Accounting for topography in the calculation of quasigeoidal heights and plumb-line deflections from gravity anomalies

A calculation of quasigeoidal heights and plumb-line deflections according to Molodensky formulae was carried out under elimination of the effect of topography from gravity anomalies. After the masses of topography had been removed a smoothed-out surface passing through astronomical and gravity stations was considered as representing the physical surface of the Earth. Thus it has been practically rendered possible to use the first-approximation formulae of Molodensky, and, in many cases, also the “zero-approximation” formulae analogous to the formulae of Stokes and Vening-Meinesz. The effect of the restored masses of topography was then added to the quantities found; the said effect was expressed as the effect of topography condensed on the normal equipotential surface passing through the point under investigation, plus a correction for condensation. Following some transformations, the resulting formulae (13) and (18) were obtained which formulae differ in their “zero-approximation” (15) and (20) from traditional formulas in that they contain terrait reductions added to free-air anomalies. Moreover, in the calculation of plumb-line deflections directly in mountain regions a correction for differing effects of topography before and after its condensation is to be introduced. A tentative expansion of terrain reduction in terms of spherical harmonics up to the third order is given; it can be seen therefrom that the Stokes series in its usual form is subject to a mean arror about 15–20%. It is also shown that the expansion of free-air anomalies in terms of spherical functions contains a first-order harmonic with a mean values about ±0.3 mgl. The said harmonic practically disappears in the expansion of the sum of free-air anomalies and terrain reductions.     

Methods for computing deflections of the vertical by modifying Vening-Meinesz' function

Summary The application of combined data (satellite and terrestrial data) to the practical computation of height anomalies or the deflections of the vertical was originally suggested by (Molodensky et al. 1962). This idea usually leads to the modification of Stokes' or Vening-Meinesz' functions in the integration procedure. In the recent decade there were various suggestions in this regard especially for the computation of height anomalies. For example, a considerable mathematical insight into the modification of Stokes' function and the truncation of its integral has been provided by (Meissl 1971, Houtze et al. 1979, Rapp 1980, Jekeli 1980). Five different methods for computing deflections of the vertical by modifying Vening-Meinesz' function are studied and compared with each other. The corresponding formulae, the values of the coefficients in each method and the estimations of their corresponding potential coefficient error and truncation error are given in this article. This paper was written at the Institut f. Angewandte Geod?sie, Technische Universit?t Graz, Austria.     

Systematic errors in levelings of mountainous areas

Sources of errors in the precise leveling influencing the results of measurements especially strongly in mountains are considered in this study. Data are given on new error sources, including (1) the difference in temperatures of invar bands of rods and of the air; and (2) displacements of rock bench marks during diurnal variations in temperature of rocks. The ranges of possible total systematic error in leveding are estimated.     

PM2.5浓度插值中不同空间插值方法对比

针对不同插值方法对于重点大气颗粒物污染源PM_(2.5)大区域内整体分布情况的插值效果和精度存在差异性的问题,该文以石家庄市赵县100个点的PM_(2.5)的数据作为样本点,利用反距离权重法、普通克里格插值法和协同克里格插值法,分别进行PM_(2.5)浓度的空间插值。利用研究区内另外20个PM_(2.5)的数据点进行插值精度的检验。研究结果表明:协同克里格插值的精度最高,但可视化效果不如其他两种方法。     

不同卫星定位加权方法的比较与分析

测量值随机误差加权模型是卫星定位的重要组成部分,它能够更加合理地分配各卫星在解算中所起的作用大小,并获得更高的定位精度。该文对目前基于卫星仰角与载噪比或信噪比两大影响因素的多种主流定权方法进行了系统阐述与讨论。通过GPS实测定位实验,对9种不同定权模型的效果进行了综合比较与分析。实验结果表明,各加权模型基本均能够在不同程度上提高定位精度,其中综合考虑仰角与载噪比或信噪比的加权模型具有最优的性能表现。另外,当定位条件较差时,由于测量值误差构成更为复杂,因此期待更加有效的加权模型与方法。     

机载激光雷达在密林山区测绘中的应用

机载激光雷达是近年来发展迅速的高新测绘技术,具有机动性高、数据覆盖量大、作业效率高和精度可靠等特点。针对当前山区沟壑且有大量植被覆盖区域进行传统测量作业较为困难,危险性大的问题,采用机载激光雷达技术获取研究区原始点云数据,在此基础上,对比分析四种滤波算法的点云分类效果,得到适用于密林沟壑区的点云滤波方法,进而通过人机交互和地面点内插实现了测区高精度数字高程模型（digital elevation model,DEM）的构建,最终获得的DEM高程中误差为0.09 m,满足实际测绘生产需求,生产效率大大提高。研究结果表明,机载激光雷达技术应用于复杂危险地形测绘具有极大优势。     

Iterative vector methods for computing geodetic latitude and height from rectangular coordinates

 Two iterative vector methods for computing geodetic coordinates (φ, h) from rectangular coordinates (x, y, z) are presented. The methods are conceptually simple, work without modification at any latitude and are easy to program. Geodetic latitude and height can be calculated to acceptable precision in one iteration over the height range from −10⁶ to +10⁹ m. Received: 13 December 2000 / Accepted: 13 July 2001     

单基站GPS差分系统在山区线路测量中的应用探讨

RTK技术的出现,使得野外实时测量精度达到厘米级,RTK测量具有实时性好、精度高、速度快等优点,是常规测量所无法比拟的,RTK已经作为快速采集数据与定位的有效工具。本文比较分析了常规RTK系统和网络RTK的优缺点,并详细介绍了单基站GPS差分系统的特点,并在实际工程应用中对其精度和有效距离进行了探讨。     

CAD数据向GIS数据转换的方法比较

针对传统的CAD地形图数据向ArcGIS数据转换的需求越来越高的现状,该文以某市的计算机辅助设计地形图为实例,讨论了ArcGIS工具模块、FME软件、C/S转换平台、编程这4种数据转换方法的优缺点和适用范围。利用这几种方法对计算机辅助设计地形图数据进行转换,并将转换结果进行对比分析。实验结果表明,基于FME软件的转换方法最为简便、可行,在一定的条件下转换的结果精度更高、更可靠。     

GPS高程拟合的方法比较

GPS高程拟合的方法有很多,各有其优点和适用范围。本文在最小二乘估计算法的基础上,讨论主成分估计法和半参数模型估计法及各自的优点,并利用六参数模型的最小二乘估计、主成分估计和半参数模型三种拟合方法对GPS高程进行拟合,通过实例计算结果比较分析,得出半参数估计方法优于其他方法,在一定条件下精度高的优点。最后得出半参数估计方法精度达毫米级,论证了其在实际应用中的优越性。     

Evaluation of different topographic correction methods for Landsat imagery

The recent free availability of Landsat historical data provides new potentials for land-cover change studies. Multi-temporal studies require a previous radiometric and geometric homogenization of input images, to better identify true changes. Topographic normalization is one of the key steps to create consistent and radiometricly stable multi-temporal time series, since terrain shadows change throughout time. This paper aims to evaluate different methods for topographic correction of Landsat TM-ETM+ data. They were assessed for 15 ETM+ images taken under different illumination conditions, using two criteria: (a) reduction of the standard deviation (SD) for different land-covers and (b) increase in temporal stability of a time series for individual pixels. We observed that results improve when land-cover classes where processed independently when applying the more advanced correction algorithms such as the C-correction and the Minnaert correction. Best results were obtaining for the C-correction and the empiric–statistic correction. Decreases of the SD for bare soil pixels were larger than 100% for the C-correction and the empiric–statistic correction method compared to the other correction methods in the visible spectrum and larger than 50% in the IR region. In almost all tests the empiric–statistic method provided better results than the C-correction. When analyzing the multi-temporal stability, pixels under bad illumination conditions (northern orientation) improved after correction, while a deterioration was observed for pixels under good illumination conditions (southern orientation). Taken this observation into account, a simple but robust method for topographic correction of Landsat imagery is proposed.     

ON THE EVALUATION OF DEFLECTIONS OF THE VERTICAL USING FFT TECHNIQUE

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云南及周边地区GNSS数据处理方法优化

采用麻省理工学院开发的GAMIT／GLOBK软件,将2015年-2016年全球347个IGS站观测数据分七个子网解算,得到一个固定的参考框架来解算云南及周边地区的35个全球卫星导航系统（GNSS）基准站的坐标,测站坐标均方根误差水平方向在0.7 mm以内,垂直方向在0.3 mm以内,水平方向的坐标重复性精度在5 mm以内,垂向坐标的重复性精度大多数在2.5 cm以内;与在ITRF2014下解算的测站坐标、基线长度、水平速度场结果对比表明:测站坐标存在系统误差,水平方向上的差异在8.5 mm以内,垂直方向上在3 cm以内;基线长度差异在2 mm以内,水平速度场在数值上存在毫米级的差异,方向上基本一致．      

Evaluation of deflections of the vertical using topographic-isostatic and astrogeodetic data for the area of Greece

The evaluation of deflections of the vertical for the area of Greece is attempted using a combination of topographic and astrogeodetic data. Tests carried out in the area bounded by 35°≤ϕ≤42°, 19°≤λ≤27° indicate that an accuracy of ±3″.3 can be obtained in this area for the meridian and prime vertical deflection components when high resolution topographic data in the immediate vicinity of computation points are used, combined with high degree spherical harmonic expansions of the geopotential and isostatic reduction potential. This accuracy is about 25% better than the corresponding topographic-Moho deflection components which are evaluated using topographic and Moho data up to 120 km around each station, without any combination with the spherical harmonic expansion of the geopotential or isostatic reduction potential. The accuracy in both cases is increased to about 2″.6 when the astrogeodetic data available in the area mentioned above are used for the prediction of remaining values. Furthermore the estimation of datum-shift parameters is attempted using least squares collocation.     

Determination of geoidal heights and deflections of the vertical for the hellenic area using heterogeneous data

Mean gravity anomalies, deflections of the vertical, and a geopotential model complete to degree and order180 are combined in order to determine geoidal heights in the area bounded by [34°≦ϕ≤42°, 18°≦λ≦28°]. Moreover, employing point gravity anomalies simultaneously with the above data, an attempt is made to predict deflections of the vertical in the same area. The method used in the computations is least squares collocation. Using empirical covariance functions for the data, the suitable errors for the different sources of observations, and the optimum cap radius around each point of evaluation, an accuracy better than±0.60m for geoidal heights and±1″.5 for deflections of the vertical is obtained taking into account existing systematic effects. This accuracy refers to the comparison between observed and predicted values.     

On the evaluation of deflections of the vertical using FFT technique

There exist three types of convolution formulae for the efficient evaluation of gravity field convolution integrals, i.e., the planar 2D convolution, the spherical 2D convolution and the spherical 1D convolution. The largest drawback of both the planar and the spherical 2D FFT methods is that, due to the approximations in the kernel function, only inexact results can be achieved. Apparently, the reason is the meridian convergence at higher latitudes. As the meridians converge, the ??,?λ blocks do not form a rectangular grid, as is assumed in 2D FFT methods. It should be pointed out that the meridian convergence not only leads to an approximation error in the kernel function, but also causes an approximation error during the implementation of 2D FFT in computer. In order to meet the increasing need for precise determination of the vertica deflections, this paper derives a more precise planar 2D FFT formula for the computation of the vertical deflections. After having made a detailed comparison between the planar and the spherical 2D FFT formulae, we find out the main source of errors causing the loss in accuracy by applying the conventional spherical 2D FFT method. And then, a modified spherical 2D FFT formula for the computation of the vertical deflections is developed in this paper. A series of numerical tests have been carried out to illustrate the improvement made upon the old spherical 2D FFT. The second part of this paper is to discuss the influences of the spherical harmonic reference field, the limited capsize, and the singular integral on the computation of the vertical deflections. The results of the vertical deflections over China by applying the spherical 1D FFT formula with different integration radii have been compared to the astro-observed vertical deflections in the South China Sea to obtain a set of optimum deflection computation parameters.     

InSAR中大气改正方法的对比研究

描述了InSAR中大气改正的几种主要方法,对各种方法的优缺点进行了深入的分析,并讨论了各种方法的使用条件和使用中应该注意的问题。改正方法的选择取决于数据条件、研究区域状况、精度要求,也可以多种方法结合使用。最后展望了InSAR中大气改正技术的发展趋势。