Quantitative assessment on the requirements of DESDynI mission for crustal deformation study

Sang-Ho Yun, Julian Chaubell, Eric Fielding, Zhen Liu,

Scott Hensley, Frank Webb, Paul RosenJet Propulsion Laboratory

David Bekaert, Shizhuo LiuDelft University of Technology

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National Aeronautics and Space Administration

Jet Propulsion LaboratoryCalifornia Institute of Technology

Atmosphere in InSAR for solid earth study

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Considered as noise

Ignored

Covariance function assumed Covariance matrix

Corrected using independent measurements (MODIS,MERIS,GPS) or time series analysis (PS-InSAR, SBAS)

Mean velocity from PS-InSAR time series analysis

3Bekaert & Yun, 2010

4.8

-23.6

cm / yr

Central californiaJuly 2007 – December 2009

When removing atmosphere with PS-InSAR

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Processed with StaMPSFilter length: 2 month

Bekaert & Yun, 2010

When removing atmosphere with PS-InSAR

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Bekaert & Yun, 2010

Processed with StaMPSFilter length: 12 month

Outline

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Covariance and structure function

Prediction-Error Filter

Atmospheric error budget in Los Angeles basin

MODIS data

Conclusions

Why Covariance?

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- Interferogram (double difference): Δρ(x1,y1) – Δρ(x2,y2) - How much is due to deformation?- How much is due to differential tropospheric delay variation?

Δρ(x1,y1)

Δρ(x2,y2)

Covariance Matrix

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Yun, 2007

Objective function in inverse problems:

(d – Gm)T(d – Gm) d – Gm ~ N(0,I) (d – Gm)TC-1(d – Gm) d – Gm correlated

Data usage

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Geophysical Modeling

Error budget analysisQuantitative assessment of mission requirements

Atmosphere in InSAR Covariance function

Structure functionMODIS NIR

Prediction-Error Filter Interpolation

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Yun et al., 2005

2 km

Prediction-Error Filter Interpolation

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Claerbout & Fomel, 2002; Yun et al., 2005

PE Filter Interpolation (1-D example)

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PE Filter Interpolation (2-D example)

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Original image Image with a hole

Interpolated image Interpolated - Original

PE Filter Interpolation (2-D example)

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PE Filter Interpolation of Real Data

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Zenith delay converted from interferometric phase (2008/11/20 – 2009/01/05, Bp = 275 m)

(mm)

PE Filter Interpolation of Real Data

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Original image Image with a hole Interpolated image Interpolated - Original

(mm)

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PE Filter Interpolation of Real Data

Study Area: Los Angeles basin

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Some statistics

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Envisat interferograms

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35 Envisat interferograms from ascending track 392 (2002.10.28 – 2007.01.15)

104 Envisat interferograms from descending track 170 (2003.09.27 – 2010.02.27)

Envisat interferograms

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Interpretation

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For example, | Δρ(x1,y1) – Δρ(x2,y2) | = 5 mm

30 % probability of the measurement value placed below the mean atmospheric noise level

Δρ(x1,y1)

Δρ(x2,y2)

| Δρ(x1,y1) – Δρ(x2,y2) |

How much is the signal against atmospheric noise

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- Mw 5.4 earthquake at a depth of 1 km.- Interferogram reduced with variance-equalizing method (quadtree)- 71 % of reduced data values above 5 percentile of atmospheric noise level

MODIS (Moderate Resolution Imaging Spectroradiometer)

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Terra (launched on 1999.12.18)Aqua (launched on 2002.05.04)

Wide swath: 2000 km

Spatial resolution: 1 km

Near daily global coverage

NIR channel has PWV (precipitable water vapor)

Cloud mask

OSCAR project team at JPL: Paul Von Allmen, Eric Fielding, Zhangfan Xing, Lei Pan

Li & Fielding

Conclusions

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Covariance function is useful for geophysical modeling and structure function is useful for quantitative assessment of mission requirements and error budget analysis.

Prediction-Error filter is tested for image recovery of tropospheric delay variation and turned out to be useful for robust production of spectral analysis.

The structure functions of tropospheric signal from Los Angeles basin from 2002 through 2010 derived from 139 Envisat interferograms are bounded within one order of magnitude.

MODIS data are being tested against the InSAR data analysis and be used to characterize and produce global library of covariance and structure functions; Fcov(r,t,lat,lon), Fstr(r,t,lat,lon).

23 ALOS interferograms (asc. 2006.06.30 – 2010.01.08)

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