正常重力场的确定以及相关的一个理论问题

给定参考椭球体的四个基本参数,椭球体产生的外部正常重力位场可利用传统方法确定。本文基于WGS84参考椭球的四个基本参数和压缩恢复法,确定了一个定义在半径为6000km内部球的外部正则调和的虚拟正常场。在mm级精度水平下,所确定的虚拟正常场在椭球体外部与真实正常场一致。基于虚拟正常场,可解决物理大地测量学中存在的一个无定义问题。     

大区域似大地水准面模型的建立方法研究

在充分研究现有几何方法确定局域似大地水准面的基础上,根据独立网内点间高程异常差的不变性和独立网间大地高起算基准面与WGS84椭球面的平行性,提出通过两步处理,获得大区域连续似大地水准面的思想和方法,即首先统一相邻两个独立GPS网大地高起算基准面,然后再利用几何方法确定大区域似大地水准面.该方法在长江口北岸得到了很好的验证,并取得了比较理想的精度.     

航空重力确定大地水准面的研究

随着近年来航空重力的发展,航空重力数据的精度和分辨率不断提高,其精度可达1 mGal,分辨率可达10km,这使得用航空重力数据计算精密大地水准面成为可能。本研究介绍利用满足一定条件的稳定、精确的航空重力数据计算大地水准面的一种新途径。它根据布隆公式,分离大地水准面与参考椭球,把航空重力观测值转换为大地水准面上的重力位,从而确定大地水准面。其具体步骤如下: 1.对重力扰动观测数据进行低通滤波,除去高频观测噪声; 2.利用全球重力场模型从低通滤波的重力     

一种确定大地水准面重力位漂移δW的方法

理论上,大地水准面上的重力位常数W0决定了大地水准面的形状及大小。源于大地水准面重力位W0的系统误差将直接导致大地水准面的漂移,如何精确确定W0一直是大地测量学家极为感兴趣的问题。本文基于虚拟压缩恢复法,提出了一种不同于传统的确定大地水准面重力位漂移δW的方法。     

重力加密测量中的若干问题

前言大地测量的成果整理,计算工作是在参考椭球面上进行的,因此,在进行天文-大地网平差及其他计算工作之前,必须将在地面上直接量测得到的水平角和基线长度归算到所采用的参考椭球面上。为此,就需要求出各三角点及基线到达参考椭球面的高程,即大地高。它是由下面两部分组成的：（1）由地面到达似大地水准面的正常高;（2）由似大地水准面到达参考椭球面的高程异常。正常高可由精密水准测量加入重力改正求得,而高程异常则采用天文重力水准测量的方法求之。     

国际高程参考系统在珠峰地区的实现

2020珠峰高程测量,首次确定并发布了基于国际高程参考系统(IHRS)的珠峰正高。在珠峰地区实现国际高程参考系统,采用的方案是建立珠峰区域高精度重力大地水准面。利用地球重力场谱组合理论和基于数据驱动的谱权确定方法,测试优选参考重力场模型及其截断阶数和球冠积分半径等关键参数,联合航空和地面重力等数据建立了珠峰区域重力似大地水准面模型,61点高精度GNSS水准高程异常检核表明,模型精度达3.8 cm,加入航空重力数据后模型精度提升幅度达51.3%。提出顾及高差改正的峰顶高程异常内插方法,采用顾及地形质量影响的高程异常——大地水准面差距转换改正严密公式,使用峰顶实测地面重力数据,基于国际高程参考系统定义的重力位值W₀和GRS80参考椭球,最终确定了国际高程参考系统中的高精度珠峰峰顶大地水准面差距。     

2000国家大地坐标系椭球参数与GRS 80和WGS 84的比较

根据2000国家大地坐标系(CGCS 2000)的定义及其所定义的4个基本椭球常数,推导CGCS 2000椭球的主要几何和物理参数,比较这些参数与GRS 80和WGS 84椭球相应参数之间的差异,给出CGCS 2000椭球与GRS 80及WGS 84椭球定义的正常重力值的差异,并分析在CGCS 2000及WGS 84系下同一点坐标的差异.研究表明:CGCS 2000椭球上的正常重力值与GRS 80,WGS 84椭球上的正常重力值的差值分别约为-143.54×10-8m/s2和0.02×10-8m/s2.同一点在CGCS 2000与GRS 80和WGS 84下经度相同,纬度的最大差值分别为8.26×10-11"(相当于2.5×10-6 mm)和3.6×10-6"(相当于0.11 mm).     

区域与全球高程基准差异的确定

全球高程基准统一是继全球大地测量坐标系及其参考基准统一之后,大地测量学科面临和亟待解决的一个重要问题,也是全球空间信息共享与交换的基础。本文针对区域高程基准与全球高程基准间基准差异确定的理论、方法及实际问题开展研究。利用物理大地测量高程系统的经典理论方法,给出了高程基准差异的定义,并推导了计算基准差异的严密公式,该公式可将高程基准差异确定的现有3种方法统一起来。在此基础上,分析顾及了不同椭球参数对于计算基准差异的影响及量级,同时,高程异常差法还需考虑全球高程基准重力位与模型计算大地水准面位值不一致引起的零阶项改正。利用青岛原点附近152个GPS水准点数据,分别选择GRS80、WGS-84、CGCS2000参考椭球以及EGM2008、EIGEN-6C4、SGG-UGM-1模型,采用位差法和高程异常差法,确定了我国1985高程基准与全球高程基准的差异。其中,EIGEN-6C4模型计算的我国高程基准与WGS-84参考椭球正常重力位U0定义的全球高程基准之间的差异约为-23.1cm。也就是说,我国高程基准低于采用WGS-84参考椭球正常重力位U0定义的全球高程基准,当选取基于平均海面确定的Gauss-Listing大地水准面作为全球高程基准时,我国1985高程基准高于全球基准约21.0cm。从计算结果还可看出,当前重力场模型在青岛周边不同GPS/水准点的精度差别依然较大,这会导致选择不同数据对确定我国85国家高程基准与全球基准之间的差异影响较大,因此,若要实现厘米级精度区域高程基准与全球高程基准的统一,全球重力场模型的精度和可靠性还需要进一步提高。     

联合GRACE/GOCE重力场模型和GPS/水准数据确定我国85高程基准重力位

GRACE、GOCE卫星重力计划的实施,对确定高精度重力场模型具有重要贡献。联合GRACE、GOCE卫星数据建立的重力场模型和我国均匀分布的649个GPS/水准数据可以确定我国高程基准重力位,但我国高程基准对应的参考面为似大地水准面,是非等位面,将似大地水准面转化为大地水准面后确定的大地水准面重力位为62 636 854.395 3m~2s~(-2),为提高高阶项对确定大地水准面的贡献,利用高分辨率重力场模型EGM2008扩展GRACE/GOCE模型至2190阶,同时将重力场模型和GPS/水准数据统一到同一参考框架和潮汐系统,最后利用扩展后的模型确定的我国大地水准面重力位为62 636 852.751 8m~2s~(-2)。其中组合模型TIM_R4+EGM2008确定的我国85高程基准重力位值62 636 852.704 5m~2s~(-2)精度最高。重力场模型截断误差对确定我国大地水准面的影响约16cm,潮汐系统影响约4~6cm。     

陆海交界区域厘米级精度似大地水准面的确定

为了得到我国某陆海交界区厘米级精度的区域（似）大地水准面,利用43个高精度GPS／水准点和1045个实测重力点数据对EGM96,WDM94和GFZ计算的局部重力（似）大地水准面进行了比较与评价。结果表明,在该测区用移去．恢复法确定重力（似）大地水准面时,EGM96应该是首选参考重力场模型。该测区处在陆海交界处,海域无GPS／水准数据。经比较发现,采用距离倒数加权平均法将该区重力似大地水准面拟合于GPS／水准数据比在大范围使用的多项式法效果更好。采用该方法计算的测区（似）大地水准面精度优于3cm。     

机载三线阵传感器航空摄影测量的坐标转换方法研究

由于机载GPS获取的数据是WGS84坐标系,定向测图时首先要进行坐标转换。本文讨论了7参数平面转换模型与GPS水准测量拟合高程异常的方法,研究了数字航空摄影测量的像控点布设问题,并对数字航空摄影测量只在测区四角布设控制点即可满足空三精度要求的观点进行了分析。实验结果表明,机载三线阵航空摄影测量中高精度的7参数转换与似大地水准面精化成果是获取高精度空三的前提。     

The Bruns formula in three dimensions

The Bruns formula is generalized to three dimensions with the derivation of equations expressing the height anomaly vector or the geoid undulation vector as a function of the disturbing gravity potential and its spatial derivatives. It is shown that the usual scalar Bruns formula provides not the separation along the normal to the reference ellipsoid but the component of the relevant spatial separation along the local direction of normal gravity. The above results which hold for any type of normal potential are specialized for the usual Somigliana-Pizzetti normal field so that the components of the geoid undulation vector are expressed as functions of the parameters of the reference ellipsoid, the disturbing potential and its spatial derivatives with respect to three types of curvilinear coordinates, ellipsoidal, geodetic and spherical. Finally the components of the geoid undulation vector are related to the deflections of the vertical in a spherical approximation.     

GPS测量坐标转换实用性问题的分析

针对ＧＰＳ测量坐标转换方法中存在的问题,提出了强制符合平面四参数法和多项式拟合法,这两种方法能够有效的克服高程系统以及椭球参数不一致造成的误差,比较适合于工程自由坐标之间的转换;同时本文给出了基于“全球大地水准面的几何中心地球质心相重合”这一假设之上的莫洛金斯坐标转换法,该法不需要联测公共点即可将ＷＧＳ－８４坐标转换成本地局部坐标。上述几种方法减少了额外联测的工作量,提高了ＧＰＳ的使用效率。     

均质椭球体的引力位以及调和延拓在边值问题中的应用

本文作者首次推导均质椭球体的内部和外部引力位的数学表达式 ,由此应用调和延拓的思想引入外大地水准面和外部位函数的概念 ;建立了关于外扰动位的边值问题 ,该问题的界面规则而且具有 O( T2 )的精度 ;作为一个整体 ,讨论了外正高的计算和将地面点的重力测量值在 O( T2 )精度下归算到外大地水准面的方法     

Topographic and atmospheric corrections of gravimetric geoid determination with special emphasis on the effects of harmonics of degrees zero and one

 The topographic and atmospheric effects of gravimetric geoid determination by the modified Stokes formula, which combines terrestrial gravity and a global geopotential model, are presented. Special emphasis is given to the zero- and first-degree effects. The normal potential is defined in the traditional way, such that the disturbing potential in the exterior of the masses contains no zero- and first-degree harmonics. In contrast, it is shown that, as a result of the topographic masses, the gravimetric geoid includes such harmonics of the order of several centimetres. In addition, the atmosphere contributes with a zero-degree harmonic of magnitude within 1 cm. Received: 5 November 1999 / Accepted: 22 January 2001     

Far-zone effects for different topographic-compensation models based on a spherical harmonic expansion of the topography

The determination of the gravimetric geoid is based on the magnitude of gravity observed at the surface of the Earth or at airborne altitude. To apply the Stokes’s or Hotine’s formulae at the geoid, the potential outside the geoid must be harmonic and the observed gravity must be reduced to the geoid. For this reason, the topographic (and atmospheric) masses outside the geoid must be “condensed” or “shifted” inside the geoid so that the disturbing gravity potential T fulfills Laplace’s equation everywhere outside the geoid. The gravitational effects of the topographic-compensation masses can also be used to subtract these high-frequent gravity signals from the airborne observations and to simplify the downward continuation procedures. The effects of the topographic-compensation masses can be calculated by numerical integration based on a digital terrain model or by representing the topographic masses by a spherical harmonic expansion. To reduce the computation time in the former case, the integration over the Earth can be divided into two parts: a spherical cap around the computation point, called the near zone, and the rest of the world, called the far zone. The latter one can be also represented by a global spherical harmonic expansion. This can be performed by a Molodenskii-type spectral approach. This article extends the original approach derived in Novák et al. (J Geod 75(9–10):491–504, 2001), which is restricted to determine the far-zone effects for Helmert’s second method of condensation for ground gravimetry. Here formulae for the far-zone effects of the global topography on gravity and geoidal heights for Helmert’s first method of condensation as well as for the Airy-Heiskanen model are presented and some improvements given. Furthermore, this approach is generalized for determining the far-zone effects at aeroplane altitudes. Numerical results for a part of the Canadian Rocky Mountains are presented to illustrate the size and distributions of these effects.     

Methods for the computation of geoid undulations from potential coefficients

The undulations of the geoid may be computed from spherical harmonic potential coefficients of the earth’s gravitational field. This paper examines three procedures that reflect various points of view on how this computation should be carried out. One method requires only the flattening of a reference ellipsoid to be defined while the other two methods require a complete definition of the parameters of the ellipsoid. It was found that the various methods give essentially the same undulations provided that correct parameters are chosen for the reference ellipsoid. A discussion is given on how these parameters are chosen and numerical results are reported using recent potential coefficient determinations.     

Ellipsoidal corrections to order e 2 of geopotential coefficients and Stokes’ formula

Assuming that the gravity anomaly and disturbing potential are given on a reference ellipsoid, the result of Sjöberg (1988, Bull Geod 62:93–101) is applied to derive the potential coefficients on the bounding sphere of the ellipsoid to order e ² (i.e. the square of the eccentricity of the ellipsoid). By adding the potential coefficients and continuing the potential downward to the reference ellipsoid, the spherical Stokes formula and its ellipsoidal correction are obtained. The correction is presented in terms of an integral over the unit sphere with the spherical approximation of geoidal height as the argument and only three well-known kernel functions, namely those of Stokes, Vening-Meinesz and the inverse Stokes, lending the correction to practical computations. Finally, the ellipsoidal correction is presented also in terms of spherical harmonic functions. The frequently applied and sometimes questioned approximation of the constant m, a convenient abbreviation in normal gravity field representations, by e ²/2, as introduced by Moritz, is also discussed. It is concluded that this approximation does not significantly affect the ellipsoidal corrections to potential coefficients and Stokes formula. However, whether this standard approach to correct the gravity anomaly agrees with the pure ellipsoidal solution to Stokes formula is still an open question.     

Geoid determination using one-step integration

A residual (high-frequency) gravimetric geoid is usually computed from geographically limited ground, sea and/or airborne gravimetric data. The mathematical model for its determination from ground gravity is based on the transformation of observed discrete values of gravity into gravity potential related to either the international ellipsoid or the geoid. The two reference surfaces are used depending on height information that accompanies ground gravity data: traditionally orthometric heights determined by geodetic levelling were used while GPS positioning nowadays allows for estimation of geodetic (ellipsoidal) heights. This transformation is usually performed in two steps: (1) observed values of gravity are downward continued to the ellipsoid or the geoid, and (2) gravity at the ellipsoid or the geoid is transformed into the corresponding potential. Each of these two steps represents the solution of one geodetic boundary-value problem of potential theory, namely the first and second or third problem. Thus two different geodetic boundary-value problems must be formulated and solved, which requires numerical evaluation of two surface integrals. In this contribution, a mathematical model in the form of a single Fredholm integral equation of the first kind is presented and numerically investigated. This model combines the solution of the first and second/third boundary-value problems and transforms ground gravity disturbances or anomalies into the harmonically downward continued disturbing potential at the ellipsoid or the geoid directly. Numerical tests show that the new approach offers an efficient and stable solution for the determination of the residual geoid from ground gravity data.