## 2 Scale Factor Calibrated Using Different AG Values
### Cross-Validation by Using Absolute Gravity (AG) Values  
Many factors can affect the drift rate of gravimeters, such as spring age, temperature inside the instrument, and transportation; therefore, using repeated observations is a practical approach when estimating the drift rate [34]. Additionally, the correlation between the mutual differences and the GD of segments can be seen as an indicator of whether the SFs of two pairs of instruments used simultaneously are preliminarily in accord. However, when the optimization of the mutual difference is not obvious, although the deviation of the SFs might exceed 150 ppm, the deviation is almost synchronous, which is not sufficient to evaluate the reliability of the SFs calibrated on the basis of the mutual differences of the GD. Therefore, high-precision AG values obtained quasi-synchronously by independent absolute gravimetry in the survey network were adopted to further verify the accuracy of the SFs and to revisit the drift rate of the gravimeters. The cross-validation method used some AG values for the gravity adjustment, while the remainder were used as validation points. Then, the calculated AG values were compared with the corresponding values obtained from the actual absolute observations to evaluate the quality of the adjustment results. The survey data of July 2020 were analyzed and the gravity deviations of the AG values were calculated separately using the CLS, BGA, and MBGA methods. As shown in Figure 10, it clearly show that the deviation of the AG values calculated using the MBGA method are smaller than those derived using either the CLS method or the BGA method. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{3}{*}{
\begin{tabular}{c} **Date of** \\ **Survey** \\ **Campaign** \\ \end{tabular} } & \multicolumn{4}{c}{**CG-169**} & \multicolumn{2}{c}{**CG-170**} & \multicolumn{2}{c}{**LCR-149**} & \multicolumn{2}{c}{**LCR-150**} \\ \cline{2-9}  & **Optimized (MBGA)** & **Difference (ppm)** & **Optimized (MBGA)** & **Difference (ppm)** & **Optimized (MBGA)** & **Difference (ppm)** & **Optimized (MBGA)** & **Difference (ppm)** \\ \hline March 2018 & 0.999956 & 297 & 0.999752 & 314 & 1.000047 & 51 & 0.988529 & 51 \\ \hline July 2018 & 0.999991 & 301 & 0.999738 & 328 & 0.999917 & 113 & 0.988404 & 109 \\ \hline March 2019 & 1.000126 & 37 & 0.999899 & 29 & 0.999959 & 62 & 0.988443 & 36 \\ \hline July 2019 & 1.000097 & 55 & 0.999835 & 29 & 0.999902 & 43 & 0.988383 & 31 \\ \hline March 2020 & 1.000094 & 139 & 0.999829 & 121 & 1.000060 & 14 & 0.989273 & 44 \\ \hline July 2020 & 1.000147 & 188 & 0.999813 & 174 & 0.999894 & 97 & 0.989136 & 92 \\ \hline Average & & 169 & 166 & & 63 & 60 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Differences in scale factors obtained using the MBGA and BGA methods. Figure 9: Variations of original scale factors obtained using the BGA method and optimized scale factors obtained from the MBGA method for the different relative gravimeters: (**a–d**) represent CG-169, CG-170, LCR-149, and LCR-150 respectively. Blue dots represent the original SF, and red dots indicate optimized SF of MBGA. For the case in which the AG stations of Kunming and Ya'an are introduced as the control stations participating in the adjustment (Figure 10a), and from the results of the CLS method, most deviations are no greater than 60 \(\upmu\)Gal, except for the stations of Ya'an, Songpan, Wanzhou, and Luzhou, which might reflect substantial influence by nonlinear drift, and there is no significant difference between the results of the BGA and MBGA methods when testing smaller numbers of starting AG stations.