利用引力梯度数据计算径向梯度的优化方法

摘要

This paper proposes an optimization method for computing the radial gravity gradient by using GOCE gradient measurements,based on the variance-covariance information of gradient observations.The approach for computing the gravity gradient and the error propagation are firstly discussed;and then by solving a conditional extremum problem,we can get an optimal combination factor which can improve the calculation accuracy for the radial gravity gradient.The advantage of the combination factor is validated by simulation data.In actual data processing,the geoid accuracy truncated to degree 250 can be improved by 2 cm by using the optimization method.The radial gravity gradient can not only be used in recovering a gravity field model,but also can be used in kinds of geophysical interpretation,so the method provided in the paper can be helpful in the related researches.%根据重力梯度观测各分量的方差及协方差信息，提出了利用 GOCE 梯度数据计算径向重力梯度的优化方法.首先给出了径向重力梯度的计算方法，并深入分析了误差传播规律，通过建立相应的条件极值问题，给出了计算径向重力梯度最优组合因子的方法；通过模拟数据验证了本文所提出的优化因子的优越性.实际数据计算表明：相对于传统方法，采用优化组合因子可使反演所得引力位模型的累积大地水准面精度在250阶时提高约2 cm.由于径向重力梯度不仅可以用于地球引力场模型的求解，也可直接应用于地球物理问题的讨论，因此本文所提出的优化方法也可对部分地球动力学问题的讨论提供方便.