针对海量卫星重力数据反演高阶次地球重力场模型的密集型计算任务与高内存耗用问题,基于MPI实现了最小二乘直接法恢复高阶次位系数的并行算法。引入并行读写、分块存储与分块计算等方式完成了设计矩阵的构建、法方程的形成与求解等密集型计算任务的并行算法,数值计算结果表明三者的并行相对效率峰值可分别达到95%、68%、63%。利用GOCE轨道跟踪和径向扰动重力梯度数据(共518 400个历元)分别反演了120、240阶次地球重力场模型,计算时间仅为40 min、7 h,内存耗用峰值仅为290 MB、1.57 GB;采用与GOCE同等噪声水平的观测数据恢复的重力场模型精度与GOCE已发布模型的解算精度相一致,联合GRACE和GOCE的解算模型能够实现二者独立信息的频谱互补,表明本文方法可高效稳定地恢复高阶次地球重力场模型。
In order to solve the intensive computing tasks and high memory demand problem in satellite gravity field model inversion on the basis of huge amounts of satellite gravity observations, the parallel algorithm for high truncated order and degree satellite gravity field model inversion with least square method on the basis of MPI was introduced. After analyzing the time and space complexity of each step in the solving flow, the parallel I/O, block-organized storage and block-organized computation algorithm on the basis of MPI are introduced to design the parallel algorithm for building design matrix, establishing and solving normal equation, and the simulation results indicate that the parallel efficiency of building design matrix, establishing and solving normal equation can reach to 95%, 68%and 63% respectively. In addition, on the basis of GOCE simulated orbits and radial disturbance gravity gradient data(518 400 epochs in total), two earth gravity models truncated to degree and order 120, 240 are inversed, and the relative computation time and memory demand are only about 40 minutes and 7 hours, 290 MB and 1.57 GB respectively. Eventually, a simulation numerical calculation for earth gravity field model inversion with the simulation data, which has the equivalent noise level with GRACE and GOCE mission, is conducted. The accuracy of inversion model has a good consistent with current released model, and the combined mode can complement the spectral information of each individual mission, which indicates that the parallel algorithm in this paper can be applied to inverse the high truncated degree and order earth gravity model efficiently and stably.
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