基于斯托克斯平面近似函数与GPU并行的海洋重力梯度模型计算

相对于其他重力场元素，扰动重力梯度能更多地反映变化的不规则地球产生的高频信息。在计算扰动重力梯度时，由于斯托克斯积分较为复杂导致被积函数复杂难以直接用牛顿-莱布尼茨公式计算、且计算的数据量过于庞大导致计算耗时过长。为有效解决该问题，文章使用高斯数值积分解决被积函数复杂的问题，同时利用统一计算设备架构(compute unified device architecture,CUDA)在计算过程中实现了在图形处理器 graphics processing unit,GPU)端的并行计算，根据拉普拉斯方程可以检验计算结果的准确性，并且选取了某海域$3^{\circ}\times 2^{\circ}$ 范围海平面的重力异常数据进行计算。结果表明，使用高斯数值积分以及CUDA并行计算的方法，提供准确计算结果的同时也提高了计算效率。

Compared to other gravitational field elements, the disturbing gravity gradients can reflect more high-frequency information produced by changing irregular Earth. When calculating the disturbing gravity gradient, due to the complexity of the Stokes integral, the integrand is complex, making it difficult to directly apply Newton-Leibniz formula, and the excessive data makes the computation too time-consuming. In order to effectively solve this problem, this paper uses the Gaussian numerical integration method to calculate the disturbing gravity gradient, and uses the compute unified device architecture(CUDA) to realize parallel computing on the graphics processing unit(GPU) side during the calculation process. According to the Laplace’s equation, the accuracy of the calculation results can be verified. This paper selects the gravity anomaly data of sea level within$3^{\circ} \times 2^{\circ}$ of a certain sea area for calculation, and the results show that the Gaussian numerical integration and CUDA parallel computing method can provide accurate calculation results and improve the computational efficiency.