# A Fast Method for Calculation of Marine Gravity Anomaly
## 3 Results
### Efficiency Test  
We compared the performance of the proposed fast method with the classical method through five tests to demonstrate the efficiency of the proposed fast method. In these tests, for convenience, we used the geoid height undulation of the South China Sea and adjacent land (Figure 3b) to implement tests and did not directly extract the geoid height undulation in the sea. The global geoid height undulation was divided into different grid intervals in each test. The geoid height undulation of the South China Sea and adjacent land was divided into the same grid intervals as the global geoid height undulation in each test. The grid parameters used in each test are displayed in Table 2. Three methods were used in every test: (1) the classical method with one CPU core, (2) the classical method with four CPU cores, and (3) the proposed fast method. In each test, each method was executed five times to obtain the corresponding average elapsed time.  
Table 3 shows the elapsed time comparison of these methods. With the increase in the numbers of calculation points and integration points, the elapsed time of every method increases. The proposed method is faster than the other two methods in all tests. Table 3 also shows the speedup ratio of the proposed fast method. Speedup ratio 1 (defined as the ratio of the elapsed time of the classical method with one CPU core to the proposed fast method) increases with the increase in the numbers of calculation points and integration points and eventually reaches 40.532074 in test 5. However, speedup ratio 2 (defined as the ratio of the elapsed time of the classical method with four CPU cores to the proposed fast method) reaches the maximum value in test 1, whose grid size is the smallest in all tests. The reason for this finding is that in test 1, the process of data allocation costs more time than the calculation process. In other tests, the calculation process is the main part, and the time required for the process of data allocation can be neglected. Therefore, speedup ratio 2 decreases in test 2 and 3 and increases in test 4 and 5.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Minimum** & **Maximum** & **Mean** & **Standard Deviation** \\ \hline \(-15.422\) mGal & 25.376 mGal & 3.990 mGal & 9.753 mGal \\ \hline \hline \end{tabular}
\end{table}
Table 1: The difference between the result in Figure 5a and the collected marine shipboard gravity data.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Test No.** & **Grid Size of the Global** & **Grid Intervals of the** & **Grid Size of Geoid** & **Grid Intervals of Geoid** \\
**Geoid Height Undulation** & **Global Geoid Height** & **Height Undulation of the** & **Height Undulation of the** \\
**1** & 360 \(\times\) 180 & 1\({}^{\circ}\times\) 1\({}^{\circ}\) & 25 \(\times\) 25 & 1\({}^{\circ}\times\) 1\({}^{\circ}\) \\
**2** & 720 \(\times\) 360 & 0.5\({}^{\circ}\times\) 0.5\({}^{\circ}\) & 50 \(\times\) 50 & 0.5\({}^{\circ}\times\) 0.5\({}^{\circ}\) \\
**3** & 1440 \(From these tests, we concluded that the proposed fast method could reduce the elapsed time to achieve the purpose of acceleration.