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:  expensive Migration velocity

4. 0X (km)60 63 0 Z (km) Problems in conventional migration image Introduction: Motivation for LSM migration artifacts imbalanced amplitude

5. 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). Problem of LSM

6. Motivation for Multisource Multisource LSM To:  Increase efficiency  Remove artifacts  Suppress crosstalk Problem: LSM is too slow Solution: multisource phase-encoding technique Many (i.e. 20) times slower than standard migration Multisource Migration Image Multisource  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 O(1/S) cost! Encoding Matrix Supergather Random source time shifts Encoded supergather modeler

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

11. Conventional Least-squares Note: subscripts agree In general, huge dimension matrix

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

13. Multisource Least-squares In general, small dimension matrix + crosstalk

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

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

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

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

18. Ratio Signal-to-noise Ratio

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 20 13.5 km 4.0 km 13.5 km Obtained by 3D boxcar smoothing

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

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

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

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

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. 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. Chapter 2: Limitations

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

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

30. 4 shots/group R  Group 1 N  frequency bands of source spectrum: Frequency Selection 2 km  Accommodate up to N  shots

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

32. Single Frequency Modeling Amplitude T T

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

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

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

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

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

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

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 inteferometric diffractions Diffracted energy contains valuable information about the subsurface structure. Goal: extract diffractions from seismic data and enhance its SNR.

42. Rotate Guide Stars

43. Step 1: Virtual Diffraction Moveout + Stacking y zw3 dt w2w1 y z y’ dt y z y’ = Super-virtual stacking theory

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

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

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

47. Super-virtual Diffraction Algorithm = w z = + * 1. Crosscorrelate and stack to generate virtual diffractions 2. Convolve to generate super-virtual diffractions 3. Stack super-virtual diffractions to increase SNR w z Virtual src excited at -t zz’ z’ w z +

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

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

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

51. Estimation of Statics 0 Offset (km)6 0.5 time (s) 1.0 Picked Traveltimes Predicted Traveltimes Estimate statics

52. Experimental Cross-well Data 0 Depth (m) 300 0.3 time (s) 1.0 180 Depth (m) 280 0.6 time (s) 0.9 Picked Moveout 0.6 time (s) 0.9 180 Depth (m) 280

53. Experimental Cross-well Data 180 Depth (m) 280 0.6 time (s) 0.9 180 Depth (m) 280 0.6 time (s) 0.9 Median Filter Time Windowed 180 Depth (m) 0.6 time (s) 0.9 280 Super-virtual Diffractions

54. Experimental Cross-well Data 0 Depth (m) 300 0.3 time (s) 1.0 180 Depth (m) 280 0.6 time (s) 0.9 Super-virtual Diffraction 0.6 time (s) 0.9 Median Filtered 180 Depth (m) 280

55. Super-virtual diffraction algorithm can greatly improve the SNR of diffracted waves.. Limitation Dependence on median filtering when there are other coherent events. Wavelet is distorted (solution: deconvolution or match filter). Chapter 4: Conclusions

56. 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

57. Chapter 2: Multisource LSRTM Multisource LSRTM is implemented with random encoding functions.  LSM produces high quality image.  Multisource technique increases computational efficiency. Multisource LSRTM, 8 Supergather

58. Chapter 2: Frequency-selection LSRTM Multisource LSRTM is implemented with frequency- selection encoding functions.  Applicable to marine data. Frequency-selection LSRTM

59. Super-virtual diffraction algorithm can extract diffraction waves and greatly improve its SNR. Chapter 4: Super-virtual inteferometric diffractions Before After

60. Acknowledgements I thank the sponsors of CSIM consortium for their financial support. I thank my advisor Prof. Gerard T. Schuster and other committee members for the supervision over my program of study. I thank my fellow graduate students for the collaborations and help over last 4 years.

61. Workflow Raw data Pick a master trace Cross-correlate all the traces with the master trace Repeat for all the shots and stack the result to give virtual diffractions Convolve the virtual diffractions with the master trace to restore original traveltime Stack to generate Super- virtual Diffractions

62. Diffraction Waveform Modeling Born Modeling 0Distance (km)3.8 0 Depth (km) 1.2 0 Depth (km) 1.2 0 time (s) 4.0 0 Distance (km) 3.8 Velocity Reflectivity

63. Diffraction Waveform Inversion 0Distance (km)3.8 0 Depth (km) 1.2 0 Depth (km) 1.2 Initial Velocity Estimated Reflectivity 0 Depth (km) 1.2 Inverted Velocity 0Distance (km)3.8 0 Depth (km) 1.2 True Velocity