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Institute of Geophysics and Tectonics

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. Why a tropospheric correction for InSAR?. Tectonic.

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Institute of Geophysics and Tectonics

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  1. 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

  2. Why a tropospheric correction for InSAR? Tectonic • To extract smaller deformation signals 100 km cm -10 13.5 Over 9 months

  3. Why a tropospheric correction for InSAR? Troposphere Tectonic • 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 100 km cm -10 13.5 Over 9 months 1 interferogram (ti –tj)

  4. Tropospheric corrections for an interferogram • Auxiliary information (e.g.): Limitations • GPS • Weather models • Spectrometer data • Station distribution • Accuracy and resolution • Cloud cover and temporal sampling

  5. 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

  6. A laterally uniform troposphere Interferogram Linear est • A linear correction can work in small regions Tropo GPS InSAR and GPS data property of IGN isolines

  7. A spatially varying troposphere Topography est: Spectrometer & Linear • However • Spatial variation of troposphere A linear correction can work in small regions + + - + isolines

  8. A spatially varying troposphere Allowing for spatial variation -9.75 rad 9.97 Interferogram (Δɸ) Why not estimate a linear function locally?

  9. A spatially varying troposphere -9.75 rad 9.97 Interferogram (Δɸ) Why not estimate a linear function locally? Does not work as: Const is also spatially-varying and cannot be estimated from original phase!

  10. A spatially varying troposphere -9.75 rad 9.97 Interferogram (Δɸ) Why not estimate a linear function locally? Does not work as: Const is also spatially-varying and cannot be estimated from original phase! We propose a power-law relationship that can be estimated locally

  11. Allowing for spatial variation 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

  12. Allowing for spatial variation Allowing for spatial variation 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

  13. Power-law example -9.75 rad 9.97 Interferogram (Δɸ)

  14. Power-law example -9.75 rad 9.97 (Y. Lin et al., 2010, G3) for a linear approach Band filtered: phase (Δɸband) & topography (h0-h)αband Interferogram (Δɸ)

  15. Power-law example (Y. Lin et al., 2010, G3) for a linear approach Band filtered: phase (Δɸband) & topography (h0-h)αband

  16. Power-law example (Y. Lin et al., 2010, G3) for a linear approach Band filtered: phase (Δɸband) & topography (h0-h)αband Anti-correlated! For each window: estimate Kspatial

  17. Power-law example (Y. Lin et al., 2010, G3) for a linear approach Band filtered: phase (Δɸband) & topography (h0-h)αband Anti-correlated! For each window: estimate Kspatial

  18. Power-law example rad/mα -1.1e-69.8e-5 Original phase (Δɸ) Tropo variability (Kspatial) Band filtered: phase (Δɸband) & topography (h0-h)αband

  19. Power-law example 1/mα rad/mα 4.7e4 2.4e5 -1.1e-69.8e-5 -9.75 rad 9.97 Power-law est (Δɸtropo) Topography (h0-h)α Original phase (Δɸ) Tropo variability (Kspatial) Band filtered: phase (Δɸband) & topography (h-h0)αband

  20. Power-law example Allowing for spatial variation -9.75 rad 9.97 -9.75 rad 9.97 -9.75 rad 9.97 Spectrometer est (Δɸtropo) Original phase (Δɸ) Power-law est (Δɸtropo)

  21. Case study regions Regions: • El Hierro (Canary Island) • GPS • Weather model • Uniform correction • Non-uniform correction • Guerrero (Mexico) • MERIS spectrometer • Weather model • Uniform correction • Non-uniform correction

  22. El Hierro Interferograms (original) -11.2 rad 10.7

  23. El Hierro Interferograms (original) -11.2 rad 10.7 WRF (weather model)

  24. El Hierro Interferograms (original) -11.2 rad 10.7 WRF (weather model)

  25. El Hierro Interferograms (original) -11.2 rad 10.7 WRF (weather model) Linear (uniform)

  26. El Hierro Interferograms (original) -11.2 rad 10.7 WRF (weather model) Linear (uniform) Power-law (spatial var)

  27. El Hierro quantification • ERA-I run at 75 km resolution • WRF run at 3 km resolution

  28. Mexico -9.75 rad 9.97 MERIS MERIS

  29. Mexico -9.75 rad 9.97 MERIS MERIS Clouds

  30. Mexico -9.75 rad 9.97 (Weather model) MERIS ERA-I MERIS ERA-I

  31. Mexico -9.75 rad 9.97 (Weather model) MERIS ERA-I MERIS ERA-I Misfit near coast

  32. Mexico -9.75 rad 9.97 (Weather model) Linear Linear MERIS ERA-I MERIS ERA-I

  33. Mexico -9.75 rad 9.97 (Weather model) Linear Linear MERIS ERA-I MERIS ERA-I

  34. Mexico -9.75 rad 9.97 (Weather model) Linear Power-law Power-law Linear MERIS ERA-I MERIS ERA-I

  35. Mexico -9.75 rad 9.97 (Weather model) Linear Power-law Power-law Linear MERIS ERA-I MERIS ERA-I

  36. Mexico techniques compared: profile AA’ MERIS ERA-I A’ A Linear Power-law

  37. Mexico quantification MERIS accuracy (Z. Li et al., 2006)

  38. Summary/Conclusions • 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. Toolbox with presented techniques will be made available to the community

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