InSAR, or Interferometric Synthetic Aperture Radar, measures ground deformation by comparing the phase difference between radar images acquired at different times. The Line of Sight, or LOS, is the path vector along which the radar signal travels from the satellite to the ground and back. This is the fundamental geometry that determines how ground displacement is measured in InSAR applications.
InSAR is sensitive only to the component of ground displacement that occurs parallel to the Line of Sight vector. When ground deformation occurs, it typically has both vertical and horizontal components. However, the radar can only measure the projection of this 3D displacement vector onto the Line of Sight direction. This means the resulting measurement represents the change in distance between the satellite and the ground target along the LOS. It is a one-dimensional measurement of what is actually a three-dimensional ground displacement vector.
The measured Line of Sight displacement can be mathematically represented as the dot product of the true 3D ground displacement vector and the unit vector in the LOS direction. This is written as Delta R LOS equals d dot u LOS. This means the measurement is influenced by both vertical and horizontal components of displacement, weighted by the satellite's look angle and heading. In this 3D representation, we can see how the actual ground displacement vector is projected onto the Line of Sight direction, resulting in the scalar measurement that InSAR actually detects.
The satellite's look angle significantly affects the sensitivity of InSAR measurements to different types of ground displacement. Vertical motion is best detected with steep look angles, where the satellite is more directly overhead. In this case, a larger component of the vertical displacement is projected onto the Line of Sight. Horizontal motion, on the other hand, is better detected with shallow look angles, where the satellite is more to the side. This directional sensitivity is a fundamental limitation of single-geometry InSAR, which is why advanced applications often combine measurements from multiple viewing geometries.
To summarize what we've learned about Line of Sight InSAR geometry: InSAR measures ground displacement along the Line of Sight direction between the satellite and the ground. The measured displacement is a one-dimensional projection of the actual three-dimensional ground movement onto the LOS vector. Mathematically, this is represented as the dot product of the displacement vector and the LOS unit vector. The satellite's look angle significantly affects measurement sensitivity, with steep angles better detecting vertical motion and shallow angles better detecting horizontal motion. For comprehensive ground deformation monitoring, advanced applications often combine measurements from multiple viewing geometries to reconstruct the full three-dimensional displacement field.