1. Overview of Multisource and Multiscale Seismic Inversion
Chaiwoot, Boonyasiriwat, Wei Dai, Ge Zhan, Yunsong Huang,
Gerard Schuster
KAUST

2. 2. Seismic Inversion Problem:
Outline
L m = d
L m = d 1 2 . N
Seismic Experiment: -1
2. Seismic Inversion Problem:
L m = d
-> m = [L L] L d T T
3. Multiscale & Multisource Inversion L 1 2 d
m = vs
N L + N L [
]m = [N d + N d ]
4. Summary and Road Ahead

3. Gulf of Mexico Seismic Survey
L m = d
L m = d 1 2 . N
Predicted data
Observed data
Time (s) 4 1 d m
6 km

4. Gulf of Mexico Seismic Survey
L m = d 1
L m = d 2
Predicted data
Observed data
L m = d . N
Goal: Solve overdetermined
System of equations for m d 2 m
6 km

5. S Details of Lm = d G(s|x)G(x|g)m(x)dx = d(g|s) s g x
Reflectivity
or velocity
model 1 s g x
G(s|x)G(x|g)m(x)dx = d(g|s)
Predicted data = Born approximation
Solve wave eqn. to get G’s S m

6. Seismic Inverse Problem
Given: d = Lm
Find: m(x,y,z)
Soln: min || Lm-d || 2
Least sq.
migration
m = [L L] L d T -1
migration
L d T

7. Seismic Inverse Problem
Given: d = Lm
Find: m(x,y,z)
Soln: min || Lm-d || 2
m = m + [L L] L d T -1
(k+1)
(k)
FWI or full waveform
inversion

8. Computational Challenges
Given: d = Lm
m = [L L] L d T -1
Find:
d > 10 7 13
words
m > 10
unknown velocity values
20x20x10 km 3
dx=1 m
# time steps ~ 10 4
# shots > 10 4 10 15
Total =

9. 2. Seismic Inversion Problem:
Outline
L m = d
L m = d 1 2 . N
Seismic Experiment: -1
2. Seismic Inversion Problem:
L m = d
m = [L L] L d T T
3. Multiscale & Multisource Inversion L 1 2 d
m = vs
N L + N L [
]m = [N d + N d ]
4. Summary and Road Ahead

10. Conventional Least Squares Solution: L= & d =1 1 L d
Given: Lm=d 2 2
In general, huge
dimension matrix
Find: m s.t. min||Lm-d|| 2
Solution: m = [L L] L d T -1
or if L is too big
m = m – a L (Lm - d)
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.
(k+1)
(k)
(k) T
(k)
= m – a L (L m - d )
(k) [ ] T
+ L (L m - d ) T 1 1 1 2 2 2
Non-Linear Optimization =
Full Waveform Inversion
Linear Optimization =
Least Squares Migration 10

11. 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
e=||d-d|| 2
Model Parameter
Data misfit function
4. To prevent getting stuck in local minima:
a). Invert early arrivals initially
mute
Time
b). Use multiscale: low freq high freq.
e=||d-d|| 2
Model Parameter
e=||d-d|| 2
Model Parameter

12. 2. Multiscale Waveform Inversion 3. Multisource Waveform Inversion
Numerical Results
1. Land and Marine MLSM
2. Multiscale Waveform Inversion
3. Multisource Waveform Inversion

13. Boonyasiriwat et al., 2009, TLE
0 km
6 km/s
6 km
3 km/s
0 km
20 km

14. Waveform Tomograms Initial model 5 Hz 10 Hz 20 Hz 0 km 6 km 0 km 20 km
6 km/s
Initial model
6 km
3 km/s
0 km
20 km
0 km
5 Hz
6 km/s
6 km
3 km/s
0 km
6 km/s
10 Hz
6 km
3 km/s
0 km
6 km/s
20 Hz
6 km
3 km/s

15. Waveform Tomograms Initial model 5 Hz 10 Hz 20 Hz 0 km 6 km 0 km 20 km
6 km/s
Initial model
6 km
3 km/s
0 km
20 km
0 km
5 Hz
6 km/s
6 km
3 km/s
0 km
6 km/s
10 Hz
6 km
3 km/s
0 km
6 km/s
20 Hz
6 km
3 km/s

16. Traveltime Tomogram Depth (km) 3000 2.5 Velocity (m/s)
Depth (km)
3000
2.5
Velocity (m/s)
Waveform Tomogram
1500
Depth (km)
2.5
X (km) 20 20

17. Vertical Derivative of Waveform Tomogram
3000
Waveform Tomogram
Velocity (m/s)
Depth (km)
1500
2.5
Vertical Derivative of Waveform Tomogram
Depth (km)
2.5
X (km) 20 21

18. Kirchhoff Migration Images

19. 2. Multiscale Waveform Inversion 3. Multisource Waveform Inversion
Numerical Results
1. Land and Marine MLSM
2. Multiscale Waveform Inversion
3. Multisource Waveform Inversion

20. Multi-Source Waveform Inversion Strategy
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

21. 3D SEG Overthrust Model (1089 CSGs)
15 km
3.5 km
15 km

22. 2. Multiscale Waveform Inversion 3. Xwell Waveform Inversion
Numerical Results
1. Land and Marine MLSM
2. Multiscale Waveform Inversion
3. Xwell Waveform Inversion

23. Dynamic Polarity Tomogram
Numerical Results
1000x
300x
3.5 km
Dynamic QMC Tomogram
(99 CSGs/supergather)
Static QMC Tomogram
(99 CSGs/supergather)
15 km
Dynamic Polarity Tomogram
(1089 CSGs/supergather)

24. Ray Tracing Tomograms S P A C Depth (m) B 210 90 90 Offset (m)A
1150
2300 C
Depth (m) B
3650
m/s
1825
m/s
210 90 90
Offset (m)
Offset (m)

25. Elastic Tomograms P S Depth (m) 210 90 90 Offset (m) Offset (m) 1150
1150
2300
Depth (m)
3650
m/s
1825
m/s
210 90 90
Offset (m)
Offset (m)

26. Viscoelastic Tomograms S P A AA A
1150
2300 C C D
Depth (m) B B
3650
m/s
1825
m/s
210 90 90
Offset (m)
Offset (m)

27. Elastic Tomograms P S A B Depth (ft) D C 500 184 184 Offset (ft)A
7750
14000 B
Depth (ft) D
12700
ft/s
22500
ft/s C
500
184
184
Offset (ft)
Offset (ft)

28. P S A B Depth (ft) D C 500 184 184 Offset (ft) Offset (ft)
Viscoelastic Tomograms P S A
7750
14000 B
Depth (ft) D
12700
ft/s
22500
ft/s C
500
184
184
Offset (ft)
Offset (ft)

29. Poisson Ratio
Visco. D
0.35
Depth (ft) C
0.05
250
184
Offset (ft)

30. Poisson Ratio
Elastic D
0.35
Depth (ft) C
0.05
250
184
Offset (ft)

31. Seismic Inverse Problem
Given: d = Lm
Find: m(x,y,z)
Soln: min || Lm-d || 2
waveform
inversion
m = m + [L L] L d T -1
(k+1)
(k)
Biggest Challenges: Convergence+Cost