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1 Differential Semblance Optimization for Common Azimuth Migration Alexandre KHOURY TRIP Annual meeting.

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Presentation on theme: "1 Differential Semblance Optimization for Common Azimuth Migration Alexandre KHOURY TRIP Annual meeting."— Presentation transcript:

1 1 Differential Semblance Optimization for Common Azimuth Migration Alexandre KHOURY TRIP Annual meeting

2 2 Prestack Wave Equation depth migration Wavefield extrapolation method Automating the velocity estimation loop (time-consuming) Context of the project

3 3 Motivation of the project Encouraging results in 2D for Shot-Record migration (Peng Shen, TRIP 2005) Efficiency of the Common Azimuth Migration in 3D enables sparse acquisition in one direction very economic algorithm Goal of the project: Implement DSO for Common Azimuth Migration in 3D after a 2D validation

4 4 Common Azimuth Migration Wavefield extrapolation in depth: “survey sinking” in the DSR equation h M Subsurface offset Variable used for Velocity Analysis : Subsurface offset

5 5 Subsurface Offset SR M R’=S’ M' SR M R’S’ h’ For true velocity For wrong velocity

6 6 Example: two reflectors data set

7 7 True velocity common image gather Offset gather at x=1000 m

8 8 Example: two reflectors data set One gather at midpoint x=1000m

9 9 Differential Semblance Optimization Fromwe define the objective function : For Criteria for determining the true velocity !

10 10 Differential Semblance Optimization Plot of the objective function with respect to the velocity c=c true

11 11 Gradient calculation The objective function : Gradient calculation : Adjoint-state calculation (Lions, 1971): code operator

12 12 Migration: Structure of the Common Azimuth Migration Wavefield at depth z+  z Phase-Shift Lens-Correction General Screen Propagator or FFD H1 H2 H3 Imaging condition Image at depth z+  z DSR equation: in the Fourier domain Wavefield at depth z in the space domain

13 13 H H H *, B* Algorithm of the gradient calculation Wavefield p z Wavefield p z+  z Wavefield p z+2  z MIGRATION Gradient at depth z+2  z H -1 Gradient at depth z+  z H -1 Adjoint variables propagation Dp, Dc

14 14 Algorithm of the gradient calculation Velocity representation on a B-spline grid: Gradient calculation respect to Fine Grid B-Spline transformation Fine grid B-Spline grid Adjoint B-Spline transformation Gradient calculation respect to B-Spline grid LBFGS Optimizer

15 15 Several critical points - Avoid wrap-around in the subsurface offset domain -Avoid artifacts propagation by tapering the data -Constrain the optimization to keep the velocity in a specified range - Careful choice of migration parameters for the accuracy of the gradient (not necessarily for the migration)

16 16 Several critical points - Avoid wrap-around in the subsurface offset domain -Avoid artifacts propagation by tapering the data -Constrain the optimization to keep the velocity in a specified range - Careful choice of migration parameters for the accuracy of the gradient (not necessarily for the migration)

17 17 Wrap-around in the subsurface offset domain For wrong velocity h ImageGather

18 18 Wrap-around in the subsurface offset domain Effect of padding and split-spread for wrong velocity h ImageGather

19 19 Several critical points - Avoid wrap-around in the subsurface offset domain -Avoid artifacts propagation by tapering the data -Constrain the optimization to keep the velocity in a specified range - Careful choice of migration parameters for the accuracy of the gradient (not necessarily for the migration)

20 20 Artifacts propagation Necessity to taper the data on both offset and midpoint axes and in time

21 21 Several critical points - Avoid wrap-around in the subsurface offset domain -Avoid artifacts propagation by tapering the data -Constrain the optimization to keep the velocity in a specified range - Careful choice of migration parameters for the accuracy of the gradient (not necessarily for the migration)

22 22 Several critical points - Avoid wrap-around in the subsurface offset domain -Avoid artifacts propagation by tapering the data -Constrain the optimization to keep the velocity in a specified range - Careful choice of migration parameters for the accuracy of the gradient (not necessarily for the migration)

23 23 Differential Semblance Optimization Tests on different data sets: -Test on flat reflectors with a constant background velocity -Test on the top of a salt model -Test on a 4-Reflectors model

24 24 Differential Semblance Optimization Tests on different data sets: -Test on flat reflectors with a constant background velocity -Test on the top of a salt model -Test on a 4-Reflectors model

25 25 Differential Semblance Optimization Image Gather Start of the optimization: V=2300

26 26 Differential Semblance Optimization 10 iterations: Right position GatherImage

27 27 Differential Semblance Optimization Tests on different data sets: -Test on flat reflectors with a constant background velocity -Test on the top of a salt model -Test on a 4-Reflectors model

28 28 Differential Semblance Optimization Top of salt : image x=5000

29 29 Differential Semblance Optimization Top of salt : one gather

30 30 Differential Semblance Optimization Plot of : localization of the energy of the objective function

31 31 Differential Semblance Optimization Tests on different data sets: -Test on flat reflectors with a constant background velocity -Test on the top of a salt model -Test on a 4-Reflectors model

32 32 Differential Semblance Optimization True velocity

33 33 Differential Semblance Optimization Starting velocity

34 34 Differential Semblance Optimization Starting image

35 35 Differential Semblance Optimization Optimized image

36 36 Differential Semblance Optimization True image

37 37 Differential Semblance Optimization Optimized velocity

38 38 Conclusion Is the DSR Migration precise enough for optimization of complex models ? Can we deal with complex velocity model ? Migration is critical and has to be artifacts free. Next: test on the Marmousi data set and on a 3D data set.

39 39 Acknowledgment Prof. William W. Symes Total E&P Dr. Peng Shen, Dr Henri Calandra, Dr Paul Williamson


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