虚拟压缩恢复法应用于航空重力向下延拓的适用性问题

Applicability of Fictitious Compress Recovery Method for Downward Continuation of Airborne Gravity Data

为了求解不规则边界面的大地测量边值问题,我国学者提出了虚拟压缩恢复法,并尝试将其应用于航空重力测量数据的向下延拓解算。在对虚拟压缩恢复法进行模型化分析基础上,从理论上证明了在求解地球内部Bjerhammar球上的虚拟重力异常时,虚拟压缩恢复法与基于逆Poisson积分的逐步迭代解是完全等价的,利用数值计算验证了两种解算结果的一致性,同时通过数值仿真计算,分析探讨了数据观测噪声对虚拟压缩恢复法解算结果的影响。检验结果表明,虚拟压缩恢复法应用于航空重力向下延拓计算,一方面可能增加边缘效应的影响,另一方面同样存在数据误差累积放大问题,因此其适用性有待做进一步的研究。

In order to solve the geodetic boundary value problems with an irregular boundary surface, the scholars of our country have put forward a new approach called fictitious compress recovery method for determining the Earth＇ s external gravity field.And they have tried to expand the application of the new method for the downward continuation of airborne gravity data. In this paper, based on the model analysis of fictitious compress recovery method, it is theoretically proved that the solution of fictitious compress recovery method is equal to that of inverse Poisson integration when fictitious gravity anomalies on the Bjerhammar sphere completely included in the Earth are solved.And it is shown with numerical tests that the computational results from above two models are coincident with each other. The influence of surveyed data errors on the solution of fictitious compress recovery method is analyzed and tested through simulated data.The conclusions are：when the fictitious compress recovery method is used to the downward continuation of airborne gravity data, more edge effects will be added to the downward continuation results, and there still exists an uncertainty in the solution of downward continuation due to its ill-posedness. So the applicability of fictitious compress recovery method for downward continuation of airborne gravity data is needed to be studied in the future.