重力异常向上延拓严密改化模型及向下延拓应用

重力异常向上延拓全球积分模型在航空重力测量数据质量评估和向下延拓迭代计算等领域具有广泛的应用。为了消除积分核函数奇异性影响，需要对该模型进行基于积分恒等式的移去-恢复转换及全球积分域的分区改化处理。在此过程中，传统改化处理方法往往忽略了全球积分过渡到局域积分引起的积分恒等式偏差影响，从而导致不必要的计算模型误差，最终影响向上延拓计算结果的可靠性，甚至影响向下延拓迭代解算结果的稳定性。针对此问题，本文开展了重力异常向上延拓积分模型改化及向下延拓应用分析研究，依据实测数据保障条件和积分恒等式适用条件要求，导出了重力异常向上延拓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，并将最终的严密改化模型应用于重力异常向下延拓迭代解算。使用超高阶地球位模型EGM2008作为标准位场开展数值计算检验，分别对重力异常向上延拓分步改化模型的计算精度及在向下延拓迭代解算中的应用效果进行了检核评估，验证了采用严密改化模型的必要性和有效性。

Rigorous modification model of upward continuation and its applications on the downward continuation of gravity anomaly

The global integral model of upward continuation for gravity anomaly is often used in the data quality assessment for airborne gravity measurement and the iterative solution of downward continuation.In order to eliminate the singularity of the integral kernel function,we have to make a remove-restore transformation to the integral model based on an equation of integral identity.And at the same time,the global integral domain has to be divided into two parts of near and far zones.During this processing,the deviation of identical formula caused by the transformation of integral domain from global to local integration is often ignored in the traditional modified method,which leads to unnecessary model errors and ultimately affects the reliability of upward continuation solution,and even affects the stability of iterative solution of downward continuation.In response to this problem,some analysis and research have been made on the integral model modification of upward continuation and its application of downward continuation for gravity anomaly in this paper.Based on the measured data situation and the applied condition of the integral identity,a set of step-by-step modified formulas of the upward continuation integral model are derived,and a correction formula is proposed to compensate the omission of the traditional modified model.Finally,the rigorous modified model is applied to the iterative solution of downward continuation for gravity anomaly.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 calculated accuracy of step-by-step modified models of the upward continuation and the applied effect in the iterative solution of downward continuation for gravity anomaly are estimated and evaluated separately.It proves the necessity and effectiveness of adopting the rigorous modified model.