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

def_mod_pt

ANSI-C programs: def_mod_pt.c and multi_def_pt.c

NAME
def_mod_pt - estimation of linear deformation, delta height and residual phase over an area
multi_def_pt - multi-patch estimation of linear deformation, delta height and residual phase

SYNOPSIS
def_mod_pt <plist> <pmask> <pSLC_par> <ppos> <itab> <pbase> <bflag> <pdiff> <pdiff_type> <np_ref> <pres> <pdh> <pdef> <punw> <psigma> <pmask_out> [dh_max] [def_min] [def_max] [sigma_max] [model] [bmax] [dtmax]

multi_def_pt <plist> <pmask> <pSLC_par> <ppos> <itab> <pbase> <bflag> <pdiff> <pdiff_type> <np_ref> <pres> <pdh> <pdef> <punw> <psigma> <pmask_out> [dh_max] [def_min] [def_max] [rpatch] [sigma_max] [sigma_max2] [model] [bmax] [dtmax]

EXAMPLES
def_mod_pt plist pmask pSLC_par - itab pbase 1 pdiff 1 814 pres pdh pdef punw psigma pmask2 20. -0.005 0.005 1.2 2

Conducts a point-wise investigation of the baseline and time dependence of the interferometric phase (relative to the phase of the reference point) and estimates height corrections, linear deformation rates, residual phases, and a quality measure for the regression.

multi_def_pt plist pmask pSLC_par - itab pbase 1 pdiff 1 814 pres pdh pdef punw psigma pmask2 20. -0.005 0.005 100 1.2 2

Conducts a point-wise investigation of the baseline and time dependence of the interferometric phase (relative to the phase of the reference point) and estimates height corrections, linear deformation rates, residual phases, and a quality measure for the regression using a multi-patch approach with a patch size of 100 range pixels.

DESCRIPTION

def_mod_pt and multi_def_pt conduct an investigation of the baseline and time dependence of the interferometric phase (relative to the interferometric phase of the indicated reference point) and estimates various parameters conducting a regression analysis using either a one dimensional (linear dependence on perpendicular baseline component) or two dimensional (linear dependences on perpendicular baseline component and linear deformation rate) linear regression function. In this regression analysis it is accounted for that wrapped phases are provided in the case of a complex valued interferogram. The slopes of the regression functions determined are directly related to the relative height correction, also called delta height value, and the linear deformation rate.

The standard deviation from the regression function serves as a quality measure for the regression function and the derived parameters. The standard deviation of the phase from the regression funnction is expressed in radian. The residual phase, this is the deviation from the regression function, contains phase terms related to the atmospheric phase delay, baseline errors, non-linear deformation, and signal noise. The residual phase is written to an output file for further investigation.

For the stack of differential interferograms unwrapped interferometric phases are derived and written out to a stack of unwrapped phases. As input to def_mod_pt and multi_def_pt interferometric data in point data format is required. This input is further discussed in the following.

The point coordinates are defined in a point list. Optionally, a point data stack of interpolated point target positions can be provided. If not provided, the point coordinates of the point list are used. Furthermore, a mask can be provided to indicate for each point if it shall be considered (mask value 1) or not (mask value 0). The interferometric pairs are defined in the itab, a table associating interferogram stack records with pairs of SLC stack records (ascii). Acquisition times and other SLC parameters are provided in the stack of SLC/MLI parameters (binary) and baseline parameters in the stack of baseline parameters (binary). The differential interferogram is provided in another point data stack. Complex valued or unwrapped differential interferograms can be provided (but the same type for all records). Typically, a simulated interferometric phase images were subtracted in the calculation of the stack of differential interferograms. Early on in an IPTA investigation initial simulated phases may contain only the topographic and orbital phase terms calculated from an initial DEM and initial baseline estimates from orbit data. Later on improved height values, precision baselines, atmospheric corrections, linear deformation trends etc. may be considered.

On the command line a number of parameters can be indicated to configure and optimize the regression analysis. These parameters are discussed in the following paragraphs.

For the interferometric baselines the user can select if either initial estimate or the precision estimate shall be used. The point number of the reference point must be entered; def_mod_pt also allows to set - instead of a reference point number to set the reference phase to 0.0 . The index of the reference point can be determined by using dis_ipta.  To minimize spatial distances it is usually adequate to select a reference point near the center of the area of interest.  It is, however, often preferred to select a point known to be stable or known to be a reference point of a leveling network, as reference. To identify the point number of a point at or near the desired coordinate the programs dis_ipta or prox_pt can be used.

In the case of the wrapped phase values the regression analysis is done in two steps. The best regression function among a predefined set of functions is determined. In a second step the least squares analysis is conducted. The predefined regression functions for the first step are derived based on the indicated maximum height correction and maximum deformation rate difference values indicated. Indicating larger values means that more predefined regression functions are tested which will make the process slower. Indicating a too small value may result in failure to resolve the regression for a point with a high height correction or deformation rate value. It has to be kept in mind that the height correction and deformation rates are relative to the reference point. Consequently, the regression analysis is generally more robust for points near the reference point.

The records considered in the regression analysis can be constrained to short perpendicular baselines and short time intervals.

As phase regression models there are several options:

  1. 1-d model depending on height differentials include a phase constant
  2. 2-d model depending on both height differentials, deformation rate including a phase constant
  3. 1-d model depending on height differentials without a phase constant
  4. 2-d model depending on both height differentials, deformation rate without a phase constant
  5. 1-d model depending of deformation rate and phase constant
  6. 1-d model depending on deformation rate without phase constant 

Each of these three models can include an optional phase constant parameter. The phase constant is required if a single SLC used as the reference for all interferograms. If there are different SLCs are used as the reference for the for the interferograms in the stack the phase constant is 0.0 and does not need to be estimated. Use of the one-dimensional regression models constrains the regression and gives better results for small stacks or early on in the analysis when large height corrections are expected.

The output of def_mod_pt and multi_def_pt includes the determined regression functions, the phase residuals from the regression, the phase standard deviation from the regression, the unwrapped differential interferometric phase, and a mask indicating points for which the quality of the regression is above the indicated threshold.

The slope of the phase to baseline dependence is used to calculate a height correction value. This height correction value is the height correction of the current point under the assumption that the height of the reference point is correct. The height corrections are indicated in meter (m). Corrected heights can be calculated by adding the height model and the height corrections. It is important to note that this improvement is done relative to the selected reference point. The accuracy of the height of a specific point depends on the accuracy of the height of the reference point plus the error in the height correction (and not only the second term).

The slope of the phase to time dependence is used to calculate a linear deformation rate. This linear deformation rate is the deformation rate of the current point relative to the reference point. The deformation rates are indicated in meter per year (m/year). It is important to note that the linear deformation rate is in addition to the deformation model which may already be considered in the calculation of the differential interferogram.

The regression calculates the delta height, deformation rate, and phase constant that minimizes the least-squared difference between the phase model and the observed unwrapped phase values.  The residual phase is the difference between the phase values and the regression model. The residual phase includes terms related to atmospheric delay, non-linear deformation, baseline errors, and signal noise and is therefore not called "atmospheric phase" as this may be mis-leading.

For each point the standard deviation of the (unwrapped) phases from the regression function is calculated and used as measure for the quality of the regression. An optional output mask file can be generated indicating points with a quality above an indicated minimum threshold. Such a mask can be used to only disply or further process data of "reliable" or "good" points.

We also calculate the covariance matrix that provides the scale factors relating the standard deviation of the phase error distribution to the estimation uncertainty of the height correction (pdh_err), the estimation uncertainty of the deformation rate (pdef_err), and estimation uncertainty of the phase offset (ppc_err). If the actual deformation is not linear then the estimated errors  will be higher than they actually are.

Furthermore, the unwrapped interferometric phases are determined and can be written to an output point data stack. The unwrapped differential phases can be added to the phase model which was subtracted to retrieve the unwrapped phases of the original interferograms. These phases together with the improved height values can be used for example in the estimation of precision baselines using base_ls_pt.

multi_def_pt conducts the same type of regression analysis as def_mod_pt, but using a multi-patch strategy. The image area is divided into different patches. For each patch a new local reference point is determined and used in the regression analysis. The use of this local reference point has the advantage that distances to this reference point can be kept short. Over short distances the residual phase terms caused by the atmospheric path delay, and inaccurate baselines remain small. Furthermore the relative deformation rates remain smaller.  Overall the approach with the local references is more robust. Region growing is used to adjust the height corrections and deformation rates estimated over the grid of patches so that they are always relative to the global reference point. This permits investigating large areas while still having the advantage of a local reference.

There are two modes for finding the local reference point. The first approach is to find the first point that has a residual phase standard deviation sigma that is less than the specified threshold sigma_max2. The other approach is to search all the points in the patch for the point that has the lowest value
of sigma and is also less than sigma_max2. The second approach requires more computation, but is generally more robust.

As compared to def_mod_pt, multi_def_pt has an additional parameter, the patch size in range pixels. The patch size in azimuth pisels is calculated from the range pixels by setting the azimuth patch size to a value corresponding to the ground-range patch size.

Individual regression analyses can be carried out for interactiviely selected point pairs (one point is the reference), using the program dis_ipta. The regression algorithms used in dis_ipta, def_mod_pt and multi_def_pt are identidcal.

SEE ALSO
base_ls_pt, dis_ipta,prox_pt, ipta.h.