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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)

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Amplitude-preserved wave-equation migration

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  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

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