I was wondering if you can help me understand what is meant by spatial correlation of deformation and temporal correlation of atmospheric contribution while the noise is neither correlated in time nor space. Three assumptions proposed by Hooper 2012 Recent advances in SAR interferometry time series analysis for measuring crustal deformation - ScienceDirect
and were carried on forward by later authors who were studying atmospheric mitigations in InSAR time series.
Most processes of deformation within the Earth that cause displacement of the surface affect adjacent areas in very similar ways. This causes a spatial correlation of the surface displacement measurements by InSAR. The geological processes also tend to either move slowly in time or have a sharp change in time like an earthquake, but the signal stays similar for long periods of time so there is temporal correlation.
There is also a spatial correlation of the atmospheric effects because the atmosphere generally varies over spatial scales of many kilometers. There are some atmospheric effects that are correlated with topography because they are caused by vertical variations of water vapor. Some part of the atmospheric variations are due to the change of seasons so they will have temporal correlation, but most atmospheric variations are random in time.
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I really appreciate your explanation, but there are a few points I couldnāt quite understand. So the deformational phase mostly displays non-randomly distributed pattern if the lateral phase delay greatly varies between adjacent pixels due to the nonuniform localized deformation such as landslides or sinkholes, and therefore the backscattered signals from such adjacent pixesl would be considered spatially uncorrelated . Am I correct?
If so, what is difference between by the spatially uncorrelated DEM (look angle) error that is filtered at StaMPS step 3, removed at Step 5, and spatially correlated look angle error that is removed at Stamps Step 7
Yes, there are some types of deformation at shallow depths, including landslides and sinkholes, that will cause sharp changes in surface displacements with space. Surface ruptures on faults are another example of a sharp discontinuity in surface displacements. Some InSAR filtering algorithms may consider these spatially uncorrelated pixels to be likely errors.
I donāt know any details of the steps in the StaMPS system. I use the SBAS system MintPy for my work. The DEM or topographic errors are usually detected by comparing the InSAR phase with the perpendicular baseline of the interferograms. The component of phase that is proportional to the baseline length is considered to be due to the topographic correction not being correct for that pixel. MintPy has an option to estimate this and I am sure that StaMPS does a similar calculation. I believe all of the DEM or topographic error estimates are done independently for each pixel because there could be a small feature like a building that is affecting the phase of that pixel but not adjacent pixels.
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