## 6 Evaluation of Seismological Parameters from the Re-Evaluated Isoseism Map  
In the previous Section, we first estimated intensity values and showed them on a map, and then defined isoseismals of individual degrees of intensity \(I_{i}\) (see Figure 6). In this Section, we will use the areas \(A_{i}\) circumscribed by the isoseismal lines \(I_{i}\) to calculate the magnitude of the 8 April 1893 earthquake, using the following three macroseismic field equations:  
1. the equation from UNESCO [12], developed for former Yugoslavia, Romania, Albania, Central, and Western Bulgaria, and Southwestern Turkey, \"normal\" foci--10 km \(<h<\) Ha (Ha--depth of the upper boundary of the asthenosphere channel, Ha = 50-100 km) \[I_{i}=1.5\cdot M_{LH}-4.5\cdot\log\sqrt{r_{i}^{2}+h^{2}}+4.5,\] (1) \[I_{0}=1.5\cdot M_{LH}-4.5\cdot\log h+4.5,\] (2) where \(I_{i}\) is the intensity degree (MSK-64) of the \(i\)-th isoseismal and \(I_{0}\) is the epicentral intensity, \(M_{LH}\) is the magnitude defined by [PERSON] et al. [26], \(h\) is the hypocentral depth (in km), and \(r_{i}\) (in km) is the equivalent radius of \(i\)-th isoseismal area, calculated as \[r_{i}=\sqrt{\frac{A_{i}}{\pi}},\] (3) (2) the equation proposed by [PERSON] et al. [5], developed for Europe south of 47\({}^{\circ}\) N, also with the intensity degrees in MSK-64 scale: \[I_{i}=1.5\cdot M_{S}-4.0\cdot\log r_{i}+3.8,\] (4) \[I_{0}=1.5\cdot M_{S}-4.0\cdot\log h+3.8,\] (5) (3) the equation we developed specifically for this study, derived from a database of recent earthquakes in Serbia for which there were instrumentally determined epicenter locations, focal depths, earthquake magnitudes (\(M_{W}\)), and the intensity values estimated according to the EMS-98 scale: \[I_{i}=1.443\cdot M_{W}-3.310\cdot\log\sqrt{r_{i}^{2}+h^{2}}+3.136,\] (6) \[I_{0}=1.443\cdot M_{W}-3.310\cdot\log h+3.136.\] (7) As for the hypocentral depth, \(h\), we will use the equation suggested for Serbia by [PERSON] et al. [3]: \[h=3.25\cdot\sqrt{A_{2}^{2}+A_{3}^{2}}\] (8) where \(A_{2}\) and \(A_{3}\) (in km\({}^{2}\)/1000) are the areas circumscribed by the second and the third isoseismal lines (in our case, these are the isoseismal lines for intensities VIII and VII, respectively). By using Equations (1)-(7), the magnitude of the analyzed earthquake is obtained as the median value for all analyzed isoseismal lines. The macrosismic magnitudes calculated by Equations (1) and (2) were then converted to \(M_{W}\) using [PERSON] (2017) equations. The \(M_{5}\) magnitudes calculated by Equations (3) and (4) were converted to \(M_{W}\) using [PERSON] et al. 's (2018) equations. Table 5 shows the final estimates of both magnitude \(M_{W}\) and hypocentral depth \(h\) (calculated using Equation (8)) for five different sets of the equivalent radii of isoseismal areas. The first two sets are those we found in the available literature ((19) and (20), respectively), while the last three represent our lowest (the most conservative), medium, and highest estimates. For the estimation of the isoseisimals, we used only discrete intensity values. As for the interval intensity values shown in Figures 6 and 7 and in Table 11, we defined our lowest isoseismal estimate (the fourth column in Table 5) using only lower interval values, our medium isoseismal estimate (the fifth column in Table 5) using the values we determined to be more likely (based on the intensity values assigned to nearby locations), and our highest isoseismal estimate (the last column in Table 5) using only higher interval values. At this juncture, it is interesting to note that the area comprising locations with reported ground fractures and liquefaction (see Figure 7) is similar to our highest estimate of I = VIII isoseismal area, which is 4164 km\({}^{2}\) and also extends 45 km to the north (Malo Crnice), 40 km to the south (Donje Vidovo), 25 km to the east (Petrovac na Mlavi), and 30 km to the west (Velika Plana) from the epicenter.