## 2 Scale Factor Calibrated Using Different AG Values
#### 4.2.2 Correlation Analysis of GD Mutual Differences  
In practice, the accuracy of SF calibration can be analyzed from the mutual difference of the GD between two instruments. Normally, if the calibrated SF of two instruments is accurate, the mutual difference of the GD between each instrument pair will not increase with increase of the GD, that is, there is a weak correlation between GD and mutual difference of GD. Figure 7 shows the mutual difference of the GD of the two CG-5 relative gravimeters and the two LCR-G gravimeters in July 2020. As shown in Figure 7a, the range of the mutual difference between the two CG-5 instruments is constrained to within \(\pm\)30 uGal. Because the SF of this measurement period is the result of the long baseline calibration, the fitting line obtained using the MBGA method is just slightly better than that of the BGA method, and the slope of both fitting lines is broadly horizontal, i.e., the mutual differences do not increase notably with increase of the GD. In contrast, the range of the mutual difference between the LCR-G instruments is relatively small (Figure 7b), i.e., constrained to within \(\pm\)15 uGal. However, it is evident that there is significant correlation between the GD and the mutual difference of the GD when using the BGA method, but that the correlation is significantly weaker when using the MBGA method. The SFs calibrated using the MBGA method are improved obviously in the gravity segment with a GD of \(>\)100 mGal, in which the deviation of the mutual difference obtained using the BGA method and the MBGA method can reach 15 uGal, and the range of the mutual difference has decreased from \(\pm\)15 uGal to \(\pm\)10 uGal. However, for the segments with small GD, the optimization effects of the MBGA method are not obvious. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**AG Stations Applied in the Calibration**} & \multirow{2}{*}{**Gravity Interval of AGs (mGal)**} & \multicolumn{4}{c}{**Scale Factors**} \\ \cline{3-8}  & & \multicolumn{2}{c}{**BGA**} & \multicolumn{2}{c}{**MBGA**} \\ \cline{3-8}  & & **CG-169** & **CG-170** & \multicolumn{2}{c}{**Values of ABIC**} & \multicolumn{2}{c}{**CG-169**} & \multicolumn{2}{c}{**CG-170**} & \multicolumn{2}{c}{**Values of ABIC**} \\ \hline Case 1: All 10 stations & 403 & 1.000335 & 0.999987 & \(-\)7120 & 1.000147 & 0.999813 & \(-\)7209 \\ \hline Case 2: Lijiang, Kunming & \multirow{2}{*}{364} & \multirow{2}{*}{1.000335} & \multirow{2}{*}{0.999987} & \multirow{2}{*}{\(-\)7094} & \multirow{2}{*}{1.000146} & \multirow{2}{*}{0.999813} & \multirow{2}{*}{\(-\)7174} \\ \cline{1-1} Funing, Gengma, Ruili & & & & & & & \\ \hline Case 3: Lijiang, Funing & 302 & 1.000335 & 0.999987 & \(-\)7071 & 1.000122 & 0.999788 & \(-\)7142 \\ \hline Case 4: Lijiang, Gengma & 150 & 1.000335 & 0.999987 & \(-\)7067 & 1.000087 & 0.999754 & \(-\)7137 \\ \hline Case 5: Lijiang, Kunming & 56 & 1.000335 & 0.999987 & \(-\)7030 & 0.999881 & 0.999548 & \(-\)7106 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Scale factors and corresponding Akaike’s Bayesian information criterion (ABIC) values by using the modified Bayesian gravity adjustment (MBGA) method and the Bayesian gravity adjustment (BGA) method with different absolute gravity (AG) values. Similarly, we also analyzed the GD residuals obtained using the BGA method (Figure 4b,d,f,h) and the MBGA method (Figure 8). It can be seen that because the nonlinear drift characteristics of the instruments have been taken into account in both methods, the GD residuals of the two results all show nonrandom variation characteristics, i.e., the changes in GD with time are broadly independent of nonlinear drift rate variations. For some gravity segments, the results obtained using the MBGA method can decrease the GD residuals. Owing to the small improvement in the correlation between the GD and mutual differences of the GD of the CG-5 instruments when using the MBGA method, the reduction of the GD residuals is not significant.