1. Multi-source Least Squares Migration and Waveform Inversion
Wei Dai, Ge Zhan, Xin Wang, and G. Schuster
KAUST and University of Utah
This is an overview of some salient results from our 2003 UTAM research.

2. Outline Fast Multisource+Precond. Theory
Multisource Least Squares Migration
Multisource Waveform Inversion
Conclusion

3. RTM Problem & Possible Soln.
Problem: RTM computationally costly
Partial Solution: Multisource LSM RTM
Preconditioning speeds convergence by factor 2-3
LSM reduces crosstalk
My talk is organized in the following way:
1. The first part is motivation. I will talk about a least squares migration (LSM ) advantages and challenges.
2. The second part is theory for a deblurring filter, which is an alternative method to LSM.
3. In the third part, I will show a numerical result of a deblurring filter.
4. The fourth is the main part of my talk.
Deblurred LSM (DLSM) is a fast LSM with a deblurring filter.
I will explain how to use the filter in LSM algorithm.
5. Then I will show numerical results of the DLSM.
6. Then I will conclude my presentation.
Each figure has a slide number is shown at the footer. 3 3

4. Multisource Migration: Multisrc-Least Sq. Migration :
Multisource Least Squares Migration d { L {
d +d =[L +L ]m 1 2
Forward Model:
Multisource Migration:
mmig=LTd
m =[LTL]-1LTd
Multisrc-Least Sq. Migration :
multisource preconditioner
multisource modeler+adjoint
m’ = m LT[Lm - d]
f ~ [LTL]-1 f
Steepest Descent
Preconditioned

5. Outline Fast Multisource+Precond. Theory
Multisource Least Squares Migration
Multisource Waveform Inversion
Conclusion

6. SEG/EAGE Salt Model 4500 Velocity (m/s) Depth (km) 4 X (km) 16 1500 9
Velocity (m/s)
Depth (km) 4
X (km) 16
1500
CSG
Multisource CSG
Time (s) 9
X (km)
X (km)

7. Generate ~200 CSGs, Born approx: Random Time Shifted CSG and Add :
Multisource Least Squares Migration Workflow
d and d 1 2
Generate ~200 CSGs, Born approx:
d =d + d 1 2
Random Time Shifted CSG and Add :
*f =
Compute Preconditioner : f =
[LTL] -1
Iterate Preconditioned Regularized CG:
m’ = m LT[Lm - d] + reg. f

8. Model, KM, and LSM Images Z (km) 1.5 0 3km Model LS M (30 its)
Kirchhoff Migration
90x 1x
1.5x 9x
0.1x
Z (km)
Z (km) 3
1.5 km
LSM 10 srcs (5 its)
LSM 10 srcs (30 its)
KM 10 Srcs
Those are velocity and density models.
Velocity and density values are assigned to the layers based on the rock and fluid types.
I created a zero-offset section from these models.
I will explain how I created the data in the next a couple of figures. 8 8

9. Model, KM, and LSM Images Z (km) 1.5 0 3km Model LS M (30 its)
Kirchhoff Migration
90x 1x
1.5x
2.5x
0.02x
Z (km)
Z (km) 3
1.5 km
LSM 10 srcs (5 its)
LSM 40 srcs (30 its)
KM 40 Srcs
Those are velocity and density models.
Velocity and density values are assigned to the layers based on the rock and fluid types.
I created a zero-offset section from these models.
I will explain how I created the data in the next a couple of figures. 9 9

10. Did Deblurring Help? Iteration # Standard precond. CG CG deblurring
1.4
Standard precond. CG
||Data Residual||
Those are velocity and density models.
Velocity and density values are assigned to the layers based on the rock and fluid types.
I created a zero-offset section from these models.
I will explain how I created the data in the next a couple of figures.
CG deblurring
Iteration # 30 10

11. Conclusions
1. Empirical Results: Multisrc. LSM effective in suppressing crosstalk for up to 40 source supergather, but at loss of subtle detail. Did not
achieve breakeven 2.5x > 1x.
2. Deblurring precond. >> Standard 1/r precond. 2
3. Blending Limitation: Overdetermined>Undetermined
Second I compute reflectivity model within this offset range from the velocity and density models.
I also created a source wavelet that mimics an air gun source signature.
Fdom = 25 Hz. T
4. Future: Better deblurring [L L] and regularizer -1 11

12. Outline Fast Multisource+Precond. Theory
Multisource Least Squares Migration
Multisource Waveform Inversion
Conclusion

13. Multiscale Waveform Tomography
1. Collect data d(x,t)
2. Generate synthetic data d(x,t) by FD method
syn.
3. Adjust v(x,z) until ||d(x,t)-d(x,t) || minimized by CG.
syn. 2
4. To prevent getting stuck in local minima:
a). Invert early arrivals initially
mute
b). Use multiscale: low freq high freq. 7

14. Multi-Source Waveform Inversion Strategy
(Ge Zhan)
Generate multisource field data with known time shift
144 shot gathers
Initial velocity model
Generate synthetic multisource data with known time shift from estimated velocity model
Using multiscale, multisource CG to update the velocity model with regularization
Multisource deblurring filter

15. Acoustic Marmousi Model and Multiscale Waveform Inversion
Single-Source Waveform Tomogram
Marmousi Model
m/s
5000
Z (m)
2000
595
X(m)
1910
Smooth Starting Model
12-Source Waveform Tomogram
m/s
12x
5000
50 iterations
Z (m)
2000
595
X(m)
1910

16. 12-Source Misfit Gradient vs Deblurred Gradient
Standard 12-Src Gradient
19.5% Error
2000
Deblurred 12-Src Gradient
7.1% Error
2000

17. Residual Gradient vs # of Shots

18. Summary Multisource+Precond. +CG Reduces Crosstalk
Multisource Waveform Inversion: reduces
computation by 12x for Marmousi
Multisource LSM: Reduces LSM computation $$
but still costs > standard mig.
Problem: Need Formulas for S/N vs dx
Potential O(10) speedup with 3D

19. Outline Fast Multisource+Precond. Theory
Multisource Least Squares Migration
Multisource Waveform Inversion
Multisource MVA
Conclusion