Help Content > Interferometric Stacking > SBAS & E-SBAS > 3

Purpose

This functionality implements the first model inversion to derive the residual height and the displacement velocity. They are used to flatten the complex interferograms, redo the phase unwrapping and generate better products to input in the following step. This step is mandatory.

Technical Note

The re-flattened interferograms, together with the phase-height pair-by-pair proportionality factors (_k_factor files, which are stored in the work_interferogram_stacking folder), are used to estimate the residual height and the displacement related information (i.e. velocity, acceleration, acceleration variation and periodic model parameters), which are known as low pass components. These components are removed from the re-flattened interferograms before the second unwrapping process takes place.

The available model options are:

•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).

When the Connection Graph has been executed with the "Delaunay 3D" option, the unwrapped products corresponding to the connections shown in the "Time-Position Delaunay 3D plot" are marked by the _3D_upha extension.

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.

The refinement (and subsequent re-flattening) can be performed either manual (when the user inserts external Ground Control Point file) or automatic (default processing) for all the pairs.

In order to apply the manual refinement, a Ground Control Point file (i.e. "Orbital GCP file") must be previously generated; the points must be located onto the Super Reference image geometry (typically the _fint or _upha files are the best products for the GCP location). It is suggested to use the "Polynomial Refinement" option (Preferences>Flattening>Refinement and Re-flattening>Refinement Method) in order to make the system more robust.

The Ground Control Points in the "Orbital GCP file" are selected with the same criteria and for the same purpose of the Ground Control Points used in the Refinement and Re-flattening step. Note that the criteria for the GCPs selection must be fulfilled for all possible (or most of them) interferometric pairs. As result of this processing step, the re-flattened unwrapped phases (_reflat_upha) and the re-flattened filtered interferograms (_reflat_fint) are written in the corresponding step SBAS folder and “interf_tiff” subfolder, and in the corresponding step work subfolder. The "_reflat_upha_list.series" and the "_reflat_fint_list.series", are both generated with the link the re-flattened products.

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. Please, see the Additional information paragraph

Displacement Model Type

The choice is given between the following models:

•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

Refer to the Technical Note for further information.

Estimate Residual Height

If selected, it estimates the residual topography height. This parameter should set to false on two situations:

1-In case of good quality high reference resolution DEM, topography component estimation is not necessary.

2-In case of less than 20 images, this could lead to a pour residual height estimation, and consequently a wrong velocity estimation, due to strong atmospheric artifacts (suitable for stack with small normal baseline as Sentinel). The most simply model selection (with just one free term) increases the result reliability.

When this parameter is selected, and the Displacement Model Type selected is no displacement, the SBAS is used for the generation of precise DEMs.

Spatial Wavelet Size (m)

It preserves the estimated residual topography data resolution till the specified value. It removes the low pass distortion under this resolution value and preserves the spatial details by using wavelet decomposition. If this value is smaller or equal to 0 is not considered.

Allow Disconnected Time Series

This option allows avoiding to discard separate group of acquisitions: the voids in the retrieved displacement temporal series will be interpolated by using the model chosen in the Displacement Model Type field (e.g. linear, quadratic or cubic). Anyway, the recommended setting to obtain more reliable results is to disable the Allow Disconnected Time Series option. Usually it may helps is increasing the coverage over low coherence areas.

The choices are the following:

oFalse: when the time series is not fully connected it is rejected.

oAllow: the results are provided even if the time series is not fully connected.

Min Valid Interferograms (%)

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

Stop Before Unwrapping

By setting this flag, the phase unwrapping (last step of the processing sequence) is not executed.

Number of Parallel Unwrapping

Defines the number of unwraps that will be performed in parallel (one interferogram for each thread). This parameter must not exceed the total number of CPU threads. The user should consider the available system memory before increasing the number of parallel processes, as the memory consumption is directly related to the number of unwraps performed in parallel.

Unwrapping Method Type

The choice is given between the following unwrapping methods:

•Region Growing, the Region Growing unwrapping method is used.

•Minimum Cost Flow, the Minimum Cost Flow (square grid) unwrapping method is used.

•Delaunay MCF, the Minimum Cost Flow (triangular grid) unwrapping method is used.

Unwrapping Decomposition Level

The number of under sampling levels to be applied to the complex interferogram before performing the phase unwrapping can be specified. Refer to Phase Unwrapping, Technical Notes for further information

Unwrapping Coherence Threshold

Pixels with coherence values smaller than this threshold are not unwrapped.

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 Poly 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 - Phase Unwrapping

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

Parameters - Cluster

It brings to the cluster 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

first_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 “interf_tiff” sub-folder with the tiff files of intermediate interferometric SBAS results.

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

Generated meta and series files:

•FI_model_first_meta, FI_model_first.series which refers to the residual height and displacement velocity (plus ancillary layers), obtained from the SVD inversion, in slant range geometry .

•FI_second_fint_meta, FI_second_fint.series, which refers to all re-flattened filtered interferograms. From these interferograms the estimated displacement model and the estimated residual topography has been removed. Note that this same extension is used for the 1st level unwrapped products, which are generated during the Interferometric Process step.

•FI_second_upha_meta, FI_second_upha.series, which refers to all unwrapped phases. From these unwrapped phases the estimated model has been removed. Note that this same extension is used for the 1st level unwrapped products, which are generated during the Interferometric Process step.

The output results in the inversion folder consist of:

•height related products which are:

oFI_H_correction, corresponding to the correction (in meters) with respect to the input Digital Elevation Model.

oFI_H_precision, corresponding to the estimate in meters of the height measurement average precision (refer to the Phase to Height conversion for more details).

oFI_srdem, corresponding to the corrected Digital Elevation Model in slant range geometry.

•displacement related products which are:

oFI_term_1, corresponding to the first-degree term of the inversion polynomial [mm/year].

oFI_term_2, corresponding to the second-degree term of the inversion polynomial [mm/year2].

oFI_term_3, corresponding to the third-degree term of the inversion polynomial [mm/year3].

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

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

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

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

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

oFI_V_precision, corresponding to the estimate in millimeter/year of the velocity measurement average precision (refer to the Phase to Displacement conversion for more details).

•general products which are:

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

oFI_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.

oFI_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_first_inversion folder

Directory used to store intermediate processing results.

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 - 3 - Inversion: First Step

Interferometric Stacking - SBAS - 3 - Inversion: First Step