第二大地边值问题引论  

Introduction to the second geodetic boundary value problem

作　　者：魏子卿 WEI Ziqing(Shenzhen University, Shenzhen 518060, China;Xi an Research Institute of Surveying and Mapping, Xi an 710054, China)

机构地区：[1]深圳大学,广东深圳518060 [2]西安测绘研究所,陕西西安710054

出　　处：《测绘学报》2022年第6期797-803,共7页Acta Geodaetica et Cartographica Sinica

摘　　要：在空间大地测量时代,GNSS可以测定地面点的大地高,使重力扰动变成了直接观测量,以重力扰动为边界条件的第二边值问题在大地测量中得以实用化。它的解与GNSS组合正在成为一种颇有应用前景的海拔高测量方法。本文原理性地讨论了有两种不同边界面的球近似第二大地边值问题。第一种以地形面为边界面,给出了高程异常与地面垂线偏差的解析延拓解;第二种以参考椭球面为边界面,将其外部地形质量按照Helmert第二压缩法移至参考椭球面,然后将Hotine函数与从地球表面延拓至边界面的Helmert重力扰动进行卷积,并顾及地形间接影响,最后得到大地水准面高、椭球面垂线偏差、高程异常与地面垂线偏差的Helmert解。在讨论部分,进行了第二与第三大地边值问题的比较,提出了现有重力点高程从正高或正常高到大地高的改化方法,并展望了它的应用前景。In space geodesy time,GNSS is capable of determining geodetic heights for ground points,enabling gravity disturbances to be direct observables.As a result,the second geodetic boundary value problem(GBVP)with gravity disturbances as the boundary condition can be applied in geodesy.The combination of its solution with GNSS is becoming a new approach to measuring the elevation above sea level,which is expected to have a bright future in application.The paper briefly discusses in principle the spherical approximation the 2nd GBVPs with two different boundary surfaces.The first kind uses the topographic surface as the boundary,and gives the analytical continuation solutions of surface height anomalies and deflections of the vertical.The second kind,with the surface of the reference-ellipsoid as the boundary,first moves topographic masses outside the reference ellipsoid onto it according to the Helmerts second condensation method,and then convolutes the Hotine function with Helmert gravity disturbances at the boundary,which are analytically downward-continued from the earths surface,and after considering the indirect effects of topography gives finally the Helmert solutions of geoidal heights,ellipsoid vertical deflections,height anomalies and surface deflections of the vertical.In the discussion part a comparison between the 2nd GBVP and the 3rd GBVP is made,and an approach is presented to converting the orthometric or normal height into the geodetic height for existing gravity points,and the application prospect of the 2nd GBVP is looked into the future.

关 键 词：第二大地边值问题 大地水准面起伏 高程异常 垂线偏差 解析延拓解 Helmert解 

分 类 号：P227[天文地球—大地测量学与测量工程]