1. The Boom and Bust Cycles of Full Waveform Inversion: Is
FWI a Bust, a Boom, or
Becoming a Commodity?
Gerard Schuster
KAUST
Dow Jones Index Avg/decade
1.0
Normalized DJI
0.0
1930s s s s s s s s

2. Outline . 1. Inversion Overview: 2. Seismic Experiment: L m = d
3. FWI, History, Examples L 1 2 d
m =
4. Summary

3. Medical vs Seismic Imaging
CAT Scan
MRI
Full Waveform Inversion Tomogram

4. Traveltime Tomogram & Migration Images
Vshallow = L/t
Vdeep = L/t

5. Traveltime Tomogram & Migration Images
Vshallow = L/t
Intersection
of down & up rays
Vdeep = L/t

6. Traveltime Tomogram & Migration Images
Vshallow = L/t
Vdeep = L/t

7. Traveltime Tomogram & Migration Images
Problems: Hi-Freq. ray tracing, picking traveltimes, tedious,
low resolution, fails in complex earth models
Shot gather = d(x,t)
time
Vshallow = L/t
migration image
Vdeep = L/t

8. Full Waveform Inversion
Given: d(x,t) =
predicted traces
Find: v(x,y,z) minimizes e=S[d(x,t)-d(x,t)obs]2
x,t - =
observed
predicted
residual
Time
Problems: Hi-Freq. ray tracing, picking traveltimes, tedious,
low resolution, fails in complex earth models

9. Outline . 1. Inversion Overview: 2. Seismic Experiment: L m = d
3. FWI, History, Examples L 1 2 d
m =
4. Summary
4. Summary and Road Ahead

10. Gulf of Mexico Seismic Survey
L m = d
L m = d 1 2 . N
Predicted data
Observed data
Goal: Solve overdetermined
System of equations for m
Time (s)
X (km) 4 1 d m

11. Outline . 1. Inversion Overview: 2. Seismic Experiment: L m = d
3. FWI, History, Examples L 1 2 d
m =
4. Summary
4. Summary and Road Ahead

12. Details of Ldm = d-dobs dm(k) = LT(d-dobs)(k)
c2 dt2
1 d2
[ ] 2 - -1
d(g|s) =
Reflectivity
or velocity
model
Time (s)
X (km)
dobs
– 1 d2 d(g|s) = F
c2 dt2 2
[ ]
Predicted data
Observed data m

13. Conventional FWI Solution L is too big for IO bound hardware
L= & d = 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
Problem:
L is too big for IO bound hardware 13

14. Outline . 1. Inversion Overview: 2. Seismic Experiment: L m = d
3. FWI, History, Examples L 1 2 d
m =
4. Summary
4. Summary and Road Ahead

15. Dow Jones Index vs FWI Index
Dow Jones Industrial Avg/decade
FWI Index Avg/decade
18.0
0.0
Tarantola
+ French School
1930s s s s s s s s
Bunks
Multiscale
Exxon+
BP+Pratt
Mora

16. Dow Jones Index vs FWI Index
0.0
18.0
1930s s s s s s s s
FWI Index Avg/decade

17. What Caused the 1st FWI Boom?
0.0
18.0
1930s s s s s s s s
FWI Index Avg/decade
True v(x,z)
FWI v(x,z) 2
Z (km)
X (km)

18. What Caused the 1st FWI Bust?
0.0
18.0
1930s s s s s s s s
FWI Index Avg/decade
True v(x,z)
FWI v(x,z) 2
Z (km)
X (km)
X (km)

19. What Caused the 1st FWI Bust?
0.0
18.0
1930s s s s s s s s
FWI Index Avg/decade
predicted
observed
residual =
Waveform Misfit V
Vtrue
Vstart 1
Time (s)
5.0
0.0 x -

20. What Caused the 1st FWI Bust?
0.0
18.0
1930s s s s s s s s
FWI Index Avg/decade
observed
predicted
residual 1 = =
Time (s)
5.0
0.0 x
Waveform Misfit V
Vtrue
Vstart -

21. What Caused the 1st FWI Bust?
0.0
18.0
1930s s s s s s s s
FWI Index Avg/decade
observed
predicted
residual 1
Gradient opt. gets
stuck local minima = =
Time (s)
5.0
0.0 x
Waveform Misfit V
Vtrue
Vstart -

22. How to Cure the 1st FWI Bust?
0.0
18.0
1930s s s s s s s s
FWI Index Avg/decade
observed
predicted
residual 1 = =
Time (s)
5.0
0.0 x
Waveform Misfit V
Vtrue
Vstart
Low-pass filter -
Gradient opt
 global minima

23. How to Cure the 1st FWI Bust?
0.0
18.0
1930s s s s s s s s
FWI Index Avg/decade
observed
predicted
residual 1 =
Multiscale FWI v(x,z) =
Time (s)
5.0
0.0 x
Waveform Misfit V
Vtrue
Vstart
Window early events -

24. How to Cure the 1st FWI Bust? 2004 EAGE Meeting Started New Boom
0.0
18.0
1930s s s s s s s s
FWI Index Avg/decade
True v(x,z)
FWI v(x,z) 2
Z (km)
X (km)
X (km)
Multiscale FWI v(x,z)

25. 3. FWI, History, Examples: Transmission FWI Norway
Outline
1. Inversion Overview:
2. Seismic Experiment:
L m = d
L m = d 1 2 . N
3. FWI, History, Examples: Transmission FWI Norway L 1 2 d
m =
4. Summary
4. Summary and Road Ahead

26. Transmission 3D FWI Norway Marine Data
2300 buried hydrophones, 50,000 shots, sea bottom 70 m
16 km
8 km
4.5
gas
Gas cloud
1.5 km/s
3.5 km/s
 Small dimensions of structures such as sandy outwash channels to 175m depth (Figure 1c) and the scars left on the sea paleo-bottom by drifting icebergs to 500m depth (Figure 1d). A wide low speed region defines the geometry of the gas cloud (Figure 1a, e) the periphery of which a fracture network is identified (Figure 1b, e). The image of a deep reflector, defining the base of the Cretaceous chalk under the tank (Figure 1a, b, white arrows), is uniquely identifiable despite the screen formed by the overlying gas cloud that opposes penetration seismic wave.
 S. Operto, A. Miniussi, R. Brossier, L. Combe, L. Metivier, V. Monteiller, Ribodetti A., and J. Virieux,  2015, GJI.

27. Transmission 3D FWI Norway Marine Data
2300 buried hydrophones, 50,000 shots, sea bottom 70 m
16 km
8 km
4.5
gas
1.5 km/s
3.5 km/s

28. 2D FWI R+T Gulf of Mexico Marine Data
Transmission 3D FWI Norway Marine Data
2300 buried hydrophones, 50,000 shots, sea bottom 70 m
Transmissions 10x
stronger than reflections
Therefore gradients will spend greater
effort updating shallow v(x,y,z)
Vshallow
Vshallow
Vshallow
Vdeep ??????

29. 3. FWI, History, Examples: R+T FWI Gulf of Mexico
Outline
1. Inversion Overview:
2. Seismic Experiment:
L m = d
L m = d 1 2 . N
3. FWI, History, Examples: R+T FWI Gulf of Mexico L 1 2 d
m =
4. Summary
4. Summary and Road Ahead

30. 2D FWI R+T Gulf of Mexico Marine Data
Reflection Rabbit Ears
Transmission Cigars
observed
predicted
predicted
Abdullah AlTheyab (2015)

31. 2D FWI R+T Gulf of Mexico Marine Data
Transmission Cigars
0.0
observed
predicted
Z (km)
3.6
X (km) 19
Migration Image with Initial V(x,z)
Migration Image with FWI V(x,z)
Migration Image with FWI V(x,z)
Abdullah AlTheyab (2015)

32. 3. FWI, History, Examples: Phase FWI Surface Waves
Outline
1. Inversion Overview:
2. Seismic Experiment:
L m = d
L m = d 1 2 . N
3. FWI, History, Examples: Phase FWI Surface Waves L 1 2 d
m =
4. Summary
4. Summary and Road Ahead

33. 2D KSA Potash Model Test 10 m surface waves 1D Vs Tomogram m/s
True 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)

34. Problem & Solution
Problem: 1D Dispersion inversion assumes layered medium
(Xia et al. 1999).
Solution: v(x,y,z) minimizes e=S[c(k,w)-c(k,w)obs]2 (Li & Schuster, 2016)
FWI: e=S[d(x,t)-d(x,t)obs]2
x (m)
t(s)
CSGs
w(Hz)
C (m/s)
Dispersion Curves
Radon
(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
w(Hz)
Dispersion Curves
C (m/s)
Radon
Z (m)
v (m/s) 1D
Inversion

35. Seismic Imaging of Olduvai Basin
Kai Lu, Sherif Hanafy, Ian Stanistreet, Jackson Njau, Kathy Schick ,Nicholas Toth and Gerard Schuster

36. 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)

37. Summary Multiscale+Skeletonized FWI:
e =S |di –di pred |2  v(x,y,z), r(x,y,z) i
2. History
1930s
3. Is FWI a commodity? Almost according to 2 industry experts
Is FWI a black box? Not yet, works ~80% time (2 experts)
Challenges? Deeper imaging, CPU cost, multiparameter

38. Summary 4. Road Ahead 3D Elastic Inversion & Adaptive Grid. Worth it?
3D Viscoelastic Inversion. Worth it?
Clever Skeletonized FWI
Anisotropic Inversion
Multiples????
Inversion Deeper than src-rec offset/depth<2

39. (We need faster migration algorithms & better velocity models)
Summary
(We need faster migration algorithms & better velocity models)
Stnd. FWI Multsrc. FWI
IO vs 1/20 or better
Cost vs /20 or better
Sig/MultsSig ?
Resolution dx vs 1

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

41. 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)

42. How to Cure the 1st FWI Bust? 2004 EAGE Meeting Started New Boom
0.0
18.0
1930s s s s s s s s
FWI Index Avg/decade
True v(x,z)
FWI v(x,z) 2
Z (km)
X (km)
X (km)
Multiscale FWI v(x,z)

43. Full Waveform Inversion
Given: d(x,t) =
Find: v(x,y,z) minimizes e=S[d(x,t)-d(x,t)obs]2
x,t
time
Vshallow = L/t
migration image
Vdeep = L/t

44. Transmission 3D FWI Norway Marine Data
2300 buried hydrophones, 50,000 shots, sea bottom 70 m
16 km
8 km
4.5
gas
Gas cloud
1.5 km/s
3.5 km/s
 Small dimensions of structures such as sandy outwash channels to 175m depth (Figure 1c) and the scars left on the sea paleo-bottom by drifting icebergs to 500m depth (Figure 1d). A wide low speed region defines the geometry of the gas cloud (Figure 1a, e) the periphery of which a fracture network is identified (Figure 1b, e). The image of a deep reflector, defining the base of the Cretaceous chalk under the tank (Figure 1a, b, white arrows), is uniquely identifiable despite the screen formed by the overlying gas cloud that opposes penetration seismic wave.
 S. Operto, A. Miniussi, R. Brossier, L. Combe, L. Metivier, V. Monteiller, Ribodetti A., and J. Virieux,  2015, GJI.