1. ADAPTIVE LOCAL KRIGING (ALK)
TO RETRIEVE THE SLANT RANGE
SURFACE MOTION MAPS OF
WENCHUAN EARTHQUAKE
Department of Earth Science and Engineering
Imperial College London
Meng-Che Wu
meng-che.wu08@imperial.ac.uk
Jian Guo Liu
j.g.liu@imperial.ac.uk

2. Outline
•Background & Purpose
•Method Development
•Experimental Results
•Conclusions
•Future works

3. Background & Purpose

4. Background & Purpose Path 472 Path 471
Path 474
Path 475
Path 476
2π
Path 473
Azimuth
0
Range

5. Background & Purpose Path 472 Path 471
Path 474
Path 475
Path 476
≈1m
Path 473
Azimuth
≈ -1 m
Range

6. Ordinary kriging concept
Ordinary kriging:
Γ*λ=g
Γ is a matrix of the semivariance between each sampled point.
λ is a vector of the kriging weights.
g is a vector of the semivariance between a unknown point and
each sampled point.
Semivariance = FSM(D)
FSM is the fitted semivariogram model.
D is the distance bewteen each sampled point or the distance
between a unknown point and each sampled point.
N
Z(s0 ) Σ λi Z(si ) S = (x, y) is a location
i 1

7. Example of semivariogram model
Gaussian model
≈1m
≈ -1 m

8. Method: Adaptive Local Kriging
Hang wall 1. Window based
kriging scan to
calculate the linear
fitting of local
semivariance.
2. Window size is
≈1m locally adaptive to
ensure adequate
data points and
high processing
Azimuth
efficiency.
Foot wall ≈ -1 m
Range

9. ALK local semivariogram model:
Towards the seismic fault (Hang
wall side)
Semivariance Local gradient: 1.258 10-5
Distance
Averaged semivariance Fitted semivariance
x = 1024, y = 230

10. ALK local semivariogram model:
Towards the seismic fault (Hang
wall side)
Semivariance Local gradient: 5.812 10-5
Distance
Averaged semivariance Fitted semivariance
x = 1024, y = 460

11. ALK local semivariogram model:
Towards the seismic fault (Hang
wall side)
Semivariance Local gradient: 7.313 10-5
Distance
Averaged semivariance Fitted semivariance
x = 1024, y = 580

12. ALK local semivariogram model:
Towards the seismic fault (Foot
wall side)
Semivariance Local gradient: 1.624 10-5
Distance
Averaged semivariance Fitted semivariance
x = 745, y = 1200

13. ALK local semivariogram model:
Towards the seismic fault (Foot
wall side)
Semivariance Local gradient: 3.613 10-5
Distance
Averaged semivariance Fitted semivariance
x = 745, y = 1000

14. ALK local semivariogram model:
Towards the seismic fault (Foot
wall side)
Semivariance Local gradient: 7.652 10-5
Distance
Averaged semivariance Fitted semivariance
x = 745, y = 870

15. ALK multi- H
Give some sampled
points in the large
step Ordinary decoherence gaps
kriging
processing F Coherence
flow chart thresholding
Input Hang wall Final
Coherence
data & foot wall ALK
thresholding
separation result
ALK
(Decoherence
zone)
H
ALK
F Artificial discontinuity
elimination

16. ALK data
≈1m
Azimuth
≈ -1 m
Range

17. ALK rewrapped interferogram
2π
Azimuth
0
Range

18. Original interferogram
2π
Azimuth
0
Range

19. ALK results assessment
A
Path 471 profiles
A A’
RMSE:
0.0053591572
meters Original unwrapped
Correlation image profile
coefficient:
0.99999985
A’
Azimuth
ALK data profile
Range
≈1m ≈ -1 m

20. ALK results assessment
Path 472 profiles
A A A’
RMSE:
0.00909682429
meters Original unwrapped
Correlation image profile
coefficient:
0.99939712
Azimuth
A’ ALK data profile
Range
≈1m ≈ -1 m

21. ALK results assessment
Path 473 profiles
A A’
A
RMSE:
0.0083477924
meters Original unwrapped
Correlation image profile
coefficient: Traced fault line Initial fault
0.99973365
Azimuth
A’ ALK data profile
Range
≈1m ≈ -1 m

22. ALK results assessment
Path 474 profiles
A A’
A
RMSE:
0.017175553
meters Original unwrapped
Correlation image profile
Traced fault line
coefficient: Initial fault
0.99792644
Azimuth
A’
ALK data profile
Range
≈1m ≈ -1 m

23. ALK results assessment
Path 475 profiles
A A A’
RMSE:
0.0059325138
meters Original unwrapped
Correlation image profile
coefficient: Initial fault Traced fault line
0.99969193
Azimuth
A’
ALK data profile
Range
≈1m ≈ -1 m

24. ALK results assessment
Path 476 profiles
A A’
A
RMSE:
0.0071013203
meters Original unwrapped
Correlation image profile
coefficient:
0.99929831
Azimuth
A’
ALK data profile
Range
≈1m ≈ -1 m

25. 3D visualization of ALK data
≈1m
≈ -1 m

26. Refined ALK data
≈1m
Azimuth
≈ -1 m
Range

27. Refined ALK rewrapped data
2π
Azimuth
0
Range

28. 3D view of refined ALK unwrapped data
≈1m
≈ -1 m

29. Conclusions
 Local semivariogram is more representive to
the local variation of spatial pattern of the
interferogram than a global semivariogram
model.
 Dynamical local linear model represents a
nonlinear global model for the whole
interferogram.
 ALK multi-step processing procedure
avoids the error increases in large
decoherence gaps.

30. Conclusions
 The ALK interpolation data revealed dense
fringe patterns in the decoherence zone and
show high fidelity to the original data
without obvious smoothing effects.
 The initial fault line separating the data does
not affect the final interpolation result of ALK
processing.
 The seismic fault line that can be denoted in
the ALK is different from that in publications.
The discrepancy needs further investigation.

31. Future works
 Geological structural numerical
modeling to explain the discrepancy
of trend of seismic fault line.
 Three dimensional surface
deformation maps development.

32. Any questions ?