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 475Path 476

Azimuth

Range

2π

0

Background & Purpose

≈ 1 m

≈ -1 m

Azimuth

Range

Path 471Path 472

Path 473

Path 474

Path 475Path 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

Coherencethresholding

Coherencethresholding

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:0.0053591572meters

Correlationcoefficient:0.99999985

≈ 1 m ≈ -1 m

ALK results assessment

Original unwrapped image profile

ALK data profile

A A’

Azimuth

RangeA’

APath 472 profiles

RMSE:0.00909682429meters

Correlationcoefficient: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:0.0083477924meters

Correlationcoefficient:0.99973365

≈ 1 m ≈ -1 m

ALK results assessment

Original unwrapped image profile

ALK data profile

Traced fault lineInitial fault

A A’

Azimuth

RangeA’

A

Path 474 profiles

RMSE:0.017175553meters

Correlationcoefficient: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’

APath 475 profiles

RMSE:0.0059325138meters

Correlationcoefficient: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

APath 476 profiles

RMSE:0.0071013203meters

Correlationcoefficient: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

THANK YOU

Any questions ?