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Fast Least Squares Migration with a Deblurring Filter

Fast Least Squares Migration with a Deblurring Filter. Naoshi Aoki Feb. 5, 2009. Outline. Motivation Theory Deblurring filter theory Deblurred LSM theory Numerical results of the deblurred LSM Marmousi2 model test 2D marine data test Conclusions. Outline. Motivation Theories

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Fast Least Squares Migration with a Deblurring Filter

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  1. Fast Least SquaresMigrationwith a Deblurring Filter Naoshi Aoki Feb. 5, 2009

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

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

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

  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 apriori model for a regularized LSM. • Use an MD filter as a preconditioner for LSM.

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

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

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

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

  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)

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

  12. Marmousi2 Velocity Model 0 Anticline Structures Z (km) 3 0 15 X (km) 1.5 4.5 P wave velocity (km/s)

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

  14. Data Preparation Part Velocity Model Reflectivity Model Migration Image Poststack KM Image 0 0 Actual Reflectivity Model Z (km) Z (km) 3 3 6 6 12 12 X (km) X (km)

  15. Reference Reflectivity Model Deblurring Filter Part Reference Migration Image Find deblurring operator Reference Migration Image Geological Reference Model 0 0 Z (km) Z (km) 3 3 6 6 12 12 X (km) X (km)

  16. Reference Reflectivity Model Deblurring Filter Part Reference Migration Image Find deblurring operator Deblurred Migration Image Actual Migration Image Deblurred Migration Image 0 0 Z (km) Z (km) 3 3 6 6 12 12 X (km) X (km)

  17. DLSM Part Compute LSM Method 1: RDLSM after 20 Iterations Method 2: PDLSM after 12 Iterations 0 0 Z (km) Z (km) 3 3 6 6 12 12 X (km) X (km)

  18. Image Comparison Migration Image Migration Image after Deblurring Filter Method 2: PDLSM after 12 Iterations Method 1:RDLSM after 20 Iterations 0 0 0 0 Z (km) Z (km) Z (km) Z (km) 3 3 3 3 6 12 6 12 6 12 6 12 X (km) X (km) X (km) X (km)

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

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

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

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

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

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

  25. Comparison of Images: Box B Migration LSM after 3 Iterations 1 1 1 1 DLSM after 3 Iterations LSM after 10 Iterations Z (km) Z (km) Z (km) Z (km) 1.2 1.2 1.2 1.2 11 11 11 11 12 12 12 12 X (km) X (km) X (km) X (km)

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

  27. Conclusions • A deblurring filter provides a fine apriori 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.

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

  29. Thanks

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