# Interpretation of Bridge Health Monitoring Data from Satellite InSAR Technology
## 3 Method  
### Multi-Temporal InSAR for Bridge Monitoring  
InSAR is a remote sensing technique that uses the phase information of radar signals emitted by Synthetic Aperture Radar (SAR) sensors mounted on satellites and backscattered by the Earth's surface to measure the displacement of reflective targets along the Line of Sight (LoS) of the satellites [28]. A SAR image is a collection of complex numbers organised in pixels over the investigated portion of the Earth's surface. The module of the complex number represents the signal amplitude and is related to the target reflectivity; the phase of the complex number is related to the distance between the radar sensor and the reflective target in the pixel. By comparing two or more SAR images of the same area taken at different times (repeat-pass interferometry), it is possible to calculate the phase differences of pixels between the images, which are related to the deformation of the Earth's surface. The phase differences can be converted into a displacement map showing the spatial distribution of the reflective targets' displacements along the LoS. Those reflective targets are called Scatterers (PSs) and are point-like targets that exhibit high reflectivity and stable phase behaviour over time). The standard InSAR approach is affected by many different limitations, so different Multi-Temporal InSAR (MT-InSAR) techniques have been developed in the last decades [8; 9; 10; 15]. The MT-InSAR technique is a method of processing SAR images that allows for detecting small changes in the Earth's surface over long periods. This technique involves analysing a series of radar images of the same area taken over several years and comparing the phase differences between them and a reference image called master. After the coregistration of all 109 SAR images and the preliminary analysis aimed at deriving the dataset's main statistics, we performed the actual MT-InSAR processing. The following are the main steps involved in our MT-InSAR workflow and the main choices we made during the analysis of our dataset:  
1. _Atmospheric-phase removal_. One advantage of MT-InSAR compared to standard InSAR is the possibility to estimate and remove the atmospheric phase disturbance from the SAR images. This step is critical because the atmospheric phase contribution is one  
Figure 7: Star Graph of the dataset with red marks highlighting dates of first, master, and last images. of the primary sources of error in InSAR data. An initial selection of pixels related to potential candidate targets (the PSs) is processed by connecting them in a spatial graph and estimating the main parameters affecting the interferometric phase along the connections (for our case, deformation velocity, thermal expansion, and height of the targets). After this estimation, the residual phase signal is used to estimate and remove the Atmospheric Phase Screen (APS) contribution from the original SAR images [28]. 2. _Persistent Scatterer Selection._ Once the APS phase contribution is removed from the images, a higher number of pixels can be analysed with the MT-InSAR algorithm to derive the parameters with respect to a common reference point (RP)--a specific PS used to anchor the estimated deformation time series. The RP is selected based on high temporal coherence and limited deformation over time [15; 28]. After estimating the parameters, we filtered out all PSs with a temporal coherence lower than 0.6. We recall that temporal coherence is a quality metric of the extracted displacement time series with respect to the model used and ranges from 0 (low quality) to 1 (high quality) [28]. As a result, we included 8426 PSs in our analysis, most of them located over roads and villages. 3. _Time series analysis._ Deformation time series can be extracted for every PSs based on the filtered phase data. Displacements are relative in time and space. In time, they are relative to the date of the master image; in space, they are relative to the displacement of the common RP (the same used in the previous step of the analysis).