school of earth and environment institute of geophysics and tectonics robust corrections for...

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


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?


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


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


A linear correction can work in small regions Interferogram

Tropo

GPS

InSAR and GPS data property of IGN

Linear est

isolines

€


A laterally uniform troposphere


However

• Spatial variation of troposphere

est: Spectrometer & Linear

isolines

+ +

- +

A linear correction can work in small regions

€


A spatially varying troposphere

Topography


Allowing for spatial variation

Interferogram (Δɸ)Why not estimate a linear function locally?

€


-9.75 rad 9.97A spatially varying troposphere


€


-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)


€

Δφtropo =Kspatial ⋅ h0 − h( )α

€


-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!



€


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




€


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


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



-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



€


α

band




Band filtered: phase (Δɸband) & topography (h0-h)αband €


α

band

For each window:estimate Kspatial


Anti-correlated!


€


α

band


For each window:estimate Kspatial


Anti-correlated!


Original phase (Δɸ)

Power-law example

Band filtered: phase (Δɸband) & topography (h0-h)αband Tropo variability (Kspatial) €


α

band

rad/mα -1.1e-6 9.8e-5


Original phase (Δɸ)

Power-law example

Band filtered: phase (Δɸband) & topography (h-h0)αband Tropo variability (Kspatial) €


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


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


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


-11.2 rad 10.7

Interferograms(original)

El Hierro


WRF(weather model)

El Hierro

-11.2 rad 10.7



WRF(weather model)

Linear(uniform)

El Hierro

-11.2 rad 10.7



WRF (weather model)

Linear(uniform)

Power-law(spatial var)

El Hierro

-11.2 rad 10.7


School of Earth and Environment El Hierro quantification

ERA-I run at 75 km resolution WRF run at 3 km resolution


MERIS MERIS

Mexico-9.75 rad 9.97


MERIS MERIS

Clouds

Mexico-9.75 rad 9.97


MERIS ERA-I MERIS ERA-I

Mexico-9.75 rad 9.97(Weather model)


MERIS ERA-I MERIS ERA-I

Misfit near coast



MERIS ERA-I Linear MERIS ERA-I Linear



MERIS ERA-I Linear Power-law MERIS ERA-I Linear Power-law



MERIS ERA-I

Linear Power-law

Mexico techniques compared: profile AA’


MERIS accuracy

(Z. Li et al., 2006)

Mexico quantification


• 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

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