GAMMA Interferometric Point Target Analysis Software (IPTA): Reference Manual

mb

ANSI-C programs: mb.c

NAME
mb - Calculate phase time series from a set of multi-reference unwrapped continuous interferograms (mb stands for multi-baseline (temporal and spatial))

SYNOPSIS
mb <DIFF_tab> <RMLI_tab> <itab> <sigma> <itab_ts> <diff_ts> <sim_flg> <sigma_ts> <hgt_flg> <hgt_out> <roff> <loff> <nr> <nl> <gamma> <MLI_ref_par>

<DIFF_tab>	(input) list of unwrapped differential interferograms (including path) that match the entries in the itab file (text)
<RMLI_tab>	(input) list MLI images and parameter files that are associated with the entries of the itab NOTE: the number of range and azimuth looks must match the values used for the input interferograms
<itab>	(input) multi-reference table associating interferogram stack records with pairs of SLC stack records (text) (line entries are: pSLC_rec1 pSLC_rec2 itab_rec_num switch_flag)
<sigma>	(input) input values to calculate layer weights of the multi-reference input data for use in the least-squares solution. (enter - for all equal to 1.0) (text)
<itab_ts>	(output) single-reference table associating output deformation stack records with pairs of SLCs (text). (line entries are: pSLC_rec1 pSLC_rec2 itab_rec_num switch_flag)
<diff_ts>	(output) ) root file name of unwrapped differential phase time series for pairs listed in the itab_out file. Output files are named: filename_001, filename_002... NOTE: a TS_tab file is created containing the names of these output files: filename.tab
<sim_flg>	(input) simulate input DIFF interferograms flag: file names of the simulated phases are the same as those the DIFF_tab with _sim appended 0: no simulation of the input interferograms using the solution (default) 1: simulate phase of input interferograms using the solution phase history
<sigma_ts>	(output) standard deviation of the phase residuals (enter - for none)
<hgt_flg>	estimate interferometric height corrections: 0: no estimation of height correction from interferometric phase 1: estimate height corrections using interferometric phase
<hgt_out>	(output) height corrections estimated from the interferometric phase (enter - for none)
<roff>	range pixel offset to center of the phase reference region
<loff>	line offset to center of the phase reference region
[nr]	number of range pixels to average in the phase reference region (enter - for default: 16)
[nl]	number of lines average in the phase reference region (enter - for default: 16)
[gamma]	weighting factor for smoothing of the first deformation velocity: (enter - for default: 0.500)
[MLI_ref_par]	(input) MLI parameter file of the image used for geometric coregistration (enter - for none)

EXAMPLE mb DIFF_tab RMLI_tab itab_mb - itab_ts diff1_ts/diff1_ts 1 diff1_ts/sigma1_ts 1 hgt_out 50 280 9 9 1.0 rmli/2030404.rmli.par

calculates the time series of unwrapped phase using unwrapped differential interferograms in the DIFF_tab. The output itab is itab_ts, and the output time series is a set of files starting with names diff_out_001, diff_out_002....diff_out_n. Simulated phase calculated from the time series solution are placed in the same directory as the files in the DIFF_tab with _sim appended. The standard deviation of the solution sigma_out is estimated using the residuals of the time series phase minus the input interferograms. Height corrections are calculated for each point in the scene and stored in the file hgt_out. The reference region is located at 50, 280 and is set to be 9x9 samples. The smoothing parameter gamma for the first-derivative of the deformation is set by default to 0.5. The file rmli/2030404.rmli.par describes the geometry of the reference scene.

A TS_tab list is generated containing the names of the output differential interferograms generated by mb.

DESCRIPTION
This program solves for the time-series of the deformation phase given a set of multi-reference unwrapped deformation phases. An optional smoothing parameter on the deformation history can be applied that constrains the abrupt changes in he deformation rate. The program can calculate a height correction relative to the DEM heights for each point in the scene given that the smoothing parameter is > 0.1.

The input set of deformation phases are typically over specified such that more than one interferogram contains information from each of the SLCs in the input data set and that the observations can be linked together. Implicit is the idea that the total deformation phase at time t₂ is the sum of deformations from t₀ to t₁ and from t₁ to t₂. Therefore the total deformation phase at some time time t_n can be expressed as a linear combination of measurements in the input data if t_n exists in the set of input deformation phases and the the set of measurements is connected.

The program mb generates a times-series of unwrapped deformation phase given a multi-temporal reference stack of unwrapped phases. The deformation phase data are derived from pairs of SLC images covering the time intervals of interest. mb estimates the deformation phase time-series using a weighted least-squares algorithm that minimizes the sum of squared weighted residual phases. The residuals are the differences between input phases (the observations) and the differential phases derived from the time-series solution. Smoothing of the time series solution is acheived by introduction of constraints on the change in velocity as described by Schmidt and Burgmann (Journal of Geophysical Research, VOL. 108, NO. B9, 2416, doi:10.1029/2002JB002267, 2003). Higher values of gamma lead to smoother solutions. Values of gamma =1 are moderately smoothed, while gamma=100 leads to an essentially linear deformation curve. The use of the smoothing parameter gamma can significanly reduce atmospheric related variations in the solution. Rapid fluctuations in the deformation phase are often related to atmosphere rather than deformation.

We also include estimation of a DEM height correction parameter (hgt_flg=1). The phase model includes a height related term proportional to the derivative of the interferometric phase with respect to height. This additional degree of freedom permits calculation of a height correction for all the interferograms that minimizes the phase residuals in a least-squares sense. If the value of the smoothing parameter is set to 0, then the value of the height correction will be very close to 0.0 since the phase can then be fully attributed to motion of the surface or atmosphere. Only when the smoothing parameter is > 0 can height corrections be calculated. The height corrections are consistent over a range of values of the smoothing parameter gamma > 1. The network of measurements should not have phase unwrapping errors or gaps when estimating the height corrections. Larger values of gamma > 1 up to 10, will result in better height estimates especially when the deformation is essentially linear.

Input to mb is the multi-reference itab file that provides information on the pairs of SLCs used to create each of the interferogram layers in the diff_in stack. Also input is the stack of SLC parameters for the images referenced in the itab, and the corresponding unwrapped deformation phases diff_in. Typically the input deformation phases are from differential interferograms with the topographic and residual orbital phases removed.

An example of a multi-reference itab is:

1 3 1 1 1 4 2 1 1 5 3 1 3 5 4 1 4 7 5 1 4 8 6 1 5 7 7 1 5 9 8 1 6 8 9 1 6 10 10 1 6 11 11 1 ... 22 25 35 1 22 27 36 1 23 27 37 1 24 27 38 1 25 27 39 1 25 28 40 1

The entries in the multi-reference itab were selected such that they satisfy specific criteria with respect to perpendicular baseline and time interval. The program base_calc, can be used to construct the multi-reference itab with entries that fulfill baseline, and time interval criteria. Note that the minimum time interval should be set to 1 day to avoid having auto-interferograms that contain no phase information.

Gaps in interferometric times series occur if there is no interferogram connecting different dates in the input data set. In a connected set of observations it is possible to synthesize an interferogram for any set of dates covered by the input measurements by taking a linear combination of the existing interferograms. If this is not possible then the network is not fully connected. The gap can be interpolated under the assumption that the phase rate does not change discontinuously. Setting the smoothing parameter gamma > 0 adds a cost associated with a change in the deformation rate. The least-squares minimization will then interpolate across the gap. If no smoothing is performed, then the deformation rate will be 0 across the gap and lead to errors in the total deformation.

An example of an input itab with a temporal gap would be:

1 2 1 1 1 3 2 1 4 5 3 1 4 6 4 1

As can be seen by inspection there is no interferometric phase information covering the period between the times when SLC-3 and SLC-4 were acquired. There is no connection between the interferometric data for acquisitions {1, 2, 3} and acquisitions {4, 5, 6} and hence there is no change in the output time series phase during the time interval from SLC-3 to SLC-4.

The output deformation phase time-series is calculated at each acquisition time of SLCs used to create the input interferogram stack. The solution is only available for times covered in the input interferogram data set. The phase time-series values are obtained by summing up the phase contribution for each time interval from the start of the series. In the example, the output single reference itab_out has entries:

1 3 1 1 1 4 2 1 1 5 3 1 1 6 4 1 ... 1 27 23 1 1 28 24 1

Note that each differential interferogram in the output is referenced to the time of the earliest scene in the series. By definition, the deformation is set to 0 at the initial epoch for the series. The phase series values can be converted to deformation along the line of sight (LOS) using the program dispmap. The IPTA script disp2ras can be used to generate a set of Sun raster images of displacement files in a text list of input files.

Observation of the time series requires creating a point data stack. The point list on rectangular grid can be created using mk_grid. Points can then be extracted using the IPTA script mk_d2pt and displayed using dis data.

If phase values are desired for other times, these can be obtained by linear interpolation using the program t_interp_pt for the point data stack derived from the continuous data.

The program mb uses Singular Value Decomposition (SVD) (see http://en.wikipedia.org/wiki/Singular_value_decomposition ) to obtain the least-squares solution for the phase time-series. As part of the screen output mb generates a list of the singular values of the design matrix constructed from the itab and observation times. The design matrix contains the coefficients of the set of linear equations that express the relationships between the observed phase data and the desired times series values. The number of singular values is equal to the number of times in the output time series. If a value is less than the largest singular value/1.e5, the value is set to 0. A singuler value indicates that the constraints in the design matrix are insufficient to fully define the output time series. Setting the singular value to zero forces the time-series output to remain constant over the unconstrained gap in the input observations.

mb also calculates the set of simulated deformation phase for each of the input interferograms using the estimated deformation phase-time series. Subtracting the simulated deformation phase from the input interferogram using sub_phase (from the DIFF/GEO package) leaves a combination of residual baseline phase, noise, and phase unwrapping errors. This suggests the use of mb for iterative improvement of the processing results.

Redundancy in the the differential interferogram input data reduces errors in the time-series due to phase errors due to baseline, topographic phase correction, and interferometric decorrelation. The effect of atmospheric phase on the other hand is not reduced by this estimation procedure. The reason for this is that the atmospheric phase cannot be distinguished from random deformation since it is directly related to path delay. A low-pass spatial filter such as bpf for the ISP can be used to find large-scale atmospheric related features in the simulated interferograms and subtracted from the input multi-reference data.

Individual interferogram layers in the input stack can be switched on and off using the switch_flag value (last column) in the input itab. Setting the switch_flag to 0 removes that particular layer from the solution. Note that if a particular acquisition occurs only in this layer, then it will not appear in the solution. Also realize that removing a particular interferogram has a good chance of destroying the connectivity of the input interferogram network causing a gap in the output time-series. However even if the the switch_flag is set to 0 for a particular layer, the deformation phase for that layer is simulated when possible. The simulated phase can then be subtracted from the input interferogram and help with unwrapping that layer. If the unwrapped phase for a single point is 0.0 in a layer that is turned on (switch_flag = 1), then no time-series solution is generated for that point.

The output stack sigma_out contains an estimate of the standard deviation of time series phase values obtained from the residuals simulated phases and the input observations. For each point sigma is evaluated over the number of layers in the input differential interferograms Contributions to the standard deviation include interferometric decorrelation, residual baseline error, and possibly phase unwrapping errors.

The program generates a list of the output time-series files that is required by the program vu_disp2d. The name of this file is the route file name "diff_out".tab.

To determine a linear deformation phase rate for the unwrapped phase time-series, use the program ts_rate.

SEE ALSO
base_calc, ts_rate, dispmap, dis_data, mk_grid, tpf_pt, t_interp_pt, mb_pt, ipta.h.