# Expanding Moment Magnitude Pools for Earthquake Magnitude Homogenization
## 3 Results
### South Korea
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Magnitude** & **Pool** & **Slope, \(\beta_{1}\)** & **Intercept, \(\beta_{0}\)** & **Correlation, R2** & **Standard** & **Number of Data** \\
**Type** & & & & & **Deviation, \(\sigma\)** & **Pairs** \\ \hline M\({}_{\text{S,ISC}}\) & M\({}_{\text{W,GCMT}}\) & 0.663 & 1.988 & 0.885 & 0.169 & 14 \\ M\({}_{\text{W,GCMT-related}}\) & 0.624 & 2.161 & 0.919 & 0.164 & 16 \\ M\({}_{\text{W,GCMT-hypothesis}}\) & 0.613 & 2.221 & 0.923 & 0.157 & 18 \\ \hline M\({}_{\text{S,NEC}}\) & M\({}_{\text{W,GCMT}}\)1 & 0.635 & 2.321 & 0.941 & 0.076 & 4 \\ M\({}_{\text{W,GCMT-related}}\)1 & 0.635 & 2.321 & 0.941 & 0.076 & 4 \\ M\({}_{\text{W,GCMT-hypothesis}}\)1 & 0.635 & 2.321 & 0.941 & 0.076 & 4 \\ \hline M\({}_{\text{S20,NEC}}\) & M\({}_{\text{W,GCMT}}\)1 & N/A & N/A & N/A & 2 \\ M\({}_{\text{W,GCMT-related}}\)1 & N/A & N/A & N/A & N/A & 2 \\ M\({}_{\text{W,GCMT-hypothesis}}\)1 & N/A & N/A & N/A & N/A & 2 \\ \hline M\({}_{\text{S2,NEC}}\) & M\({}_{\text{W,GCMT}}\)1 & N/A & N/A & N/A & N/A & 1 \\ M\({}_{\text{W,GCMT-related}}\)1 & N/A & N/A & N/A & N/A & 1 \\ M\({}_{\text{W,GCMT-hypothesis}}\)1 & N/A & N/A & N/A & N/A & 1 \\ \hline \hline \end{tabular} \({}^{1}\) Pool of M\({}_{\text{W}}\) data did not change for the corresponding magnitude type. N/A = not applicable.  
\end{table} 
Table 9: Magnitude homogenization regression results from all moment magnitude pools for surface wave magnitude types. The resultant magnitude homogenization regressions for all body wave magnitude types considered herein, i.e., \(m_{b,\text{JSC}}\), \(m_{b,\text{NEC}}\) are shown in Table 10. Both \(m_{b,\text{JSC}}\) and \(m_{b,\text{NEC}}\) had identical moment magnitude pools between \(M_{W,\text{CGMT}}\) and \(M_{W,\text{CGMT-related}}\). Regression \(\sigma\)s are noticeably high for each regression given the number of data points available. Since \(M_{W,\text{CGMT}}\) and \(M_{W,\text{CGMT-related}}\) contained identical records against \(m_{b,\text{JSC}}\) and \(m_{b,\text{NEC}}\), there was no need to conduct hypothesis testing on their regression parameters. Hypothesis testing conducted on regression parameters derived from \(M_{W,\text{CGMT-hypothesis}}\) found no significant differences for \(m_{b,\text{JSC}}\) and \(m_{b,\text{NEC}}\) results. The resultant magnitude homogenization regressions for \(M_{W,\text{CGMT-hypothesis}}\) against \(m_{b,\text{JSC}}\) and \(m_{b,\text{NEC}}\) are shown in Figure 13a,b, respectively. Additionally shown in the figures are the data from \(M_{W,\text{CGMT}}\) for comparison. Since regression results using \(M_{W,\text{CGMT}}\) and \(M_{W,\text{CGMT-hypothesis}}\) pools are identical, they are not plotted in the figure. Even though there appear to be some differences in regression results for each magnitude type, the differences appear negligible when plotted. The resultant magnitude homogenization regressions for \(M_{W,\text{CGMT-hypothesis}}\) against (**a**) \(m_{b,\text{JSC}}\) and \(m_{b,\text{NEC}}\). Data from \(M_{W,\text{CGMT}}\) are also shown. Black line is the regression against \(M_{W,\text{CGMT-hypothesis}}\) while the dashed red line is the regression against \(M_{W,\text{CGMT}}\). The resultant magnitude homogenization regressions for \(M_{L,\text{KMA}}\) are shown in Table 11. Moment magnitude pools \(M_{W,\text{CGMT}}\) and \(M_{W,\text{CGMT-related}}\) are identical and therefore produced the same regression results. Although, the \(M_{W,\text{CGMT-hypothesis}}\) pool contains an additional two events, the regression results appear quite different even at a similar \(\sigma\)