## 2 Materials and Methods
### Spatiotemporal Analysis of Collapsed Buildings  
With the increasing number of sensors and geospatial data availability worldwide, spatiotemporal data mining becomes an important method to extract new interesting and useful patterns from geographical data [15; 16]. However, extracting meaningful spatiotemporal patterns is more difficult than extracting regular patterns from traditional numeric and categorical data. The complexity of spatiotemporal data types and relationships results in challenges in data storage, management, analysis, and knowledge discovery [13; 16]. Data storage in a space-time cube is one of the most effective ways to manage and analyze spatiotemporal patterns. Points are aggregated into so-called bins, based on their location and time, where each bin has a specific location. All bins within the same time create a time step (or slice), and time data of each bin creates a bin time series. Each bin has input points based on its location within the bin size and the time step interval. The oldest time step is at the bottom of the cube while the upper time step represents the most recent time data [25]. In this study, we converted the vertical velocity maps of Alexandria for the last 120 days before the collapse incident to points with their corresponding dates. A buffer of 200 meters from the collapsed building was created for processed points to reduce the processing time of each incident. A netCDF data structure cube was then created with a bin size of ten meters and a time step interval of twelve days. The bin size was selected as twice the size of the previously processed vertical velocity maps for Alexandria (5 m). Furthermore, the time step interval value was selected based on the average of Sentinel-1 data availability average over the city during the study period. In case of no data availability for a specific time step, we decided to spatially and temporally interpolate bin values of the slice based on the mean of space-time neighbors. A Mann-Kendall trend test [26; 27] was calculated during the space-time cube creation to investigate the time series trend of each bin. It simply compares the bin value to the previous one. If it is smaller, its result is -1, if it is larger, its result is +1, and if the two bins are equal, then the result is 0. The results of all pairs in the space-time cube are then summed for each bin. If the sum is zero, then it means no trend over time was detected. The other bins are compared to the no-trend ones based on the variance for the values in the bin time series, the number of ties, and the number of time steps to measure its statistical significance based on z-score and \(p\)-value with confidence levels. The \(p\)-value of a bin indicates whether it is statistically significant or not, while the z-score shows if the trend is positive or negative based on the increase or decrease of bin values, respectively [28; 29]. We used the netCDF space-time cube to extract spatiotemporal patterns of vertical velocity surrounding collapsed buildings by using emerging hot spot analysis. It is a regular hot spot analysis with the addition of time as a third dimension [28]. Emerging hot spot analysis [30; 31] calculates the Getis-Ord \(Gi^{\star}\) statistic based on the neighborhood in space (bins in the same time step), and time (bins in different time steps) [32]. A simple form of the \(Gi^{\star}\) statistic as defined by [PERSON] [31]:  
\[G_{i}^{\star}\frac{\sum_{j=1}^{n}w_{ij}x_{j}}{\sum_{j=1}^{n}x_{j}} \tag{3}\]  
where \(Gi^{\star}\) is a statistic that describes the spatial dependency of the incident \(i\) over all \(n\) events, \(x_{j}\) is the magnitude of variable \(x\) at incident location \(j\) over all \(n\) (\(j\) may equal \(i\)), and \(w_{ij}\) is a weight value between event \(i\) and \(j\) that represents their spatial interrelationship. In this study, we kept the default value of neighborhood distance, which was about 30 meters, and selected one neighborhood time step for the emerging hot spot analysis.