# Methods for Underwater Gravity Measurement Error Compensations Based on Correlation Analysis
## 3 Results  
In order to test the performance and technical indices of the towing system and the underwater dynamic gravimetry system mounted on the towed body, our research group conducted an underwater gravimetry test in a deep-sea area of the South China Sea in 2019. The area is challenging and has a variety of topographic and geomorphic features. The water depth in the test area is about 2200 m, and underwater gravimeter performs gravity measurements at a depth of about 2000 m with an average speed of 2.5 knots. The round-trip measurement of the test line SHEW1 produced two repeated test lines SHEW1-1 and SHEw1-2, and the round-trip measurement of the test line SHEW2 also produced two repeated test lines SHEW2-1 and SHEW2-2. The experimental results show that the inner coincidence accuracy of SHEW1 is 1.06 mGal/180 m. The consistency accuracy of SHEW2 in two repeated lines is 1.15 mGal/180 m. For the detailed introduction of the experiment, please refer to [5]. The error analysis and compensation involved in this paper are carried out on the basis of gravity anomaly processing; for the specific processing process of gravity anomaly, please refer to [6], which will not be repeated in this paper. The statistical results of depth standard deviation along survey line SHEW1 and survey line SHEW2 are 12.8 m and 24.4 m, respectively. The depth curve of one east-west survey line SHEW2-2 and the gravity-measurement results after 300 s finite impulse response (FIR) low-pass filtering are shown in Figures 2 and 3, respectively. It can be seen from Figure 2 that there are two peaks in the depth curve of survey line SHEW2-2; these were caused by the project team continuously retracting and releasing the cable during the acquisition of survey line SHEW2-2 to prevent the towing body from being too close to the bottom. The drastic change in depth also leads to two spikes in gravity-measurement results; these are gravity-measurement errors caused by dynamics (Figure 3). Since the depth standard deviation of survey line SHEW2-2 is the largest and its dynamic property is the worst, it was used as the target survey line to fit the reconstructed gravity-measurement result curve, as shown in Figure 4.  
The parameters of each model in Formula (3) were estimated by the least-squares fitting method, and parameters of the fitting model are shown in Table 1.  
Since the fitting curves of gravity-measurement results of all survey lines in the survey area are primary curves, the reconstructed gravity-measurement results according to the error model are compensated according to Formula (4) to obtain the compensated gravity-measurement results. Figure 5 is a comparison diagram of gravity-measurement results (300 s low-pass filtering) before and after the compensation of repeated survey line SHEW2; Figure 6 shows gravity-measurement results (300 s low-pass filtering) before and after the compensation of the SHEW1-repeated survey line. \[ \begin{array}{l}\delta g_{compensate}=\delta g_{1}+0.05f-0.03\dot{v}+0.82 df-7.45\dot{e}-05 dp-1.96\dot{e}-04 dh-55.13\dot{f}^{2}-171.08\dot{v}^{2}\\ \qquad\qquad+2492.97 df^{2}-0.01 dp^{2}-1.76\dot{e}-04 dh^{2}+160.98f\dot{v}+2068.0 8 fdf-1.89 fdp\\ \qquad\qquad+0.72 fdh-2807.23\dot{v}df+3.78\dot{v}dp-1.07\dot{v}dh+24.52 dfdp-2. 70 dfdh+0.01 dydh\end{array}  \tag{4}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline \(k_{1}\) & \(0.05\) & \(k_{11}\) & \(160.98\) \\ \(k_{2}\) & \(-0.03\) & \(k_{12}\) & \(2068.08\) \\ \(k_{3}\) & \(0.82\) & \(k_{13}\) & \(-1.89\) \\ \(k_{4}\) & \(-7.45\times 10^{-5}\) & \(k_{14}\) & \(0.72\) \\ \(k_{5}\) & \(-1.96\times 10^{-4}\) & \(k_{15}\) & \(-2807.23\) \\ \(k_{6}\) & \(-55.13\) & \(k_{16}\) & \(3.78\) \\ \(k_{7}\) & \(-171.08\) & \(k_{17}\) & \(-1.07\) \\ \(k_{8}\) & \(2492.97\) & \(k_{18}\) & \(24.52\) \\ \(k_{9}\) & \(-0.01\) & \(k_{19}\) & \(-2.70\) \\ \(k_{10}\) & \(-1.76\times 10^{-4}\) & \(k_{20}\) & \(0.01\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Statistics of error fitting parameters.