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ADAPTIVE LOCAL KRIGING (ALK)
TO RETRIEVE THE SLANT RANGE
SURFACE MOTION MAPS OF
WENCHUAN EARTHQUAKE
Department of Earth Science and EngineeringImperial College LondonMeng-Che [email protected] Guo [email protected]
Outline
•Background & Purpose
•Method Development
•Experimental Results
•Conclusions
•Future works
Background & Purpose
Background & PurposePath 471Path 472
Path 473
Path 474
Path 475
Path 476
Azimuth
Range
2π
0
Background & Purpose
≈ 1 m
≈ -1 m
Azimuth
Range
Path 471Path 472
Path 473
Path 474
Path 475
Path 476
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.
Ordinary kriging concept
)Z(sλΣ )(sZ ii
N
1i0
S = (x, y) is a location
Example of semivariogram model
≈ 1 m
≈ -1 m
Gaussian model
Method: Adaptive Local Kriging
≈ 1 m
≈ -1 m
Azimuth
Range
Hang wall
Foot wall
1. Window based
kriging scan to
calculate the linear
fitting of local
semivariance.
2. Window size is
locally adaptive to
ensure adequate
data points and
high processing
efficiency.
Semivariance
Distance
Averaged semivariance Fitted semivariance
x = 1024, y = 230
Local gradient: 1.258 10-5
ALK local semivariogram model:
Towards the seismic fault (Hang
wall side)
Semivariance
Distance
Averaged semivariance Fitted semivariance
ALK local semivariogram model:
Towards the seismic fault (Hang
wall side)
x = 1024, y = 460
Local gradient: 5.812 10-5
Semivariance
Distance
Averaged semivariance Fitted semivariance
ALK local semivariogram model:
Towards the seismic fault (Hang
wall side)
x = 1024, y = 580
Local gradient: 7.313 10-5
Semivariance
Distance
Averaged semivariance Fitted semivariance
ALK local semivariogram model:
Towards the seismic fault (Foot
wall side)
x = 745, y = 1200
Local gradient: 1.624 10-5
Semivariance
Distance
Averaged semivariance Fitted semivariance
ALK local semivariogram model:
Towards the seismic fault (Foot
wall side)
x = 745, y = 1000
Local gradient: 3.613 10-5
Semivariance
Distance
Averaged semivariance Fitted semivariance
ALK local semivariogram model:
Towards the seismic fault (Foot
wall side)
x = 745, y = 870
Local gradient: 7.652 10-5
ALK
(Decoherence
zone)
ALK multi-
step
processing
flow chart
Input
data
Hang wall
& foot wall
separation
Final
ALK
result
Ordinary
kriging
ALK
Give some sampled
points in the large
decoherence gaps
Artificial discontinuity
elimination
H
F
H
F
Coherence
thresholding
Coherence
thresholding
ALK data
≈ 1 m
≈ -1 m
Azimuth
Range
2π
0
ALK rewrapped interferogram
Azimuth
Range
Original interferogram
2π
0
Azimuth
Range
ALK results assessment
Azimuth
Range
Original unwrapped
image profile
ALK data profile
A
A’
A A’
Path 471 profiles
RMSE:
0.0053591572
meters
Correlation
coefficient:
0.99999985
≈ 1 m ≈ -1 m
ALK results assessment
Original unwrapped
image profile
ALK data profile
A A’
Azimuth
RangeA’
APath 472 profiles
RMSE:
0.00909682429
meters
Correlation
coefficient:
0.99939712
≈ 1 m ≈ -1 m
ALK results assessment
Original unwrapped
image profile
ALK data profile
Traced fault line Initial fault
A A’
Azimuth
RangeA’
A
Path 473 profiles
RMSE:
0.0083477924
meters
Correlation
coefficient:
0.99973365
≈ 1 m ≈ -1 m
ALK results assessment
Original unwrapped
image profile
ALK data profile
Traced fault lineInitial fault
A A’
Azimuth
Range
A’
A
Path 474 profiles
RMSE:
0.017175553
meters
Correlation
coefficient:
0.99792644
≈ 1 m ≈ -1 m
ALK results assessment
Original unwrapped
image profile
ALK data profile
Traced fault lineInitial fault
A A’
Azimuth
Range
A’
A
Path 475 profiles
RMSE:
0.0059325138
meters
Correlation
coefficient:
0.99969193
≈ 1 m ≈ -1 m
ALK results assessment
Original unwrapped
image profile
ALK data profile
A A’
Azimuth
Range
A’
≈ 1 m ≈ -1 m
A
Path 476 profiles
RMSE:
0.0071013203
meters
Correlation
coefficient:
0.99929831
3D visualization of ALK data
≈ 1 m
≈ -1 m
Refined ALK data
≈ 1 m
≈ -1 m
Azimuth
Range
2π
0
Azimuth
Range
Refined ALK rewrapped data
3D view of refined ALK unwrapped data
≈ 1 m
≈ -1 m
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.
Conclusions
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.
Geological structural numerical
modeling to explain the discrepancy
of trend of seismic fault line.
Three dimensional surface
deformation maps development.
Future works
Any questions ?