Correcting for satellite looking angles.

What is actually measured in interferometric applications is the projection of a target’s motion onto the satellite’s Line Of Sight (LOS). If the direction of ground movement is close to the angle of the LOS, then the actual and measured motions are similar. However, the LOS motion can often differ noticeably from the real value of motion, especially in cases where the ground motion is not vertical. See Figure 1.

Figure 2 shows an example of LOS measurements over a landslide, Italy. The ground measurement points are colored according to their displacement rate. Data has been analyzed using a single geometry (in this case from a descending satellite orbit), hence displacement velocities are in the satellite LOS direction.

Figure 1

Figure 2

Measuring true vertical and horizontal components of motion is difficult with a single geometry of acquisition, unless a priori information is available on the true vector of movement (not a common situation).

By acquiring imagery on both ascending and descending orbits, it is possible to view a point on the Earth’s surface from two different perspectives, from the east and from the west. This is an important element of measuring vertical and horizontal motion.

However, by using both ascending and descending data, it is possible to combine the measured motion information to obtain an accurate estimate of the true vertical motion and of the east-west component of the motion. See Figure 3.

Figure 4 shows true vertical and east-west horizontal data over a delpeting oil field, Middle East, calculated by combining ascending and descending satellite geometry data. Calculating vertical and horizontal ground displacement vectors allows the actual ground motion to be analyzed. In the case of the delpeting oil field in Figure 4, vertical subsidence over the extraction area (red area) and horizontal movement towards center of the extraction area (arrows) highlights ground subsidence as a result of hydrocarbon extraction.

Figure 3

Figure 4

Figure 5 illustrates how features on an undulating landscape will be viewed by a satellite. In pixels (or resolution cells) 1 and 2, the equilateral triangles on the landscape appear slightly distorted in the LOS range (also referred to as slant-range).

As the signal reaches pixel 3, there is a marked change in ground slope and many more triangles appear in the pixel, even though they are all of the same size. The effect is to compress these triangles in the LOS, referred to as foreshortening. When the radar progresses to pixels 4 and 5, at which point the ground slope and LOS are parallel, the triangles now appear stretched at their base.

This distortion in the appearance of land use can be seen in Figure 6, which is an amplitude image of Mount Vesuvius, Italy, viewed in SAR coordinates (range and azimuth corresponding to the vertical and horizontal axis respectively).

In hilly or mountainous terrain, it sometimes occurs that the projection of steep slopes on to the LOS is reversed. Figure 7 illustrates how this phenomenon manifests itself in radar imagery. In pixel 1, the radar images object A normally. However, when the radar reaches pixels 2, 3 and 4, the objects E, F, and G are present in the same pixels as objects B, C, and D, the latter being masked by the former.

This phenomenon is referred to as layover and generates noise. In an amplitude image, it appears as a bright white layer (Figure 6 shows this effect around the caldera of Mount Vesuvius). As the radar progresses from pixels 4 to 7, the slope of the ground is greater than that of the LOS and so the area in question cannot be imaged by the sensor. Figure 6 shows this area to be black. This effect is referred to as shadow.

Figure 5

Figure 6

Figure 7