# Integrated Earthquake Catalog of the Eastern Sector of the Russian Arctic
## 3 Results
### Merging Catalogs
#### 3.1.1 Stage 1. Merging YAK and NER  
YAK was considered as the main catalog and NER as the additional one. The preliminary analysis of duplicates was performed with the distribution parameters \(\sigma_{\rm T}=0.05\) min and \(\sigma_{X}=\sigma_{Y}=15\) km. As a result, 1834 absolute duplicates and about 370 potential duplicates (events with a small metric) were identified. The preliminary threshold was determined by the minimum distribution of the metric. Absolute duplicates were not used to determine the dispersions (Figure 3). It was verified that each of the parameters followed a normal distribution and that the mean was small compared to the standard deviation for all three parameters (\(DT\), \(DX\), and \(DY\)). It was also verified that the variance was almost independent of the event magnitude and time (Figure 3). The final duplicate analysis was performed with the parameters \(\sigma_{T}=0.041\) min, \(\sigma_{X}=17.4\) km, and \(\sigma_{Y}=16.3\) km. The metric values between the nearest events of the YAK catalog were also calculated. This made it possible to estimate the probability that  
Figure 3: Distributions of \(DT\), \(DX\), and \(DY\) for the nearest events from the YAK and NER catalogs, and the dependence of the standard deviations \(\sigma_{T}\), \(\sigma_{X}\), and \(\sigma_{Y}\) and the mean values \(\overline{DT}\), \(\overline{DX}\), and \(\overline{DY}\) on the time and magnitude of the events. The red dots and bars are the population mean values and standard deviations, respectively. the duplicate was chosen incorrectly due to the high density of earthquakes. Figure 4a shows the distributions of metric (1) for the YAK/NER pairs and the same metric for the YAK/YAK earthquakes (the algorithm for calculating the metric is the same as for two different catalogs, but only the comparison of the earthquake with itself is excluded). A group of anomalously close YAK/NER events is identified well. The optimization of the threshold value of the metric is illustrated in Figure 4b. The red line is the probability of missing a duplicate in the 3D normal distribution model (error of the first kind) and the blue line is the probability of a false duplicate (error of the second kind), which is defined as the ratio of the number of YAK/YAK pairs for a given value of the metric \(Ro\) to the number of events in the YAK catalog. An equal number of errors of the first and second kind is achieved at \(Ro\) = 5.8. In the NER catalog, only 15 earthquakes have a distance to the nearest neighbor of \(Ro\) < 5.8. This made it possible to estimate the probability that the duplicate was chosen incorrectly due to the high density of earthquakes. The upper estimate of the probability of false duplicates \(P\) = 15/6600 = 0.0023 is approximately 0.25%. At \(Ro\) = 7.9, the number of such earthquakes increases to 26, which corresponds to a probability of 0.4% (see the blue line in Figure 4b). The choice of the metric threshold for identifying duplicates depends on the objective of further research of the integrated catalog. If it is important to ensure that duplicates are removed, then a higher \(Ro\) threshold is preferable. If it is important to keep the integral characteristics of the catalog, then the \(Ro\) threshold that ensures the equality of errors of the first and second kind is preferable. We chose the threshold \(Ro\) = 5.8. In this case, in addition to 1834 absolute duplicates, 319 more duplicates were identified. In total, 5515 unique events were identified in the NER catalog in the study area. These events were added to the YAK catalog, and thus a merged YAK_NER catalog containing 12,115 events was obtained. Figure 5 shows the spatio-temporal structure of the YAK/NER duplicates and the naturally grouped events in the YAK catalog. The metric values for earthquakes in the YAK catalog are significantly larger than those for the YAK/NER duplicates.