 km 13.5 km

  22. LSRTM 400 Shots, 25 Shots/Supergather 13.5 km 4.0 km 13.5 km

  23. Conventional RTM 100 Shots 13.5 km 4.0 km 13.5 km

  24. LSRTM 100 Shots, 10 Shots/Supergather 13.5 km 4.0 km 13.5 km

  25. Chapter 2: Conclusions • MLSM can produce high quality images efficiently. • LSM produces high quality image. • Multisource technique increases computational efficiency. • SNR analysis suggests that not too many iterations are needed.

  26. Chapter 2: Limitations • Random encoding is not applicable to marine streamer data. Fixed spread geometry (synthetic) Marine streamer geometry (observed) 6 traces 4 traces Mismatch between acquisition geometries will dominate the misfit.

  27. Outline Introduction and Overview Chapter 2: Multisource least-squares reverse time migration Chapter 3: Frequency-selection encoding LSRTM Chapter 4: Super-virtual inteferometric diffractions Summary

  28. Problem with Marine Data erroneous misfit misfit = observed data simulated data

  29. Solution • Every source is encoded with a unique signature. • Every receiver acknowledge the contribution from the ‘correct’ sources. observed simulated

  30. Frequency Selection R(w) Nwfrequency bands of source spectrum: Accommodate up to Nwshots w 4 shots/group Group 1 2 km

  31. Single Frequency Modeling Helmholtz Equation Acoustic Wave Equation Harmonic wave source • Advantages: • Lower complexity in 3D case. • Applicable with multisource technique.

  32. Single Frequency Modeling Amplitude T T

  33. Single Frequency Modeling Amplitude 0 Freqency (Hz) 50 Amplitude 20 Freqency (Hz) 30

  34. Marmousi2 • Model size: 8 x 3.5 km • Freq.: 400 (0~50 hz) • Shots: 301 • Receivers: 201 • Cable: 2km km/s 0 4.5 Z (km) 3.5 1.5 8 0 X (km)

  35. LSRTM Image (iteration=20) LSRTM Image (iteration=80) Conventional RTM 0 Z (km) 3.5 8 0 X (km) LSRTM Image (iteration=1) Cost: 2.4 0 Z (km) 3.5 8 0 X (km)

  36. Frequency-selection LSRTM of 2D Marine Data • Model size: 18.7 x 2.5 km • Freq: 625 (0-62.5 Hz) • Shots: 496 • Cable: 6km • Receivers: 480 km/s 0 2.1 Z (km) 2.5 1.5 18.7 0 X (km)

  37. Conventional RTM 0 Z (km) 2.5 Frequency-selection LSRTM 0 Z (km) 2.5 18.7 0 X (km)

  38. Zoom Views Conventional RTM Conventional RTM Freq. Select LSRTM Freq. Select LSRTM

  39. Chapter 3: Conclusions • MLSM can produce high quality images efficiently. • LSM produces high quality image. • Frequency-selection encoding applicable to marine data. • Limitation: • High frequency noises are present.

  40. Outline Introduction and Overview Chapter 2: Multisource least-squares reverse time migration Chapter 3: Frequency-selection encoding LSRTM Chapter 4: Super-virtual inteferometric diffractions Summary

  41. Chapter 4: Super-virtual inteferometricdiffractions Diffracted energy contains valuable information about the subsurface structure. • Goal: extract diffractions from seismic data and enhance its SNR.

  42. Guide Stars Rotate

  43. Super-virtual stacking theory Step 1: Virtual Diffraction Moveout + Stacking dt dt = dt dt w2 w1 w3 y z y z y z y’ y’

  44. Super-virtual stacking theory Step 2: Redatum virtual refraction to known surface position x y z y z x y z = * y’ x y z x y z i.e. = y’

  45. Super-virtual stacking theory Step 3: Repeat Steps 1&2 for a Different Master Trace x y z y z x y z = * y’ x y z x y z i.e. = y’

  46. z x Super-virtual stacking theory Stacking Over Master Trace Location Desired shot/ receiver combination Common raypaths

  47. Super-virtual Diffraction Algorithm 1. Crosscorrelate and stack to generate virtual diffractions w z w z w z = Virtual src excited at -tzz’ z’ 2. Convolve to generate super-virtual diffractions w z w z * = 3. Stack super-virtual diffractions to increase SNR w z w z w z + +

  48. Synthetic Results: Fault Model km/s 0 3.4 Z (km) 1.8 3 0 X (km) 6

  49. Synthetic Shot Gather: Fault Model 0 Diffraction time (s) 3 0 Offset (km) 6

  50. Synthetic Shot Gather: Fault Model Raw Data 0.5 0.5 time (s) time (s) Our Method 1.5 1.5 Median Filter Offset (km) 0 6 0.5 time (s) 1.5 0 Offset (km) 6

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