GAMMA DIFF/GEO Reference Manual

stacking.c

ANSI-C program: stacking.c

NAME
stacking - Stacking of multiple unwrapped differential interferometric phases to estimate deformaton rate in units of radians/year

SYNOPSIS
stacking <diff_tab> <width> <ph_rate> <sig_ph_rate> <sig_ph> <roff> <loff> [nr] [nl] [np_min] [tscale]

data_tab	(input) 2 column list of unwrapped differential interferograms and delta_T values in days (text)
<width>	number of samples/line of the interferograms in the stack
<ph_rate>	(output) average phase rate determined from a weighted sum of phases (radians/year, float)
<sig_ph_rate>	(output) standard deviation of the estimated phase rate (radians/year, float)
<sig_ph>	(output) standard deviation of the residual phases (enter - for none, radians, float)
[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)
[np_min]	min. number of phase values required to accept phase rate estimate (enter - for default = nfiles)
[tscale]	time scale used for phase rate calculation (enter - for default): 0: radians/day 1: radians/year (default)

EXAMPLE:

stacking diff_tab 600 ph_rate ph_rate_sigma ph_sigma 148 304 8 8 9

calculates the stacked phase of unwrapped interferograms listed in the diff_tab file with entries:

20030404_20020924.adf.unw -192

  20030404_20021018.adf.unw -168

  20030404_20021111.adf.unw -144

  20030404_20021229.adf.unw  -96

  20030404_20030122.adf.unw  -72

  20030404_20030311.adf.unw  -24

  20030404_20030428.adf.unw   24

  20030404_20030522.adf.unw   48

  20030404_20030615.adf.unw   72

  20030404_20030709.adf.unw   96

  20030404_20030802.adf.unw  120

The phase reference point region is centered at range pixel 148, line 304 in the interferogram stack. The reference region is 8 x 8 in size.

DESCRIPTIONstacking is used to estimate the linear rate of differential phase using a set of unwrapped differential interferograms. A set of unwrapped differerential interferograms are isted in the diff_tab along with the time interval in days of SLC-2 relative to the reference SLC-1. There is one line/per differential interferogram with the path to the differential interferogram in column 1, and the time interval (in days) of the interferogram in column 2. If a # is placed in the first column of the line, the line is ignored. The program also calculates the standard deviation of the phase rate (sigma) relatives.

The individual interferogram phases are weighted by the time interval in estimating the phase rate (ph_rate). The underlying assumption is that atmospheric statistics are stationary for the set of N interferograms. The formulas for the estimated phase rate and the varience for each point in the image are given by:

where the time interval for each interferogram is delta_t. The phase rate can be converted to deformation rate using the program dispmap.

The phase measurments are relative to a spatial reference point as specified on the command line. Each interferogram has its own phase offset that is determined by averaging interferogram values about the reference point. The size of the reference region is also specified on the command line in terms of width and height. This offset is subtracted from the phase values used in estimating the deformation rate. Typically the error of the phase rate will increase with increasing distance from the the reference point as the contribution of the phase errors due to atmosphere and baseline error increases. All differential phases are estimated relative to the reference point.

The user can specify the minimum number of interferograms with valid phase values that are required to estimate the phase. The default value for np_min is conservatively set by default to the number of interferograms in the diff_tab. Setting a lower threshold value for np_min increases the coverage for the ph_rate estimates because each nterferogram may not have been entirely unwrapped.

The user can select the time scale for the output to be either days or years using the tscale parameter

SEE ALSO:

dispmap