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 Jian Guo Liu

Outline Background & Purpose Method Development Experimental Results Conclusions Future works

Background & Purpose

Path 471 Path 472 Path 473 Path 474 Path 475 Path 476 Azimuth Range 2π2π 0

Background & Purpose ≈ 1 m ≈ -1 m Azimuth Range Path 471 Path 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 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 semivarianceFitted 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 semivarianceFitted 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 semivarianceFitted 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 semivarianceFitted 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 semivarianceFitted 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 semivarianceFitted 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 (Decoherence zone) ALK multi- step processing flow chart Input data Hang wall & foot wall separation Final ALK result Ordinary kriging 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

2π2π 0 ALK rewrapped interferogram Azimuth Range

Original interferogram 2π2π 0 Azimuth Range

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

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

ALK results assessment Original unwrapped image profile ALK data profile Traced fault lineInitial fault AA’ Azimuth Range A’ A Path 473 profiles RMSE: meters Correlation coefficient: ≈ 1 m≈ -1 m

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

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

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

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

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

2π2π 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

 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

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