# A Fast Method for Calculation of Marine Gravity Anomaly
## 3 Results
### Precision and Accuracy Test  
Figure 2(a) shows the geoid height undulation of the South China Sea. The global geoid height undulation is depicted in Figure 4. To obtain accurate marine gravity anomalies with high resolution, we chose the gridded data with \(2.5^{\prime}\times 2.5^{\prime}\) intervals of global geoid height  
Figure 2: The MATLAB code for the fast method of the ISF (inverse Stokes formula) method.  
undulation and the geoid height undulation of the South China Sea. The geoid height undulation in the sea was extracted from the gridded data in the South China Sea and used in the calculation. A total of 228,368 points of gravity anomaly needed to be calculated.  
The result from the proposed fast method is shown in Figure 5a. The values of the gravity anomalies increase from northwest to southeast as a whole. The gravity anomalies in the middle of the South China Sea extend along the NE or NEE direction, and those in the east and west strike along the NS direction. The gravity anomalies in the local area, whose values vary, show the characteristics of typical marine gravity anomalies, which are associated with continent-ocean transitional zones, spreading ocean ridges, etc.  
Figure 4: The global geoid height undulation.  
Figure 5: The marine gravity anomalies in the South China Sea calculated from (**a**) the proposed fast method; (**b**) the classical method.  
Figure 3: (**a**) The geoid height undulation of the South China Sea. (**b**) The geoid height undulation of the South China Sea and adjacent land.  
In GPU parallel computing technology, single-precision produces a result with low precision [26]. Although the result in Figure 5a was calculated in double precision to improve its precision, we still compared it with the result from the classical CPU method to estimate its precision. The result from the classical CPU method is shown in Figure 5b. Figure 5b is similar to Figure 5a, and they have the same trends and characteristics of gravity anomalies. Figure 6 shows the difference between the results in Figure 5a,b. The differences range from \(-6.47\times 10^{-11}\) to \(7.83\times 10^{-11}\) mGal, the mean value is \(-3.77\times 10^{-15}\) mGal, and the RMS (root mean square) is \(2.78\times 10^{-12}\) mGal. Therefore, the precision of the result in Figure 5a is high.  
The comparison with the classical CPU method showed that the proposed fast method can calculate the gravity anomalies with high precision, similar to the classical CPU method, but cannot show the accuracy of the result in Figure 5a. A comparison with marine shipboard gravity data can show the accuracy of the result in Figure 5a. Therefore, we collected marine shipboard gravity data. The result in Figure 5a was compared with shipboard gravity data, and Figure 7 shows the spatial distribution of the difference between the result in Figure 5a and the collected marine shipboard gravity data. At the same time, we recorded the statistical parameters of their differences in Table 1, which were satisfying and demonstrated that the result in Figure 5a is highly accurate.  
Figure 6: The difference between the results in Figure 5a,b.  
Figure 7: The spatial distribution of the difference between the result in Figure 5a and the collected marine shipboard gravity data.