## 3 Results
OLS regressions on the M\({}_{\text{S}}\) data result in the following relationships:  
\[\text{M}_{\text{w,proxy}}=0.723\ \text{M}_{\text{S,ISC}}+1.661;\ \sigma_{\text{OLS}}=0.184;\ 3.0\leq\text{M}_{\text{S,ISC}}\leq 7.0 \tag{3a}\] \[\text{M}_{\text{w,proxy}}=0.550\ \text{M}_{\text{S,NEC}}+2.772;\ \sigma_{\text{OLS}}=0.237;\ 4.4\leq\text{M}_{\text{S,NEIC}}\leq 6.7\] (3b) \[\text{M}_{\text{w,proxy}}=0.815\ \text{M}_{\text{S,BJI}}+0.859;\ \sigma_{\text{OLS}}=0.158;\ 3.9\leq\text{M}_{\text{S,BJI}}\leq 6.5\] (3c) \[\text{M}_{\text{w,proxy}}=0.681\ \text{M}_{\text{S,MOS}}+1.820;\ \sigma_{\text{OLS}}=0.149;\ 4.0\leq\text{M}_{\text{S,MOS}}\leq 6.9\] (3d) \[\text{M}_{\text{w,proxy}}=0.777\ \text{M}_{\text{S,IDC}}-1.565;\ \sigma_{\text{OLS}}=0.198;\ 2.6\leq\text{M}_{\text{S,IDC}}\leq 6.5 \tag{3e}\]  
Additionally, TLS regressions on the M\({}_{\text{S}}\) data result in the following relationships:  
\[\text{M}_{\text{w,proxy}}=0.741\ \text{M}_{\text{S,ISC}}+1.579;\ \sigma_{ \text{TLS}}=0.149;\ 3.0\leq\text{M}_{\text{S,ISC}}\leq 7.0 \tag{4a}\] \[\text{M}_{\text{w,proxy}}=0.601\ \text{M}_{\text{S,NEIC}}+2.513;\ \sigma_{ \text{TLS}}=0.206;\ 4.4\leq\text{M}_{\text{S,NEIC}}\leq 6.7 \tag{4b}\] \begin{table}
\begin{tabular}{c c} \hline \hline
**Agencies** & **Number of Equivalent M\({}_{\text{W}}\)–M Pairs Used in Regression** \\ \hline ISC & 79 \\ NEIC & 45 \\ IDC & 139 \\ JMA & 132 \\ BJI & 80 \\ MOS & 43 \\ KEA & 14 \\ KMA & 46 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Number of earthquakes with a listed M\({}_{\text{W}}\) as well as another magnitude type categorized by agency. Figure 2 shows that both OLS and TLS regressions produce similar relationships for the magnitude ranges presented. Similar to Figure 2, a plot of \(\mathrm{M_{w}}\) and \(\mathrm{m_{b}}\) pairs from multiple agencies is shown in Figure 3. \(\mathrm{m_{b}}\) data from ISC, NEIC, BJI, MOS, and IDC is shown in Figure 3a-e, respectively. The data show some scatter but appear linear with \(\mathrm{R^{2}}\) = 0.891, 0.806, 0.814, 0.821, and 0.804 for ISC, NEIC, BJI, MOS, and IDC, respectively. The data also hint at potential magnitude saturation at \(\mathrm{m_{b}}\)\(\sim\) 6, which is what is expected. Similar to the \(\mathrm{M_{S}}\) data, the figure shows NEIC, BJI, and MOS to have no data pairs \(\mathrm{m_{b}}\)\(<\) 4, while ISC and IDC have data pairs for \(\mathrm{m_{b}}\)\(<\) 4. Additionally, the ISC data generally plot closer to the right-side boundary of a global earthquake catalog data set [19], similar to that shown in Figure 2.  
Figure 2: Relationships between \(\mathrm{M_{w}}\) against \(\mathrm{M_{S}}\) from (**a**) ISC, (**b**) NEIC, (**c**) BJI, (**d**) MOS, and (**e**) IDC. The solid and dashed lines represent the regression type as indicated in the graph. N is the number of data points used for regression. Data by [PERSON] et al. (2015) from a larger earthquake compilation related to \(\mathrm{M_{w}}\) versus \(\mathrm{M_{S,ISC}}\) is shown in gray symbols in the background for comparison [19]. OLS regressions on the \(\rm m_{b}\) data result in the following relationships:  
\[\rm M_{w,proxy}=0.898\ m_{b,ISC}+0.649;\ \sigma_{OLS}=0.198;\ 3.3\leq m_{b,ISC}\leq 5.9 \tag{5a}\] \[\rm M_{w,proxy}=1.064\ m_{b,NEIC}-0.233;\ \sigma_{OLS}=0.263;\ 3.7\leq m_{b,ISC}\leq 5.9\] (5b) \[\rm M_{w,proxy}=1.360\ m_{b,BJI}-1.555;\ \sigma_{OLS}=0.260;\ 4.0\leq m_{b,BJI}\leq 5.8\] (5c) \[\rm M_{w,proxy}=1.057\ m_{b,MOS}-0.312;\ \sigma_{OLS}=0.224;\ 4.1\leq m_{b,MOS}\leq 6.2\] (5d) \[\rm M_{w,proxy}=1.090\ m_{b,IDC}+0.113;\ \sigma_{OLS}=0.281;\ 3.1\leq m_{b,IDC}\leq 5.1 \tag{5e}\]  
Additionally, TLS regressions on the \(\rm m_{b}\) data result in the following relationships:  
\[\rm M_{w,proxy}=0.948\ m_{b,ISC}+0.430;\ \sigma_{TLS}=0.157;\ 3.3\leq m_{b,ISC}\leq 5.9 \tag{6a}\] Figure 3.0 (6b) Figure 3.1 (6c) Figure 3.2 (6d) Figure 3.3  
Figure 3.4 Relationships between \(\rm M_{w}\) against \(\rm m_{b}\) from (**a**) ISC, (**b**) NEIC, (**c**) BJI, (**d**) MOS, and (**e**) IDC.