珠穆朗玛峰地区的地壳运动,地壳厚度,张性冰川的探讨

珠穆朗玛峰是世界最高峰，基高程一直受到世人关注。同时珠穆朗玛峰及其毗邻地区位于欧亚板块和印度板块边缘的冲撞挤压地带，地壳运动，剧烈，地形。复杂，三十年来我国对珠穆朗玛峰高程及其毗邻地区进行了三次大规模大地测量，现将珠穆朗玛峰高程和该地区的地壳运动研究介绍于后。     

珠穆朗玛峰地区的地壳运动,地壳厚度,张性冰川的探讨

珠穆朗玛峰是世界最高峰，基高程一直受到世人关注。同时珠穆朗玛峰及其毗邻地区位于欧亚板块和印度板块边缘的冲撞挤压地带，地壳运动，剧烈，地形。复杂，三十年来我国对珠穆朗玛峰高程及其毗邻地区进行了三次大规模大地测量，现将珠穆朗玛峰高程和该地区的地壳运动研究介绍于后。     

在板块边缘的冲撞地区重力场的求定

在陆地上，板块边的冲撞地区一般都是呈现地形复杂，地表和地下的质量分布不均衡、有强烈的地壳运动和构造运动，因此，该地区的重力场（重力异常、垂线偏差，大地水准面）变化剧烈。对它的归算和推估都需要作特殊的考虑。本文以位于欧亚板块和印度板块边缘冲撞地区的珠穆朗玛峰测区的重力场求定为例，进行讨论。     

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。     

全球高程基准研究进展

建立统一的全球高程基准是国际大地测量科学界的核心目标之一,也是全球尺度地球科学研究、跨境工程应用等的必要基础设施。国际大地测量协会（international geodesy association,IAG）2015年发布了国际高程参考系统的定义,并于2019年提出了建立国际高程参考框架的目标。从全球高程参考系统的理论基础和定义出发,对国际高程参考系统与框架的理论、方法和实际问题开展论述与研究,主要包括全球大地水准面重力位$W_{\mathrm{0}}$的确定、基于高阶重力场模型的重力位确定、基于区域重力场建模的重力位确定,并重点论述和分析了IAG组织的科罗拉多大地水准面建模试验和中国2020珠峰高程测量实现国际高程参考系统2项典型案例研究。结果表明,在平坦地区和一般山区,重力大地水准面模型精度能达到1 cm（重力位0.1 m2/s2）,即使在珠穆朗玛峰这样的特大山区,也有望达到2~3 cm精度（重力位0.2~0.3 m2/s2）。综合典型案例研究结果、观测技术、数据资源和区域分布等因素,提出了建立国际高程参考框架的初步策略,包括IHRF参考站布设、重力位确定方法、数据要求、应遵循的标准/约定和预期精度指标等,展望了光学原子钟与相对论大地测量对于全球高程基准统一的潜在贡献。     

珠穆朗玛峰峰顶大地水准面与似大地水准面差值计算及其验证

本文利用登山路线上的实测重力点,通过试算分析确定了珠穆朗玛峰地区应采用的均衡模型及均衡深度,并利用该均衡模型推估了珠穆朗玛峰峰顶地形均衡重力异常与珠穆朗玛峰峰顶重力值。根据正常高和正高换算关系的需要,计算了珠穆朗玛峰峰顶沿垂线方向至黄海平均海平面的重力值的平均值与正常重力值的平均值,在此基础上完成了珠穆朗玛峰峰顶正常高和正高的换算,即大地水准面与似大地水准面差值计算,并对此结果采用其他方法进行了验证。     

珠峰及邻近区域第四次大地测量

叙述了我国大地测量工作者于 1998年对珠穆朗玛峰及邻近区域进行的第四次大规模的大地测量外业概况和取得的成果 ,以及数据处理方法和最终结果。经过对 1998、196 6 - 196 8、1975、1992年珠峰及邻近区域四次大地测量数据综合分析 ,从地学方面进行研究 ,得出青藏块体在印度板块的推动下 ,仍向北东东方向运动 ;珠峰地区相对垂直运动在整体抬升的过程中伴有波浪式的起伏等结论。     

超定边值问题的差分法

物理大地测量面临着越来越多的数据:高程异常、垂线偏差、重力异常、重力梯度等,因此出现了超定边值问题,本文采用求解偏微分方程最简单而又最常用的差分法,对这一问题进行了初步的研究。     

确定高程异常的GPS／水准重力内插法

本文介绍了在局部地区借助于一定数量的GPS／水准点上的高程异常和该地区及周围的重力数据和地形数据内插试地区内任一点高程异常的原理和方法，该方法仅需利用6个或以上的GPS／水准点并利用该地区及周围一定密度分布的重力点和地形高数据，就能以一定的精度内插出该地区内任一点的高程异常。     

对我国35年来珠峰高程测定成果的思考

20世纪60年代以来，我国曾单独或与外国合作，在1966年，1975年，1992年，1998年及1999年对珠穆朗玛峰高程进行了5次测定，开展了大规模的大地测量外业作业、数据处理和科学研究，其中包括天文、重力、平面、高程和气象等方面。本文对我国近35年来的珠峰高程测定的成果和最新进展作分析研究，将我国35年来所精确测定的珠峰峰顶雪面高程值取中数，以我国60(似)大地水准面为基准面，得珠峰海拔高为8849.0m±0.5m；若以接近全球高程系统的EGM96大地水准面为基准面，珠峰海拔高为8850.1m±0.5m。     

Determination of Indian absolute geodetic datum by least-square solution technique

The Everest spheroid, 1830, in general use in the Survey of India, was finally oriented in an arbitrary manner at the Indian geodetic datum in 1840; while the international spheroid, 1924, in use for scientific purposes; was locally fitted to the Indian geoid in 1927. An attempt is here made to obtain the initial values for the Indian geodetic datum in absolute terms on GRS 67 by least-square solution technique, making use of the available astro-geodetic data in India, and the corresponding generalised gravimetric values at the considered astro-geodetic points, as derived from the mean gravity anomalies over1°×1° squares of latitude and longitude in and around the Indian sub-continent, and over5° equal area blocks covering the rest of the earth’s surface. The values obtained independently by gravimetric method, were also considered before actual finalization of the results of the present determination.     

On estimating gravity anomalies— A comparison of least squares collocation with conventional least squares techniques

The least squares collocation algorithm for estimating gravity anomalies from geodetic data is shown to be an application of the well known regression equations which provide the mean and covariance of a random vector (gravity anomalies) given a realization of a correlated random vector (geodetic data). It is also shown that the collocation solution for gravity anomalies is equivalent to the conventional least-squares-Stokes' function solution when the conventional solution utilizes properly weighted zero a priori estimates. The mathematical and physical assumptions underlying the least squares collocation estimator are described.     

Interpolation and integration of the normal free air anomalies

Conclusion If we want to compute the height anomalies and the deflections of the vertical for a point where there are height differences exceeding one kilometer in the neighborhood, a very dense net of gravity values must be observed, even when the topographic corrections are used. In smoother regions, the simple Bouguer anomalies with a moderate spacing and with the estimation of the mean heights give reliable results without further reductions.     

重力均衡与地形波长——兼论均衡理论不适宜于珠峰重力值的推估

150多年来，重力均衡的理论已得到很大的发展，均衡异常与大地水准面差距在地球科学诸多学科中已得到了广泛的应用，各种均衡理论及其相应的重力异常在各种文献中已作了比较和评论；不同波长地形的重力效应，包括短波长的地形不能构成补偿也作了进一步研究。因此，在局部场中不宜用均衡补偿的方法作山区重力点值的推估，而曾经仅用地形（高程）的数据推估珠穆朗玛峰顶上的重力倒是适合的。     

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.     

Gravity anomalies from satellite altimetry: comparison between computation via geoid heights and via deflections of the vertical

The accumulation of good quality satellite altimetry missions allows us to have a precise geoid with fair resolution and to compute free air gravity anomalies easily by fast Fourier transform (FFT) techniques.In this study we are comparing two methods to get gravity anomalies. The first one is to establish a geoid grid and transform it into anomalies using inverse Stokes formula in the spectral domain via FFT. The second one computes deflection of the vertical grids and transforms them into anomalies.The comparison is made using different data sets: Geosat, ERS-1 and Topex-Poseidon exact repeat misions (ERMs) north of 30°S and Geosat geodetic mission (GM) south of 30°S. The second method which transforms the geoid gradients converted into deflection of the vertical values is much better and the results have been favourably evaluated by comparison with marine gravity data.     

On the gravimetric inverse problem in geodetic gravity field estimation

Gravity field estimation in geodesy, through linear(ized) least squares algorithms, operates under the assumption of Gaussian statistics for the estimable part of preselected models. The causal nature of the gravity field is implicitly involved in its geodetic estimation and introduces the need to include prior model information, as in geophysical inverse problems. Within the geodetic concept of stochastic estimation, the prior information can be in linear form only, meaning that only data linearly depending on the estimates can be used effectively. The consequences of the inverse gravimetric problem in geodetic gravity field estimation are discussed in the context of the various approaches (in model data spaces) which have the common goal to bring into agreement the statistics between these two spaces. With a simple numerical example of FAA prediction, it is shown that prior information affects the accuracy of estimates at least equally as the number of input data. Received: 25 April 1994; Accepted: 15 October 1996     

第二大地边值问题引论EI北大核心CSCD

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。     

利用大地边值问题方法统一全球高程基准

为解决世界各国高程基准差异的问题,提出联合卫星重力场模型、地面重力数据、GNSS大地高、局部高程基准的正高或正常高,按大地边值问题法确定局部高程基准重力位差的方法。首先推导了利用传统地面"有偏"重力异常确定高程基准重力位差的方法;接着利用改化Stokes核函数削弱"有偏"重力异常的影响,并联合卫星重力场模型和地面"有偏"重力数据,得到独立于任何局部高程基准的重力水准面,以此来确定局部高程基准重力位差;最后利用GNSS+水准数据和重力大地水准面确定了美国高程基准与全球高程基准W₀的重力位差为-4.82±0.05 m²s^-2。