1. paul@sep.stanford.edu Amplitude-preserving wave-equation migration Paul Sava* Stanford University Biondo Biondi Stanford University

2. paul@sep.stanford.edu The problem Recover reliable migration amplitudes: i.e. reflectivity as a function of incidence angle Reflectivity description Describe reflectivity as a function of incidence angle Migration algorithm Apply amplitude corrections to the migration operator Illumination balance Restore amplitudes in shadow zones

3. paul@sep.stanford.edu Agenda Amplitude corrections Angle-domain common image gathers Imaging effects Propagation effects Acquisition effects Definitions Methods Applications

4. paul@sep.stanford.edu Common image gathers z h flat events z h focused events z  flat events z  Wave-equationKirchhoff Offset domain Angle domain

5. paul@sep.stanford.edu Angle-Domain Common Image Gathers SourceReceiver V(x,y,z)     2h v  S-G migration Prucha et al., 1999 Sava et al., 2001 Shot-profile migration de Bruin et al., 1990 Rickett & Sava, 2001

6. paul@sep.stanford.edu ADCIG: S-G migration

7. paul@sep.stanford.edu Agenda Amplitude corrections Angle-domain common image gathers Imaging effects Propagation effects Acquisition effects Definitions Methods Applications

8. paul@sep.stanford.edu Modeling operator modeling migration

9. paul@sep.stanford.edu Jacobian weighting: arbitrary geometry  2h s  image space data space

10. paul@sep.stanford.edu Jacobian weighting: flat reflectors (Wapenaar et al., 1999)  2h s image space data space

11. paul@sep.stanford.edu Jacobian weighting Ideal offset-gather Ideal angle-gather Reflection angle Offset ray parameter

12. paul@sep.stanford.edu Jacobian weighting Ideal offset-gather Ideal angle-gather Reflection angle Offset ray parameter

13. paul@sep.stanford.edu Agenda Amplitude corrections Angle-domain common image gathers Imaging effects Propagation effects Acquisition effects Definitions Methods Applications

14. paul@sep.stanford.edu WKBJ & scattering operators Clayton & Stolt (1981) Stolt & Benson (1986)

15. paul@sep.stanford.edu Agenda Amplitude corrections Angle-domain common image gathers Imaging effects Propagation effects Acquisition effects Definitions Methods Applications

16. paul@sep.stanford.edu Stationary-phase operator 2-D CAM Bleistein & Handelsman (1975)

17. paul@sep.stanford.edu Agenda Amplitude corrections Angle-domain common image gathers Imaging effects Propagation effects Acquisition effects Definitions Methods Applications

18. paul@sep.stanford.edu Applications Pseudo-unitary migrationTrue-amplitude migration

19. paul@sep.stanford.edu Example: vertical section

20. paul@sep.stanford.edu Example: vertical section

21. paul@sep.stanford.edu Example: horizontal section uncorrected

22. paul@sep.stanford.edu Example: horizontal section corrected

23. paul@sep.stanford.edu Summary Amplitude-preserving transformation to the angle domain Amplitude corrections –imaging effects –propagation effects –acquisition effects