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<< Click to Display Table of Contents >> Interferometric Stacking - Post Processing Tools - Time Series Classification - Parametrical Analysis |
  
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Interferometric Stacking - Post Processing Tools - Time Series Classification - Parametrical Analysis
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<< Click to Display Table of Contents >> Interferometric Stacking - Post Processing Tools - Time Series Classification - Parametrical Analysis |
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Purpose
This tool fits the SBAS raster deformation time series using three analytical displacement models. It retrieves the best fitting coefficients and its RMS for each pixel in the time series. These coefficients represent different characteristics of the displacement such as speed, acceleration, oscillation amplitude and frequency.
These results can be sequentially used to perform a displacement classification using the Model Classification panel.
Technical Notes
The available models are linear, quadratic or periodical.
The linear model is defined by:
With:
the displacement [mm]
time [year]
an initial displacement offset [mm]
the deformation speed [mm/year]
The quadratic model is defined by:
With:
the displacement [mm]
time [year]
an initial displacement offset [mm]
the deformation speed [mm/year]
the deformation acceleration [mm/year 2]
The periodical model is defined by:
With:
the displacement [mm]
time [year]
an initial displacement offset [mm]
the deformation speed independent of the periodical trend [mm/year]*
the deformation acceleration [mm/year 2]
the oscillation amplitude [mm]
a delay [days]
the oscillation period [days]
* This estimated speed corresponds to the deformation process not described by the oscillating process. For example, a structure may sink at constant speed and oscillate at the same time. This velocity corresponds to the sinking process.
The heavyside model is defined by:
the displacement [mm]
time [year]
an initial displacement offset [mm]
the deformation speed for both sides of the step[mm/year]
a step magnitude [mm]
time of the discontinuity relative to the first measurement [days]
The two-slope model is defined by:
Where 
, the new y-intercept is defined as.
With:
the displacement [mm]
time [year]
an initial displacement offset [mm]
the deformation speed before the inflection date [mm/year]
the deformation speed after the inflection date [mm/year]
inflection point date [days].
The two-slope model is defined by:
Where 
, the new y-intercept is defined as.
With:
the displacement [mm]
time [year]
an initial displacement offset [mm]
the deformation speed before the inflection date [mm/year]
the deformation speed after the inflection date [mm/year]
inflection point date [days]
Input Files
Input File
The displacement meta file (*_meta). Both decomposed or LOS meta files are supported
Parameters - Principal Parameters
Analyze time subset
By setting this flag only the period defined by From and To will be analyzed.
Generate fitted TS
By setting this flag the fitted time series for each model will be saved. This may be useful to analyze different model performance.
Linear fit
By setting this flag the linear model fitting will be performed.
Quadratic fit
By setting this flag the quadratic model fitting will be performed.
Periodical fit
By setting this flag the periodical model fitting will be performed.
Parameters - Other Parameters
Limits for the possible fitting parameters can be introduced.
Output Files
A directory is created for each executed model combining the Output Root Name and the model’s name (I.e.: projectXXX_Linear, projectXXX_Periodical, projectXXX_Quadratic). Inside each of these directories you will find:
modelName_aN
Images with fitting parameter of order N.
modelName_daic
Image with the delta Akaike Information criterion to compare the goodness off fitting among models.
modelName_rms
Image with the fitting RMS error.
modelName_meta
Meta file of fitting parameters and the fitted time series (if selected).
modelName_input_TS
Fitted time series images (if selected).
General Functions
Cancel
The window will be closed.
Help
Specific help document section.
Specific Function(s)
None.
Task, SARscapeBatch object, SARscapeBatch script example
References A. De Grandi (2019): PASTA - Phenomena Aware Spatial-Temporal Analysis, Bsc Thesis, Università degli Studi dell’Insubria, Italy.