The laplace condition in the adjustment of a chain of triangles

Summary The purpose of this treatise is to study in detail the influence of the approximations usually applied in the Laplace condition, on the adjusted elements of a chain of triangles. In § 1 the Laplace condition is derived once again from the well-known Laplace equation, because in our opinion the usual deriviations are not quite correct. In §§ 2–6 the Laplace condition is converted to a form—terms containing first powers of s: R inclusive—suitable for an application in the adjustment of a chain of triangles. The usual approximate form is derived from it by omitting the terms mentioned. In § 7 the influence of these approximations is examined by adjusting a chain of triangles twice over: applying the exact resp. the approximate Laplace condition and comparing the results. From this it is concluded that in all normal cases the influence of applying the approximations is negligible and that the validity of this conclusion is independent of a possible future increase of the accuracy of observation.     

Numerical solution to the oblique derivative boundary value problem on non-uniform grids above the Earth topography

The paper presents a numerical solution of the oblique derivative boundary value problem on and above the Earth’s topography using the finite volume method (FVM). It introduces a novel method for constructing non-uniform hexahedron 3D grids above the Earth’s surface. It is based on an evolution of a surface, which approximates the Earth’s topography, by mean curvature. To obtain optimal shapes of non-uniform 3D grid, the proposed evolution is accompanied by a tangential redistribution of grid nodes. Afterwards, the Laplace equation is discretized using FVM developed for such a non-uniform grid. The oblique derivative boundary condition is treated as a stationary advection equation, and we derive a new upwind type discretization suitable for non-uniform 3D grids. The discretization of the Laplace equation together with the discretization of the oblique derivative boundary condition leads to a linear system of equations. The solution of this system gives the disturbing potential in the whole computational domain including the Earth’s surface. Numerical experiments aim to show properties and demonstrate efficiency of the developed FVM approach. The first experiments study an experimental order of convergence of the method. Then, a reconstruction of the harmonic function on the Earth’s topography, which is generated from the EGM2008 or EIGEN-6C4 global geopotential model, is presented. The obtained FVM solutions show that refining of the computational grid leads to more precise results. The last experiment deals with local gravity field modelling in Slovakia using terrestrial gravity data. The GNSS-levelling test shows accuracy of the obtained local quasigeoid model.     

二维复合介质Laplace方程解的本征函数方法

在Ｂｅｒｇｍａｎ表示的基础上,对二维复合介质找到一套基函数,利用本征函数展开建立了基于第一性原理的计算二维复合介质Ｌａｐｌａｃｅ方程的求解方法。得到了这类Ｌａｐｌａｃｅ方程解的一般结果。     

基于俯仰轴相交和球拟合的天线旋转中心测量方法

针对传统天线旋转中心测量时,俯仰轴生成方式不严密对其精度和可靠性产生不利影响的问题,提出了俯仰轴相交和球拟合两种新的旋转中心测量方法。对不同方位下标志点绕俯仰轴的运动轨迹进行圆拟合,得到含有方位信息的俯仰轴,多条俯仰轴求交点作为旋转中心,称之为俯仰轴相交法,较传统方法可靠性更高。对标志点的运动轨迹进行球拟合,取所有球心的均值作为旋转中心,称之为球拟合法,避免了圆拟合及求交点的过程,方法更为严密。以3台φ3 m上行阵天线为实验对象,应用全站仪和工业摄影测量技术获取标志点在规划姿态下的坐标,采用两种新方法处理观测数据,均得到了内符合精度达亚毫米级的旋转中心。     

地球主惯性矩

地球主惯性矩属于大地测量学和天文学的基本地球参数.研究地球主惯性矩及有关问题.第一节研究主惯性矩和地球扁率的计算公式;第二节研究主惯性轴坐标系中2阶位系数的计算;第三节研究地球主惯性轴方向的确定方法,第四节给出地球主惯性矩、主惯性轴方向和地球扁率的数值结果.     

关于天体平衡形状问题

利用拉梅谐和函数理论,证明了共焦椭球成层分布三轴椭球体的外部引力位与均质三轴椭球体的外部引力位具有一致的形式。因而,若不顾及天体的内部静力平衡假设仅考虑天体表面平衡时,有关天体平衡形状的马克劳林理论、雅哥比理论和骆熙极限等对共焦椭球成层分布模型也是成立的。     

Coerciveness of the linear gravimetric boundary-value problem and a geometrical interpretation

In this paper the linear gravimetric boundary-value problem is discussed in the sense of the so-called weak solution. For this purpose a Sobolev weight space was constructed for an unbounded domain representing the exterior of the Earth and quantitative estimates were deduced for the trace theorem and equivalent norms. In the generalized formulation of the problem a special decomposition of the Laplace operator was used to express the oblique derivative in the boundary condition which has to be met by the solution. The relation to the classical formulation was also shown. The main result concerns the coerciveness (ellipticity) of a bilinear form associated with the problem under consideration. The Lax-Milgram theorem was used to decide about the existence, uniqueness and stability of the weak solution of the problem. Finally, a clear geometrical interpretation was found for a constant in the coerciveness inequality, and the convergence of approximation solutions constructed by means of the Galerkin method was proved. Received: 21 June 1996 / Accepted: 14 April 1997     

Method of reducing HASM boundary error

High accuracy surface modeling (HASM) constructed based on the fundamental theorem of surface is more accurate than the classical methods. However, because of boundary error, location error, etc, HASM has a big accuracy loss in real-world examples. In former researches we solved the location error with Taylor expansion. In order to reduce the HASM boundary error and improve its accuracy further, this paper presents a new method of Laplace interpolation to compute the region boundary value. Gaussian synthetic surface and the real world test region are employed to validate the efficiency of this method. Results show that the boundary value computed with Laplace interpolation is more accurate than the classical methods, which can be regarded as an alternative for boundary value computation.     

南京奥体中心主轴线的测设

结合南京奥体中心主轴线的测设实践介绍了一种不同于常规的归化法轴线测设方法,结合测量误差理论对该方法进行了精度分析,给出了相应的精度估算式,通过工程实例的具体数据说明该方法具有较高的归化精度。     

大型建筑物主轴线相关性问题研究

随着现代建筑施工技术的发展,建筑物的结构越来越复杂,对施工测量技术和方法的要求也越来越高.对于大型建筑群,尤其是连体建筑,要保证工程质量,不仅要对各建筑主轴线进行准确定位,还要考虑各主轴线的相关性.本文结合中新城上城项目,提出建筑主轴线相关性研究的一些方法,取得了预期的效果.     

改进Laplace的无人机图像边缘检测算法研究

当图像灰度发生急剧变化时,常规算法存在"阈值检测不敏感"的问题.针对这一问题,借鉴RGB三相分解变换的思路,基于Laplace算法基本原理,文中提出BRGB-ALaplace算法.该算法先进行图像增强,并用高斯滤波器平滑图像和抑制噪声;再对RGB 3个相位分量方向进行拉普拉斯模板锐化拉伸,对这3个分量进行相位重组,实现...     

地面网与空间网联合平差中起算边长和起算方位角权的确定

本文全面分析了拉普拉斯方位角和起算边长的精度，指出了联合平差中这两类元素不能作为固定值，而应视为变量且赋予相应的权，并对权的取法进行了探讨。     

Tectonic inferences from the statistical treatment of the remote sensing lineament fabric data associated with the Great Boundary Fault of Rajasthan,India

A systematic statistical analysis of the lineament fabric data associated with the Great Boundary Fault of Rajasthan provides 26 axes of high density girdles. Further statistical treatment of these isolated axes following the methods of analysis of directional data indicates that the lineament can be classified into genetic categories. The result indicates that the Great Boundary Fault and the Chambal Fault are genetically related and that the majority of the lineaments are the result of the reactivation of the Great Boundary Fault under a southward directed dominant stress field.     

一种适用大旋转角的GPS网三维平差方法

在工程测量中往往采用工程坐标系,该坐标系坐标轴可能与GPS采用的WGS84坐标系的相应坐标轴间存在较大的旋转角,此时若仍直接按照一般方法进行三维约束平差计算会给结果带来不利影响,本文给出了一种适用大旋转角的GPS网三维平差方法,该方法能够很好地处理大旋转角时直接采用一般三维平差模型计算带来的不利影响,同时又能够获得平差后工程网中各点的点位精度。工程应用表明该方法非常有效,具有很好的应用价值。     

L_1-范估计的无偏性

根据一元Laplace分布的概率密度函数及分布函数公式 ,推导了当观测值个数n为偶数时 ,中位数的概率密度函数 ;在此基础上证明了L1 范估计的无偏性     

New Solution for the Earth’s Free Wobble and Its Geophysical Implications

In this paper, the theory of the free wobble of the triaxial Earth is developed and new conclusions are drawn: the Euler period should be actually expressed by the first kind of complete elliptic integral; the trace of the free polar motion is elliptic and the orientations of its semi-minor and major axes are approximately parallel to the Earth’s principal axes A and B, respectively. In addition, the present theory shows that there is a mechanism of frequency-amplitude modulation in the Chandler wobble, whi...     

大气折射的精确计算

不少著名学者,如牛顿、布拉得雷、拉普拉斯和贝塞耳等都对大气折射进行过研究,然而其精确计算,至今仍是一个尚未解决问题。本文在设立一个新的变量的基础上,导出了高精度的计算公式。     

Influence of sample size on line-based positional assessment methods for road data

Sample size influences considerably the variability of results of estimation processes, but this issue has never previously been analyzed for line-based positional assessment methods. The basis of the analysis is a simulation process which extracts homologous road axes from the product and from the control survey and applies the four methods. Sample sizes of road axes range from 10 Km up to 200 Km, and for each sample size 1000 simulations were run. Results for each sample size were compared to population parameters or population distribution functions by means of statistical tests. The variability of estimations was reduced in the order of 2.5-4.5 times when sample size increased from 10 Km to 200 Km.     

The geodetic boundary value problem and the coordinate choice problem

Summary The geodetic boundary value problem (g.b.v.p.) is a free boundary value problem for the Laplace operator: however, under suitable change of coordinates, it can be transformed into a fixed boundary one. Thus a general coordinate choice problem arises: two particular cases are more closely analyzed, namely the gravity space approach and the intrinsic coordinates (Marussi) approach.     

Remote detection of geological structures: an application to the Aravalli region,western India

Optical and microwave remote sensing data are used in conjunction with a digital elevation model to map lineaments in the central parts of the Aravalli region, Rajasthan, western India. Lineament maps interpreted from each data-set are subsequently combined to derive a composite lineament map of the area. Rose plots are used to identify the prominent trends of the lineaments and compared with published structural map of the study area. Three major trends are identified, namely, the NE–SW, NNE–SSW and EW, which are interpreted to be, related to the DF1, DF2 and DF4 deformation phases identified by the previous workers through field studies. The lineaments are classified as fold axes or faults, and a total of 10-fold axes and 30 faults mapped in the area.