地球外部扰动重力严密改化模型及分析检验

直接积分模型是计算地球外部扰动重力的主要数学工具，将全球积分模型改化为局域积分模型是实现地球外部重力场赋值的前提条件.相比表层积分模型和向上延拓积分模型，Stokes积分模型要求的输入信息种类最少，故在减轻数据保障压力方面具有比较明显的优势.在实施Stokes积分模型工程化应用过程中，我们发现扰动重力径向分量积分模型从地球外部逼近边界面时存在比较严重的数值不连续性问题，本文研究并指出了存在该问题的内在原因，同时提出了保持该模型连续性的修正方法；针对三分量计算模型存在的积分奇异性问题和传统改化方法存在的理论缺陷，提出综合采用移去恢复运算和积分恒等式转换技术，同时依据实测数据保障条件，分步实施扰动重力三分量全球积分模型改化的技术流程和方法，推出了三分量积分模型的分步改化公式，提出了补偿传统改化模型缺陷的修正公式.以超高阶地球位模型EGM2008作为检核参考位场，开展模型对比计算数值试验，分别对本文推出的扰动重力三分量不同阶段改化模型的计算精度进行了分析检验和评估，验证了采用严密改化模型的必要性和有效性.

Analysis and test on the rigorous modification models for computing the external disturbance gravity

Direct integral model is a major mathematical tool for calculating the disturbance gravity outside the earth.It is a prerequisite for realizing the computation of external gravity field to transform a global integral model to a local integral model.Compared with the surface layer integral model and the upward continuation integral model,the Stokes integral model requires the least types of input information,so it has obvious advantages in meeting the requirements of gravity data.When realizing the engineering application of the Stokes integral model,we find that there exists a serious discontinuity in the integral model for computing the radial component of disturbance gravity from the external space to the boundary surface.We analyze and point out the reason for the discontinuity of the model on the boundary surface,and propose a correction method to maintain its continuity.In view of the integral singularity problem of the three-component calculation models and the theoretical flaws of the traditional modification method,we suggest a comprehensive remove-restore transformation to the integral model based on an equation of integral identity,and a step-by-step modification process to the global integration models for the three-component disturbance gravity according to the measured data conditions.Then a set of step-by-step modification formulae of the three-component integration models are derived,and a corrected formula to compensate the omission of the traditional modification model is proposed.The ultra-high-degree geopotential model EGM2008 is used as a standard potential field to carry out a set of numerical calculation test,and the calculation accuracy of step-by-step modified models of the three-component disturbance gravity is estimated and evaluated.It is shown that adopting the rigorous modified model is necessary and effective.