顾及地形效应的重力向下延拓模型分析与检验

向下延拓是航空重力测量数据实际应用中必不可少的技术环节。向下延拓属于不适定反问题,其解算过程具有较大的不确定性,故该问题一直是大地测量领域国内外学者的研究热点。本文深入分析研究了当前国内外最具代表性的3种向下延拓计算模型的技术特点和适用条件,提出了应用超高阶位模型、局部地形改正和移去—恢复技术顾及地形效应,以及位场延拓结果球面化曲面的工程化方法,重点探讨了计算模型的稳定性及数据观测误差对延拓计算结果的影响。通过理论分析、数值仿真和实测数据计算等手段,定量评估了不同向下延拓模型的解算精度及其可靠性。其主要结论是:传统逆Poisson积分模型解严重受制于输入数据观测噪声的干扰,在现有作业条件下,该模型至多只能用于1km以下高度的延拓解算;频谱截断积分和位模型加地改两种延拓新模型具有良好的计算稳定性,完全适用于2′分辨率和5km飞行高度条件下的航空重力测量数据向下延拓解算,其延拓计算精度可达2×10~(-5) m/s~2,可满足各方面实际应用需求。

Test and Analysis of Downward Continuation Models for Airborne Gravity Data with Regard to the Effect of Topographic Height

Downward continuation is an essential technical step of data processing in airborne gravimetry for further applications.It is known that the solution of downward continuation is uncertain due to its ill-posedness.So it has been a topic of general interest for many scholars at home and abroad in geodesy.The main purpose of this paper is to give 3 representative models for downward continuation including traditional inverse Poisson integration and two modern methods,and make a comprehensive comparison and analysis on their property and applicability among the different models.Ultra-high-degree geopotential model,local topographic correction and remove-restore technique are suggested to be used for regard to the effect of topographic height,and for the realization of downward continuation combining with a transformation from spherical to undulating surface.We pay our attention to the influence of surveyed data errors on the stability of downward continuation solutions.Theoretical analysis,simulated data and real numerical computations are carried out to evaluate the stability and accuracy of downward continuation models.And some useful conclusions are obtained.Under existing working conditions,the traditional inverse Poisson integration method can only be used to the continuation computation under 1 km due to the serious disturbing of surveying noise.Excellent computation stability can be achieved by using the band-limited spectrum and the geopotential model plus topographic correction methods.The two new models can be used to the downward continuation of airborne gravity data on 5 km height and 2′data resolution.And the accuracy of corresponding continuation solutions can be reach 2 × 10-5 m/s2.It can meet the requirements from different applications.