重力异常垂向梯度严密改化模型及应用

A rigorous modification model and its application for computing the vertical gradient of gravity anomaly

积分奇异性和数值不连续性是改化重力异常垂向梯度全球积分模型面临的两大主要难题.本文研究并指出了积分模型传统改化方法存在的理论缺陷,同时依据实测数据保障条件,联合采用积分恒等式转换和移去恢复运算技术,分别推出了计算地球外部及地面重力异常垂向梯度全球积分模型的分步改化公式,提出了补偿传统改化模型理论缺陷的修正公式.以超高阶地球位模型EGM2008作为数值试验标准场,分别开展改化模型精度比对分析和向下延拓应用效能评估试验,从不同侧面验证了采用严密改化模型的必要性和有效性.

Integral singularity and numerical discontinuity are two major problems in the modification model for computing the vertical gradient of gravity anomaly.We study the method of model modification and point out the theoretical flaws of the traditional modification method.Then a comprehensive remove-restore transformation to the integral model is suggested based on an equation of integral identity,and a set of step-by-step modification formulae of the global integration model for computing the vertical gradient of gravity anomaly are derived according to the measured data conditions.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 and their application effect to downward continuation are analyzed and evaluated.It is shown from different aspect that adopting the rigorous modified model is necessary and effective.