地心坐标反解大地坐标的非线性方程组牛顿迭代法分析     

李琦  王小辉 《测绘科学》2009,34(6)

目前的一些地心坐标向大地坐标的转换模型在计算速度,稳定性或精度方面存在一定的局限性。本文探讨了非线性方程组数值迭代的求解方法及其在MATLAB 7.0中的编程实现,并将结果与基于一元三次方程求解的严密方法做了比较分析,结果证明该方法是可以在实际中参考应用的。  相似文献   

图形坐标转换方法与实现     

周卫  张彦彦  龙毅 《地球信息科学学报》2007,9(2):101-105

图形坐标转换是CAD和GIS开发与应用的基本问题,涉及基础地理数据标准的统一、共享程度的提高和服务面的拓宽等重要问题,是地图制图输出、基础地理信息系统和专业信息系统建设中的重要功能。本文以CAD和GIS的图形坐标转换与配准为例,介绍了相关的数学模型和实现方法。  相似文献   

旋转椭球面上的应变与转动张量表达   总被引：6，自引：1，他引：5       下载免费PDF全文

刘序俨  黄声明  梁全强 《地震学报》2007,29(3):240-249

以旋转椭球体面上某点为原点建立一个大地坐标单位活动坐标架. 通过平移, 使活动坐标架的原点与以椭球中心为原点的笛卡尔单位标架的原点相重合. 然后再通过两次标架旋转, 使活动坐标架与笛卡尔单位标架完全重合. 本文给出了使两个单位标架相重合的转换关系式, 以及该点位移在两个单位标架中的坐标转换式; 在此基础上, 考虑该点的位移及活动坐标架皆为该点大地坐标的函数, 经复杂推导, 分别给出了该点位移向量的微分在大地坐标系中的分量以及该点分别沿坐标曲线的弧微分表达式, 继而导出了该点的位移梯度矩阵; 最后推导出了椭球坐标系的应变张量与转动张量表达式, 并对转动张量的几何含义进行了较详细的解释, 且采用曲面理论对球面与椭球面的应变张量间的内在关系进行了讨论.   相似文献   

Least squares and integral methods for the spherical harmonic analysis of theSq-field     

Koji Kawasaki  S. Matsushita  J. C. Cain 《Pure and Applied Geophysics》1989,131(3):357-370

Spherical harmonic coefficients (SHCs) for the daily magnetic variation fields (solar and lunar) and the main field of the earth are usually estimated by the method of least squares applied to a truncated spherical harmonic series. In this paper, an integral method for computing the SHCs for the solar quiet daily magnetic variation fieldSq is described and applied toSq data for May and June 1965. TheSq SHCs thus derived are then compared with the results obtained using both unweighted and weighted versions of the least squares method. The weighting used tends to orthogonalize the least squares terms. The integral and weighted least squares results agree closely for terms up to order 4 and degree 30, but both disagree considerably for the higher degree terms with the results of the unweighted least squares. Errors introduced by the numerical integration can be shown to be small, hence the disagreement between integral and unweighted least squares coefficient sets arises from improper weighting. Also, it is concluded that discrepancies between the geomagnetic northward and eastward component-derived coefficient sets arise from either time-dependent external sources that produce non-local-time, based fields or nonpotential sources and not from truncation of the spherical harmonic series as has previously been suggested.Deceased.  相似文献   

Descriptive statistics for N -dimensional closed arrays: A spherical coordinate approach     

Clifford R. Stanley 《Mathematical Geology》1990,22(8):933-956

Recent publications have demonstrated that the composition of a system can be described by the angles which define the vector resulting from the projection of the composition onto the unit hypersphere. Although published trigonometric relationships allow determination of the angles in any number of dimensions, no general hyperdimensional recursive formulae exist for the calculation of these quantities and their variances and covariances. A general methodology for calculating the angles which describe the compositions of systems in any number of dimensions is presented. These angles can be used to calculate statistics (central moments and resultant vectors) describing the central tendency and dispersion among rock compositions, as well as to quantify the angular differences between compositions. Equations that relate the variances and covariances of these angular variables to the variances and covariances of the actual component proportion variables are presented, allowing projection of these measurements from one reference frame to another (cartesian to spherical and vice versa).  相似文献   

地图数字化数据坐标变换的相关性分析   总被引：4，自引：0，他引：4  

余晓红  刘大杰 《武汉大学学报(信息科学版)》2002,27(5):456-461

将用于求定地图数字化坐标转换参数的已知点的地面坐标和数字化坐标都当作观测值，用随有参数的条件平差求定转换参数，对采用4个已知点、9个已知点分别进行相似与仿射变换进行了分析，计算了格网点之间的相关系数，进一步分析了格网点间相关系数的分布规律，对转换后的坐标相关性进行了讨论。  相似文献   

带缓和曲线的特大桥坐标计算及放样方法     

夏冬君  王鑫  杨继禹 《测绘与空间地理信息》2001,24(4):44-46

介绍一种带缓和曲线的特大桥桥墩在测量坐标系下的坐标计算及桥墩放样方法 ,以及Leica全站仪在桥梁施工放样中的应用  相似文献   

一个压力坐标下的海洋环流模式   总被引：5，自引：0，他引：5  

Huang Ruixin  Jin Xiangze  Zhang Xuehong 《大气科学进展》2001,18(1):1-22

A new oceanic general circulation model in pressure coordinates is formulated. Since the bottom pressure changes with time, the vertical coordinate is actually a pressure-σ coordinate. The numerical solution of the model is based on an energy-conservation scheme of finite difference. The most important new feature of the model is that it is a truly compressible ocean model and it is free of the Boussinesq approxima tions. Thus, the new model is quite different from many existing models in the following ways: 1) the exact form of mass conservation, 2) the in-situ instantaneous pressure and the UNESCO equation of state to calculate density, 3) the in-situ density in the momentum equations, 4) finite difference schemes that conserve the total energy. Initial tests showed that the model code runs smoothly, and it is quite stable. The quasi-steady circulation patterns generated by the new model compare well with existing models, but the time evolution of the new model seems different from some existing models. Thus, the non-Boussinesq models may provide more accurate information for climate study and satellite observations.  相似文献   

外部质量产生的扰动位的球谐展开式     

于锦海 《测绘学院学报》1996,(3)

本文讨论了参考椭球面之外，地球质量产生的扰动位的球谐展开式。分别在地球的平均球面上以及地球表面之外，给出了该扰动位的球谐展开式，为进一步研究外部质量对扰动位的影响建立了理论基础。  相似文献   

地磁场模型和冠谐分析   总被引：4，自引：2，他引：4  

安振昌 《地球物理学进展》1992,(3)

地磁场是由内源场(地核场和地壳场)和外源场(电离层场和磁层场)组成的,地磁场模型是表示地磁场时空分布的数学表达式.本文简述了地磁场全球模型和区域模型的计算方法和应用;评述了冠谐分析方法及其在地磁学中的应用;介绍了地磁场模型误差的主要来源.  相似文献