1. Propagation delays in InSAR
GE California Institute of Technology, 2013

2. Propagation delays in InSAR
TerraSAR-X
CosmoSkyMed
Envisat
ERS-1/2
RadarSat
Sentinels
Kollias et al, 2007, BAMS

3. An example... - One month temporal baseline (no deformation)
- Topography <=> Atmospheric delay

4. An example...

5. An example...

6. An example...

7. Differential delay
First pass
Second Pass

8. Differential delay
First pass
Second Pass

9. A bit of theory Air Refractivity: : Total Pressure : Temperature
Refraction index
: Total Pressure
: Temperature
: Cloud Water Content
: Electron Density
: Frequency
: Constants

10. A bit of theory - Small perturbation - Very hard to estimate
Air Refractivity:
: Total Pressure
: Temperature
: Cloud Water Content
: Electron Density
Real-life range
: Frequency
- Small perturbation
- Very hard to estimate
: Constants
Hanssen, 2001

11. A bit of theory - Small perturbation - Very hard to estimate
Air Refractivity:
: Total Pressure
: Temperature
: Cloud Water Content
: Electron Density
Real-life range
: Frequency
- Small perturbation
- Very hard to estimate
: Constants
Hanssen, 2001

12. A bit of theory Air Refractivity: : Total Pressure : Temperature
- Dispersive effect
- Long wavelength perturbations (~100 km)
- Effect is small in C-band (too short wavelength)
- Significant in L-band
: Cloud Water Content
: Electron Density
: Frequency
: Constants

13. Ionospheric perturbation
Shen et al., 2009, Nat. Geosci.

14. Ionospheric perturbation
“clean”
Interferogram
Azimuth
offsets
Phase gradient
- Estimate the azimuth offset
- Compute the phase gradient
- Extract the proportionality factor
- Correct the interferogram
Problem: Only works where there is no deformation along azimuth
Interferogram
Ionospheric
phase screen
Raucoules & de Michele, IEEE GRSL

15. Ionosphere (not today)
A bit of theory
Air Refractivity:
: Total Pressure
: Temperature
Ionosphere (not today)
: Cloud Water Content
: Electron Density
Troposphere (today)
: Frequency
: Constants

16. A bit of theory Air Refractivity: Nadir Delay: and : Dry Air Pressure
: Total Pressure
: Temperature
: Specific Constant for dray air and vapor
: Cloud Water Content
: Gravitation
: Electron Density
: Partial pressure in Water Vapor
: Frequency
: Constants

17. A bit of theory Delay along the Line-Of-Sight wrt. reference altitude:
: Dry Air Pressure
: Total Pressure
: Temperature
: Specific Constant for dray air and vapor
: Cloud Water Content
: Gravitation
: Electron Density
: Partial pressure in Water Vapor
: Frequency
: Constants

18. A bit of theory If I had a pressure profile...
Delay along the Line-Of-Sight wrt. reference altitude:
If I had a
pressure profile...

19. ... and a temperature profile...
A bit of theory
Delay along the Line-Of-Sight wrt. reference altitude:
... and a temperature profile...

20. ... and a Water Vapor Partial Pressure profile...
A bit of theory
Delay along the Line-Of-Sight wrt. reference altitude:
... and a Water Vapor Partial Pressure profile...

21. ... I could compute the total delay:
A bit of theory
Delay along the Line-Of-Sight wrt. reference altitude:
... I could compute the total delay:

22. ? A bit of theory ... I could compute the total delay:
Delay along the Line-Of-Sight wrt. reference altitude: ?
... I could compute the total delay:
But usually, I don’t have all those things (actually, never...).

23. Do we really need to correct for that delay?
Can’t we just filter it, or whatever?

24. Do we really need to correct for that delay?
Can’t we just filter it, or whatever?
Yes, you can...

25. Do we really need to correct for that delay?
Can’t we just filter it, or whatever?
Yes, you can...
... but you should not.

26. Single interferograms
Mw 7.7
Depth ~ 100 km

27. Time filtering, then...?
Stacking:

28. Time filtering, then...? Stacking:
If we have independent interferograms,
with random noise (in time)

29. Time filtering, then...? Stacking:
If we have independent interferograms,
with random noise (in time)
Doin et al, 2009, J. App. Geophy.

30. Now that we can do better, still no!!!
Time filtering, then...?
Stacking:
If we have independent interferograms,
with random noise (in time)
Now that we can do better, still no!!!

31. ==> Stacking or Time Series
How to correct then?
Turbulent
Delay
Stratified
Tropospheric
Delay +
==> Stacking or Time Series
- Random in Space and Time
- Numerous Acquisitions to average or smooth
the signal

32. ==> Stacking or Time Series
Separating the delay
Turbulent
Delay
Stratified
Tropospheric
Delay +
==> Stacking or Time Series 2

33. ==> Stacking or Time Series
Separating the delay
Turbulent
Delay
Stratified
Tropospheric
Delay +
==> Stacking or Time Series
Semivariogram:
Covariance:

34. ==> Stacking or Time Series
Separating the delay
Turbulent
Delay
Stratified
Tropospheric
Delay +
==> Stacking or Time Series

35. Estimating a phase/elevation relationship
Empirical Correction
Estimating a phase/elevation relationship

36. Empirical Methods Estimating a phase/elevation relationship
Joint inversion model/orbit/troposphere
Cavalie et al, 2008; Jolivet et al., 2012

37. Empirical Methods Estimating a phase/elevation relationship
Joint inversion model/orbit/troposphere
Cavalie et al, 2008; Jolivet et al., 2012

38. Estimating a phase/elevation relationship
Empirical Methods
Estimating a phase/elevation relationship
Multi-scale approach
Lin et al, 2010

39. - Deformation/Topography correlation
Empirical Methods
- Deformation/Topography correlation

40. Prediction Methods
- Most methods focus on constructing vertical profiles of delay
Available Data:
GPS zenith delays
Local Atmospheric data
Multi-spectral imagery systems
Global Re-analysis
Available Methods:
Interpolation (2D / 3D / Ray tracing)
Meso-scale modeling

41. Local Atmospheric Data
Prediction Methods
Local Atmospheric Data
- Data from a meteorological station
- Radio sounding profile
Delacourt et al. 1998, GRL

42. Prediction Methods
GPS zenith delays
Onn & Zebker, 2006, JGR

43. Prediction Methods
GPS zenith delays
Onn & Zebker, 2006, JGR

44. Puyssegur et al, 2007, JGR; Li et al, 2012, GJI
Prediction Methods
Multispectral Images
Multi-spectral imagery system onboard Envisat:
- Passive system (captures the electro-magnetic field reflected by the ground surface)
- 15 Bands
- Combination of band 14 and 15 gives the Integrated Precipitable Water Vapor
- Integrated Wet delay
and
and
: Specific Constant for dray air and vapor
: Ratio of molecular masses of water vapor and dry air
: Constants
Puyssegur et al, 2007, JGR; Li et al, 2012, GJI

45. Prediction Methods Multispectral Images Good:
Does not only correct for stratified features
Predicts turbulence
Bad:
Does not work for night-time acquisitions
Does not work if dense cloud cover
Li et al, 2012, GJI

46. Goal: Reproduce the turbulences using fine modeling
Prediction Methods
Meso-Scale Modeling
Goal: Reproduce the turbulences using fine modeling
MM5 Modeling
Interferogram
Puyssegur et al, 2007, JGR

47. Prediction Methods ERA-Interim Dee et al, 2011 Available Data:
GPS zenith delays
Local Atmospheric data
Multi-spectral imagery systems
Global Re-analysis
These data are not always available
This is fine over SoCal, but Tibet is another story
ERA-Interim Dee et al, 2011
- ECMWF atmospheric model
- Global ~75 km grid
- 4 solutions a day at 0 am, 6 am, 12 pm and 6 pm
- Altitude, temperature and water vapor partial pressure at 37 pressure levels (surface to 50 km alt.)

48. Computing Delay Maps from GAM
1 - Computing delay functions

49. Computing Delay Maps from GAM
1 - Computing delay functions
2 - Spatial bilinear interpolation and
spline interpolation for altitude

50. Computing Delay Maps from GAM
One month temporal baseline == no deformation expected

51. Computing Delay Maps from GAM

52. Computing Delay Maps from GAM
ERA-Interim Dee et al, 2011
- ECMWF atmospheric model
- Global ~75 km grid
- 4 solutions a day at 0 am, 6 am, 12 pm and 6 pm
- Altitude, temperature and water vapor partial pressure at 37 pressure levels (surface to 50 km alt.)
North AmeRican Re-analysis Mesinger et al, 2006
- NOAA atmospheric model
- North America (Canada, USA + Hawaii, Mexico), Lambert Conic grid, ~0.3 degrees
- 8 solutions a day
- Altitude, temperature and water vapor partial pressure at 29 pressure levels.
Modern Era-Restrospective Analysis Rienecker et al, 2011
- NASA atmospheric model
- Global ~0.5 deg
- 4 solutions a day
- Altitude, temperature and water vapor partial pressure at 42 pressure levels.
Probably other models available, need to try these...

53. Removing the atmosphere is great because...
... it allows to unwrap the phase
where we thought it was impossible.
- Atmosphere introduces high fringe rate over areas with rough topography.
- High fringe rate is a problem for unwrapping (aliasing of fringe rates)
- Correction “flattens” the phase field and allows for unwrapping
Jolivet et al, 2011, GRL

54. Removing the atmosphere is great because...
... it removes the seasonal oscillations in time series.

55. Removing the atmosphere is great because...
... it removes the bias in rate estimates.

56. Removing the atmosphere is great because...
... I hope it will allow to measure long wavelength deformations.
- Long-wavelength tropospheric perturbation mimic orbital artifacts
- Usually, we fit a first order polynomial function on the interferogram, pretending it comes from orbital errors
- This long-wavelength is actually a combination of orbits + troposphere + tides (Hilary??)

57. Bibliography
- Kollias, P. et al., Millimeter-Wavelength Radars. Bulletin of the American Meteorological Society, pp.1–17.
- Hanssen, R.F., Radar Interferometry, Data Interpretation and Error Analysis, Kulwer Academic Publishers.
- Shen, Z.-K. et al., Slip maxima at fault junctions and rupturing of barriers during the 2008 Wenchuan earthquake. Nature Geoscience, 2(10), pp.718–724.
- Raucoules, D. & de Michele, M., Assessing Ionospheric Influence on L-Band SAR Data: Implications on Coseismic Displacement Measurements of the 2008 Sichuan Earthquake. IEEE Geoscience and Remote Sensing Letters, 7(2), pp.286–290.
- Doin, M.P. et al., Corrections of stratified tropospheric delays in SAR interferometry: Validation with global atmospheric models. Journal of Applied Geophysics, 69(1), pp.35–50.
- Cavalié, O. et al., Measurement of interseismic strain across the Haiyuan fault (Gansu, China), by InSAR. Earth and Planetary Science Letters, 275(3-4), pp.246–257.
- Lin, Y.-N.N. et al., A multiscale approach to estimating topographically correlated propagation delays in radar interferograms. Geochemistry Geophysics Geosystems, 11(9), p.Q09002.
- Jolivet, R. et al., Shallow creep on the Haiyuan Fault (Gansu, China) revealed by SAR Interferometry. Journal of Geophysical Research, 117(B6).
- Delacourt, C., Briole, P. & Achache, J., Tropospheric corrections of SAR interferograms with strong topography. Application to Etna. Geophysical Research Letters, {25}({15}), pp.{2849–2852}.
- Onn, F. & Zebker, H.A., Correction for interferometric synthetic aperture radar atmospheric phase artifacts using time series of zenith wet delay observations from a GPS network. Journal of Geophysical Research, 111(B9).
- Puysségur, B., Michel, R. & Avouac, J.-P., Tropospheric phase delay in interferometric synthetic aperture radar estimated from meteorological model and multispectral imagery. Journal of Geophysical Research, 112(B5).
- Li, Z.W. et al., Correcting atmospheric effects on InSAR with MERIS water vapour data and elevation-dependent interpolation model. Geophysical Journal International, 189(2), pp.898–910.
- Dee, D.P. et al., The ERA-Interim reanalysis: configuration and performance of the data assimilation system. Quarterly Journal of the Royal Meteorological Society, 137(656), pp.553–597.
- Mesinger, F. et al., North American Regional Reanalysis. Bulletin of the American Meteorological Society, 87(3), pp.343–360.
- Rienecker, M.M. et al., MERRA: NASA’s Modern-Era Retrospective Analysis for Research and Applications. Journal of Climate, 24(14), pp.3624–3648.
- Jolivet, R. et al., Systematic InSAR tropospheric phase delay corrections from global meteorological reanalysis data. Geophysical Research Letters, 38(17).