ADAPTIVE LOCAL KRIGING (ALK)

TO RETRIEVE THE SLANT RANGE

SURFACE MOTION MAPS OF

WENCHUAN EARTHQUAKE

Department of Earth Science and EngineeringImperial College LondonMeng-Che Wumeng-che.wu08@imperial.ac.ukJian Guo Liuj.g.liu@imperial.ac.uk

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 ?