异构并行算法快速构建全球扰动重力梯度全张量图

Fast Constructing Full Tensor Maps of Global Disturbing Gravity Gradient Using Heterogeneous Parallel Algorithm

扰动重力梯度是扰动重力位的二阶导数,相对于其他重力场元素能更多地反映变化的不规则地球产生的高频信息。在使用高阶次球谐系数模型获取大范围高分辨率的扰动重力梯度数据时,存在重复运算多、计算效率低下、耗时较长的问题。针对该问题,推导了简化计算公式,将中间变量提取出来作为全局参数和局部参数单独进行计算、存储,从而有效减少重复运算;并在简化公式的基础上,提出了扰动重力梯度张量快速异构并行算法,利用CUDA(compute unified device architecture)实现了梯度全张量在GPU端的并行计算。根据T_(xx)、T_(yy)、T_(zz)三个分量满足Laplace条件验证了算法可靠性,并与传统串行算法进行了计算效率对比,实验结果表明,相较于串行算法,所提算法可减少90%以上计算耗时,可将计算效率提高60倍以上。最后利用该算法基于2 190阶EIGEN-6C4模型快速构建了5′×5′分辨率的全球扰动重力梯度全张量图,计算结果显示了扰动重力梯度同地形、地球质量分布变化的相关性及其在全球范围内的数值特征。

Disturbing gravity gradient is the second derivative of disturbing potential,containing more high-frequency information of the changing and irregular earth gravity field with respect to other sort of gravity data.Using high-order spherical harmonic coefficient model to obtain large-scale and high-resolution disturbing gravity gradient data is time-consuming and inefficient caused by repetitive computation.To solve this problem,a simplified method was proposed which computed and saved some intermediate variables that can be converted into global and local parameters separately.Based on this method,a fast heterogeneous parallel algorithm for calculating disturbing gravity gradient tensors was proposed.The parallel calculation of gradient tensor on GPU was realized by CUDA(compute unified device architecture),and by using this algorithm,a full tensor map of the global disturbing gravity gradient with 5′×5′ resolution was quickly constructed based on the 2 190-order EIGEN-6 C4 model,which shows the numerical characteristics of the disturbing gravity gradient on a global scale and its correlation with changes in topography and Earth’s mass distribution.The reliability of this algorithm was validated by checking whether the calculated T_(xx),T_(yy) and T_(zz) met the Laplace constrain,and the computational efficiency was compared with the traditional serial algorithm.The experimental result shows that using this algorithm can reduce time consumption by 90% and increase computational efficiency by 60 times.