## 3 Multi-Track/Multi-Satellite InSAR Methodologies
\right) \tag{46}\]  
Figure 16: Multi-angle InSAR observations. Deformation is discriminated with respect to its horizontal East-West (\(d_{H}\)) and vertical Up-Down (\(d_{V}\)) components. We may observe that the vertical displacement is associated with the sum of the two LOS deformation measurements whereas the E-W component is related to the difference between the two deformation measurements, respectively. Note that this method is beneficial if we are interested in merely combining the rate of deformations from ascending and descending orbits. More challenging is the generation of combined deformation time-series (see Section 4) because, apart from rare exceptions, ascending and descending orbits are not coeval over the same region (i.e., SAR data are not acquired simultaneously from the two complementary observation points). A way to overcome this problem is to interpolate LOS time-series acquired on ascending and descending orbits over the whole set of time acquisitions. However, such solution, in general, is of a low precision because of atmospheric, orbital, thermal and interpolation noise presented in original and recreated by the interpolation data. To illustrate the results achieved through the basic combination technique described by Equations (43)-(46), we show in Figure 17a,b the E-W and U-D displacement maps obtained by combing ascending and descending COSMO-SkyMed DInSAR products related to the Mount Etna volcano area, Italy (see Table 1). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & & **Mt. Etna Volcano** & & \\ \hline _Sensor_ & _Orbit_ & _Start Time_ & _End Time_ & \
\begin{tabular}{c} _Number of_ \\ _Acquisitions_ \\ \end{tabular} &
\begin{tabular}{c} _Number of_ \\ _Interferograms_ \\ \end{tabular} \\ \hline CSK & Descending & 23 July 2011 & 15 January 2015 & 87 & 198 \\ CSK & Ascending & 12 July 2009 & 10 January 2015 & 146 & 309 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Data used for generating the E-W and U-D DInSAR maps shown in Figure 17.  
Figure 17: Estimated COSMO-SkyMed horizontal E-W (**left** side) and vertical U-D (**right** side) mean displacement velocity maps for the Mt. Etna volcano area, Italy, relevant to the 2011–2015 period. Let us now address the issue of combining multi-track InSAR data in a more general way, by referring to the achievements proposed in the literature. In the work of [PERSON] et al. [124], a global approach to recover 3-D displacements from the combination of ascending/descending and right/left looking SAR acquisitions was initially discussed. In particular, the authors combined five RADARSAT-1 interferograms generated from four right-looking ascending/descending passes and recovered the U-D and the E-W deformation field induced by the 23 October 2002, Nenana Mountain (Alaska) earthquake. In their investigation, they voluntarily neglected the N-S deformation, which is assumed to be very small. Resolving the N-S components of deformation, as said, is very critical, because space-borne satellites move along N-S oriented orbits. Such a limitation in recovering the N-S components was circumvented in the work of [PERSON] [125] by combining LOS displacements derived from the extra-low and the extra-high beams of the RADARSAT-2 sensor to estimate the full 3-D movements of the Henrietta Nesmith Glacier. The whole 3-D deformation components were also inferred in [126; 127] by complementing LOS displacements with GPS measurements. To overcome the problem due to the low sensitivity of LOS measurements to N-S displacements, Pixel Offset (PO) tracking techniques have also been exploited. In particular, in [128; 129], the 3-D co-seismic displacements were derived for the 1999 Hector Mine and 2001 Bam earthquakes, based on the combination of ascending/descending interferograms and Azimuth Pixel Offset (AZPO) measurements. The accuracy of estimating the azimuth offsets with amplitude matching can reach a fraction (i.e., 1/30 th) of the pixel spacing; henceforth, it is greater than 10 cm [137; 138; 139].