School of Earth and Environment Institute of Geophysics and Tectonics Robust corrections for topographically-correlated atmospheric noise in InSAR data from large deforming regions By David Bekaert Andy Hooper, Tim Wright and Richard Walters
School of Earth and Environment
Institute of Geophysics and Tectonics
Robust corrections for topographically-correlated atmospheric noise in InSAR data from large deforming regions
By David Bekaert
Andy Hooper, Tim Wright and Richard Walters
School of Earth and Environment Why a tropospheric correction for InSAR?
Tectonic
Over 9 months
100 km
cm
-10 13.5
To extract smaller deformation signals
School of Earth and Environment
To extract smaller deformation signals
Tropospheric delays can reach up to 15 cm
With the tropospheric delay a superposition of
- Short wavelength turbulent component
- Topography correlated component
- Long wavelength component
Troposphere
1 interferogram
(ti –tj)
Tectonic
Over 9 months
100 km
cm
-10 13.5
Why a tropospheric correction for InSAR?
School of Earth and Environment
Auxiliary information (e.g.): Limitations
• GPS
• Weather models
• Spectrometer data
Station distribution
Accuracy and resolution
Cloud cover and temporal sampling
Tropospheric corrections for an interferogram
School of Earth and Environment
Auxiliary information (e.g.): Limitations
• GPS
• Weather models
• Spectrometer data
Interferometric phase
• Linear estimation (non-deforming region or band filtering)
Station distribution
Accuracy and resolution
Cloud cover and temporal sampling
Assumes a laterally uniform troposphere
isolines
€
Δφtropo =Kuniform ⋅ h +Const
Tropospheric corrections for an interferogram
School of Earth and Environment
A linear correction can work in small regions Interferogram
Tropo
GPS
InSAR and GPS data property of IGN
Linear est
isolines
€
Δφtropo =Kuniform ⋅ h +Const
A laterally uniform troposphere
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However
• Spatial variation of troposphere
est: Spectrometer & Linear
isolines
+ +
- +
A linear correction can work in small regions
€
Δφtropo =Kuniform ⋅ h +Const
A spatially varying troposphere
Topography
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Allowing for spatial variation
Interferogram (Δɸ)Why not estimate a linear function locally?
€
Δφtropo =Kuniform ⋅ h +Const
-9.75 rad 9.97A spatially varying troposphere
School of Earth and Environment
€
Δφtropo =Kuniform ⋅ h +Const
-9.75 rad 9.97A spatially varying troposphere
Why not estimate a linear function locally?
Does not work as:
Const is also spatially-varying and
cannot be estimated from original phase!
Interferogram (Δɸ)
School of Earth and Environment
€
Δφtropo =Kspatial ⋅ h0 − h( )α
€
Δφtropo =Kuniform ⋅ h +Const
-9.75 rad 9.97
We propose a power-law relationship
that can be estimated locally
A spatially varying troposphere
Why not estimate a linear function locally?
Does not work as:
Const is also spatially-varying and
cannot be estimated from original phase!
Interferogram (Δɸ)
School of Earth and Environment
€
Δφtropo =Kspatial ⋅ h0 − h( )α
With h0 the lowest height at which the relative
tropospheric delays ~0
• 7-14 km from balloon sounding
Sounding data provided by the University of Wyoming
Allowing for spatial variation
School of Earth and Environment
Allowing for spatial variation
€
Δφtropo =Kspatial ⋅ h0 − h( )α
With h0 the lowest height at which the relative
tropospheric delays ~0
• 7-14 km from balloon sounding
With α a power-law describing the decay of
the tropospheric delay
• 1.3-2 from balloon sounding data
Allowing for spatial variation
Sounding data provided by the University of Wyoming
School of Earth and Environment Power-law example
€
Δφ =Kspatial ⋅ h0 − h( )α+ Δφdefo + ...
-9.75 rad 9.97
Interferogram (Δɸ)
School of Earth and Environment Power-law example
-9.75 rad 9.97
€
Δφband≈ Kspatial ⋅ h0 − h( )
α
band
Band filtered: phase (Δɸband) & topography (h0-h)αband
(Y. Lin et al., 2010, G3) for a linear approach
Interferogram (Δɸ)
School of Earth and Environment Power-law example
€
Δφband≈ Kspatial ⋅ h0 − h( )
α
band
Band filtered: phase (Δɸband) & topography (h0-h)αband
(Y. Lin et al., 2010, G3) for a linear approach
School of Earth and Environment Power-law example
Band filtered: phase (Δɸband) & topography (h0-h)αband €
Δφband≈ Kspatial ⋅ h0 − h( )
α
band
For each window:estimate Kspatial
(Y. Lin et al., 2010, G3) for a linear approach
Anti-correlated!
School of Earth and Environment Power-law example
€
Δφband≈ Kspatial ⋅ h0 − h( )
α
band
Band filtered: phase (Δɸband) & topography (h0-h)αband
For each window:estimate Kspatial
(Y. Lin et al., 2010, G3) for a linear approach
Anti-correlated!
School of Earth and Environment
Original phase (Δɸ)
Power-law example
Band filtered: phase (Δɸband) & topography (h0-h)αband Tropo variability (Kspatial) €
Δφband≈ Kspatial ⋅ h0 − h( )
α
band
rad/mα -1.1e-6 9.8e-5
School of Earth and Environment
Original phase (Δɸ)
Power-law example
Band filtered: phase (Δɸband) & topography (h-h0)αband Tropo variability (Kspatial) €
Δφtropo =Kspatial ⋅ h0 − h( )α
Topography (h0-h)α
-1.1e-6 9.8e-5rad/mα
-9.75 rad 9.97
Power-law est (Δɸtropo)
4.7e4 2.4e51/mα
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Allowing for spatial variation-9.75 rad 9.97 -9.75 rad 9.97 -9.75 rad 9.97
Original phase (Δɸ) Power-law est (Δɸtropo) Spectrometer est (Δɸtropo)
Power-law example
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Regions:
• El Hierro (Canary Island)
- GPS
- Weather model
- Uniform correction
- Non-uniform correction
• Guerrero (Mexico)
- MERIS spectrometer
- Weather model
- Uniform correction
- Non-uniform correction
Case study regions
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WRF(weather model)
El Hierro
-11.2 rad 10.7
Interferograms(original)
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WRF(weather model)
El Hierro
-11.2 rad 10.7
Interferograms(original)
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WRF(weather model)
Linear(uniform)
El Hierro
-11.2 rad 10.7
Interferograms(original)
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WRF (weather model)
Linear(uniform)
Power-law(spatial var)
El Hierro
-11.2 rad 10.7
Interferograms(original)
School of Earth and Environment El Hierro quantification
ERA-I run at 75 km resolution WRF run at 3 km resolution
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MERIS ERA-I MERIS ERA-I
Misfit near coast
Mexico-9.75 rad 9.97(Weather model)
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MERIS ERA-I Linear MERIS ERA-I Linear
Mexico-9.75 rad 9.97(Weather model)
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MERIS ERA-I Linear MERIS ERA-I Linear
Mexico-9.75 rad 9.97(Weather model)
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MERIS ERA-I Linear Power-law MERIS ERA-I Linear Power-law
Mexico-9.75 rad 9.97(Weather model)
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MERIS ERA-I Linear Power-law MERIS ERA-I Linear Power-law
Mexico-9.75 rad 9.97(Weather model)
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MERIS ERA-I
Linear Power-law
Mexico techniques compared: profile AA’
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• Fixing a reference at the ‘relative’ top of the troposphere allows us to deal with spatially-varying tropospheric delays.
• Band filtering can be used to separate tectonic and tropospheric components of the delay in a single interferogram
• A simple power-law relationship does a reasonable job of modelling the topographically-correlated part of the tropospheric delay.
• Results compare well with weather models, GPS and spectrometer correction methods.
• Unlike a linear correction, it is capable of capturing long-wavelength spatial variation of the troposphere.
Summary/Conclusions
Toolbox with presented techniques will be made available to the community