nternational Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B2. Istanbul 2004
Co-registered DInSAR
interferograms
Phase unwrapping
on sparse data
and coherence to
weight transform
Coherence
images
Re-weight
: Maps of the
the observations p
residuals
Weight of the
observations
Unwrapped DInSAR
interferograms
Model estimation
- Stepwise linear deformation
- Topographic component
- Weighted least squares
adjustment
Compensated
velocity field(s)
Qualits
map(s)
Iterate
Error analysis
Data interpretation
Figure 2: Scheme of the LS adjustment procedure based on multiple interferograms.
Q,,, is usually temporally correlated, while the atmospheric
effects are supposed to be uncorrelated in time. A specific
strategy can be implemented dealing with small-scale
deformations, when a priori information on the subsidence area
is available, see Crosetto et al. (2002).
The main features of the DInSAR estimation procedure
employed in this work are briefly summarized below. The
implemented model includes for each pixel the DEM error and
a stepwise linear function to describe the temporal evolution of
the deformation. The unknown parameters are computed by LS
adjustment. A scheme of the procedure is shown in Figure 2.
The procedure supports the classical data snooping proposed by
Baarda (1968), useful to detect the unwrapping-related errors.
The outputs of the procedure include the compensated velocity
fields, the corresponding quality maps (with the standard
deviations of the velocities), and the maps of the residuals. It
must be noted that in the so-called screening analysis, which is
based on a reduced set of images, usually only one velocity
field is estimated: different intervals can be considered in the
subsequent in-depth analysis based on larger datasets. The
residuals are used to check the errors associated with the
unwrapped interferograms (i.e. the input observations), like the
unwrapping-related errors, the atmospheric effects, etc. In order
to improve the estimates of the compensated velocity fields, the
procedure can be run iteratively, by re-weighting the
observations or eliminating some of them.
2.3 Geometric aspects
The DInSAR technique requires an accurate geometric model
to connect the SAR image space to the object space. This
geometric model is required in two key processing stages: the
computation of d , based on a DEM of the imaged
Topo Sim
scene, which involves the object-to-image transformation, and
the geocoding of the DInSAR products, which is based on the
image-to-object transformation. In our procedure we have
implemented a rigorous SAR model that connects the image
166
coordinates of a given pixel, azimuth and range (az, rg), to the
object space coordinates P(X,Y.Z) with three equations:
T=T, +AT -(az-1) (3)
MP=R,+AR-(rg-1) (4)
Em RR T
MP- Vy 2-4: MP- EM (5)
where (3) provides the time of acquisition T of a given image
point (az, rg); (4) and (5) are the two basic SAR mapping
equations, namely the range and Doppler equations. These
equations include important parameters like the first line
acquisition time To, the azimuth pixel size AT, the near slant
range R,, the range pixel size AR, the master velocity vector
Vy, the radar wavelength A, and the Doppler frequency of the
master image fr y. These parameters are usually known with
an inadequate accuracy. Their direct use in the model may
result in important distortions in the transformations between
the image and object spaces. In order to get an accurate
geometric model, the model parameters have to be refined by
LS adjustment using ground control points (GCPs). The
original implementation of the calibration worked with one
image at the time. The procedure is now extended in order to
fuse data coming from multiple images, e.g. ascending and
descending SAR images. The multiple adjustment allows
reducing the number of required GCPs using tie points, in full
analogy with the photogrammetric procedures. After the LS
calibration, the residuals on the GCPs are typically of the order
of one pixel: using a $-look azimuth compression this
corresponds to about 20 m on the ground, see e.g. Crosetto et
al. (2003). It is worth mentioning that other SAR calibration
strategies can be implemented. One of the most interesting
approaches only requires as input a DEM of the scene. The
calibration of T, and R, is achieved by image correlation of the
given SAR image and a synthetic amplitude image simulated
from the DEM. This approach is implemented in different
softwares, e.g. the DIAPASON software developed by the
c
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