# Advanced Unified Earthquake Catalog for North East India
## 4 Regression Analysis for Magnitude Conversion
### Surface Wave and Body Wave Conversions  
The GOR1 methodology has been used to convert magnitudes such as \(\mathrm{M_{s}}\) and \(\mathrm{m_{b}}\) to \(\mathrm{M_{wgGCMT}}\). The GOR1 relationship for \(\mathrm{M_{s,ISC}}\) to \(\mathrm{M_{wg,GCMT}}\) has been developed in the range \(4.1\leq\mathrm{M_{s,ISC}}\leq 6.1\), using 93 case data and assuming \(\eta=0.6\), is obtained as follows:  
\[\mathrm{M_{wg,GCMT}}=0.680(\pm 0.002)\ \mathrm{M_{s,ISC}}+1.69(\pm 0.08). \tag{1}\]  
\[\mathrm{R_{xy}}=0.94,\quad\mathrm{RMSE}=0.094,\quad\mathrm{n}=93\]  
The regression plot for \(\mathrm{M_{s,ISC}}\) to \(\mathrm{M_{wg,GCMT}}\) has been shown in Figure 3. The above obtained GOR1 relationship is found with the lowest error values in terms of slope, intercept, standard deviation, and root means square error as compared to SLR and GOR2 (Tables 2 and 3, Figure 4). The correlation coefficient value (\(\mathrm{R_{xy}}\)) obtained using the GOR1 methodology shows significant improvement as compared to GOR2 and SLR (Tables 2 and 3). The maximum difference between \(\mathrm{M_{wg}}\) estimation using \(\mathrm{M_{s,ISC}}\), and the corresponding \(\mathrm{M_{w}}\) estimation of Ref. [5] is found to be 0.4. Figure 3: The (\(\mathrm{M_{S,ISC}}-\mathrm{Mwg}\)) data, as well as the GOR1, GOR2, and SLR regression lines. Similarly, to convert M\({}_{\rm S,NEIC}\) to M\({}_{\rm wg,GCMT}\), we are taking into account 57 earthquake events in the range \(4.2\leq\) M\({}_{\rm S,NEIC}\leq 6.1\), and the GOR1 relationship is shown below. \[\rm M_{wg,GCMT}=0.771(\pm 0.003)M_{S,NEIC}+1.193(\pm 0.126). \tag{2}\]  
\[\rm R_{xy}=0.94,\quad RMSE=0.092,\quad n=57\]  
The regression plots for the relationships between M\({}_{\rm S,NEIC}\), and M\({}_{\rm wg}\) are shown in Figure 5. We observed GOR1 methodology for conversion of M\({}_{\rm S,NEIC}\) towards M\({}_{\rm wg}\) shows significant improvement in terms of error of slope, intercept, RMSE and R\({}_{\rm xy}\) as compared to the other two methods (Tables 2 and 3 and Figure 6). \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline
**Regression** & **Magnitude** & **Slope** & **Intercept** & **Slope** & **Intercept** & **Slope** & **Intercept** & **R\({}_{\rm xy}\)** & **R\({}_{\rm xy}\)** & **R\({}_{\rm xy}\)** & **RMSE** & **RMSE** & **RMSE** \\
**Relation** & **Range** & **(GOR1)** & **(GOR1)** & **(GOR2)** & **(  
Figure 4: Comparison of the uncertainty in regression parameters for (M\({}_{\rm S,ISC}\)\(-\) M\({}_{\rm wg}\)) data pairs using GOR1, GOR2, and SLR approaches considering function of error variance ratio: (**a**) Correlation Coefficient determination (R\({}_{\rm xy}\)), (**b**) Root mean square error (RMSE), (**c**) uncertainty values of slope and (**d**) uncertainty of intercept. For changeover of \(\rm m_{b,ISC}\) to \(\rm M_{wg,GCMT}\) for magnitude range \(4.8\leq m_{b,ISC}\leq 6.1\), and \(\rm m_{b,NEC}\) to \(\rm M_{wg,GCMT}\) for magnitude range \(4.8\leq m_{b,NEC}\leq 6.1\), the same methodology has been adopted by datasets of 116 and 106 for the period 1964-2012, respectively. The GOR1 relationship between \(\rm M_{wg,GCMT}\), and \(\rm m_{b,ISC}\) is obtained using \(\eta=0.2\) and is given below. The regression plot is shown in Figure 7.  
\[\rm M_{wg,GCMT}=1.19(\pm 0.014)m_{b,ISC}-1.190(\pm 0.347). \tag{3}\]  
\[\mathrm{R_{xy}}=0.94,\quad\mathrm{RMSE}=0.094,\quad\mathrm{n}=93\]0  
\[\mathrm{R_{xy}}=0.94,\quad\mathrm{RMSE}=0.094,\quad\mathrm{n}=93\]1 Comparison of the uncertainty in regression parameters for (\(\rm M_{S,NEC}-M_{wg}\)) data pairs using GOR1, GOR2, and SLR approaches considering function of error variance ratio: (**a**) Correlation Coefficient determination (\(\rm R_{xy}\)), (**b**) Root mean square error (RMSE), (**c**) uncertainty values of slope and (**d**) uncertainty of intercept. \[\mathrm{R_{xy}}=0.94,\quad\mathrm{RMSE}=0.094,\quad\mathrm{n}=93\]2 The (\(\rm m_{b,ISC}-M_{wg}\)) data, as well as the GOR1, GOR2, and SLR regression lines.