1. Fast Least Squares Migration with a Deblurring Filter Naoshi Aoki Feb. 5, 2009 1

2. Outline Motivation Theory –Deblurring filter theory –Deblurred LSM theory Numerical results of the deblurred LSM –Marmousi2 model test –2D marine data test Conclusions 2

3. Outline Motivation Theories –Deblurring filter theory –Deblurred LSM theory Numerical results of the deblurred LSM –Marmousi2 model test –2D marine data test Conclusions 3

4. Deblurring Migration Image Migration Two methods to deblur the migration image –Least Squares Migration (e.g., Nemeth et al.,1999) –Migration Deconvolution (Hu and Schuster, 2001) 4

5. Motivation Problems –LSM can be more than an order of magnitude more costly than standard migration. –MD filter is characterized by image artifacts known as MD edge artifacts. Solution –Use an MD image as an a priori model for a regularized LSM. –Use an MD filter as a preconditioner for LSM. 5

6. Outline Motivation Theories –Deblurring filter theory –Deblurred LSM theory Numerical results of the deblurred LSM –Marmousi2 model test –2D marine data test Conclusions 6

7. Deblurring Filter Theory (1) 1. Actual Migration Image 2. Reference migration image 7 Migration Model ? Reference MigrationReference Model

8. Deblurring Filter Theory (2) 3. Find non-stationary matching operator 4. Apply the deblurring filter 8 Reference MigrationReference Model Migration Model ?

9. Outline Motivation Theories –Deblurring filter theory –Deblurred LSM theory Numerical results of the deblurred LSM –Marmousi2 model test –2D marine data test Conclusions 9

10. Deblurred LSM (DLSM) Theory DLSM is a fast LSM with a deblurring filter. Two types of DLSM algorithms are proposed: –Method 1: Regularized DLSM (or RDLSM) where is, and is a regularization parameter. –Method 2: Preconditioned DLSM (or PDLSM) 10

11. Outline Motivation Theories –Deblurring filter theory –Deblurred LSM theory Numerical results of the deblurred LSM –Marmousi2 model test –2D marine data test Conclusions 11

12. Marmousi2 Velocity Model 0 3 015 Z (km) X (km) 4.51.5 P wave velocity (km/s) Anticline Structures

13. Test Workflow 13 Migration Image Velocity Model Reflectivity Model Reference Migration Image Reference Reflectivity Model Compute LSM Deblurred Migration Image Find deblurring operator Data Preparation Part Deblurring Filter Part DLSM Part

14. Data Preparation Part Poststack KM Image 0 3 Z (km) 612 X (km) Actual Reflectivity Model 0 3 Z (km) 612 X (km) 14 Migration Image Velocity Model Reflectivity Model

15. Deblurring Filter Part Reference Migration Image 0 3 Z (km) 612 X (km) Geological Reference Model 0 3 Z (km) 612 X (km) 15 Reference Migration Image Reference Reflectivity Model Find deblurring operator

16. Deblurred Migration Image 0 3 Z (km) 612 X (km) Actual Migration Image 0 3 Z (km) 612 X (km) 16 Deblurred Migration Image Reference Migration Image Reference Reflectivity Model Find deblurring operator Deblurring Filter Part

17. Method 2: PDLSM after 12 Iterations Method 1: RDLSM after 20 Iterations 17 0 3 Z (km) 612 X (km) 0 3 Z (km) 612 X (km) Compute LSM DLSM Part

18. Image Comparison 0 3 Z (km) 612 X (km) Method 2: PDLSM after 12 Iterations 0 3 Z (km) 612 X (km) Method 1:RDLSM after 20 Iterations 18 Migration Image after Deblurring Filter 0 3 Z (km) 612 X (km) Migration Image 0 3 Z (km) 612 X (km)

19. DLSM Residual Curves Method 2: Preconditioned DLSM 1 0 1 30 Iteration Number Residual Method 1: Regularized DLSM 1 0 1 30 Iteration Number Residual 20 12 Damping parameter: Γ= 200000x0.5n-1, n=1,2,…,30 19 Noise level

20. Outline Motivation Theories –Deblurring filter theory –Deblurred LSM theory Numerical results of the deblurred LSM –Marmousi2 model test –2D marine data test Conclusions 20

21. 2D Poststack Kirchhoff Migration 8 1 1.5 Z (km) X (km) 13 10.5 0.5 21

22. Test Workflow 22 Migration Image Field Data Reference Migration Image Reference Reflectivity Model Compute LSM Deblurred Migration Image Find deblurring operator Standard Processing Part Deblurring Filter Part DLSM Part

23. Comparison of Imaging Results 23 8 1 1.5 Z (km) X (km) 13 10.5 0.5

24. Comparison of Images: Box A 0.5 0.7 Z (km) 9.6 10.6 X (km) Migration 0.5 0.7 Z (km) 9.6 10.6 X (km) LSM after 3 Iterations 0.5 0.7 Z (km) 9.6 10.6 X (km) DLSM after 3 Iterations 0.5 0.7 Z (km) 9.6 10.6 X (km) LSM after 10 Iterations 24

25. Comparison of Images: Box B Migration 1 1.2Z (km) 1112 X (km) LSM after 3 Iterations 1.2 Z (km) 1112 X (km) 1 DLSM after 3 Iterations 1.2 Z (km) 1112 X (km) 1 LSM after 10 Iterations 1.2 Z (km) 1112 X (km) 1 25

26. Outline Motivation Theories –Deblurring filter theory –Deblurred LSM theory Numerical results of the deblurred LSM –Marmousi2 model test –2D marine data test Conclusions 26

27. Conclusions A deblurring filter provides a fine a priori model for a regularized LSM, and can be used as an effective preconditioning filter. DLSM algorithms provide acceptable LSM images with 1/3 – 2/3 the cost of standard LSM. 27

28. Continued Works 3D DLSM is tested by Wei Dai. An improved migration deconvolution technique is presented in my next talk. 28

29. Thanks 29