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<< Click to Display Table of Contents >> Interferometrick Stacking - Stacking Tools - SBAS Variogram |
  
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<< Click to Display Table of Contents >> Interferometrick Stacking - Stacking Tools - SBAS Variogram |
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Purpose
The interferometric phase error due to tropospheric propagation effects can be investigated by averaging variograms of interferograms that are expected to measure mainly atmospheric delay, exhibiting a negligible displacement signal and ensuring good temporal coherence. This result can be achieved imposing a bound on the maximum temporal baseline of the interferograms to be considered for variogram analysis. Generating the average empirical variogram before and after execution of the atmospheric correction tools, enables characterization of tropospheric disturbances on displacement measures and assessment of the filtering gain as well. The rationale of variograms exploitation to address atmospheric noise impact on displacement maps derived through differential interferometric approaches can be found in [Parizzi, 2020]. This kind of analysis is also recommended in the Product Specification Document and Service Implementation Plan for the Preparation of the Implementation of the European Ground Motion Service (EGMS) [Larsen-NORCE]. The idea is that since a variogram measures the variance of differences between pair of points extracted from a given interferogram, such estimates can be related to uncertainties in displacement measurements. This is true because all figures derived from interferometric computations are intrinsically obtained by phase differences both in space and time. Whenever such uncertainties are assumed to be related only to propagation delay, we can characterize the impact of atmosphere on the impossibility to reduce the final products dispersion below a desired level. On the other side, a comparison of such residual dispersions before and after the application of specific atmospheric correction approaches, enables to verify the performance of filtering methods.
Technical Note
The theoretical variogram of a random field is defined as the variance of the difference between pairs of samples from the field at different distances:
Where, dx and dy are the lags on the horizontal and vertical axis, respectively and d is the lag magnitude.
For a random process having constant mean and covariance only dependent on the distance, the variogram is equal to:
Where, Cov(0) is the covariance at distance zero, thus simply the constant variance of the random process, and Cov(d) is the covariance between a pair of points at distance d. From this it follows that a typical variogram of a correlated random field shows an increasing trend with distance towards a plateau region where any two samples are uncorrelated and thus the variogram is equal to twice the variance.
The classical Matheron's variogram estimator, used by the tool for the empirical variograms calculation, is defined as:
Where, N(d) is the number of distinct pairs at a distance lag
Input Files
Auxiliary File
Reference file generated as output of the "Connection Graph" step. The Interferometric Process and the atmospheric removal through external sensors must must have been performed.
This file is mandatory.
Principal Parameters
Apply Re-Flattening
Apply re-flattening on unwrapped data (_upha files), using the reflattening parameters of the SBAS processing.
Rebuild-All
By setting this flag the whole process is started from scratch.
Max Temporal Speration (days)
The variogram is computed only when the number of days between the reference and secondary image (of the SBAS interferogram set) is below this threshold.
Max normal baseline
The variogram of an interferogram of the SBAS set is computed only when the perpendicular baseline is below this threshold. The threshold is expressed in meters (please ignore the % sign). The default value can be too small in this beta version, please select a reasonable baseline.
Reference Processing Level
The type of interferogram to be considered as the first term of comparison when performing the variogram gain analysis. Original interferogram is the one before any atmospheric filtering. External atmosphere sensor corrected is typically the one corrected with GACOS, height correlation atmosphere corrected is the correction of the atmospheric component correlated with height, Displacement HP LP is the actual SBAS High-Pass, Low-Pass filtering.
Comparison Processing Level
The type of interferogram to be considered as the second term of comparison when performing the variogram gain analysis. Original interferogram is the one before any atmospheric filtering. External atmosphere sensor corrected is typically the one corrected with GACOS, height correlation atmosphere corrected is the correction of the atmospheric component correlated with height, Displacement HP LP is the actual SBAS High-Pass, Low-Pass filtering.
Start Validity Month
The variogram will be computed only on interferograms for which both the reference and secondary image belong to the temporal interval defined by start validity month and end validity month.
End Validity Month
The variogram will be computed only on interferograms for which both the reference and secondary image belong to the temporal interval defined by start validity month and end validity month.
Max Abs Velocity Threshold
For any given interferogram the variogram will computed discarding pairs of points for which the corresponding velocity of one or both points is larger than this threshold.
Distance Bin Size
The distance measured in pixels of the 1D variogram bin. When the variogram is computed, pairs of points are considered; the first point is at any one of the grid locations, the second point is at distance equal to an integer number of distance bin size divided by the oversampling factor.
Samples Grid Step
Distance between grid points.The pairs of points for the variogram computation have the first point at one of the grid locations
Maximum Distance (%)
The maximum distance between two points for the variogram computation expressed as percentage of the maximum available distance. Although the maximum distance between two points in an interferogram is equal to the largest diagonal, it is recommended to set this parameter to 50% or slightly more. The problem with large distances is that too few pairs of points are averaged making the variogram estimate unreliable.
Coherence Threshold
For any given interferogram the variogram will computed discarding pairs of points for which the corresponding velocity of one or both points is larger than this threshold.
Variogram
Distance Bin Size
The distance measured in pixels of the 1D variogram bin. When the variogram is computed, pairs of points are considered; the first point is at any one of the grid locations, the second point is at distance equal to an integer number of distance bin size divided by the oversampling factor.
Samples Grid Step
Distance between grid points.The pairs of points for the variogram computation have the first point at one of the grid locations
Maximum Distance (%)
The maximum distance between two points for the variogram computation expressed as percentage of the maximum available distance. Although the maximum distance between two points in an interferogram is equal to the largest diagonal, it is recommended to set this parameter to 50% or slightly more. The problem with large distances is that too few pairs of points are averaged making the variogram estimate unreliable.
Distance Bin Oversampling Factor
The oversampling factor for averaging points in the 1D variogram bin. When the variogram is computed, pairs of points are considered; the first point is at any one of the grid locations, the second point is at distance equal to an integer number of distance bin size divided by the oversampling factor.
Coherence Threshold
For any given interferogram the variogram will computed discarding pairs of points for which the corresponding velocity of one or both points is larger than this threshold.
Generate 2D Variogram
Set this flag to true to compute also the 2D variograms. A 2D variogram is a raster, the horizontal (vertical) axis represents horizontal (vertical) distance in pixels unit. The central pixel of the raster represents 0 distance..
Distance unit
The unit of measurement for the 1D variogram plot. Please note that all parameters are considered in pixels units even if this parameter is set to meters. It is suggested to leave this parameter set to meters.
Output type
This parameter decides if the variogram or the semi-variogram is computed. The variogram is the variance of the difference between points of a random field. The semi-variogram is half the variogram.
Output Files
Outputs 1D:
•Output_root_name_mean_1D_reference.png: plot of the mean variogram for the reference processing level unwrapped phase
•Output_root_name_mean_1D_comparison.png: plot of the mean variogram for the comparison (after filtering) processing level unwrapped phase
•Output_root_name_mean_1D_reference_multiple_plots.png: multiple plots of the mean variogram and the single variograms for the reference processing level unwrapped phase
•Output_root_name_mean_1D_comparison_multiple_plots.png: multiple plots of the mean variogram and the single variograms for the comparison (after filtering) processing level unwrapped phase
Outputs 2D:
•Output_root_name_mean_2D_reference: raster of the mean 2D variogram for the reference processing level unwrapped phase
•Output_root_name_mean_2D_comparison: raster of the mean 2D variogram for the comparison (after filtering) processing level unwrapped phase
Task, SARscapeBatch object, SARscapeBatch script example
References Parizzi, Alessandro, Ramon Brcic, and Francesco De Zan. "InSAR Performance for Large-Scale Deformation Measurement." IEEE Transactions on Geoscience and Remote Sensing (2020). Larsen, Y., et al. "European Ground Motion Service: Service Implementation Plan and Product Specification Document." Report to CLMS, ver 1 (2020).