# Expanding Moment Magnitude Pools for Earthquake Magnitude Homogenization
## 4 Discussion  
It is interesting to see that the techniques presented in expanding the pool of available moment magnitudes for magnitude homogenization only increased the pool size by at most 2% for the body and surface wave-related magnitude types and almost no increase for local magnitude types. These increases were primarily seen in the high seismicity study region. For a region of low seismicity such as South Korea, these techniques did not significantly influence regressed parameters.  
It should be noted that in a previous study on magnitude homogenization in South Korea [4], the moment magnitude pool expansion technique was slightly biased in that it included data from NIED, which in this study was not directly related to the base M\({}_{\text{W,GCMT}}\) and did not pass hypothesis testing for inclusion. However, other studies suggest that M\({}_{\text{W}}\) from NIED is similar to M\({}_{\text{W}}\) from HRVD and GCMT [3; 30; 31]. Although the use of literature was accepted in estimating seismic moments and thus moment magnitudes for M\({}_{\text{W,GCMT-related}}\) herein, it is not sure if the use of literature in verifying consistency in agency magnitude types is warranted. For example, M\({}_{\text{W,HRVD}}\) should be similar to M\({}_{\text{W,GCMT}}\), but hypothesis testing conducted previously demonstrates the linear regression parameters were significantly different.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Magnitude** & **Pool** & **Slope, \(\beta_{1}\)** & **Intercept, \(\beta_{0}\)** & **Correlation, R2** & **Standard** & **Number of** \\
**Type** & & & & & **Deviation, \(\sigma\)** & **Data Pairs** \\ \hline M\({}_{\text{L,KMA}}\) & M\({}_{\text{W,GCMT}}\)1  & 0.596 & 2.027 & 0.814 & 0.181 & 12 \\ M\({}_{\text{W,GCMT-related}}\)1  & 0.596 & 2.027 & 0.814 & 0.181 & 12 \\ M\({}_{\text{W,GCMT-related}}\)1  & 0.755 & 1.371 & 0.882 & 0.174 & 14 \\ \hline \hline \end{tabular}
\end{table}
Table 11: Magnitude homogenization regression results from all moment magnitude pools for local magnitude types from DJA.  
Figure 14: Resultant magnitude homogenization regressions for M\({}_{\text{W,GCMT-hypothesis}}\) against M\({}_{\text{L,KMA}}\). Data from M\({}_{\text{W,GCMT}}\) are also shown. Black line is the regression against M\({}_{\text{W,GCMT-hypothesis}}\) while the dashed red line is the regression against M\({}_{\text{W,GCMT-}}\).  
It is noted that some works use bilinear regressions for their magnitude homogenization, such as the work by [PERSON] [2]. Their work applied bilinear regression for MS data. However, their regression combined ISC and NEIC data and the inflection point where the regression is separated into two sections was subjectively chosen. The issue with the bilinear approach is that the standard deviations for each portion are different. Another team also implied this concern in their work [3]. Moreover, accounting for these differences ventures into the realm of nonlinear, or semi-nonlinear regression, which might violate some of the assumptions in hypothesis testing. This is a problem depending on how the resultant earthquake catalog is used and, to our knowledge, no one has provided a robust treatment of bilinear regressions for magnitude homogenization yet. We do not doubt there are better models out there, but these appear out of our scope.  
In addition to limitations on linear regression models, there may be limitations due to ergodicity. Indonesia and South Korea do not represent all regions of varying seismicity. Even though the results suggest independence from seismicity, it may not ring true for other regions, especially those that have lower seismicity than South Korea. Moreover, the data for this study was taken from ISC, which did not record many low magnitude events. The verification of low magnitude events could significantly change the results.