# A Fast Method for Calculation of Marine Gravity Anomaly
## 1 Introduction  
With the gradual deepening of global exploration, the ocean, which covers about 70% of the Earth [1], has become a key study area for future resource detection [2]. When studying specific marine areas, large amounts of basic data are usually required due to their wide range. However, collecting gravity data over an extensive marine area is expensive and inefficient. After decades of development, resolving gravity anomalies from the satellite altimetry data has gradually become the mainstream approach for obtaining marine gravity anomalies [3; 4; 5; 6]. For this method, the satellite altimetry data are processed to obtain the sea surface height [3; 7; 8]. The geoid height undulation can be calculated by subtracting the mean sea height from the obtained sea surface height. Then, the marine gravity anomalies can be inverted from the geoid height undulation. In the literature, the main methods for transforming the geoid height undulation to marine gravity anomalies are: the least squares collocation (LSC) method [9; 10], the inverse Stokes formula method (ISF) [11; 12], the inverse Hotine formula (IHF) method [13], and the inverse Vening Meinesz formula (IVMF) method [14; 15]. The LSC method is a statistical method that involves the calculation of the matrix inversion of corresponding covariance functions and covariance matrices. The sizes of the covariance matrices are related to the numbers of the predicted marine gravity anomalies and the given geoid height undulation. For the calculation of large-scale marine gravity anomalies, the LSC generates large covariance matrices, which leads to the problem of large matrix inversion. Therefore, the LSC method is time-consuming when calculating large-scale marine gravity anomalies. The other three methods all belong to integral equation methods. For the implementation of these methods, both study areasand the integral areas should be divided into many smaller grids. All the divided grids should be involved in the calculation process, which is time-consuming. The singularity problem exists in these three methods. The judgment statements should be used to solve the singularity problem in the calculation, which further increases the computing time. To accelerate the calculation of marine gravity anomalies, many scholars have employed the fast Fourier transform (FFT) technique into the calculation: [PERSON] et al. [16] studied marine gravity anomalies from satellite altimetry using the ISF method in the spectral domain via the FFT technique; [PERSON] and [PERSON] [13] used the IHF method with the FFT technique to determine marine gravity in the Labrador Sea region; [PERSON] and [PERSON] [17] computed marine gravity in the Labrador Sea area using the IHF method with the FFT technique; [PERSON] and [PERSON] [4] applied the FFT technique into the LSC method to determine the global marine gravity field; [PERSON] [14] implemented the IVMF method using the FFT technique to compute the gravity anomalies over the South China Sea. The FFT technique is sensitive to noise, which would amplify high-frequency errors [4; 18]. Therefore, it is necessary to filter the results of the FFT technique. However, the filtering process would remove useful information from the results calculated by the FFT technique. Besides, sometimes, the FFT technique would produce unstable gravity anomalies. To address the time-consuming geosciences problems, the graphics processing unit (GPU) provides a feasible solution. For example, [PERSON] et al. [19] used GPU parallel computing and the CUDA platform to present a parallel program, GICUDA, a rapid inversion of large-scale gravity and gravity gradiometry data; [PERSON] et al. [20] introduced a fast forward calculation method of gravity, which was further accelerated using GPU. Based on the platform of GPU, [PERSON] et al. [21] proposed a fast inversion of gravity interface. [PERSON] and [PERSON] [22] used a GPU in CUDA to implement prestack Kirchhoff time migration, and so on [23; 24].