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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B2. Istanbul 2004 
   
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Figure 1: Amplitude SAR image (left) and coherence image (right) of an interferogram with AT — 210 days, where the dark pixels 
correspond to low coherence areas. The images cover the airport and a small portion of the metropolitan area of Barcelona (Spain). 
2. A DInSAR PROCEDURE BASED ON IMAGE STACKS man-made structures: urban and industrial areas (bright 
amplitude values), and the runways of the Barcelona airport 
The key factor to achieve a quantitative DInSAR deformation (dark). All these structures are characterized by high coherence 
monitoring is the number of available SAR images over the values (Fig. I, right), while the rural Areas and the water 
same study area. The classical DInSAR technique is based on surfaces show low coherence values. 
two SAR images, i.e. a single interferogram. With this simple 
configuration is not possible to separate the deformation 2.2 Least Squares adjustment 
contribution from the other phase components. In this work we 
describe a new DInSAR procedure, which is based on multiple Let us assume that from a stack of co-registered SAR images a 
interferograms over the same scene (image stacks). Three main set of N differential interferograms has been computed. For 
aspects of the procedure are discussed below: the each pixel that remains coherent over the observation period it 
interferometric processing steps to exploit SAR image stacks; is possible to write N equations (1), one for cach interferogram. 
the least squares procedure employed to estimate the terrain In order to estimate the terrain movement, ®,,, has to be 
deformation; and the DInSAR geometric aspects, which affect o E Mo Lal ; 
i ; separated from the other components: O,., uno: Pan and 
the computation of O;,, ., and the geocoding of the 2 e = 
D x. - Different modelling and estimation procedures can be 
DInSAR products. - : = Ar : 
employed for this purpose. Without going into technical details, 
i i '€ briefly discuss s important issues of our procedure. 
2.1 Interferometric processing we briefly discuss some important issues of our procedure 
In order to derive deformation maps from stacks of complex The residual component due to DEM errors Dres Topo has à 
SAR images, the original SAR data have to undergo several 
: | : known geometric relationship with the DEM error, ej, : 
processing steps, see e.g. Crosetto et al. (2003). In this section 
. 4 ; d.7. DB 
we briefly discuss two important steps: the image co- Ds nam 4-7-8, “Orr (2) 
. . ; es Topo ; if DEN = 
registration and the phase unwrapping. Another key step, the MP :sinO 
q] 1 > 1c I1 iselv discussed 1 “2011 7) . . ; 33 : 
simulation of. 7, , , is concisely discussed in section 2.3. where B, is the normal baseline and O is the off-nadir angle. 
In order to exploit the phase information of a series of complex For each coherent pixel of the N interferograms we have an 
SAR images covering the same area, it is necessary to unknown parameter ep, . Since its effect in cach 
accurately co-register all images over the same master image, 
AVhitpar! . > . : interferogram is modulated by. B, , the wider is the spectrum of 
arbitrarily chosen as geometric reference. It is worth noting that interierogr: x m p | 
this operation only concerns the geometric reference: after the B, , the better is the configuration to estimate e,,, . 
co-registration each interferogram can be chosen by taking as 
master image M any of the co-registered SAR image. Note that Modelling the terrain deformation represents a quite complex 
other techniques, e.g. (Ferretti et al., 2000; Ferretti et al., 2001), task. In fact, in principle we need a 3D model, with. two 
use the same master for all the interferograms. A second key dimensions in the image space, plus a component to describe 
step of the procedure is the phase unwrapping, which is based the temporal evolution of the deformation. A general discussion 
on an implementation of the Minimum Cost Flow method of of 3D models for DInSAR analysis is beyond the scope of this 
Costantini et al. (1999), The most relevant. property of this paper. We just mention that often the temporal evolution of the 
unwrapping is that it works on irregular networks of sparse deformation is modelled with polynomial functions of the time. 
pixels. The unwrapping is only performed on the pixels whose In our procedure the deformation of each pixel is modelled by a 
coherence is above a certain threshold, while it is not computed stepwise linear function, which is computed by least squares 
over low coherence pixels, where it is expected to have high (LS) adjustment. 
o, values. With this procedure the long-term deformation 4 
Different approaches to estimate the atmospheric component 
monitoring is limited to the areas that remain coherent over ; : 
= iv : have been proposed, see e.g. Ferretti et al. (2000). In order to 
long time periods. This typically occurs over urban, suburban 
and industrial areas. An example is illustrated in Figure |, 
where on the amplitude image (left) on may recognize different employed: both components are (usually) spatially correlated, 
separate ,,, and ®,, the following property is often 
im 
165