FWI without tears: a forward modeling-free gradient
- 1. www.crewes.org Supervisors: Dr. Larry Lines Dr. Robert Ferguson Presenter: Marcelo Guarido de Andrade
- 2. Outline • Introduction • Gradient approximation •Impedance inversion •Forward modeling-free (pre-stack) •Forward modeling-free (post-stack) • All results • Conclusions www.crewes.org
- 5. Introduction www.crewes.org C 𝑚 ≡ ∆𝑑 𝑚 2Minimize Least Squares
- 6. Introduction www.crewes.org C 𝑚 ≡ ∆𝑑 𝑚 2Minimize Least Squares 𝒅 𝒐𝒃𝒔 − 𝒅 𝒔𝒚𝒏
- 7. Introduction www.crewes.org C 𝑚 ≡ ∆𝑑 𝑚 2Minimize Least Squares 𝒅 𝒐𝒃𝒔 − 𝒅 𝒔𝒚𝒏
- 8. m0
- 9. m0
- 10. m0 ∆dm
- 11. m0 ∆dm g0
- 12. m0 ∆dm g0 α0
- 13. m0 ∆dm g0 m1 α0
- 14. m0 ∆dm g0 m1 α0
- 15. 𝒎(𝒏+𝟏) = 𝒎(𝒏) − 𝜶(𝒏) 𝒈(𝒏) m0 ∆dm g0 m1 α0
- 16. Introduction www.crewes.org The final update is assumed to be the closest one to the true model
- 17. Introduction www.crewes.org Velocity(m/s) Velocity(m/s) The final update is assumed to be the closest one to the true model
- 19. Gradient Approximation: Impedance Inversion www.crewes.org • Gradient -> reflection coefficients or impedance? • Impedance inversion • FWI as processing tools • I – impedance inversion • S – stacking • M – migration
- 20. Gradient Approximation: Impedance Inversion www.crewes.org • Pratt et al. (1990): • Step length: Forward modeling over a small perturbation of the model
- 21. Gradient Approximation: Impedance Inversion www.crewes.org
- 22. Gradient Approximation: Impedance Inversion www.crewes.org
- 23. Gradient Approximation: Impedance Inversion www.crewes.org
- 24. Gradient Approximation: Impedance Inversion www.crewes.org
- 25. Gradient Approximation: Forward Modeling-Free (Pre-Stack) www.crewes.org
- 26. Gradient Approximation: Forward Modeling-Free (Pre-Stack) www.crewes.org • Linear operators Current Model And: Step length requires 2 forward modeling No forward modeling is required to estimate the gradient Separate the terms
- 27. Gradient Approximation: Forward Modeling-Free (Pre-Stack) www.crewes.org
- 28. Gradient Approximation: Forward Modeling-Free (Pre-Stack) www.crewes.org
- 29. Gradient Approximation: Forward Modeling-Free (Pre-Stack) www.crewes.org
- 30. Gradient Approximation: Forward Modeling-Free (Pre-Stack) www.crewes.org
- 31. Gradient Approximation: Forward Modeling-Free (Post-Stack) www.crewes.org
- 32. Gradient Approximation: Forward Modeling-Free (Post-Stack) www.crewes.org • Seismic processing workflow • Commute the order of the Migration and Stacking processes
- 33. Gradient Approximation: Forward Modeling-Free (Post-Stack) www.crewes.org • Seismic processing workflow • Commute the order of the Migration and Stacking processes
- 34. Gradient Approximation: Forward Modeling-Free (Post-Stack) www.crewes.org • Seismic processing workflow • Commute the order of the Migration and Stacking processes Theoretically, same thing Pre-stack migration Post-stack migration
- 35. Gradient Approximation: Forward Modeling-Free (Post-Stack) www.crewes.org Input: Stacked observed data
- 36. Gradient Approximation: Forward Modeling-Free (Post-Stack) www.crewes.org
- 37. Gradient Approximation: Forward Modeling-Free (Post-Stack) www.crewes.org
- 38. Gradient Approximation: Forward Modeling-Free (Post-Stack) www.crewes.org
- 39. Gradient Approximation: Forward Modeling-Free (Post-Stack) www.crewes.org
- 40. Gradient Approximation: Forward Modeling-Free (Post-Stack) www.crewes.org
- 41. Gradient Approximation: Forward Modeling-Free (Post-Stack) www.crewes.org Simple exponential of trace integration as impedance inversion
- 42. Gradient Approximation: Forward Modeling-Free (Post-Stack) www.crewes.org
- 43. Gradient Approximation: Forward Modeling-Free (Post-Stack) www.crewes.org
- 44. Gradient Approximation: Forward Modeling-Free (Post-Stack) www.crewes.org Velocity analysis output as initial model
- 45. Gradient Approximation: Forward Modeling-Free (Post-Stack) www.crewes.org
- 46. Gradient Approximation: Forward Modeling-Free (Post-Stack) www.crewes.org
- 47. Gradient Approximation: Forward Modeling-Free (Post-Stack) www.crewes.org 2nd pass of the FWI processing tool
- 48. Gradient Approximation: Forward Modeling-Free (Post-Stack) www.crewes.org • Improves initial model • Better on the shallow • 2nd pass -> good choice • Fast • Simple • Cheap
- 50. All Results www.crewes.org Standard approximation with BLIMP
- 53. All Results www.crewes.org Simple exponential of trace integration as impedance inversion
- 55. Conclusions www.crewes.org • Impedance inversion of the gradient is reasonable • Forward modeling-free gradient is good enough and stable • No source estimation for gradient • Two forward modeling runs is required to estimate step length • Possibility for a post-stack approximation • Trace integration has higher resolution on simpler models • Requires reasonable good initial model • Promising results
- 56. Acknowledgments www.crewes.org • NSERC • CREWES Sponsors • Students and staff