1. Machine Learning and Wave Equation Inversion of Skeletonized Data
G. Schuster and Jing Li
King Abdullah University Science and Technology

2. Outline Motivation Theory of Skeletonized Inversion Example Summary
Inverting Vp from Guided-Wave C(w)
Summary

3. Machine Learning &Wave Equation Inversion of Skeletonized Data
Input
Data d
[LTL]-1LT
Model m
FWI
Input
Data d
[LTL]-1LT
Model m
Skeletonized
Wave Eqn. Inv.
Skeletal
Features SW GW
Implicit
Function
Theorem
(Luo+Schuster, 1991)

4. Machine Learning &Wave Equation Inversion of Skeletonized Data
Input
Data d
[LTL]-1LT
Model m
FWI
Input
Data d
[LTL]-1LT
Model m
Skeletonized
Wave Eqn. Inv.
Skeletal
Features
Input
Data d
Target
Model m
Neural
Network
Features
Machine
Learning
Machine
Learning

5. Outline Motivation Theory of Skeletonized Inversion Example Summary
Inverting Vp from Guided-Wave C(w)
Summary

6. ? Skeletonization of Geophysical Data
Skeletonization Problem:   dc
Solution: Implicit Function Theorem 2 ¶P
P + (w/c)2 P = F  Fre’chet deriv. (easy) ¶c
What about ? ? ? / ? …
¶t/ ¶c
¶C/ ¶c
¶z/ ¶c
¶AVO
Constraint: F(P,c,t) = 0  dF = dc dt = 0 dF dt dc
F(P,c,t)=P Ä Pobs = 0
dP Ä Pobs dt . dc
= -
= - dt dc
dF/dc
dF/dt

7. Outline Motivation Theory of Skeletonized Inversion Example Summary
Inverting Vp from Guided-Wave C(w): Theory
Summary

8. Wave Equation Dispersion Inversion of Guided P-Waves (WDG)
Problem: Near-surface P-velocity imaginglow resolution & cycle skipping in FWI.
Solution: Invert phase velocity C(w) of waveguide P-waves SW GW
GW: Guided wave
SW: Surface wave
Misfit function:
Gradient (RTM):
Theory:
Conjugate Gradient method: w C DC

9. Outline Motivation Theory of Skeletonized Inversion Example Summary
Inverting Vp from Guided-Wave C(w)
Synthetic Example without Machine Learning
Summary

10. Wave Equation Dispersion Inversion of Guided P-Waves (WDG)
Parameter:
 V1=1000 m/s V2=2500 m/s.
 f=40 Hz,
 Dominate wavelength=25 m
 Sr=60, Re=120; 20 40
True P-velocity Model
z (m) 20 40
z (m)
Starting P-velocity Model
l=25m
2500
2000
1500
1000
X(m) 20 40
z (m)
WDG P-velocity tomogram
l=25m
Courtesy of Jing Li

11. Pred. vs Obs. CSGs 190 X (m) Pred. vs Obs. CSGs .02 s .18 s obs. CSGs
Observed
Inverted
.18 s
190
X (m)
Courtesy of Jing Li

12. Pred. vs Obs. Traces
0.1
0.2
Time (s)
X (m)
Courtesy of Jing Li

13. Outline Motivation Theory of Skeletonized Inversion Example Summary
Inverting Vp from Guided-Wave C(w)
Synthetic Example with Machine Learning
Summary

14. Wave Equation Dispersion Inversion of Guided P-Waves (WDG)
120 m
30 m Vs Vs
120 m
0.9
0.3
C (km/s)
Kernel
SVM
FK Filter
+ Picking w
0.9
0.3
C (km/s)
Pie
FK Filter
+ Manual
Picking
CSG
120 m
0.4 s
120 m

15. Outline Motivation Theory of Skeletonized Inversion Example Summary
Inverting Vp from Guided-Wave C(w)
Field Data Example without Machine Learning
Summary

16. Wave Equation Dispersion Inversion of Guided P-Waves (WDG)20 40
Ray Tracing P-velocity Tomogram
z (m)
2900 m/s
1800 m/s
700 m/s
0.1
0.2
COG Profile (x=20 m)
t (s) 20 40
WDG P-velocity Tomogram
X (m)
z (m)
2900 m/s
1800 m/s
700 m/s
Courtesy of Jing Li

17. Summary FWI Neural Network [LTL]-1LT Skeletonized [LTL]-1LT
Input
Data d
[LTL]-1LT
Model m
FWI
Input
Data d
[LTL]-1LT
Model m
Skeletonized
Wave Eqn. Inv.
Skeletal
Features
Unsupervised
Input
Data d
Target
Model m
Neural
Network
Features
Machine
Learning
Machine
Learning

18. Summary FWI Neural Network [LTL]-1LT Skeletonized [LTL]-1LT
Input
Data d
[LTL]-1LT
Model m
FWI
Input
Data d
[LTL]-1LT
Model m
Skeletonized
Wave Eqn. Inv.
Skeletal
Features
Unsupervised
Skeletal
Features
Machine
Learning
Unsupervised NN
Input
Data d
Target
Model m
Neural
Network
Features
Machine
Learning
Input
Data d
Machine
Learning

19. Thanks to sponsors of CSIM
consortium

20. Summary
1. Skeletonize data  more robust convergence but typically less resolution
but typically less resolution
complex
complex
simple
simple
complex x kx t
C(kx )
Dispersion
curve 2.
Multidimensional implicit function theorem opens new doors
F(t, dz, AVO, df, c(w), attr.,..) NxN equations
3. All that glitters is not gold: