## 3 Method
### Dual Polarization Coherence Change Detection  
The damaged buildings can be determined by the actual investigation, image interpretation and other methods. The most accurate method is the actual survey of the disaster site because closer observation can better characterize the extent of the damage. However, it is an extremely difficult challenge to assess the extent of damage from a remote sensing perspective, especially from low- and medium-resolution spaceborne platforms. Therefore,the \"damaged change detection\" in this study emphasizes explicitly the state that the building is determined to collapse or not collapse, though it does not accurately detect slight or moderate damage, such as wall cracks and outer walls being burnt. Nevertheless, from the point of view of emergency disaster assessment, this may not be important because of the need to quickly assess the number and spatial distribution of highly damaged buildings. In the absence of ground survey data and high-resolution optical images, SAR imaging makes it possible to perform this work because of its all-weather and all-weather characteristics and the availability of coherence detection changes. In SAR images, buildings in different states have completely different scattered structures. Figure 6 illustrates common types of damage and the corresponding SAR intensity images before and after the damage occurred. (a) is a healthy building, usually with strong backscattering due to the presence of dihedral angles, specular reflection occurs on the roof, and the walls block the signal to form shadows. (b) is the damaged building, the roof and wall collapse formed a disorderly distribution so that the SAR echo signal lost the rule, and the backscattering intensity was significantly weakened. (c) is the damaged type of some large warehouses or factories. The top of the building is damaged, but the rest of the structure is relatively intact. The residual walls and ground may form an angular reflector and cause a strong double-reflection effect [46], and the backscattering intensity is enhanced. Under ideal geometric conditions, the capability of SAR coherence change detection in building damage detection is better than that of intensity change detection [47]. Phase coherence represents the coherence amount of complex phase signals of SAR images with two different simultaneous phases at the same position. The coherence coefficient \(\gamma\) is 0 to 1, which can be defined as  
\[\gamma=\frac{E\langle ab*\rangle}{\sqrt{E\langle aa*\rangle E\langle bb*\rangle}} \tag{6}\]  
where \(a\) and \(b\) are the relative complex values of the preceding time and the following time in the interference analysis, \(a*\) and \(b*\) are complex conjugate values of the images. \(E\) is the mathematical expectation. In the study area, areas with high vegetation coverage, such as farmland and forest land, often exhibit decoherence due to short-term effects, such as wind disturbance, or long-term effects, such as vegetation growth. The sea surface, rivers and other water bodies  
Figure 6: Comparison of buildings in different damaged states on SAR images before and after conflict. will also cause decoherence because the water surface waves constantly change. In urban areas, the main features are artificial buildings, and the coherence is usually at a high level under the condition of not being destroyed by external forces. The damaged buildings in conflicts can be detected more robustly by synthesizing different polarization modes. In this study, The DPNCI was constructed by a weighted combination of the coherence maps in the VV polarization and VH polarization modes. We selected two SAR images before the conflict, with the image on 4 February 2022, as the master image and the image on February 16 as the slave image, and calculated the coherence coefficient within the artificial building land (Red Area in Figure 7, land types include: commercial, construction, education, gas station, factory, military, religious and residential).