## 2 Differential Radar Interferometry for Deformation Monitoring in Cultural Heritage Sites
### Local-Scale Structural Deformation Monitoring for Heritage Monuments
#### 2.2.1 Ground-Based Radar Interferometry Measurements  
There are two types of ground-based radar interferometry approaches for deformation monitoring: one is the Ground-Based SAR Interferometry (GB-InSAR) to perform static measurements [10, 37]; the other is GB-InRAR for dynamic measurements, such as structural vibration monitoring [38, 39, 40, 41] (in this paper, we write \"Ground-Based Real Aperture Radar Interferometry\" as GB-InRAR for short).  
GB-InSAR is a well-known technique, which has been widely used in deformation monitoring in civil structures and natural phenomena [42, 43, 44]. Due to its capabilities of offering optimal observing geometry and a significantly high-frequency data acquisition rate, GB-InSAR overcomes the limitations of space-borne DInSAR, such as a fixed revisit cycle and observation angle constraints. In light of its flexible placement, GB-InSAR can be used to measure deformation in the chosen direction with precision at the millimeter and even sub-millimeter level [10, 45]. Furthermore, the high-frequency data acquisition rate of GB-InSAR allows us to detect rapid-deformation data needed in emergency situations, where most of the space-borne radar interferometry systems may not be effective due to their relatively long revisit cycle. GB-InSAR can also operate in areas shadowed or not perfectly observable from a space-borne SAR imaging system, such as steep slopes and north-facing surfaces [45]. Hence, GB-InSAR can be used to perform multi-direction and quasi-real time monitoring. Till now, it has been successfully applied in deformation monitoring of cultural heritage in some places [35, 36]. However, since GB-InSAR can only measure the LOS displacements, the choice of the installation site of the GB-InSAR system is critical.  
On the other hand, in the last decade, some researchers have exploited the potential capabilities of GB-InRAR in monitoring the dynamic behavior of large structures [46, 47, 48, 49, 50, 40]. Owing to its high sampling frequency (up to hundreds of Hz) and spatial resolution (a range resolution with accuracy up to sub-meter level) compared to conventional radar, this approach is able to measure the frequency of structural vibration and to estimate its amplitude of displacement with a precision at the sub-millimeter level. In cultural heritage sites, particularly with regard to the conservation of historic buildings, a number of common vibration sources, including road and rail traffic, sonic booms, blasting and earthquakes, as well as long-term effects due to material wear-and-tear and weakening of the foundations of buildings have become major concerns [51, 52]. In order to evaluate the influences of the vibration sources on cultural heritage, GB-InRAR can be used as a remote sensing tool to retrieve the vibration characteristics of heritage structures; an example is the dynamic monitoring of an ancient building with different tourism loads or impacts from other sources of vibration. The main challenge of this application is that the radar measurement can be affected by different factors due to the propagation itself and its high sensitivity to the context changes. Thus, it is necessary to make sure that the radar responses of disturbing factors remain weak and do not interfere with the responses of the targeted object. Besides,data interpretation can be improved by careful analyses of the spectral and temporal characteristics of the target [38; 40; 49]. Successful applications include oscillation monitoring of ancient bridges, historic towers and monuments, either induced by natural or anthropogenic activities [53; 54; 55; 56].