slide 47

The sensitivity of light-of-sight displacements in different directions can be determined by decomposing the displacement and projecting it onto the light-of-sight direction. Vertical displacement is the most sensitive, followed by east displacement, and north displacement is the least sensitive. InSAR is not sensitive to displacement in the north-south direction. To see the sensitivity of light-of-sight displacements to east, north, up directions, we can further decompose the light-of-sight direction. For better visualization, I convert the light-of-sight displacement from satellite to ground to ground to satellite. I draw a figure about the projection from east, north, and up displacement onto light-of-sight direction. The geometry is ascending track. Theta is the azimuth angle starting from the north. Theta is incident angle. We can know the light-of-sight displacement consists of horizontal displacement and vertical displacement. The relation is shown in the first equation. The horizontal displacement can be further decomposed into east and north displacement. For the angle between north and horizontal vector, it is computed by 90 degrees minus 360 degrees plus beta. The angle is beta minus 270 degrees. For the angle between east and horizontal vector, it is computed by 90 degrees minus beta plus 260 degrees. The angle is 360 degrees minus beta. Once we know the angles, we can do the projection. The final projection from east, north, and up to the light-of-sight is shown in the third line of the equation. We can know that light-of-sight displacement is more sensitive for up displacement. That is the reason why many researches use SAR to measure vertical displacement, such as length-of-sight. The second sensitivity is the east displacement and the last is north displacement. We can use the real case to see the difference of sensitivity. If incident angle is 35 degrees and azimuth angle is 350 degrees, we can see the proportion of each direction projected on light-of-sight direction. As you can see, InSAR is not less sensitive to the displacement in the north direction. So if you want to use InSAR to measure the displacement in the north-south direction, you probably cannot obtain any signals.