Presentation of the Wave Equation Migration tool

1. Presentation of the Wave Equation Migration tool 75th SEG Annual Meeting, Houston, TX. November 6 - 11, 2005.

2. Long term R&D effort • 2D Paraxial propagator (Collino, 1989) • Constrained least squares migration (Ehinger and Lailly, 1991; Duquet et al., 1994) • Common offset wavefield migration (Ehinger et al.; 1996) • 3D paraxial propagator (Collino and Joly, 1995) • 3D prestack wavefield migration (Duquet et al., 2001) • Comparison of 3D wavefield propagator (Lavaud and Duquet, 2001) • True amplitude wavefield migration (Joncour et al., 2005)

3. WE Method • Shot record Migration • Accurate • No assumption on the propagation complexity • No assumption on the acquisition geometry • Easy parallelization (shot, frequencies, ...) • Various One-Way propagation kernel • Finite Difference methods, Wavenumber methods, Mixed methods

4. One-Way propagation methods • Two main approaches : Finite Difference and Wavenumber • Finite difference (paraxial) : • Handle strong lateral velocity variations • Dip limited • Anisotropic Error in 3D (splitting method) • Wanenumber (SSF, PSPI) : • Handle gentle velocity variations • High dip accurate • Isotropic Error • Mixed method (FFD, Li) : • Combine both approaches

5. Accuracy of FD propagation 2 splitting directions 4 splitting directions 45 ° 68 °

6. Accuracy vs. Velocity contrasts

7. Accuracy vs. Velocity contrasts (2)

8. One-Way propagation method • All these methods are implemented in our software namely: • SSF, PSPI, FD, FFD, LI, Optimized Li • FD propagation kernel: • 2 or 4 splitting directions • Unconditionally stable

9. Synthetic model Strong velocity contrasts + High dips Layer 1 = homogeneous velocity 1.5 km/s Layer 2 = layer 4 = lateral velocity gradient from 2 to 3 km/s Layer 3 = vertical velocity gradient from 3 to 4 km/s Layer 5 = homogeneous velocity 4 km/s

10. SSF propagation

11. FD propagation

12. FFD propagation

13. PSPI propagation

14. Synthetic model

15. Splitting directions : 2 vs. 4

16. WE software • 2D/3D shot record migration • Common Angle Gather • Different parallelization level • Optimization strategy • Designed for huge size problem

17. Master Node Shot parallelization Slave Node n Slave Node 1 Frequency parallelization proc 1 proc 1 proc n proc n Two level parallelization

18. Two level parallelization • Coarse grain parallelization over shots • Masternode assign and send shared shots to each Slave node • Finer grain parallelization over frequency • Slavenode can be a dual/quadri processor or a cluster subset • mpi parallelization: each processor takes a subset of the frequencies • Reduced communication: • data reading + image condition

19. Optimization strategy • Shared shot allow to save cost associated with propagation matrix construction • Large step through water • Propagation depth step can be bigger than imaging depth step using an ad'hoc interpolation • ...

20. dz image=10m / dz propagation=10m

21. dz image=40m / dz propagation=40m  4 times faster

22. dz image=10m / dz propagation=40m+ ad'hoc interpolation  3 times faster

23. dz image=10m / dz propagation=10m

24. Designed for huge size problem • Memory requirement • Lateral propagation domain : 15km x 10km • Spatial sampling dx=dy=25m • Recording time= 10s • Frequency band = 40Hz (400 frequencies) • ~2 Gb core memory • Flexibility on the frequency range to be migrated

25. WE software • Shot record migration • accurate method • Fast and flexible algorithm • Various propagation kernels • handle high dips and strong velocity contrasts