GPS Strain Transient Detection with a Filter-Window-Eigenvalue MethodGPS 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

1. Initial approachA. Eigenvalue-only methodB. Difficulties

2. Improved approachA. Noise attenuationB. Eigenvalue criterionC. Windowing

3. Detection threshold

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)

Filter-Window-Eigenvalue Method

1. Noise attenuation2. Eigenvalue Criterion3. Windowing

1. Noise attenuation2. Eigenvalue Criterion3. Windowing

Noise attenuation (1/3)Two observed types of GPS noise:•Residual, seasonally-correlated noise [e.g. Langbein 2008, Lipovsky 2011]•High-frequency “chatter”

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

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

Eigenvalue Criterion (2/3)

1~

This criterion implies that episodes of transient deformation show a

characteristic type of simplicity(space-time separability).

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

Method: use this criterion as an indicatorof transient deformation

Windowing (3/3)

Goal: Find subsets of the data that maximize λ1/λ2

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.

Dataset 3f

Dataset 3g

Relationship with Least Squares