A data-driven approach to local gravity field modelling using spherical radial basis functions

We propose a methodology for local gravity field modelling from gravity data using spherical radial basis functions. The methodology comprises two steps: in step 1, gravity data (gravity anomalies and/or gravity disturbances) are used to estimate the disturbing potential using least-squares techniques. The latter is represented as a linear combination of spherical radial basis functions (SRBFs). A data-adaptive strategy is used to select the optimal number, location, and depths of the SRBFs using generalized cross validation. Variance component estimation is used to determine the optimal regularization parameter and to properly weight the different data sets. In the second step, the gravimetric height anomalies are combined with observed differences between global positioning system (GPS) ellipsoidal heights and normal heights. The data combination is written as the solution of a Cauchy boundary-value problem for the Laplace equation. This allows removal of the non-uniqueness of the problem of local gravity field modelling from terrestrial gravity data. At the same time, existing systematic distortions in the gravimetric and geometric height anomalies are also absorbed into the combination. The approach is used to compute a height reference surface for the Netherlands. The solution is compared with NLGEO2004, the official Dutch height reference surface, which has been computed using the same data but a Stokes-based approach with kernel modification and a geometric six-parameter “corrector surface” to fit the gravimetric solution to the GPS-levelling points. A direct comparison of both height reference surfaces shows an RMS difference of 0.6 cm; the maximum difference is 2.1 cm. A test at independent GPS-levelling control points, confirms that our solution is in no way inferior to NLGEO2004.     

基于庄河市空间大地全面控制网谈似大地水准面的确定及精度分析

介绍了通过布设足够密度且分布均匀的GPS水准联测点,建立庄河市辖区4086 km2的高精度、高分辨率的似大地水准面数学模型的原理和方法.     

精化区域似大地水准面技术方法与设计

2003年至2006年国家测绘局与地方测绘部门合作,在华东、华中、华北15个省、市开展区域似大地水准面精化项目,文中论述了该项目采用的技术路线、项目设计所顾及的有关问题,以及所取得的成果。     

GPS-RTK用于矿山高精度沉陷监测的可行性研究

针对复杂地表条件下采用水准测量和导线测量等常规方式进行地表变形周期观测、任务量大甚至无法实施等问题,提出了建立研究区域的似大地水准面精化模型,同时采用GPS-RTK技术获取观测站三维空间信息,进而获得概率积分法预计参数。最后以内蒙古准格尔旗某煤矿的生产实践说明该技术的有效性和可行性,极大地提高了工作效率,为保护煤柱的留设提供了科学的依据。     

区域似大地水准面的非均匀B样条拟合方法探讨

介绍了建立似大地水准面模型的原理,讨论了非均匀B样条函数方法的基本原理。根据中部某地区的已知点的大地高和正常高,分别用非均匀三次B样条函数和三次曲面函数对该地区的似大地水准面进行高程拟合,结果表明了该方法具有更好的精度和稳定性。     

Molodensky potential telluroid based on a minimum-distance map. Case study: the quasi-geoid of East Germany in the World Geodetic Datum 2000

 A potential-type Molodensky telluroid based upon a minimum-distance mapping is derived. With respect to a reference potential of Somigliana–Pizzetti type which relates to the World Geodetic Datum 2000, it is shown that a point-wise minimum-distance mapping of the topographical surface of the Earth onto the telluroid surface, constrained to the gauge W(P)=u(p), leads to a system of four nonlinear normal equations. These normal equations are solved by a fast Newton–Raphson iteration. Received: 7 February 2000 / Accepted: 23 October 2001     

珠峰地区似大地水准面精化与珠峰顶正高的确定

本文使用珠峰及其周边地区的重力数据与SRTM3、1∶50000 DEM、GTOPO30地形数据,以该地区的44个GPS水准点为控制,选择国内外的EGM96、WDM94、IGG05B、DQM2000D和CG03C作为参考重力场模型,采用移去-恢复技术,首次完成了珠峰地区分辨率为2.5′×2.5′高精度似大地水准面,其精度达到±9 cm,并据此推算了珠峰顶高程异常值. 再利用登山线路上的新测重力点与珠峰地形数据,依据严格的重力归算理论及移去-恢复技术,完成了珠峰顶似大地水准面与大地水准面差值计算,即珠峰正常高与正高的换算.     

GPS/重力边值问题的求解及应用

从分析GPS技术在确定地球形状中的作用入手，论述了建立一类新的大地边值问题——GPS/重力边值问题的意义，给出了GPS/重力边值问题的定义及数学描述，推导出GPS/重力边值问题的逼近解式，并给出了应用GPS/重力边值问题确定（似）大地水准面、地面垂线偏差及外部重力场的基本公式. 对GPS技术用于物理大地测量的优势及有待解决的问题进行了简要归纳.     

几种确定似大地水准面方法比较

利用GPS点水准联测数据,通过曲面拟合的方法得到高程异常值;重点探讨了在同一组数据下分别采用二次曲面、多面函数、神经网络和样条函数等拟合方法;通过实例验证这些方法的可行性,同时对各种方法的精度进行了比较。