1. Skeletonized Wave-Equation Surface Wave Dispersion (WD) Inversion
Jing Li*, Gerard Schuster, Zongcai Feng
and Sherif Hanafy
King Abdullah University of Science and Technology (KAUST)

2. Outline Motivation Theory Radon Transform Skeletonized WD Inversion
Checkerboard Test
Results (Synthetic and Field Data)
Conclusions and Future Work
z (m)
x (m)
z (m)
x (m)
Predicted
Observed
Frequency (Hz)
Phase velocity (m/s)
x (m)
z (m)
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. 2

3. Background V(z)s inverted from surface wave dispersion curve.
Key point: Dispersion curve is mostly sensitive to Vs, not Vp or density.
Key point: Dispersion curve is mostly sensitive to Vs, not Vp or density.
Test Model
x (m) 20
Dispersion of Vp
f (Hz)
800
400
Dispersion of Density
f (Hz)
Dispersion of Vs
z (m)
v (m/s)
v (m\s)
Parameters: Vp, Vs and density
Dispersion curve

4. Problem & Solution
Problem: 1D Dispersion inversion assumes layered medium (Xia et al. 1999).
Solution: Wave-equation dispersion inversion (WD) with 2D/3D data (Li and Schuster, 2016).
x (m)
t(s)
CSGs
f (Hz)
V (m/s)
Dispersion Curves RT
(Radon Transform)
v (m/s)
Z (m) 1D
Inversion
1D Vs Tomogram
x(m) 30
Z (m)
True model
x(m) 30
Z (m)
WD Vs Tomogram
x(m) 30
Z (m) 2D WD
t(s)
x (m)
CSGs
f (Hz)
Dispersion Curves
V (m/s) RT
Z (m)
v (m/s) 1D
Inversion

5. Comparison of 2D WD Inversion with FWI
Start Model
FWI of Surface Waves
Easy to get stuck in a local minimum (Solano, et al., 2014).
x (m)
z (m)
Vs True Model
x (m)
t (s)
A shot gather FD
x (m)
z (m)
Vs Tomogram
FWI
2D WD of Surface Waves
Avoid local minimum and apply in 2D/3D model.
x (m)
z (m)
Vs Tomogram WD
Dispersion curve
f (Hz)
v (m/s)
x (m)
t (s)

6. Outline Motivations Theory Radon Transform
f (Hz)
500
100
Phase Velocity
v (m/s)
Motivations
Theory
Radon Transform
Skeletonized Inversion Theory
Checkerboard Test
Results (Synthetic and Field Data)
Conclusions and Future Work
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. 6

7. Theory: Radon Transform
Synthetic Model
x (m) 30
z (m) FD
Shot Gather D(x,t)
x (m) 2
t (s)
k (m-1) 50 5
FFT
Shot Gather D(k,w)
f (Hz)
f (Hz)
500
100
Radon Transform
v (m/s)
High order
Fundamental mode
Pred. Model
x (m) 30
z (m)
Predicted
f (Hz)
500
100
Dispersion Curve
Pick
v (m/s)
Observed

8. Outline Motivations Theory Radon Transform
Predicted
Observed
Frequency (Hz)
Phase Velocity
v (m/s)
Motivations
Theory
Radon Transform
Skeletonized Inversion Theory
Checkerboard Test
Results (Synthetic and Field Data)
Conclusions and Future Work
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. 8

9. Wave-equation Traveltime (WT) vs Wave-equation Dispersion (WD)
Properties:
Wave-equation traveltime
tomography (Luo and Schuster, 1991)
Wave-equation dispersion tomography (Li and Schuster, 2016)
Misfit function: Δ𝜏
Predicted
Observed
Frequency (Hz)
k (m-1)
Wave-equation computation
Gradient:

10. Backpropagated weighted field
WD Algorithm
Predicted
Observed
Frequency (Hz)
Wavenumber-f
k (m-1)
There are 3 steps:
Gradient 1) 2) 3)
Weighted source field
Backpropagated weighted field

11. WD Workflow Weighted Source True Vs Model Residual Dispersion1 -1
t (s)
True Vs Model
x (m) 10
z (m)
800
600
400
Obs. Dispersion
f (Hz)
v (m/s) RT
Data
Pred. Dispersion
Residual Dispersion
f (Hz)
k (m-1)
RTM
Weighted Data
x (m) 2
t (s)
Pred. Vs Model
x (m) 10
z (m)
800
600
400
Update
Small ? CG
Inverted Vs
x (m) 10
z (m)
x (m) 10
z (m)
Gradient

12. Outline Motivations Theory Radon Transform Inversion Theory
Checkerboard Test
Results (Synthetic and Field Data)
Conclusions and Future Work 15
x(m)
z (m)
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. 12

13. Checkerboard Test Checkerboard Model 1 m/s WD Vs Tomogram m/s
700
600
500
x(m) 15
Checkerboard Model m/s
z (m)
700
600
500
x(m) 15
WD Vs Tomogram m/s
z (m) 15
700
600
500
x(m)
Checkerboard Model m/s
z (m) 15
700
600
500
x(m)
WD Vs Tomogram m/s
z (m)

14. Outline Motivations Theory Radon Transform Inversion Theory
Checkerboard Test
Results (Synthetic and Field Data)
Conclusions and Future Work
x (m)
z (m)
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. 14

15. 2D Potash Model Test 1D Vs Tomogram m/s True Model m/s Start Model m/s
x(m) 30
800
600
400
z (m)
Start Model m/s
x(m) 30
800
600
400
z (m)
WD Vs Tomogram m/s
x(m) 30
800
600
400
z (m)
1D Vs Tomogram m/s
x(m) 30
800
600
400
z (m)

16. Predicted Data vs Observed Data
2D Potash Model Test
Dispersion Curve
750
600
550
v (m/s)
Predicted Data vs Observed Data
x(m)
1.0
2.0
t (s)
Pred. Data
Obs. Data
Residual vs Iter. #
Iteration (#) 1
0.6
0.2
misfit

17. Qademah Fault, Saudi Arabia Field Data
P-wave Tomogram
2D WD S-wave Tomogram
1D S-wave Tomogram

18. Olduvai, Tanzania Seismic Data
3.6 km
Fifth Fault
Borehole 2A
Survey Line (Courtesy of Kai Lu et al, 2016)
The Fifth Fault
Borehole 2A

19. Olduvai, Tanzania Seismic Data
The Fifth Fault
COG
0.6
z (m)
0.6
S-wave Velocity Tomogram (WD)
1000
800
600
m/s
z (m)
P-wave Velocity Tomogram Tomogram
0.6
3500
2000
1500
m/s
z (m)

20. Outline Motivations Theory Radon Transform
Skeletonized Inversion Theory
Checkerboard Test
Results (Synthetic and Field Data)
Conclusions and Future Work
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. 20

21. Conclusions WD inversion can be applied to 2D or 3D data;
True Model m/s
x(m) 30
800
600
400
z (m)
2D WD Vs Tomogram m/s
x(m) 30
800
600
400
z (m)
x (m)
z (m)

22. Conclusions 2. Avoid the local minimum; FWI z (m) z (m) x (m) x (m) WD
Vs Tomogram
FWI
x (m)
z (m)
Vs model
x (m)
z (m)
Vs Tomogram WD
x (m)
z (m)
Start model

23. Limitations Computation costly. Moderate resolution.
Pick dispersion curve in low SNR field data.

24. Future Work Consider the effect of attenuation and topography;
x(m) 30 50
z (m)
Vs Model with Topography
f (Hz)
700
500
300
V (m/s)
Effect of attenuation
x(m) 30 50
z (m)
WD Inversion with Topography

25. Acknowledgements Sponsors of the CSIM (csim.kaust.edu.sa) consortium.
KAUST Supercomputing Laboratory (KSL) and IT research computing group.

26. Thank you