1. 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 Rosen Jet Propulsion Laboratory David Bekaert, Shizhuo Liu Delft University of Technology National Aeronautics and Space Administration Jet Propulsion Laboratory California Institute of Technology

3. Mean velocity from PS-InSAR time series analysis Bekaert & Yun, 2010 4.8 -23.6 cm / yr Central california July 2007 – December 2009

4. When removing atmosphere with PS-InSAR Processed with StaMPS Filter length: 2 month Bekaert & Yun, 2010

5. When removing atmosphere with PS-InSAR Bekaert & Yun, 2010 Processed with StaMPS Filter length: 12 month

7. Why Covariance? - Interferogram (double difference): Δρ(x 1 ,y 1 ) – Δρ(x 2 ,y 2 ) - How much is due to deformation? - How much is due to differential tropospheric delay variation?   Δρ(x 1 ,y 1 ) Δρ(x 2 ,y 2 )

8. Covariance Matrix Yun, 2007 Objective function in inverse problems: (d – Gm) T (d – Gm) d – Gm ~ N(0, I ) (d – Gm) T C -1 (d – Gm) d – Gm correlated

9. Data usage Geophysical Modeling Error budget analysis Quantitative assessment of mission requirements Atmosphere in InSAR Covariance function Structure function MODIS NIR

10. Prediction-Error Filter Interpolation Yun et al., 2005 2 km

11. Prediction-Error Filter Interpolation Claerbout & Fomel, 2002; Yun et al., 2005

12. PE Filter Interpolation (1-D example)

13. PE Filter Interpolation (2-D example) Original image Image with a hole Interpolated image Interpolated - Original

14. PE Filter Interpolation (2-D example)

15. PE Filter Interpolation of Real Data Zenith delay converted from interferometric phase (2008/11/20 – 2009/01/05, Bp = 275 m) (mm)

16. PE Filter Interpolation of Real Data Original image Image with a hole Interpolated image Interpolated - Original (mm)

17. PE Filter Interpolation of Real Data

18. Study Area: Los Angeles basin

19. Some statistics

20. Envisat interferograms 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)

21. Envisat interferograms

22. Interpretation For example, | Δρ(x 1 ,y 1 ) – Δρ(x 2 ,y 2 ) | = 5 mm  30 % probability of the measurement value placed below the mean atmospheric noise level   Δρ(x 1 ,y 1 ) Δρ(x 2 ,y 2 ) | Δρ(x 1 ,y 1 ) – Δρ(x 2 ,y 2 ) |

24. MODIS (Moderate Resolution Imaging Spectroradiometer) 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

25. Conclusions 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).

26. 23 ALOS interferograms (asc. 2006.06.30 – 2010.01.08)