## 4 Results and Discussion  
After adjusting the magnitude relation equations based on past instrumental data and known catalog earthquake locations, we proceeded to evaluate the performance of the new equations using simulated real-time replays of recorded data and real-time processing. This evaluation is necessary since missing data, delays, and other operational difficulties may affect the results, and since the accuracy of the distance R calculation in real-time depends on the correct epicenter location, if the epicenter is mis-located, it can lead to an incorrect estimation of the magnitude. However, we were able to ensure a highly robust earthquake location due to the dense seismic network used in this study for the Bursa province and its surroundings. Hereafter, we will refer to the original magnitude relation equation as \"default\" (Equations (1) and (2)) [31; 45] and the newly developed equation as \"newly developed\" (Equations (3) and (4)). Figure 4: The relationship between \(T_{p}^{max}\) (calculated for each station) and catalog magnitude (\(M\)). The epicenter distribution of earthquakes in the KOERI catalog and the epicentral distributions of the solutions obtained from the EPIC replayed dataset are shown in Figure 5. Square symbols represent KOERI solutions, and circles represent EPIC solutions. Errors are observed in the locations of some earthquakes. This is expected as performance declines for events outside the system. [PERSON] and [PERSON] [11] stated that large location errors are caused by events located further away from the network, and the system is suitable for in-network events and performs less well for out-of-network events. No parameter other than magnitude is estimated in the study. The observed difference is due to the different stations used while processing the replay solution. In real-time performance, there will be no difference in locations. Please note that in real-time playback, the algorithm uses multi-threading, which leads to different data orders each time. Figure 6 compares \(Pd\) and \(T_{p}^{max}\) calculated with the default and newly developed equations for each earthquake by observed magnitudes. When Figure 6a,b obtained with the default and newly developed equations are examined, it is observed that the scattering of the new equation is less. Although a small increase in standard deviation is observed, this is due to the scattering of some earthquakes smaller than \(M<4\). The distribution of \(T_{p}^{max}\) against the catalog size of the default and newly developed equation is different (Figure 6c,d). Scattering is high in the graph by using the default equation. It is seen that the results of the analysis made with the newly developed equation show a better agreement between \(T_{p}^{max}\) and the observed magnitudes compared to the default equation. Although an improvement in \(T_{p}^{max}\) is observed, it is clear that \(T_{p}^{max}\) is neither a good measure of magnitude estimation for default nor newly developed equations compared to \(Pd\). The problem that \(Pd\) reaching saturation for large earthquakes has been emphasized in previous studies [37,38,42]. In our study, the network's magnitudes estimates agree with the newly developed equations. This can be explained by the near-field effects emphasized by [PERSON] and [PERSON] [46]. Waveforms recorded by the strong motion sensor close to the source were used in the analysis. In this direction, values comparable to the catalog values were obtained despite the near-field effects. Figure 5: Epicenter distributions of the replayed earthquakes. In Figure 7, the errors of the magnitudes obtained by using \(Pd\) and \(T_{p}^{max}\) with the default and newly developed equations are given. When comparing \(Pd\) was examined, the mean magnitude error is \(-0.57\), the standard deviation \(0.38\), and the median \(-0.6\) using the default settings. When the newly developed coefficients were used, mean magnitude error \(-0.13\), standard deviation \(0.41\), and median \(-0.1\) values were obtained.