极空白对三类重力梯度边值问题球谐分析解的影响分析

就极空白对三类重力梯度边值问题球谐分析解的影响进行了定性探讨和定量分析,结果表明,基于球面边界的垂直-垂直重力梯度边值问题球谐分析解的零次项、垂直-水平重力梯度边值问题球谐分析解的一次项、水平-水平重力梯度边值问题球谐分析解的二次项受极空白问题的影响最为显著。     

利用Molodensky理论求解第二大地边值问题

过去由于无法获得大地高数据，传统的第三大地边值问题采用重力异常作为边值条件。GNSS技术的发展为第二边值问题的研究带来了契机。研究比较成熟的第三边值理论无疑为第二边值问题提供了很好的参考和借鉴，对此开展将第三边值问题中计算似大地水准面的Molodensky理论方法应用于第二边值问题的研究。首先推导了Hotine算子与梯度算子的关系，然后给出了基于Molodensky理论求解第二边值问题的算法。实验结果表明，该算法与传统第三边值问题中Molodensky理论的边值解精度相当，说明基于Molodensky理论求解第二大地边值问题是完全可行的。     

论交向摄影测量之构形

本文导出了交向摄影测量新的精度估算公式，并在此公式的基础上讨论了非对称情形交向摄影的构形问题。无论对于什么情形，本文总能给出该情形下的一组最优构形参数值。     

多点最小二乘匹配的可变权阵阵列松弛算法

本文详细介绍了多点最小二乘匹配的常规算法和由阵列代数表示的阵列松弛算法，并把Ｒａｕｈａｌａ限于等权的情形推广到不等权（变权）的情形，给出了实现阵列松弛的步骤，最后从计算效率，匹配精度对常规算法，等权阵列松弛和不等权阵列松弛进行了比较，分析，揭示了变权阵列松弛法巨大的实用潜力。     

保持矩形图廓的变比例尺地图投影

本文提出了一种毋需“坐标压缩”的变比例尺地图投影方法,利用它可以较好地提高投影质量,解决现有变比例尺地图投影在矩形图幅情形下所存在的变形问题,亦可避免多焦点投影各焦点局部变形的相互影响。本文所给出的投影公式以及等比例尺线的概念,在理论和实用上也有普遍意义。     

非线性混合大地边值问题的二阶项影响

本文讨论了两类非线性混合大地边值问题在级数展开中的非线性二阶项的影响，建立了关于二阶项的定解问题，并给出了单层密度扰动解。此外，以第二类混合边值问题为例，利用ＧＥＭ１０Ｂ模型，对二阶项影响予以数值实现。计算表明，非线性二阶项对大地水准面积起伏的影响约为２０￣７５厘米。     

噪声互相关情况下的Kalman滤波

考虑观测误差与动力学模型误差的相关性，本文讨论噪声互相关情形下的Kalman滤波解算问题。分别从自由极值、条件极值和相关转换三个方面导出了噪声互相关情形下的Kalman滤波解，并在噪声独立时得出标准Kalman滤波解。     

地球重力场椭球谐模型的建立

本文以参考椭球面为边界来研究下列边值问题其中Σ是参考椭球面，γ是Ｓｏｍｉｇｌｉａｎａ正常重力，ｈ是Σ的外法向。我们首先在保持扁率量级的前提下推导了问题（＊）的简化形式，然后研究了求解的方法，最后讨论了建立椭球谐重力场模型的理论。     

扰动重力数据精度对GPS/重力边值问题的影响研究

以GPS／重力边值问题为基本的数学模型，通过数值模拟方法，对不同精度的扰动重力数据对GPS／重力边值问题的影响厦误差量级进行了模拟和分析，得出了一些有意义的结论。     

地形图新旧图幅编号自动检索算法及其可视化实现

为检索地形图上指定区域各种比例尺下的新旧图幅编号提出一种详细的算法.以1:100万比例尺为基准分情形完成对指定选区覆盖的、指定比例尺下的新旧图幅编号的遍历,并借助VB和MapObjects将该算法可视化实现.     

随机Dirichlet问题解的调和展开

针对重力学随机Dirichlet问题,通过适当地对边界检验函数的分解,并在随机边界样本空间中提取确定性部分的对偶基,本文将随机Dirichlet问题的一般解展开为一随机系数的调和级数形式。     

Uniqueness and existence for the geodetic boundary value problem using the known surface of the earth

The geodetic boundary value problem using the known surface of the earth is defined and shown to have at most one solution. Furthermore it is proved that the solution exists and that its harmonic part can be represented by the potential of a simple layer under the sufficient condition that at the surface of the earth directions are known which lie differentially close to the gradients of the gravity field. The advantages of this boundary value problem are outlined in comparison to the boundary value problem formulated by Molodensky.     

The ellipsoidal correction to the Stokes kernel for precise geoid determination

Solving the geodetic boundary-value problem (GBVP) for the precise determination of the geoid requires proper use of the fundamental equation of physical geodesy as the boundary condition given on the geoid. The Stokes formula and kernel are the result of spherical approximation of this fundamental equation, which is a violation of the proper relation between the observed quantity (gravity anomaly) and the sought function (geoid). The violation is interpreted here as the improper formulation of the boundary condition, which implies the spherical Stokes kernel to be in error compared with the proper kernel of integral transformation. To remedy this error, two correction kernels to the Stokes kernel were derived: the first in both closed and spectral forms and the second only in spectral form. Contributions from the first correction kernel to the geoid across the globe were [−0.867 m, +1.002 m] in the low-frequency domain implied by the GRIM4-S4 purely satellite-derived geopotential model. It is a few centimeters, on average, in the high-frequency domain with some exceptions of a few meters in places of high topographical relief and sizable geological features in accordance with the EGM96 combined geopotential model. The contributions from the second correction kernel to the geoid are [−0.259 m, +0.217 m] and [−0.024 m, +0.023 m] in the low- and high-frequency domains, respectively.     

GPS在物理大地测量中的应用及GPS边值问题

针对GPS技术逐步用于物理大地测量的现状，从物理大地测量的基本原理及方法入手，分析了GPS对传统物理大地测量理论及方法所产生的影响、GPS在解决物理大地测量中的一些难题所发挥的作用以及对物理大地测量的一些功能所造成的变化。重点讨论了物理大地测量边值问题的基本属性的改变、第二边值问题的应用、高程系统的确定、GPS边值问题的定义、特征及求解。最后，对GPS与物理大地测量进一步结合所面临的有关问题进行了简要论述。     

On the solvability of the Stokes pseudo-boundary-value problem for geoid determination

A new form of boundary condition of the Stokes problem for geoid determination is derived. It has an unusual form, because it contains the unknown disturbing potential referred to both the Earth's surface and the geoid coupled by the topographical height. This is a consequence of the fact that the boundary condition utilizes the surface gravity data that has not been continued from the Earth's surface to the geoid. To emphasize the `two-boundary' character, this boundary-value problem is called the Stokes pseudo-boundary-value problem. The numerical analysis of this problem has revealed that the solution cannot be guaranteed for all wavelengths. We demonstrate that geoidal wavelengths shorter than some critical finite value must be excluded from the solution in order to ensure its existence and stability. This critical wavelength is, for instance, about 1 arcmin for the highest regions of the Earth's surface. Furthermore, we discuss various approaches frequently used in geodesy to convert the `two-boundary' condition to a `one-boundary' condition only, relating to the Earth's surface or the geoid. We show that, whereas the solution of the Stokes pseudo-boundary-value problem need not exist for geoidal wavelengths shorter than a critical wavelength of finite length, the solutions of approximately transformed boundary-value problems exist over a larger range of geoidal wavelengths. Hence, such regularizations change the nature of the original problem; namely, they define geoidal heights even for the wavelengths for which the original Stokes pseudo-boundary-value problem need not be solvable. Received 11 September 1995; Accepted 2 September 1996     

维格纳3-j符号在解算混合边值问题中的应用

混合边值问题的直接解算对于提高地球重力场模型的精度有着重要意义,本文主要讨论了量子力学中的维格纳3-i符号的计算方法以及利用3-i符号直接解算混合边值问题,模拟计算的结果表明,其解算精度是很高的。     

Numerical solution of geodetic boundary value problems using a global reference field

One of the most serious practical limitations of boundary element methods for gravity field determination is that they cannot make efficient use of existing satellite geopotential models. Three basic approaches to solving the problem are developed: (1) alternative representation formulas; (2) modified kernel functions of classical representation formulas; and (3) modified trial and test spaces. The three methods are tested and compared for the altimetry–gravimetry II boundary value problem. It is shown that there is in fact a significant improvement when compared to the pure boundary element solution. Most promising is the method of multiscale trial and test spaces which, in addition, yields sparse system matrices. Received: 7 September 1998 / Accepted: 16 June 1999     

超定边值问题的差分法

物理大地测量面临着越来越多的数据:高程异常、垂线偏差、重力异常、重力梯度等,因此出现了超定边值问题,本文采用求解偏微分方程最简单而又最常用的差分法,对这一问题进行了初步的研究。