1. Wave Equation Dispersion Inversion of Guided P-Waves (WDG)
Jing Li, Sherif Hanafy, and Gerard Schuster
King Abdullah University of Science
and Technology (KAUST)

2. Outline Motivation Guided-waves Inversion Theory ResultsGW
Shot Gather
Motivation
Guided-waves Inversion Theory
Results
Synthetic and Field Data
Conclusions and Limitation
WDG Tomogram
WDG P-velocity Tomogram
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. (LVL: low velocity layer)
Motivation
Guided-waves
Snapshots of wavefield
(LVL: low velocity layer)
Shot Gather
If there is great velocity difference, P-wave will be
trapped in the low velocity layer (Grant and West, 1965)
Guided-waves
P-wave reverberations

4. Different kinds of Guided-waves (Boiero, TLE, 2013).
Motivation
Different kinds of Guided-waves (Boiero, TLE, 2013).
Land Seismic data
OBC data
Towed-streamer
f (Hz)
k (1/m)
f (Hz)
k (1/m)
f (Hz)
k (1/m)

5. Problem & Solution Problem: Wave-equation traveltime inversion (WT)
Low-mid Res.Vp
Solution: Wave-equation dispersion inversion for Guided-waves (WDG)
Mid-high Res. Vp
Shot Gather
t (s)
x (m)
Traveltime map
Receiver
Source
Pick WT
WT P-velocity Tomogram
Z (m)
x (m)
Shot Gather
t (s)
x (m)
Dispersion Curve
V (m/s)
f (Hz)
Radon
Transform
WDG
WDG P-velocity Tomogram
Z (m)
x (m) GW

6. Outline Motivations Guided-waves Inversion Theory Results
Synthetic and Field Data
Conclusions and Limitation
Predicted
Observed
Frequency (Hz)
Dispersion Curves
v (m/s)
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. Guided-waves Inversion Theory (WDG)
Dispersion Curves
f (Hz)
c (m/s)
1) Misfit Function
2) Gradient
Backpropagated field
3) Velocity Update
Source field

8. Wave-equation Traveltime Inversion (WT) vs Wave-equation Dispersion Inversion for Guided-waves (WDG)
Properties:
Wave-equation traveltime
tomography (Luo and Schuster, 1991)
Wave-equation dispersion tomography (Li and Schuster, 2016)
Misfit function: Δ𝜏
Predicted
Observed
Frequency (Hz)
Wavenumber (m-1)
Frechet derivative
Gradient:

9. WDG Workflow CG Update RTM True Vp Model Obs. Dispersion
Residual Dispersion
f (Hz)
k (m-1)
True Vp Model
x (m) 10
z (m)
Obs. Dispersion
f (Hz)
v (m/s)
Pred. Dispersion
Radon Transform
Backpropagated Data
x (m)
0.5
t (s)
Weighted
Initial Vp Model
x (m) 10
z (m)
Update
x (m) 10
z (m)
Gradient
RTM CG
Inverted Vp
x (m) 10
z (m)

10. Outline Motivation Guided-waves Inversion Theory Results
WDG P-velocity Tomogram
WDG Tomogram
Motivation
Guided-waves Inversion Theory
Results
Synthetic and Field Data
Conclusions and Limitation
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. 10

11. WT vs WDG True P-velocity Model WT Tomogram WDG Tomogram Parameter:5 10 15 20
x (m)
z (m)
2500
2000
1500
1000
m/s
WT Tomogram
V1=1000 m/s
V2=1400 m/s
WDG Tomogram
Initial P-velocity Model
λ/2=12.5m
Parameter:
 V1=1000 m/s V2=2500 m/s.
 f=40 Hz,
 λ=25 m
 Sr=30, Re=60;

12. Synthetic Model Test 1 Parameter: True P-velocity Model10 20
True P-velocity Model
z (m)
Parameter:
 V1=1000 m/s V2=2500 m/s.
 f=40 Hz,
 λ=25 m
 Sr=60, Re=120;
Initial P-velocity Model
λ/2=12.5m
2500
2000
1500
1000 10 20
z (m)
m/s
WDG P-velocity Tomogram 10 20
z (m)

13. Synthetic Model Test 2 True P-velocity Model WDG Tomogram
Initial Model
Parameter:
 V1=900 m/s V2=1100 m/s, 1800 m/s.
 f=30 Hz, λ=33 m
 Sr=30, Re=30 45
True P-velocity Model
x (m)
z (m)
m/s
λ/4=8m 45
WDG Tomogram
x (m)
z (m)

14. Qademah Field Data Test
Seismic - Parameter
Equipment: Geometrics
No of Profiles:
No. of shots:
Shot Interval: m
No. of Receivers:
Receiver Interval: 2.5 m
Profile Length: m
(Sherif, et al, 2012)

15. Qademah Field Data Test
Dispersion Curves
V (m/s)
f (Hz)
Raw Shot Gather
t (s)
x (m)
Window Guided-waves
t (s)
x (m)
Adaptive window mute
Radon Transform

16. P-velocity Tomogram WT Tomogram WDG Tomogram 40 z (m) 40 z (m) 0 60040
WT Tomogram
z (m)
3.0
2.2
1.6
1.0
km/s 40
z (m)
WDG Tomogram
3.0
2.2
1.6
1.0
km/s
x (m)

17. WDG and WT COG (Offset=40 m)
T (s)
x (m)
Raw COG
WDG COG
WT COG

18. Trace Comparison
0.25
t (s)
Offset (m)
Raw Data
WT Data

19. Trace Comparison
0.25
t (s)
Offset (m)
Raw Data
WDG Data

20. Outline Motivation Guided-waves Inversion Theory Results
Synthetic and Field Data
Conclusions and Limitation
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
1. Guided-waves dispersion inversion (WDG) can accurately reconstruct the P-velocity in near surface structure.
Shot Gather
t (s)
x (m)
Traveltime map
Rec.
Source
Pick WT
WT Tomogram
Z (m)
x (m)
Shot Gather
t (s)
x (m)
Dispersion Curve
V (m/s)
f (Hz)
Radon
Transform
WDG
WDG Tomogram
Z (m)
x (m) GW

22. Conclusions 2. WDG tomogram has higher (?) resolution than WT.
WT Tomogram
WDG Tomogram
True P-velocity Model 20
z (m)
x (m)
2500
2000
1500
1000
m/s

23. Conclusions 3. Improvement P-wave statics in near surface.
Stack without applying static correction
Stack with static from high resolution P-velocity
(CGG, Florian Duret, et al, 2016, TLE}

24. Limitations WDG resolution decreases as the velocity contrast between
the two-layers becomes smaller
x (m)
z (m)
V1=1000 m/s
V2=1400 m/s
True Vp Model
Shot Gather
V1=1000 m/s
V2=2500 m/s
z (m)
WDG Tomogram
z (m)

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

26. Thank you