A computational scheme to model the geoid by the modified Stokes formula without gravity reductions

In a modern application of Stokes formula for geoid determination, regional terrestrial gravity is combined with long-wavelength gravity information supplied by an Earth gravity model. Usually, several corrections must be added to gravity to be consistent with Stokes formula. In contrast, here all such corrections are applied directly to the approximate geoid height determined from the surface gravity anomalies. In this way, a more efficient workload is obtained. As an example, in applications of the direct and first and second indirect topographic effects significant long-wavelength contributions must be considered, all of which are time consuming to compute. By adding all three effects to produce a combined geoid effect, these long-wavelength features largely cancel. The computational scheme, including two least squares modifications of Stokes formula, is outlined, and the specific advantages of this technique, compared to traditional gravity reduction prior to Stokes integration, are summarised in the conclusions and final remarks. AcknowledgementsThis paper was written whilst the author was a visiting scientist at Curtin University of Technology, Perth, Australia. The hospitality and fruitful discussions with Professor W. Featherstone and his colleagues are gratefully acknowledged.     

Soil saturation patterns in steep,convergent hill-slopes under forest and pasture vegetation

The relationships between hillslope form and the development of zones of hillslope saturation are central to studies of process hydrology. These relationships are examined in two small, steep (30°) first-order basins under forest and pasture vegetation. Hillslope saturation patterns are described using a probability analysis of observations of peak water table elevations made at individual sites in each basin. In both first-order basins, the effects of topographic convergence on the spatial variability of hillslope saturation zones are most pronounced on shallow slopes and in steeper areas where hillslope form is strongly concave. The implications of vegetation type on the formation and variation of hillslope saturation are also examined. The differences in hillslope saturation patterns in each vegetation type are attributed primarily to differences in net rainfall and not soil physical properties or other features of topography.     

Spherical harmonic analysis of the CRUST 2.0 global crustal model

The spherical harmonic analysis of the 2×2 density and stratification information contained in the global crustal model CRUST 2.0 is presented from the viewpoint of gravity field recovery and interpretation. Using a standard Airy/Heiskanen (A/H) isostatic hypothesis and a radially distributed compensation mechanism, two models of topographic/isostatic (t/i) potential harmonic coefficients are obtained up to degree and order 90. The CRUST-derived coefficients are compared with the spectrum of uncompensated topography, with the EGM96 observed gravity field, and with the t/i spectrum based on an A/H hypothesis with a constant compensation depth of 30 km. The signal degree variances of both CRUST models decrease quite smoothly towards degree 90, while the seven-layer model approaches the EGM96 spectrum for degrees 80–90. The significant deviation of the CRUST spectra from the A/H combined spectrum may prove of relevance to local and regional applications investigating the validity of current isostatic hypotheses.Acknowledgments. Sincere thanks go to Nikolaos Pavlis and three unknown referees for their thoughtful comments. Figure 1 has been produced using the mapping package m_map by R. Pawlowicz, which is a MATLAB toolbox that can be freely downloaded from http://www2.ocgy.ubc.ca/~rich/map.html     

The analytical continuation bias in geoid determination using potential coefficients and terrestrial gravity data

One important application of an Earth Gravity Model (EGM) is to determine the geoid. Since an EGM is represented by an external-type series of spherical harmonics, a biased geoid model is obtained when the EGM is applied inside the masses in continental regions. In order to convert the downward-continued height anomaly to the corresponding geoid undulation, a correction has to be applied for the analytical continuation bias of the geoid height. This technique is here called the geoid bias method. A correction for the geoid bias can also be utilised when an EGM is combined with terrestrial gravity data, using the combined approach to topographic corrections. The geoid bias can be computed either by a strict integral formula, or by means of one or more terms in a binomial expansion. The accuracy of the lowest binomial terms is studied numerically. It is concluded that the first term (of power H²) can be used with high accuracy up to degree 360 everywhere on Earth. If very high mountains are disregarded, then the use of the H² term can be extended up to maximum degrees as high as 1800. It is also shown that the geoid bias method is practically equal to the technique applied by Rapp, which utilises the quasigeoid-to-geoid separation. Another objective is to carefully consider how the combined approach to topographic corrections should be interpreted. This includes investigations of how the above-mentioned H² term should be computed, as well as how it can be improved by a correction for the residual geoid bias. It is concluded that the computation of the combined topographic effect is efficient in the case that the residual geoid bias can be neglected, since the computation of the latter is very time consuming. It is nevertheless important to be able to compute the residual bias for individual stations. For reasonable maximum degrees, this can be used to check the quality of the H² approximation in different situations.Acknowledgement The author would like to thank Prof. L.E. Sjöberg for several ideas and for reading two draft versions of the paper. His support and constructive remarks have improved its quality considerably. The valuable suggestions from three unknown reviewers are also appreciated.     

应用计算机绘制地层柱状剖面图的尝试

本文是使用计算机绘制的地层柱状剖面图和柱状剖面对比图的尝试。分析认为,表示各种岩石类型的花纹图式都是由简单的几何图形或符号组成,而这些图形、符号均可用一些简单的数学式子表述。因此,完全可以用计算机输出。文中讨论了岩石花纹符号的设计方法和输出步骤,并附有输出的柱状剖面图和剖面对比图实例。结果表明,使用本方法不仅方便可行,而且速度快、精度高、质量好。     

双频接收机C／A码与P码伪距的精确比较

采用Matlab编制的精密伪距单点定位程序，利用IGS跟踪站的源数据，对P码和C／A码伪距精密定位的精度进行了比较和分析。     

2维地图符号与3维可视化的关系

从传统的2维地图发展到电子地图和3维可视化地理环境的过程中,地理信息的表达从2维到3维是一次飞跃。2维地图符号系统作为成熟的地图表达方式在3维可视化环境中仍然有用。2维地图符号系统有其自身的特点和优点:体系成熟,易于认知,易于实现。论述了目前3维可视化环境下传统2维(电子)地图符号的应用特点和二者之间的辩证关系,探讨了3维可视化环境下地理信息表达和地图符号设计的一些原则。     

利用空间数据库概念管理地形图

随着信息技术在国土资源部门的广泛应用,空间数据库理论、技术和实践日臻成熟。在日常地形图管理服务工作中,引入空间数据库概念,在不进行矢量化的条件下,构建地形图数据模型,提供便捷的计算机查询、辅助管理服务。     

ITK应用在架空送电线路勘测中的探讨

主要通过常规传统勘测和RTK勘测的比较介绍了架空送电线路勘测技术的更替，并结合RTK专业电力软件在重庆永川110KV交流超高压输送电线路改线测量中的应用与实施，探讨RTK电力数字化有码作业方式的有效应用。     

A comparison of the tesseroid,prism and point-mass approaches for mass reductions in gravity field modelling

The calculation of topographic (and iso- static) reductions is one of the most time-consuming operations in gravity field modelling. For this calculation, the topographic surface of the Earth is often divided with respect to geographical or map-grid lines, and the topographic heights are averaged over the respective grid elements. The bodies bounded by surfaces of constant (ellipsoidal) heights and geographical grid lines are denoted as tesseroids. Usually these ellipsoidal (or spherical) tesseroids are replaced by “equivalent” vertical rectangular prisms of the same mass. This approximation is motivated by the fact that the volume integrals for the calculation of the potential and its derivatives can be exactly solved for rectangular prisms, but not for the tesseroids. In this paper, an approximate solution of the spherical tesseroid integrals is provided based on series expansions including third-order terms. By choosing the geometrical centre of the tesseroid as the Taylor expansion point, the number of non-vanishing series terms can be greatly reduced. The zero-order term is equivalent to the point-mass formula. Test computations show the high numerical efficiency of the tesseroid method versus the prism approach, both regarding computation time and accuracy. Since the approximation errors due to the truncation of the Taylor series decrease very quickly with increasing distance of the tesseroid from the computation point, only the elements in the direct vicinity of the computation point have to be separately evaluated, e.g. by the prism formulas. The results are also compared with the point-mass formula. Further potential refinements of the tesseroid approach, such as considering ellipsoidal tesseroids, are indicated.