# Integrated Earthquake Catalog of the Ossetian Sector of the Greater Caucasus
## 3 Results
### Magnitudes in the Integrated Catalog of the Ossetian Sector of the Greater Caucasus  
The magnitude scale in the integrated catalog was unified. The integrated earthquake catalog of the Ossetian sector of the Greater Caucasus contains many magnitude definitions of different types from various agencies. The seismic moment magnitude determined by GCMT was chosen as the reference scale. The analysis of the correlation relationships between different magnitudes was carried out and conversion formulas were proposed to obtain \"proxy-MW\" estimates. The simplest shift-type relations \(M=m+a\) were used. An exception was made for \(ML^{\text{AZER}}\) and \(ML^{\text{EDIC}}\). For them, linear relationships were used. The Ossetian sector of the Greater Caucasus considered (Figure 1) is not a large region at all. For this reason, there are not sufficient statistics for many magnitudes. Therefore, to obtain more reliable estimates, the relationships between magnitudes throughout the North Caucas were analyzed. The integrated catalog of the Ossetian sector of the Greater Caucasus contains 16,285 events. The \(MW^{\text{GCMT}}\) magnitude was determined for only 10 events. Magnitudes \(mb^{\text{ISC}}\) and \(mb^{\text{NEIC}}\) are known for 259 events. Magnitude \(mb^{\text{ISC}}\approx MW^{\text{GCMT}}\) (Figure 10a), which corresponds to the ISC practice of using magnitude \(mb\) as a proxy-\(MW\) for earthquakes with \(M<5.0\)[6; 30]. Also, \(mb^{\text{ISC}}\approx mb^{\text{NEIC}}\) (Figure 10b). The latest ratios make it possible to significantly increase statistics and expand the magnitude range to convert other magnitudes to proxy-\(MW\). Note that for the vast majority of events (15,872), the energy class \(k\) is determined. Thus, more than 99% of events have magnitudes \(MW^{\text{GCMT}}\), \(mb^{\text{ISC}}\), NEIC, and energy class \(k\). The relationships between these magnitudes are considered basic (Figure 10). It should be noted that the relationship between the energy class and magnitude of \(mb^{\text{ISC}}\)  
Figure 8: Stage 5: Determination of numerical parameters of metric (1) for merging the ISC_CORE and GSR_OTHER catalogs. Distributions of variables \(DT\), \(DX\), \(DY\), and the dependence of dispersion and mean values on the time and magnitude of events. turned out to be different in the ZEMSU and NC catalogs (Figure 10c,d). In turn, in the Georgian catalogs GEOR71 and GEOR04, the energy class \(k\) showed approximately the same regressions with \(mb^{\text{SC}}\) as in the ZEMSU and NC catalogs (Figure 10c,d). The energy class \(k\) was converted to magnitude \(Mk\) and the relationship between \(Mk\) and \(mb^{\text{SC}}\) is shown in Figure 10e. Figure 9: Stage 5: Merging of catalogs ISC_CORE and GSR_OTHER. (**a**) Comparison of the metric distribution ISC_CORE/GSR_OTHER pairs (blue histogram) and the same metric for GSR_OTHER/GSR_OTHER earthquakes (red histogram). (**b**) Threshold optimization: the red line shows the probability of missing a duplicate, the blue line shows the probability of a false duplicate, and the black line shows the total probability of first and second kind errors. The threshold value \(Ro=9\), which minimizes the total number of errors, approximately \(1.1\%\), is shown by a dashed line. (**c**) Distribution of normalized \(DT\) and \(DR\), and contour line of metric (1). Colored dots represent ISC_CORE/GSR_OTHER pairs (pink dots are duplicates, blue dots are unique events), and black dots are distances between GSR_OTHER/GSR_OTHER events in metric (1). The values of the metric for earthquakes in the GSR_OTHER catalog are significantly larger than for ISC_CORE/GSR_OTHER duplicates (pink dots). The contour line of metric (1), \(Ro=9\), provides close-to-optimal separation of duplicates and naturally grouped events. Absolute duplicates are not shown. A total of 145 events in the integrated catalog have other types of magnitudes. For them, relationships were built with \(mb^{\rm ISC}\) and/or \(Mk\).