Help Content > Interferometric Stacking > SBAS & E-SBAS > 4

Purpose

This is the second and final inversion, which uses the optimized unwrapped products coming from the previous step.

The second model inversion is implemented to derive the date by date displacements, which are filtered to remove the atmospheric phase components to fit the final displacement velocity model. This step is mandatory.

Technical Note

The second re-flattened interferograms are used to estimate the displacement-related information (i.e. velocity, acceleration, acceleration variation and date-specific displacements).

This is possible by selecting the type of the Displacement model within the 'Other parameters' panel. The available model options are:

•The same as first (selected by default), use the same model used in first inversion,

•No displacement, a stable area is considered, no displacement is calculated (this parameter set to true exploit the SBAS capability to calculate precise DEMs)

•Linear, the displacement velocity [mm/year] is calculated

•Quadratic, the displacement acceleration [mm/year2], and velocity [mm/year] are calculated

•Cubic, the displacement acceleration variation [mm/year3], the displacement acceleration [mm/year2] and velocity [mm/year] are calculated

•Linear Periodic, the periodic delay [days], the periodic modulation [mm] and velocity [mm/year] are calculated

The three displacement polynomial models can be synthesized as follows:

where Disp is the displacement at time t; K1 is the linear term [mm/year], corresponding to the instantaneous displacement velocity; K2 is the quadratic term [mm/year2], corresponding to the instantaneous displacement acceleration; K3 is the cubic term, corresponding to the instantaneous displacement acceleration variation [mm/year3].

The displacement periodical model can be synthesized as follow:

where Disp is the displacement at time t; K1 is the linear term, corresponding to the instantaneous displacement velocity; K2 is the modulation term [mm]; K3 delay [days]. F is the known expected frequency (1/ Model Period).

The software will also provide the average velocity, the average acceleration, and the average acceleration variation.

The average velocity is computed as average over a certain interval of the modeled values: a definite integral, that at the end is equal to the value of the modeled displacement in the last time of the interval minus the value of the modeled displacement in the first time of the interval, normalized( divided) by the interval duration time. If the model choose by the user is first order, the average velocity correspond to the linear term K1.

The average acceleration and the average acceleration variation are computed in the same way.

The multitemporal coherence is estimated as the absolute, normalized, complex sum of all the flattened (by subtracting the modeled phase) interferograms. It measures how well the model fits the measures. Smaller is the average residuals in the flattened interferograms higher is the multitemporal coherence value till a maximum value of 1 (when the model perfectly fits the measures and no residues left).

It is important to note that the No Displacement Model does not foresee the displacement calculation as well as the atmospheric removal.

It is possible to move the entire SBAS processing folder in another disk location without causing any problem in the further steps.

To avoid loading failures it is recommended not to move any file from its original repository folder.

It is worthwhile to mention that the re-flattening, which is performed on the displacement products, does not foresee the orbital refinement; it means than only a ramp (using minimum three GCPs) or a constant term (using minimum one GCP) can be removed.

A graphic, showing the extracted displacement information, can be created using the General Tools>Raster analyzer.

Input Files

Auxiliary file

Reference file generated as output of the "Connection Graph" step and possibly updated afterwards. This file is mandatory.

Optional Files

Refinement GCP file

Either a previously created Ground Control Point file (.xml) is loaded (Load GCP File) or the interface to create a new Ground Control Point file is automatically loaded (Create GCP File, refer to the "Tools>Generate Ground Control Point" for details). This file is used for manual refinement. This file is optional.

Parameters - Principal Parameters

Rebuild All

By setting the flag the whole process is performed from scratch (if not incremental mode is active).
It is advisable to leave this flag unchecked in case of process interruption, so that the products already generated have not to be computed and stored again.

Product Coherence Threshold

Pixels with coherence values smaller than this threshold will be set to dummy (NaN) in the final products.

Interpol Disconnected Time Series

By setting this flag the program provides the solution for disconnected coherent targets over the grid point. The temporal gaps, where the displacement measurement does not exist or have been rejected, are interpolated using the average trend estimated during the first inversion. The disconnected SBAS provides a higher solution spatial coverage, limited by the Min Valid Interferogram and Min Valid Acquisition percentage thresholds.

The choices are the following:

oFalse: the temporal series with gaps are rejected.

oInterpol Using Model: the gaps are interpolated using the average trend estimated during the first inversion.

oInterpol Starting from Zero: the gaps are filled with zero. The temporal series start from zero at the end of this gaps.

Min Valid Interferograms (%)

Percentage of the minimum number of valid inversion equations (interferograms over the coherence threshold) for getting an acceptable result, at each output grid point. This parameter is considered if it is equal or greater than zero valid interferogram and should be used when the Interpol Disconnected Blocks is flagged (or the Allow Disconnected Blocks has been previously flagged in the connection graph generation step).

Min Valid Acquisitions (%)

Percentage for the minimum number of valid acquisitions (covered by at least a certain amount of valid interferogram over the coherence threshold) for getting an acceptable result, at each output grid point. This parameter is considered if is equal or greater than zero and should be used when the Interpol Disconnected Blocks is flagged (or the Allow Disconnected Blocks has been previously flagged in the connection graph generation step).

Atmosphere Low Pass Size (m)

Enter the window size, in meters, to apply the spatial distribution related filter (refer to the Technical Note).

Atmosphere High Pass Size (days)

Enter the window size, in days, to apply the temporal distribution related filter (refer to the Technical Note).

Refinement Radius (m)

Maximum buffer radius for the association of Ground Control Point with respect of the slant range unwrapped phase closer valid pixel.

Refinement Residual Phase Polynomial Degree

Degree of the polynomial used to estimate the phase ramp, which will be removed from the input unwrapped phase during the Re-flattening operation. In case this value is higher that the number of input Ground Control Points, it will be automatically decreased. The default values of 3 means that a phase ramp in range and azimuth direction plus a constant phase offset will be corrected. In case only the phase offset correction is needed, the polynomial degree will be set to 1.

Parameters - Global

It brings to the general section of the Preferences parameters. Any modified value will be used and stored for further processing sessions.

Parameters - Refinement

It brings to the flattening section of the Preferences parameters. Any modified value will be used and stored for further processing sessions.

Parameters - Other Parameters

It brings to the general section of the Preferences parameters. Any modified value will be used and stored for further processing sessions.

Output Files

second_inversion folder

Directory containing the following products:

•Due to the large number of output products meta (_meta). and series (.series).files are generated. They enable to load at once all relevant output products:

•The “inversion” sub-folder with the products (second model) from SBAS inversion in slant range geometry.

•The internal copy of the input refinement and re-flattening GCP (.xml).

•The input refinement and re-flattening GCP converted in shape format in slant geometry (.shp).

•The input refinement and re-flattening GCP converted in shape format in geocoded geometry (.shp and .kml).

Generated meta and series files:

•SI_model_meta, SI_model.series, which refers to the residual height and displacement velocity (plus ancillary layers), obtained from the time series polynomial regression, in slant range geometry ..

•SI_disp_first_meta, SI_disp_first.series, which refers to the date by date displacements, measured in slant range geometry, without atmospheric correction.

•SI_disp_meta, SI_disp.series, which refers to the date by date displacements, measured in slant range geometry, after the atmospheric correction.

•SI_interf_counter_meta, SI_interf_counter.series, which refers to valid measure (interferograms with coherence higher than the Product Coherence Threshold) counter for each acquisition.

•SI_only_disp_upha_meta, SI_only_disp_upha.series, which refers to all unwrapped phases flattened by the residual height estimated component

•SI_second_reflat_upha_meta, SI_second_reflat_upha.series, which refers to all unwrapped phases re-flattened for the second SVD inversion.

The output results in the inversion consist of:

•displacement related products which are:

oSI_term_0, corresponding to the zero-degree term of the inversion polynomial [mm].

oSI_term_1, corresponding to the first-degree term of the inversion polynomial [mm/year]. SI_term_2, corresponding to the second-degree term of the inversion polynomial [mm/year2].

oSI_term_3, corresponding to the third-degree term of the inversion polynomial [mm/year3].

oSI_velocity, corresponding to the average displacement velocity [mm/year].

oSI_acceleration, corresponding to the average displacement acceleration [mm/year2].

oSI_delta_acceleration, corresponding to the average displacement acceleration variation [mm/year3].

oSI_periodical_modulation, corresponding to the periodic model modulation [mm].

oSI_periodical_delay, corresponding to the periodic model delay [days].

oSI_disp_first_est, corresponding to the date specific displacement (in millimeters) measured with respect to the first acquisition date, to which a null displacement is assigned, without atmospheric correction

oSI_disp, corresponding to the date specific displacement (in millimeters) measured with respect to the first acquisition date, to which a null displacement is assigned, after the atmospheric correction

•general products which are:

oSI_coherence, corresponding to the multitemporal coherence. It shows how much the displacement trend fits with the selected model.

oSI_RMSE_rad, which is a measure of the inversion quality. It is the RMSE expressed in radians. The higher this value the worse the fitting and inversion quality.

oSI_RMSE_mm, which is a measure of the fitting quality. It is the RMSE expressed in millimeters. The higher this value the worse the fitting and inversion quality.

oSI_norm_L1, corresponding to the cumulative sum of the date by date absolute value displacements (in millimeters).

oSI_interf_counter, counter with the valid measure number for each acquisition.

oSI_image_perc, valid acquisitions percentage (covered by at least one valid measure).

oSI_interf_perc, valid interferogram percentage.

The displacement values are reported with:

•Positive sign if the movement corresponds to a decrease of the sensor-to-target slant range distance.

•Negative sign if the movement corresponds to an increase of the sensor-to-target slant range distance.

work_second_inversion folder

Directory used to store intermediate processing results.

It is important to mention the existence of SI_atmosphere_meta, SI_atmosphere.series, which refers to date by date atmospheric related components in slant range geometry.

Details specific to the Units of Measure and Nomenclature of the output products can be found in the Data Format section.

General Functions

Exec

The processing step is executed.

Store Batch

The processing step is stored in the batch list. The Batch Browser button allows to load the batch processing list.

The window will be closed.

Help

Specific help document section.

Specific Function(s)

None.

Interferometric Stacking - SBAS - 4 - Inversion: Second Step

Interferometric Stacking - SBAS - 4 - Inversion: Second Step