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Iterative Migration Deconvolution (IMD) with Migration Green’s Functions as Preconditioners

Iterative Migration Deconvolution (IMD) with Migration Green’s Functions as Preconditioners. Naoshi Aoki Feb. 5, 2009. Outline. Introduction Theory Inexpensive IMD Numerical results 2D model IMD test 3D model IMD test When should we use IMD and LSM ? Conclusions. Outline. Introduction

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Iterative Migration Deconvolution (IMD) with Migration Green’s Functions as Preconditioners

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  1. Iterative Migration Deconvolution (IMD) with Migration Green’s Functions as Preconditioners Naoshi Aoki Feb. 5, 2009

  2. Outline • Introduction • Theory • Inexpensive IMD • Numerical results • 2D model IMD test • 3D model IMD test • When should we use IMD and LSM ? • Conclusions

  3. Outline • Introduction • Theory • Inexpensive IMD • Numerical results • 2D model IMD test • 3D model IMD test • When should we use IMD and LSM ? • 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. Migration Green’s Function or MGF Synthetic Data • is known as the migration Green’s function. • It is an impulse response of migration operator. • MGF variation depends on: • acquisition geometry, • and velocity distribution. TWT (s) Grid Reflectivity Model MGFs Z (km) X (km)

  6. Outline • Introduction • Theory • Inexpensive IMD • Numerical results • 2D model IMD test • 3D model IMD test • When should we use IMD and LSM ? • Conclusions

  7. Inexpensive IMD Theory Expensive IMD • where and represent the k+1 and k th models, is a step length, and is expensive MGF. Inexpensive IMD with Preconditioned MGFs where represents a preconditioned normal matrix that contains the preconditioned MGF in each subsection, denotes amplitude compensated migration image.

  8. Expensive and Inexpensive MGFs

  9. Outline • Introduction • Theory • Inexpensive IMD • Numerical results • 2D model IMD test • 3D model IMD test • When should we use IMD and LSM ? • Conclusions

  10. Test Workflow Data Preparation Part MGF Computation Part Point Scatterer Model Reflectivity Model Migration Image Compute MGFs IMD Computation Part Compute IMD Compare with LSM

  11. Data Preparation Part Reflectivity Model Migration Image 2D Stick Model Prestack Migration 0 0 Z (km) Z (km) 1.8 1.8 0 0 1.8 1.8 X (km) X (km)

  12. MGF Computation Part Point Scatterer Model Compute MGFs Scatterers MGFs 0 0 Z (km) Z (km) 1.8 1.8 0 1.8 0 1.8 X (km) X (km)

  13. IMD Computation Part Compute IMD IMD Image after 43 Iterations Prestack Migration 0 0 Z (km) Z (km) 1.8 1.8 0 1.8 0 1.8 X (km) X (km)

  14. IMD vs LSM Compute IMD Compare with LSM IMD Image after 43 Iterations LSM Image after 30 Iterations 0 0 Z (km) Z (km) 1.8 1.8 0 1.8 0 1.8 X (km) X (km)

  15. Model Residual 7 Residual IMD Noise level 5 43 1 30 Iteration number

  16. Computational Costs 9 640 55 860

  17. Expensive and Inexpensive MGFs Compute MGFs at Once Compute MGFs One by One A possible problem is interference from other MGFs. Clean MGFs without interference

  18. Outline • Introduction • Theory • Inexpensive IMD • Numerical results • 2D model IMD test • 3D model IMD test • When should we use IMD and LSM ? • Conclusions

  19. 3D Model Test Model Model Description Model size: 1.8 x 1.8 x 1.8 km U shape reflectivity anomaly Cross-spread geometry Source : 16 shots, 100 m int. Receiver : 16 receivers , 100 m int. ● Source ● Receiver 0 Z (km) 2 0 0 X (km) Y (km) 2 2

  20. Test Workflow Data Preparation Part MGF Computation Part Point Scatterer Model Reflectivity Model Migration Image Compute MGFs IMD Computation Part Compute IMD Compare with LSM

  21. Data Preparation Reflectivity Model Migration Image Prestack Migration Y = 1 km Prestack Migration Z = 750 m 0 0 Z (km) Y (km) 1.8 1.8 0 0 1.8 1.8 X (km) X (km)

  22. MGF Computation Part Point Scatterer Model Compute MGFs MGF Image Z = 750 m MGF Image Y = 1 km 0 0 Z (km) Y (km) 1.8 1.8 0 0 1.8 1.8 X (km) X (km)

  23. Compute IMD IMD Computation Part IMD Image after 30 Iterations Prestack Migration Y = 1000 m 0 0 Z (km) Z (km) 1.8 1.8 0 1.8 0 1.8 Z = 750 m 0 0 Y (km) Y (km) 1.8 1.8 0 1.8 0 1.8 X (km) X (km)

  24. IMD vs Prestack Migration IMD after 30 Iterations Z = 250 m 750 m 1000 m 1250 m 1500 m 0 Y (km) 1.8 0 1.8 0 1.8 0 1.8 0 1.8 0 1.8 X (km) Prestack Migration 0 Y (km) 1.8 0 1.8 0 1.8 0 1.8 0 1.8 0 1.8 X (km)

  25. Compute IMD IMD vs LSM Compare with LSM LSM Image after 30 Iterations IMD image after 30 Iterations Y = 1000 m 0 0 Z (km) Z (km) 1.8 1.8 0 1.8 0 1.8 Z = 750 m 0 0 Y (km) Y (km) 1.8 1.8 0 1.8 0 1.8 X (km) X (km)

  26. IMD vs LSM IMD Images after 30 Iterations Z = 250 m 750 m 1000 m 1250 m 1500 m 0 Y (km) 1.8 0 1.8 0 1.8 0 1.8 0 1.8 0 1.8 X (km) LSM Images after 30 Iterations 0 Y (km) 1.8 0 1.8 0 1.8 0 1.8 0 1.8 0 1.8 X (km)

  27. Model Residual 84 Residual IMD Noise level 76 1 30 Iteration number

  28. Computational Costs 190 25500 65400 15400

  29. Why Is IMD So Slow? • Computational cost of IMD is 6 times higher than that of LSM because: • the cross-spread geometry has a large MGF variation, • convolution / cross-correlation is used in the space domain.

  30. Outline • Introduction • Theory • Inexpensive IMD • Numerical results • 2D model IMD test • 3D model IMD test • When should we use IMD and LSM ? • Conclusions

  31. Difference Between LSM and IMD LSM IMD • Both methods minimize the misfit with the data.

  32. When Should We Use IMD and LSM ? IMD LSM Smaller amount of 5-D data provides larger MGF variation. Larger amount of 5-D data provides smaller MGF variation.

  33. Suitable Application

  34. Outline • Introduction • Theory • Inexpensive IMD • Numerical results • 2D model IMD test • 3D model IMD test • When should we use IMD and LSM ? • Conclusions

  35. Conclusions • Inexpensive IMD method with preconditioned MGF is developed. • 2D IMD achieves a quality almost equal to that from LSM with cheaper computational cost. • 3D IMD test suggests that IMD quality and cost depend on required MGF density, and investigationof the required MGF density is important.

  36. Continued Work • An IMD test on PEMEX RTM image is presented by Qiong Wu.

  37. Thanks

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