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GPS Strain Transient Detection with a Filter-Window-Eigenvalue Method
Brad Lipovsky (UC Riverside, now at Stanford University)Gareth Funning (UC Riverside)
1. Initial approachA. Eigenvalue-only methodB. Difficulties
2. Improved approachA. Noise attenuationB. Eigenvalue criterionC. Windowing
3. Detection threshold
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Eigenvalue-only approach
D(x,t)Data matrix with column vector time series
X(x)
T(t)
Spatial patterns of deformation (collections of vectors)
Temporal patterns of deformation(a collection of time series)
λ Relative weighting of patterns (eigenvalues)
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Filter-Window-Eigenvalue Method
1. Noise attenuation2. Eigenvalue Criterion3. Windowing
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Noise attenuation (1/3)Two observed types of GPS noise:• Residual, seasonally-correlated noise [e.g.
Langbein 2008, Lipovsky 2011]• High-frequency “chatter”
1. Band-stop filter (2-pole IIR)• Band stops at 0.5 and 2.0 cycles/year
2. Low-pass filter (FIR)• Time constant ~50-125 days
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Eigenvalue Criterion (2/3)
1~
This criterion implies that episodes of transient deformation show a
characteristic type of simplicity(space-time separability).
Method: use this criterion as an indicatorof transient deformation
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Windowing (3/3)
Goal: Find subsets of the data that maximize λ1/λ2
The latitude-longitude window and time period of transient deformation,
we define to be a transient centroid.
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Dataset 3f
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Dataset 3g
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Relationship with Least Squares