## 4 Discussion  
Building damage is one of the frequently occurring geohazards in subsidence zones [1; 11]. This study attempts to understand surface vertical motion surrounding collapsed buildings before the incident. The PS-InSAR technique is used to measure the deformation time series, and spatiotemporal data analysis is used to extract surface motion patterns before the collapse. Results show that new cold spot and new hot spot are the two common spatiotemporal patterns shown before 66 buildings collapsed between May 2015 and December 2018, out of a total of 68 buildings that were studied. Besides the high percentage of collapse incidents having at least one of these two spatiotemporal patterns close in proximity, which is 97% of the studied buildings, the rare distribution of the two spatiotemporal patterns gives confidence to the correlation obtained in this study between building collapse incidents in the city and the NCS and NHS patterns. Table 5 shows the percentage of NCS and NHS in the ninth and tenth time steps among the seventeen spatiotemporal patterns in the 4 km\({}^{2}\) area used for the validation process presented in Section 3.4. The distribution average of NCS and NHS, including the ninth and tenth time step before collapse incident dates, is 2.6% of all spatiotemporal patterns in the four square kilometer of the validation area. The highest distribution of the two patterns was before the 18 February 2019 collapse (3.5% of the validation area), while the lowest distribution obtained was before the collapse incident on 22 March 2019 (2.1%). The result of the existing new cold spot close to the collapsed building was expected, as it represents sudden subsidence in a very limited space in comparison to the overall velocity of the surrounding area. Although it is also representing a sudden deformation in the surrounding area of the collapsed building, results of the new hot spot pattern was unexpected. Many new hot spots related to collapsed buildings were observed in the winter of 2015, which raised the idea of surface uplift due to the accumulation of underground water and seawater surges during the rainy season of that year. This could be one reason for a new hot spot pattern surrounding collapsed buildings during that period. However, the existence of a new hot spot pattern in the dry season of summer suggested another technical explanation of related collapses. This might be a sudden relative failure on the surface that was higher than the applicability of PS-InSAR slow surface motion detection, which resulted in unwrapping error in this area, and presents the deformation at that time as uplift. However, a sudden failure in the surface cannot be detected due to its high velocity. Regardless, building collapse due to surface alternation between drought-flood seasons might be a reason for a high building collapse ratio [11] in a city like Alexandria. [PERSON] et al. analyzed the deformation time series of PS points close to collapsed buildings in Camaiore, Italy, and found clear subsidence in eight points before the collapse, which returned to \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Spatiotemporal Pattern**} & \multirow{2}{*}{**Time Step**} & \multicolumn{3}{c}{**Incident Date**} \\  & & **18 February 2019** & **22 March 2019** & **1 April 2019** \\ \hline \multirow{2}{*}{NCS} & 10 th & 0.3\% & 1\% & 0.5\% \\  & 9 th & 0.7\% & 0.5\% & 1.1\% \\ \hline \multirow{2}{*}{NHS} & 10 th & 1\% & 0.3\% & 0.3\% \\  & 9 th & 1.5\% & 0.3\% & 0.4\% \\ \hline \multicolumn{2}{c}{Total percentage} & 3.5\% & 2.1\% & 2.3\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Distribution percentage of NCS and NHS patterns in the validation area. random velocity after the incident. The deformation was affected by clay soil erosion and subsequent formation of cavities. In comparison, [PERSON] et al. [10] utilized relatively more images to detect deformation before two collapse incidents in Katowice, Poland, and Moscow, Russia.