## 2 Methods  
This paper focuses on the use of SAR EO data for rapid damage assessment after a natural disaster, such as an earthquake, a tsunami, a storm, _etc._ According to [PERSON] and [PERSON] [73], a \"simple\" pre- and post-disaster SAR amplitude image comparison is often not very useful, as the SAR amplitude both decreases and increases after a disaster. Buildings could be reduced to debris after a disaster (e.g., an earthquake) increasing the SAR backscatter especially in the former darker  
Figure 2: Principle of InSAR. As the distance from SAR 2 to the object on the ground is by the amount of \(\Delta R\) longer than the distance from SAR 1 to the object (\(R_{s,2}=R_{s,1}+\Delta R\)), two different phase signals are recorded at the two SAR acquisitions. This phase difference can be used to determine the topographic height \(h\) of the object on the ground.  
neighborhood of the building. On the other hand, a tsunami or flood could wash the entire building away or the debris of the building may be cleared by reconstruction activities leading to a decrease of the SAR backscatter.  
Therefore, this article concentrates on two kinds of multi-temporal SAR based damage assessment techniques, interferometric coherence and intensity correlation, being much better suited for damage assessment than a \"simple\" pre- and post-disaster SAR amplitude image comparison.  
Common for all the damage assessment procedures based on either SAR intensity correlation or interferometric coherence is the use of at least three SAR images. Two pre-disaster SAR images acquired in the ideal case shortly before the event happened and at least one post-disaster image recorded shortly after the event are required (Figure 3; The temporal baseline will be explained in detail in the Sections 2.1 and 4). Hereby, all three SAR images have to be acquired at the same imaging geometry (same incidence angle, beam, relative orbit, pass direction (ascending/descending), imaging mode, wavelength, _etc._).  
First, all three (or more) SAR images, fulfilling the requirements mentioned above, are co-registered to one common master image and resampled to its reference grid (Figure 4). Additionally, a common band filtering ensures that only the overlapping parts of the spectrums are used. Thereby, the spatial de-correlation effect (see Section 2.1.) is reduced [74]. In the next step, interferograms between the master and the two slave images are generated: One pre-disaster InSAR pair (t\({}_{1}\) and t\({}_{2}\)) and one co-disaster InSAR pair (t\({}_{2}\) and t\({}_{3}\)). Then, for both InSAR pairs the coherence is computed according to Equation (5) (see Section 2.1). Moreover, as described by Equation (9), also two SAR intensity correlations are computed using again the co-registered pre- (t\({}_{1}\) and t\({}_{2}\)) and co-disaster (t\({}_{2}\) and t\({}_{3}\)) intensity image pairs [8]. The damage caused by the natural disaster is then assessed by detecting the change between the corresponding image pairs (see Section 2.3 for more details).  
Figure 3: Three SAR images are required for the damage assessment methods interferometric coherence and SAR intensity correlation: Two images acquired before the event (time t\({}_{1}\) and t\({}_{2}\)) and at least one SAR acquisition shortly after the disaster at time t\({}_{3}\). In the optimum case the temporal baseline between each acquisition is only one repeat cycle (_cf._ also Section 4).