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Satellite SAR interferometry measures only the projection of the three‐dimensional displacement vector along the satellite line of sight. The data from any given interferogram are, therefore, single component distance measurements. However, it is possible to combine radar data acquired from different acquisition geometries to approximate two‐dimensional displacement fields (Rucci et al., 2013). In fact, all SAR sensors follow near‐polar orbits and every point on Earth can be imaged by two different acquisition geometries: one with the satellite flying from north to south (descending mode), looking westward (for right‐looking sensors) and the other with the antenna moving from south to north (ascending mode), looking eastward. This is the reason why, by combining InSAR results from both acquisition modes, it is possible to estimate two components of displacement.

To illustrate how the decomposition is performed, imagine a Cartesian reference system where the three axes correspond to the East‐West (X), North‐South (Y), and Vertical (Z) directions. Consider the case in which two estimates of the target range change are available, obtained from both ascending and descending radar acquisitions, namely r _a and r _d (Fig. 2.2). In the Cartesian reference system X‐Y‐Z, the range change of a scatterer on ground can be expressed as:

(2.4)

where d _x , d _y , and d _z represent the component of the displacement along the E‐W, N‐S, and Vertical directions, and l _x , l _y , l _z are the direction cosines of the look vector.

Given our knowledge of the satellite orbit, the line of sight of the radar antenna is known, as are the corresponding direction cosines of the velocity vector r _a and r _d . It is thus possible to write the following system of equations:

Figure 2.2 Example of motion decomposition combining ascending and descending acquisition geometry.

(2.5)

where l _{x, a} , l _{y, a} , l _{z, a} , and l _{x, d} , l _{y, d} , l _{z, d} are the direction cosines of the satellite line of sight for both ascending and descending acquisitions. The problem is poorly posed if we now want to invert for the full three‐dimensional velocity vector, as there are three unknowns (d _x , d _y , and d _z ) and only two equations. However, because the satellite orbit is almost circumpolar, the sensitivity to possible motion in the north‐south direction is usually very small (the direction cosines l _{y, a} and l _{y, d} are close to 0). This allows us to rewrite the system in the following form:

(2.6)

an equation that may be solved for d _x and d _z .