Authors:
Wietske Brouwer | Delft University of Technology, Department of Geoscience and Remote Sensing | Netherlands
Andreas Theodosiou | Delft University of Technology, Department of Geoscience and Remote Sensing | Netherlands
Dr. Paco López-Dekker | Delft University of Technology, Department of Geoscience and Remote Sensing | Netherlands
Prof. Ramon F. Hanssen | Delft University of Technology, Department of Geoscience and Remote Sensing | Netherlands
Satellite radar interferometry (InSAR) is a powerful technique for monitoring deformation phenomena. While deformation phenomena occur in a three-dimensional (3D) world, one of the limitations of the InSAR phase observations is that they are only sensitive to the projection of the 3D displacement vector onto the radar line-of-sight (LoS) direction. To uniquely estimate the three displacement components, we would require at least three sets of spatiotemporally coinciding independent (STCI) LoS observations, i.e., scatterers on an object that is not subject to internal deformations, observed at the same time. More importantly, the system of equations needs to have a full-rank coefficient matrix. Unfortunately, in most practical situations at most two STCI LoS observations are available, resulting in an underdetermined system with an infinite amount of possible solutions.
With only one LoS observation, the solution space of the inverse problem is a plane orthogonal to the LoS displacement vector, i.e., the null-space. With two LoS observations, the solution space is a null-line, the intersection of two null-planes. The local orientation of the null-line is dependent on the location on earth, and the characteristics of the satellite orbits. The null-line provides information on the type of displacement product that can be derived from the LoS observations. Therefore, it is a key metric for every InSAR study.
We developed Null-space Orientation (NO), an open-source tool that computes the orientation and geometry of the local null space, given the location on Earth and the orbits of the available satellite missions. The software leverages the Delft Radar Modelling and performance Analysis (DRaMA) software library to compute the acquisition geometry for a given location from the two-line element set of an arbitrary SAR mission. In combination, the No-DRaMA tool provides suggestions on the displacement products that can be derived from the available LoS observations.
There are many different possibilities for the information product. For cases with two LoS observations, the orientation of the null-line defines which displacement product can be derived. Since the satellites are not sensitive to the displacements into the direction of the null-line it is always possible to give unbiased displacement estimates in the row space, i.e., the plane orthogonal to the null-line. However, often the orientation of this plane does not represent the displacement directions of interest. For such cases, we may project the LoS observations onto a plane which represents the vertical and a particular horizontal direction, whereas it should be noted that the ‘projected product’ is not the same as e.g. ‘the vertical displacement’.
A valuable aspect of No-DRaMA is that it can be used prior to an InSAR study to assess what satellite mission, or combination of missions, should be used to deliver a deformation product with highest value depending on the user needs. With the orbits of the different missions, different deformation directions can be estimated, which will result in different deformation products. When those deformation products are compared a well-considered choice on the mission can be made.