# Methods for Underwater Gravity Measurement Error Compensations Based on Correlation Analysis
## 2 Materials and Methods  
The errors related to dynamics are mainly caused by changes in depth. A drastic change in depth will change the pitch angle of the carrier; the upward acceleration of the carrier will also fluctuate greatly, and the upward-specific force error will increase. The upward-specific force error can be expressed as follows [4]:  
\[\delta f=k\cdot f+\tau\cdot df+\
abla \tag{1}\]  
where \(\delta f\) is the upward-specific force error; \(k\) is the scale factor error; \(df\) is the derivative of the upward-specific force; \(\tau\) is the time delay coefficient; \(\
abla\) is Gaussian white noise. Therefore, errors related to dynamics mainly include the motion acceleration of the upward-specific force, the upward-specific force itself, the derivative of the upward-specific force, changes in the pitch angle, and depth changes (sky velocity). In order to suppress the influence of dynamics-related error terms on gravity measurement, it is necessary to model and compensate for each error term. The data flowchart of the error compensation method based on correlation analysis is shown in Figure 1. Firstly, the gravity-measurement results on the survey line are empirically mode decomposed to obtain a group of intrinsic mode functions and residual signals. Secondly, intrinsic mode functions that have no correlation with the gravity-measurement results, the upward-specific force, the upward-specific force derivative, the upward velocity, the upward acceleration, and the pitch angle change are removed; the remaining intrinsic mode functions and residual signals are then reconstructed. Thirdly, the difference between the reconstructed gravity-measurement result and its fitting curve is calculated. According to the least-squares fitting method, an error model is established between the difference and the upward-specific force, the upward-specific force derivative, the upward velocity, the upward acceleration, and the pitch angle change. Finally, the reconstructed gravity-measurement results are compensated according to the error model. The specific data-processing steps are summarized as follows:1. Obtain the depth curve of each survey line in the survey area, and calculate the standard deviation of the depth value of each survey line. The larger the standard deviation, the more drastic the depth change with respect to the survey line, and the worse the dynamics of the carrier on the survey line. Select the survey line with the largest standard deviation of the depth curve as the target survey line. 2. Calculate the upward-specific force, depth, pitch-angle change, and gravity measurement results of the gravimeter on the target survey line. The upward-specific force derivative is obtained by differentiating the upward-specific force, the upward velocity is obtained by differentiating the depth, and the upward acceleration is obtained by differentiating the upward velocity. The results of the gravity measurement, the upward-specific force, the derivative of the upward-specific force, the upward velocity, the upward acceleration, and the change in the pitch angle are taken as the influence factors. 3. Empirical mode decomposition (EMD) is performed on the gravity-measurement results of the target survey line to obtain a set of intrinsic mode functions from low frequency to high frequency and a residual signal. Correlation coefficient \(r\) is obtained by analyzing the correlation between intrinsic mode functions and gravity-measurement results, the upward-specific force, the derivative of the upward-specific force, the upward velocity, the upward acceleration, and the change in the pitch angle. When \(|r|\geq 0.7\), the correlation between the intrinsic mode functions and the influence factor is strong; when \(0.2\leq|r|<0.7\), the correlation between the intrinsic mode functions and the influence factor is weak; when \(|r|<0.2\), the correlation between the intrinsic mode functions and the influence factor is weak. 4.