# Influence of Sea Level Anomaly on Underwater Gravity Gradient Measurements
## 5 Experimental Results and Analysis  
When the relative error is less than 1%, 24, 68, and 108 m can be taken as the side lengths of the integration area to calculate the disturbing gravity gradient at 10, 30, and 50 m below the mean sea level, respectively. Since the average grid side length of the sea level anomaly data is about 20 km, which is significantly larger than the side length of the integration area, the gravity gradient value of each grid is only calculated from the mass anomaly in the central area of the grid, i.e., only one prism is calculated at each grid. Only the three components of \(\Gamma_{xx}\), \(\Gamma_{yy}\), and \(\Gamma_{zz}\) are calculated and analyzed below since the \(\Gamma_{xy}\), \(\Gamma_{zz}\), and \(\Gamma_{yz}\) of a single prism on the vertical line where the midpoint is located are zero [19]. Figure 8 shows that the sum of \(\Gamma_{xx}\), \(\Gamma_{yy}\), and \(\Gamma_{zz}\) is close to zero, satisfying the Laplace equation, and thus, the calculation process can be considered to be correct. The chart shows that the sea level anomaly considerably impacts the disturbing gravity gradient value at 10 m below the mean sea level, up to 16 E, and the difference between the disturbing gravity gradient at different locations can reach 22 E. At 30 and 50 m below the mean sea level, the spatial distribution of \(\Gamma_{xx}\), \(\Gamma_{yy}\), and \(\Gamma_{zz}\) is similar to the distribution at 10 m below the mean sea level, but the magnitude is lower; thus, only the statistics of the calculation results are listed. Table 5 shows that the disturbing gravity gradient caused by the sea level anomaly significantly decreases with increasing depth. The vertical disturbing gravity gradient can still reach 3 E at 50 m below the mean sea level, and the maximum difference of the disturbing gravity gradient at different locations can reach 4 E. Therefore, based on the measurement accuracy of the gravity gradiometer 1 E [20; 21; 22; 23; 24; 25], the local sea level anomaly will considerably affect the underwater gravity gradient measurements at the depth of 50 m below the mean sea level. The above results show that in addition to the spatial differences, the sea level anomalies will change with time. The annual range of the sea level anomalies in this area (Figure 9) is used to forward calculate the disturbing gravity gradient. The maximum and minimum values of the sea level anomaly are used as the upper and lower surfaces of the prism, respectively. The calculation process is the same as above. We obtain the change value of the disturbing gravity gradient caused by sea level anomaly within one year (Figure 10). Figure 10 and Table 6 show that if the carrier measured the gravity gradient for one year in 2020 at 10 m below the mean sea level in the study area, the variation of the vertical disturbing gravity gradient caused by the sea level anomaly variation with time could reach a maximum of 24 E and minimum of 3 E, and the variation of the horizontal disturbing \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Side Length of** **Integration Area (m)**} & \multicolumn{2}{c}{**Vertical Gravity Gradient at 50 m below Mean Sea Level (E)**} \\ \cline{2-4}  & **Position A** & **Position B** & **Position C** \\ \hline
84 & 2.966 & \(-\)1.194 & 1.242 \\
88 & 3.045 & \(-\)1.224 & 1.275 \\
92 & 3.113 & \(-\)1.251 & 1.303 \\
96 & 3.172 & \(-\)1.273 & 1.327 \\
100 & 3.220 & \(-\)1.292 & 1.347 \\
104 & 3.262 & \(-\)1.307 & 1.364 \\
**108** & **3.295** & **\(-\)1.319** & **1.377** \\
112 & 3.320 & \(-\)1.328 & 1.387 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Variation of gradient with integration range at 50 m below mean sea level.