## 3 Methods of Modified Bayesian Gravity Adjustment (MBGA)  
Generally, more than two relative gravimeters are used in a gravity survey campaign that will contain redundant observations. To resolve this problem, the CLS method adopts the least squares method to establish an adjustment model in which the drift rate is considered linear. However, in an actual field gravity campaign, drift rate always shows nonlinear characteristics that reflect the duration of the survey period and the complexity of the geological structures, especially for CG-5 relative gravimeters. Moreover, the practical solution to the problem is attributed to an overdetermined system of equations, which leads to a nonunique solution. In this study, on the basis of BGA method [36], the modified Bayesian gravity network adjustment optimization model (MBGA) [45] was applied, in which the ABIC criterion was adopted to optimize the solutions, and it was assumed that the effects of ocean tides and pole shift were removed before the adjustment. Additionally, gravity changes caused by crustal deformation and precipitation were not considered during the same observation period. Assuming that the observation error, absolute gravity error, and drift error of the gravimeter \(p\) obey the normal distribution, then:  
\[A_{p}\widetilde{x}+D_{p}\widetilde{v}_{p}-\widetilde{y}_{p}\ \sim Normal(0,\ W_{p}^{-1}) \tag{1}\]  
\[G\widetilde{x}-\widetilde{g}\ \sim Normal(0,W_{g}^{-1}) \tag{2}\]  
\[B_{p}\widetilde{v}_{p}\ \sim Normal(0,W_{b,p}^{-1}) \tag{3}\]  
Equations (1) and (2) are the assumption used by the least-squares criterion [48] which are the observation equation for relative measurements and observation equation for absolute measuremts, respectively. Equation (3) is the calculation model of nonlinear drift which added in the BGA method, in which the drift rate of the relative gravimeter is assumed temporally smoothed. Here, \(A_{p}\), \(D_{p}\), \(G\), and \(B_{p}\) are the observation order matrix of GD, observation time matrix of GD, absolute point matrix, and second-order smoothing operator, respectively. Similarly, \(\widetilde{x}\), \(\widetilde{y}_{p}\), \(\widetilde{v}_{p}\), \(\widetilde{\delta}\) represent the gravity values at all stations, vector of the observed GD values, drift rate of all the gravimeters, and the observed AG values, respectively. In the above, \(Normal(. )\) represents the normal distribution with a mean value of 0 and variance of \(W^{-1}\), and the weight matrix is expressed as: \(W_{p}=diag\Big{(}\sigma_{p}^{-2},\sigma_{p}^{-2},\cdots,\sigma_{p}^{-2}\Big{)}\), \(W_{g}=diag\Big{(}\sigma_{g}^{-2},\sigma_{g}^{-2},\cdots,\sigma_{g}^{-2}\Big{)}\), where \(\delta_{p}^{2}\), and \(\delta_{g}^{2}\) represent the observed noise variance and absolute gravity variance, respectively. \(W\) and \(W_{b}\) are regarded as the weights of the relative gravity observations and weights of the drift rate variations, respectively [45]. In Equation (1), GD of gravimeter \(p\) can be represented as:  
\[\widetilde{y}_{p}=\Delta y_{p}l_{p}-\Delta T_{p}\alpha-\Delta P_{p}\beta \tag{4}\]  
where \(\Delta y_{p}\) is the gravity reading data of GD, \(l_{p}\) is the SF of gravimeter \(p\), \(\Delta T_{p}\) is the theoretical Earth tide, \(\alpha\) is the earth tide factor, \(\Delta P_{p}\) is the gravitational load difference of atmospheric pressure, and \(\beta\) is the pressure admittance coefficient, respectively. In the process of gravity adjustment, the Earth tide factor [49] and pressure admittance coefficient [38; 50] were considered as approximations of 1.16 and \(-0.3\)\(\mu\)Gal/hPa, respectively. Here, the \(l_{p}\) is considered as a constant in the BGA method, while it is introduced as a new hyperparameter to be estimated in the MBGA method, together with the two hyperparameters (observed noise variance and drift rate variance). Equations (1)-(3) can be combined as the full Bayesian modal for the adjustment:  
\[SX-Y\sim Normal(0,\widetilde{W}^{-1}) \tag{5}\]Here,  
\[S=\left[ \begin{array}{cc}A&D\\ G&0\\ 0&B\end{array} \right],X=\left[