Investigation of sensitivity to noise in the three-dimensional displacement field retrieval problem, generated by radar interferometry (Case study: Sefidsang and Ezgeleh earthquakes of 21 March and 12 November 2017, respectively)

In recent decades, Interferometric Synthetic Aperture Radar (InSAR) technology has been an efficient tool in quantitatively measuring of the earth's deformation, influenced by natural and human factors, such as the overexploitation of water from underground aquifers, mining, subsidence, earthquake, and landslide. However, in the nature of the displacement measurement in the satellite's line of sight (LOS) in this technology, the possibility of extracting a three-dimensional displacement field has faced challenges. Especially in the study of many tectonic phenomena requiring a comprehensive understanding of the three-dimensional displacement components. Therefore, at least three independent radar geometries or InSAR-derived LOS displacements are always needed to solve the problem of retrieval of the three-dimensional (3D) displacement field. However, the polar geometry of imaging radar satellites is such that the contribution of the displacement and effect of the noise of the observations on the estimated parameters (Three-dimensional components) will be different, even in some cases, the problem will be unstable. Therefore, in this research, the noise sensitivity of the three-dimensional displacement field retrieval problem in independent and differential radar geometries is investigated and also based on the orbit overlapping method in the Sentinel radar satellite, using simulated and real data, the three-dimensional displacement of the Sefidsang and Ezgeleh earthquakes of 21 March and 12 November 2017 respectively is retrieved and the efficiency of this method is evaluated. In fact, in this study, considering the importance of knowing and measuring the components of the 3D surface displacement field, the problem of three-dimensional displacement field retrieval was investigated using a combination of independent radar geometries. Then, according to the variance-covariance matrix structure of the problem and the principal component analysis (PCA) method, the sensitivity of recovering each component of the displacement field to the input data noise by taking measurements of three independent radar geometries was discussed. The results show that the north-south displacement component has the highest sensitivity to the input data noise and has the least contribution of displacement along with the satellite LOS. Then the east-west and up-down components have approximately the same sensitivity to noise, although, for some specific incidence angles, the sensitivity to noise for the up-down component will be increased. Also, the condition number of the design matrix in the 3D field retrieval problem show that in most cases (except when the incidence angles of the two geometries are equal or have very slight differences), it is a well-established and stable problem and there is no need to solve it with regularization method. In the second part of the paper, remembering that in the Sentinel radar satellite, each sub-swath is imaged at different angles (with a difference of about 10 degrees), so the concept of overlap between the orbits (at least three different geometries) can be used to retrieve the 3D displacement field in most regions. The feasibility and efficiency of this method were evaluated with real and simulated data. The results showed that in the absence of noise components, the orbit overlap interferometry (OOI) method could be well used in 3D field reconstruction.