1 / 53

Amplitude-preserved wave-equation migration

Amplitude-preserved wave-equation migration. Paul Sava & Biondo Biondi SEP108 (pages 1-27). Wave-equation imaging. Why? Complex wavefields Sharp velocity variation sub-salt What? Reflectivity function of incidence angle Imaging Migration Velocity Analysis (MVA)

rachana-harjit
Download Presentation

Amplitude-preserved wave-equation migration

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Amplitude-preserved wave-equation migration Paul Sava & Biondo Biondi SEP108 (pages 1-27)

  2. Wave-equation imaging • Why? • Complex wavefields • Sharp velocity variation • sub-salt • What? • Reflectivity function of incidence angle • Imaging • Migration Velocity Analysis (MVA) • Amplitude vs. Angle Analysis (AVA)

  3. Angle-Domain Common Image Gathers • Applications • imaging • S/G migration (Prucha et at., 1999) • shot-profile migration (Rickett, 2001) • seismic inversion (Prucha et. al., 2001) • MVA • traveltime tomography (Clapp, 2000) • wave-equation MVA (Sava & Biondi, 2000) • C-waves • polarity reversal (Rosales, 2001) • AVA • wave-equation AVA (Gratwick, 2001)

  4. Angle-gathers vs. offset-gathers Offset gather Angle gather

  5. Agenda • ADCIG kinematics • image space • data space • Amplitude-preserved migration • general formulation • weighting function • COMAZ • ADCIG amplitudes • spatial bandwidth • temporal bandwidth • RTT • Applications • true-amplitude migration • inversion • WEMVA

  6. Reflection scheme: global view Source Receiver V(x,y,z) g g

  7. Reflection scheme: local view 2h g g a v

  8. ADCIG methods Reflection angle Offset ray-parameter x-domain (slant-stack) k-domain (RTT)

  9. ADCIG: example

  10. ADCIG methods: comparison Computation domain • image space • separated from migration • data space • mixed with migration Reflection angle • directly • indirectly • function of dip Inaccurate velocity boundaries • sensitive • less sensitive Reflection angle Offset ray-parameter

  11. Agenda • ADCIG kinematics • image space • data space • Amplitude-preserved migration • general formulation • weighting function • COMAZ • ADCIG amplitudes • spatial bandwidth • temporal bandwidth • RTT • Applications • true-amplitude migration • inversion • WEMVA

  12. Spatial bandwidth kz kh kz - gmax + gmax g -90 +90 -gmax +gmax

  13. Synthetic: ideal gather frequency domain space domain amplitude

  14. Temporal bandwidth w kz kz kz g kh kh kh narrow frequency band image data offset gather angle gather wide frequency band

  15. Temporal bandwidth frequency domain space domain amplitude

  16. RTT implementation • Two possibilities: • push: loop over input • pull: loop over output kz kz kh g offset gather angle gather

  17. push RTT offset-gather angle-gather x-domain k-domain

  18. pull RTT offset-gather angle-gather x-domain k-domain

  19. RTT amplitudes

  20. Agenda • ADCIG kinematics • image space • data space • Amplitude-preserved migration • general formulation • weighting functions • COMAZ • ADCIG amplitudes • spatial bandwidth • temporal bandwidth • RTT • Applications • true-amplitude migration • inversion • WEMVA

  21. Amplitude-preserving migration • Definition: the process of recovering the amplitude of the reflectivity vector given • perfect data • infinite bandwidth • infinite aperture

  22. Modeling operator i0: seismic image r: reflectivity d: seismic data L: modeling operator A: Amplitude operator G: Reflection operator

  23. Amplitude operator i0: seismic image r: reflectivity d: seismic data L: modeling operator A: amplitude operator G: Reflection operator Clayton & Stolt (1981)

  24. Reflection operator i0: seismic image r: reflectivity d: seismic data L: modeling operator A: amplitude operator G: reflection operator Clayton & Stolt (1981) Stolt & Benson (1986)

  25. Amplitude-preserving operator i0: seismic image r: reflectivity d: seismic data L: modeling operator A: amplitude operator G: reflection operator

  26. Weighting operator migration modeling

  27. Agenda • ADCIG kinematics • image space • data space • Amplitude-preserved migration • general formulation • weighting functions • COMAZ • ADCIG amplitudes • spatial bandwidth • temporal bandwidth • RTT • Applications • true-amplitude migration • inversion • WEMVA

  28. Amplitude correction: the problem frequency domain space domain amplitude

  29. Jacobian: general expression data space image space

  30. Jacobian: 2-D, image space 2h g g a v

  31. Jacobian: general expression data space image space

  32. Jacobian: 2-D, data space 2h g g a v

  33. Jacobian: 2-D, flat reflectors (Wapenaar et al., 1999)

  34. Amplitude correction: the problem frequency domain space domain amplitude

  35. AVA: correct amplitudes frequency domain space domain amplitude

  36. Agenda • ADCIG kinematics • image space • data space • Amplitude-preserved migration • general formulation • weighting function • COMAZ • ADCIG amplitudes • spatial bandwidth • temporal bandwidth • RTT • Applications • true-amplitude migration • inversion • WEMVA

  37. COMAZ: stationary-phase 2-D COMAZ view from above

  38. COMAZ: stationary-phase correction Phase-shift component Amplitude component

  39. COMAZ: no amplitude corrections

  40. COMAZ: all amplitude corrections

  41. Agenda • ADCIG kinematics • image space • data space • Amplitude-preserved migration • general formulation • weighting function • COMAZ • ADCIG amplitudes • spatial bandwidth • temporal bandwidth • RTT • Applications • true-amplitude migration • inversion • WEMVA

  42. True-amplitude migration i0: seismic image r: reflectivity d: seismic data L: modeling operator A: amplitude operator G: reflection operator

  43. True-amplitude migration: COMAZ OPERATORS L: modeling W: Jacobian A: amplitude Astat: stationary-phase G: reflection

  44. True-amplitude migration: real data

  45. Inversion: pseudo-unitary operators Migration Inversion

  46. Inversion: preconditioned regularization

  47. Wave-equation MVA L: Wave-equation MVA m: slowness perturbation d: image perturbation References: SEP100, SEP103, SEP105

  48. WEMVA: model

  49. WEMVA: correct amplitudes

  50. WEMVA: incorrect amplitudes

More Related