Construction of Green's function to the external Dirichlet boundary-value problem for the Laplace equation on an ellipsoid of revolution

Green's function to the external Dirichlet boundary-value problem for the Laplace equation with data distributed on an ellipsoid of revolution has been constructed in a closed form. The ellipsoidal Poisson kernel describing the effect of the ellipticity of the boundary on the solution of the investigated boundary-value problem has been expressed as a finite sum of elementary functions which describe analytically the behaviour of the ellipsoidal Poisson kernel at the singular point ψ = 0. We have shown that the degree of singularity of the ellipsoidal Poisson kernel in the vicinity of its singular point is of the same degree as that of the original spherical Poisson kernel. Received: 4 June 1996 / Accepted: 7 April 1997     

Seismic moment tensor representations and radiation patterns in unbounded media with elipsoidal cavities driven by low frequency pressure

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椭球谐和球谐系数之间一个简单的转换关系

本文推导的椭球谐系数和球谐系数相互之间转换关系的核心思想是在ε~2量级下利用Legendre函数的正交性,从球谐系数求解的积分表示出发,将积分中的椭球坐标变量与球坐标变量相互转换,从而得出椭球谐系数与球谐系数之间的转换关系。本文导出的转换关系有以下优点:①对于第二类Legendre函数的计算采用Laurent级数表示,使计算第二类Legendre函数更为简单;②保留了ε~2量级下,导出的转换关系相比文献[2]的形式更简单,满足物理大地测量边值问题线性化的要求;③顾及了余纬和归化余纬的区别。     

参数带椭球约束平差算法的应用

针对实际工程应用中遇到的参数带有范围约束的情形,提出带椭球约束的平差算法,并给出其具体模型和解算步骤。数值模拟实验和病态测边网数据计算表明,在处理病态问题时,最小二乘平差（least-squares,LS）已不适用,而与岭估计、奇异值分解法（singular value decomposition,SVD）以及不等式约束相比,本文算法精度更高。     

精确高程异常的确定

本文在顾及局部地形改正、椭球改正及大气改正的情况下,采用实测数据,应用Meissel方法和Wenzel频谱分析方法,对某盆地边缘的高程异常进行了实际计算。并将计算结果同多普勒高程异常进行了比较,证明结果是良好的。此外还对我国精确高程异常的确定提出了一些建议。     

IGS跟踪站的大地高时间序列特征分析

应用国内几个IGS跟踪站在U方向的观测数据,分析研究跟踪站大地高的变化趋势。通过对时间序列进行奇异谱分析和傅立叶变换分析,表明大地高时间序列具有一定的周期性,且周期特性明显,时间序列的时频特性表现出明显的区域性。     

铁岭县GPS控制网高程拟合精度分析

利用GPS技术测量点的平面位置可获得较高精度,但不能直接得到地面点的正常高,只能得到大地高。作者探讨了GPS高程拟合的精度与起算点的分布、整体拟合和分区拟合方法的选择、GPS高程拟合精度的分析等方法并提出了自己的见解,且通过铁岭县C级GPS网的高程拟合实例,介绍了该方法的具体应用。     

Solution to the Stokes Boundary-Value Problem on an Ellipsoid of Revolution

We have constructed Green's function to Stokes's boundary-value problem with the gravity data distributed over an ellipsoid of revolution. We show that the problem has a unique solution provided that the first eccentricity e₀ of the ellipsoid of revolution is less than 0·65041. The ellipsoidal Stokes function describing the effect of ellipticity of the boundary is expressed in the E-approximation as a finite sum of elementary functions which describe analytically the behaviour of the ellipsoidal Stokes function at the singular point = 0. We prove that the degree of singularity of the ellipsoidal Stokes function in the vicinity of its singular point is the same as that of the spherical Stokes function.     

椭球面三角形外接大地圆圆心测地坐标的另一种解法

为了在测地坐标系中确定外接大地圆圆心,采用了解非线性方程组的牛顿迭代法,解法简便,易于理解.数据验证表明,由该数值法求解的结果与由解析公式获得的结果完全一致.由此亦表明,一些繁难的大地测量计算也可改用数值法来进行.