## 2 Methods
### Change Detection--Damage Assessment  
Several damage assessment methods by means of the interferometric coherence and/or intensity correlation have been described in the literature (Section 3). Common for all is a certain comparison of the pre-disaster and co-disaster coherence and/or intensity correlation values to detect the change, _i.e._, the damage caused by the disaster. [PERSON] _et al._[91] gives a general review on change detection. For instance, first, the coherence is calculated using the pre-event InSAR pair (t\({}_{1}\) and t\({}_{2}\)). This enables the identification of urban areas and areas dominated by man-made structures, which are characterized by their relatively high coherence values compared to e.g., vegetated areas. Second, the coherence of the co-event InSAR pair t\({}_{2}\) and t\({}_{3}\) is computed. For damage assessment applications we make use of the temporal de-correlation \(\gamma_{temp}\). The concept of the method is that events causing extensive structural damage, such as earthquakes, storms, floods, _etc._, dominate the de-correlation of the interferometric coherence (and also of the intensity correlation) computed from SAR EO imagery spanning a short time period including the event [74]. Therefore, by comparing the pre-disaster coherence and the co-disaster coherence, one is able to determine the damage caused by the event. As mentioned above, only urban areas show high coherence values over a longer time period, whereas vegetated areas de-correlate within a few days. Consequently, only at areas dominated by urban structures the damage can be assessed. However, especially these regions are our area of interest. For damage assessment normalized differences \(ND\) (Equation (10)), similar to the well-known normalized difference vegetation index \(NDVI\) were proposed by several authors, e.g., including [8, 77, 84, 92]:  
\[ND\,=\,\frac{X_{pre}\,-\,X_{co}}{X_{pre}\,+\,X_{co}} \tag{10}\]  
with \(X_{pre}\) representing the pre-disaster SAR image pair (t\({}_{1}\) and t\({}_{2}\) in Figure 3) and \(X_{co}\) representing a pre- and a post-disaster image pair including the event (t\({}_{2}\) and t\({}_{3}\) in Figure 3). The normalizeddifferences approach can be applied to both, the interferometric coherence _ND\({}_{\gamma}\)_ and the intensity correlation _ND\({}_{\rho}\)_:  
\[ND_{\gamma} = \frac{\gamma_{pre}\,-\,\gamma_{co}}{\gamma_{pre}\,+\,\gamma_{co}} \tag{11}\] \[ND_{\rho} = \frac{\rho_{pre}\,-\,\rho_{co}}{\rho_{pre}\,+\,\rho_{co}} \tag{12}\]  
Crucial for all change detection techniques is the selection and determination of a useful threshold to distinguish between damaged and undamaged buildings or to determine different grades of damage classes [93]. [PERSON] [74] concentrated on the use of interferometric coherence for damage assessment and introduced a coherence change index \(\tau\), where \(\gamma_{pre}\) is the coherence of the pre-disaster SAR image pair (t\({}_{1}\) and t\({}_{2}\) in Figure 3) and \(\gamma_{co}\) is the coherence calculated from a pre- and a post-disaster image pair including the event (t\({}_{2}\) and t\({}_{3}\) in Figure 3):  
\[\tau=\frac{\gamma_{pre}}{\gamma_{co}} \tag{13}\]  
The coherence index is calculated for each pixel of the area of interest. Thereby, one has to consider that the coherence is estimated over several windows, causing a reduction of the spatial resolution compared to the original SAR imagery. However, damage assessment is much more practical at coarser units such as administrative boundaries or building codes than at the pixel values [94] (as averaging over several pixels reduces the influence of the speckle effect). The spatial resolution of the SAR sensor predetermines the minimum size of the ground target to be analyzed at the damage assessment procedure.