Attraction of the topographic masses

The attraction of a topographic mass element on a spherical earth is derived. The case of a distant mass element is treated. The procedure of calculating the attraction of the topographic masses from a combination of digital models of different grid sizes is studied. The limitation of using the point mass formula of the distant mass elements is illustrated. The results show that using an artificial very fine DHM (made by dividing each cell of the fine DHM into a very fine sub-cells having the same height as the original cell) in the neighbourhood of the computational point (about 2.5 km) reduces the errors on calculating the attraction of the topographic masses.     

A bilinear approximation of the surface relief in terrain correction computations

A new method is presented for the computation of the gravitational attraction of topographic masses when their height information is given on a regular grid. It is shown that the representation of the terrain relief by means of a bilinear surface not only offers a serious alternative to the polyhedra modeling, but also approaches even more smoothly the continuous reality. Inserting a bilinear approximation into the known scheme of deriving closed analytical expressions for the potential and its first-order derivatives for an arbitrarily shaped polyhedron leads to a one-dimensional integration with – apparently – no analytical solution. However, due to the high degree of smoothness of the integrand function, the numerical computation of this integral is very efficient. Numerical tests using synthetic data and a densely sampled digital terrain model in the Bavarian Alps prove that the new method is comparable to or even faster than a terrain modeling using polyhedra.     

基于EGM96模型的GPS水准拟合方法

用GPS测量的方法来获得一点的正高或正常高，需要知识一点的大地水准面差距或高程异常。采用的大地水准面差距或高程异常的精度，决定了GPS水准的精度。本文利用EGM96模型计算高程异常。在利用巳知水准点上的高程异常拟合区域大地水准面模型时，首先移去用EGM96模型计算得到的部分，然后对剩余的高程异常进行拟合和内插，在内插点上再利用EGM96模型把移去的部分恢复，得到该点的高程异常。通过对某线路GPS水准的计算表明，引入EGM96模型拟合高程的精度改进不大。但对于大范围测量，这种方法有望能改进GPS水准的拟合精度。     

A comparison of different mass elements for use in gravity gradiometry

Topographic and isostatic mass anomalies affect the external gravity field of the Earth. Therefore, these effects also exist in the gravity gradients observed, e.g., by the satellite gravity gradiometry mission GOCE (Gravity and Steady-State Ocean Circulation Experiment). The downward continuation of the gravitational signals is rather difficult because of the high-frequency behaviour of the combined topographic and isostatic effects. Thus, it is preferable to smooth the gravity field by some topographic-isostatic reduction. In this paper the focus is on the modelling of masses in the space domain, which can be subdivided into different mass elements and evaluated with analytical, semi-analytical and numerical methods. Five alternative mass elements are reviewed and discussed: the tesseroid, the point mass, the prism, the mass layer and the mass line. The formulae for the potential, the attraction components and the Marussi tensor of second-order potential derivatives are provided. The formulae for different mass elements and computation methods are checked by assuming a synthetic topography of constant height over a spherical cap and the position of the computation point on the polar axis. For this special situation an exact analytical solution for the tesseroid exists and a comparison between the analytical solution of a spherical cap and the modelling of different mass elements is possible. A comparison of the computation times shows that modelling by tesseroids with different methods produces the most accurate results in an acceptable computation time. As a numerical example, the Marussi tensor of the topographic effect is computed globally using tesseroids calculated by Gauss–Legendre cubature (3D) on the basis of a digital height model. The order of magnitude in the radial-radial component is about  ± 8 E.U. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

The gravitational effect of ocean tide loading at high latitude coastal stations in Norway

Gravity measurements close to the ocean are strongly affected by ocean tide loading (OTL). The gravitational OTL effect consists of three parts, i.e. a change in gravity caused by direct attraction from the variable water-masses, by displacement of the observing point due to the load, and by redistribution of masses due to crustal deformation. We compare the OTL gravitational effect of several global models to observed time-series of gravity to identify the best model for four arctic observation sites. We also investigate if the global models are sufficient for correcting gravity observations. The NAO99b model fits the observations best at three stations. At two stations (Tromsø and Bodø) the global models explain the variability in the observations well. At the other two (Honningsvåg and Andøya), a significant periodic signal remains after the OTL correction has been applied. We separate two of the gravitational effects, the direct attraction and the change in gravity due to displacement, to study the local effects. Simple geometric models of the water load and independent measurements from local tide-gauges are used to calculate these effects. This leads to improved correspondence with the OTL signal, hence demonstrating the importance of careful modelling of local effects for correction of gravity observations in coastal stations.     

海域超大范围外部重力场快速赋值模型构建

针对海域超大范围外部重力场快速赋值的特殊需求,分析了3种传统扰动引力赋值模型的适用性和局限性,分别提出了直接积分改进模型、点质量改进模型和直接积分与点质量混合模型。利用数值计算验证了3组改进模型的合理性和有效性,为实际工程应用奠定了必要的理论基础。     

GPS水准采用移去恢复技术拟合大地水准面方法的研究

精化大地水准面是现代重力场和大地测量学工作的重要任务之一。探讨了利用已知水准点上的高程异常拟合区域大地水准面模型时,首先移去EGM96模型计算得到的部分,然后基于移动曲面和多面函数方法分别对剩余高程异常进行拟合,在内插点上再利用EGM96模型把移去的部分恢复,得到该点的高程异常。通过对某局部地区水准点的计算表明,引入EGM96模型的拟合高程异常的精度有所改进,对于大范围地区,这种方法有望能更好地提高大地水准面的拟合精度。     

Computer Executed Production of a Regular Grid of Height Points from Digital Contours

One of the most frequently used sources of digital terrain models are digitized contours of topographical maps. Using computer algorithms these contour-polygons serve as input for the interpolation of a matrix of height points. This article describes a possible methodology for such an interpolation procedure. For each point of the required DTM vertical profiles of the terrain—as defined by the contours—are computed. The number of profiles can be chosen at will. For the examples of this article (PROGRAM MATCON) profiles in at least four directions are computed and the height of each DTM point is found as the weighted average of the heights of this point on each of the four profiles. This approach enables the computation of both a mean square error for each DTM point and, consequently, an average mean square error of the whole DTM.     

利用等效点质量进行(似)大地水准面拟合

基于等效源原理,提出了一种半自由点质量模型,并给出了顾及相邻点空间关系构造虚拟点质量的简单快速迭代算法。实验结果表明,利用该点质量模型对离散GPS/水准观测数据进行拟合是可行的。     

多平台点云数据的单木参数提取精度分析

以浙江省海宁市4种代表行道树(广玉兰、无患子、悬铃木、香樟树)为研究对象,结合无人机(UAV)影像和三维激光扫描数据,利用ContextCapture、LiDAR360软件完成点云拼接、滤波、降噪和编辑,通过迭代最近点算法实现点云精细匹配,完成多平台点云数据融合,进而得到数字表面模型与数字高程模型,并制作冠层高度模型;采用分水岭分割算法对不同行道树树种的冠层高度模型进行单木分割,并综合局部最大值法实现单木树高、冠幅的参数提取。结果表明,本文方法进行行道树单木分割的精度高,树高、冠幅参数提取值的效果好,满足行道树几何参数调查要求。     

Computing components of the gravity field induced by distant topographic masses and condensed masses over the entire Earth using the 1-D FFT approach

 A new method for computing gravitational potential and attraction induced by distant, global masses on a global scale has been developed. The method uses series expansions and the well known one-dimensional fast Fourier transform (1-D FFT) method. It has been proven to be significantly faster than quadrature while being equally accurate. Various quantities were studied to cover the two primary applications of the Stokes–Helmert scheme of modeling effects. These two applications (or paths), given the names R/r/D and R/D/r, are briefly discussed, although the primary objective of the paper is to provide computational information to either path, rather than choosing one path as preferable to the other. It is further shown that the impact of masses outside a 4-degree cap can impact the absolute computation of the geoid at more than 1 cm, and should therefore be included in all local geoid computations seeking that accuracy. Received: 13 December 2000 / Accepted: 3 September 2001     

河塘清淤和回填量测量及计算方法讨论

本文通过一个模型讨论了平均断面法、平均高程法及数字地面模型法三种测量及计算河塘清淤量和回填量的方法，通过比较三者计算的结果，得到一些有用的可供参考的结论。     

Analysis of the factors affecting LiDAR DTM accuracy in a steep shrub area

The creation of a quality Digital Terrain Model (DTM) is essential for representing and analyzing the Earth in a digital form. The continuous improvements in the acquisition and the potential of airborne Light Detection and Ranging (LiDAR) data are increasing the range of applications of this technique to the study of the Earth surface. The aim of this study was to determine the optimal parameters for calculating a DTM by using an iterative algorithm to select minimum elevations from LiDAR data in a steep mountain area with shrub vegetation. The parameters were: input data type, analysis window size, and height thresholds. The effects of slope, point density, and vegetation on DTM accuracy were also analyzed. The results showed that the lowest root mean square error (RMSE) was obtained with an analysis window size of 10 m, 5 m, and 2.5 m, rasterized data as input data, and height thresholds equal to or greater than 1.5 m. These parameters showed a RMSE of 0.19 m. When terrain slope varied from 0–10% to 50–60%, the RMSE increased by 0.11 m. The RMSE decreased by 0.06 m when point density was increased from 4 to 8 points/m², and increased by 0.05 m in dense vegetation areas.     

房屋震害预测数字化辅助方法

为提高房屋震害预测效率,将数字化技术应用于房屋震害预测分类工作中。利用航空摄影测量、遥感及地理信息系统技术,提出两种房屋震害预测分类数字化辅助方法。若预测区域有符合条件的遥感影像对,利用航空摄影测量技术可获得DSM及DEM模型,进一步从层数上对建筑物进行分类。另一种方法则是利用遥感技术提取有关建筑物阴影信息,由阴影计算建筑物层数,进而对建筑物进行分类。利用地理信息系统自动统计不同类建筑物总面积,画出不同类建筑的地理分布图。与传统方法相比,这种方法效率高,可以纵览全局,减少房屋震害预测现场调查工作量,提高震害预测工作效率。     

The optimum expression for the gravitational potential of polyhedral bodies having a linearly varying density distribution

When topography is represented by a simple regular grid digital elevation model, the analytical rectangular prism approach is often used for a precise gravity field modelling at the vicinity of the computation point. However, when the topographical surface is represented more realistically, for instance by a triangular irregular network (TIN) model, the analytical integration using arbitrary polyhedral bodies (the analytical line integral approach) can be implemented directly without additional data pre-processing (gridding or interpolation). The analytical line integral approach can also facilitate 3-D density models created for complex geometrical bodies. For the forward modelling of the gravitational field generated by the geological structures with variable densities, the analytical integration can be carried out using polyhedral bodies with a varying density. The optimal expression for the gravitational attraction vector generated by an arbitrary polyhedral body having a linearly varying density is known. In this article, the corresponding optimal expression for the gravitational potential is derived by means of line integrals after applying the Gauss divergence theorem.     

虚拟压缩恢复法在向下延拓问题中的应用

阐述了基于虚拟压缩恢复法的重力场向下延拓,构造了点质量处于内部球内部、内部球外部和在内部球内外各有一个点质量三种点质量异常模型,试验结果支持基于虚拟压缩恢复法的向下延拓。     

贵阳市阿哈水库库容计算方法的探讨

介绍几种库容计算方法的原理和数学模型。以阿哈水库基础数据为基础,对库容计算进行分析和验证。主要从准确性、可靠性和计算效率等几方面分析。指出三角网数字地面模型计算库容具有精度高、运算速度快、适用范围广、分析计算灵活等特点。     

基于Kalman滤波的InSAR基线估计方法

针对目前SAR干涉测量中基线估计现存的问题,提出了利用Kalman滤波和配准参数进行基线估计的方法.所提出的方法具有不需地面控制点、不受地形限制和不依赖于轨道参数等优点,并可以估计时变的基线参数.利用南京地区的ERS-1/2 tandem数据进行了试验研究,并对提出的方法进行了验证.结果表明,在精确的卫星轨道数据和地面控制点不能获取时,所提出的方法仍能有效地估计InSAR基线.这在一定程度上补偿了轨道偏移带来的误差,为获取高精度的DEM奠定了基础.     

DATA PROCESSING TECHNOLOGY OF AIRBORNE 3D IMAGE

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基于等效噪声模型的数字锁相环环路参数确定方法

理想情况下,数字锁相环(DPLL)的环路参数可以通过直接计算输入原子钟与压控振荡器(VCO)的相位噪声功率谱交点来确定.但该方法不能考虑到锁相环(PLL)其他模块的噪声,这会导致输出性能恶化.针对这一问题,文中从PLL模型出发,基于PLL环路传递函数和幂律谱模型,提出PLL模块噪声的等效方法.该方法将PLL各模块噪声分...