GPS/重力边值问题实用公式推导及分析

基于GPS/重力边值问题的连续趋近解,推导了形式上更为简单,物理意义更加明确的实用公式.同时利用扰动重力的泰勒级数展开式直接证明了GPS/重力边值问题实用公式的正确性,并且进一步阐明其物理含义.在实用公式中,我们引入了扰动重力垂直梯度这个物理量,这在观测数据多元化的今天具有积极意义.     

The GPS-gravimetry boundary value problem

Boundary value problem (BVP) plays a funda-mental role in physical geodesy that aims at determin-ing the earth’s shape and its external gravity field. TheMolodensky BVP and the Stokes BVP are typical inphysical geodesy, and the gravity anomaly is a kind ofbasic data. With the wide use of GPS, measurementaccuracy of the earth’s surface can reach one centime-ter, while that of the gravity measurement can reachμgals. Hence, it is necessary to establish a new kind ofBVP which can satisfy…     

On the boundary condition of the gravity disturbing potential

Summary The boundary condition for the gravity disturbing potential was derived upto the second-order terms and the influence of the second-order terms was investigated.Dedicated to 90th Birthday of Professor Frantiek Fiala     

On the solution of the boundary problem of the potential theory by means of the vertical derivative of the gravity anomaly

Summary The boundary problem of the potential theory is treated for the case in which the values of the vertical derivative of the gravity anomaly are known. There boundary conditions are derived and alternatives are also treated.Dedicated to RNDr. Jan Pícha, CSc., on his 60th Birthday     

Mixed boundary value problem in an elastic quarter-space

Summary The stress and displacement throughout a homogeneous, isotropic, elastic quarterspace have been evaluated when the stress is prescribed on one of the plane boundaries and the displacement on the other. The variations of the displacement and stress on the boundaries with time and distance from the origin have been shown graphically.     

地球重力场恢复中的位旋转效应

分析了地球自转引起的位旋转效应公式中采用近似速度的影响. 对一组GFZ的快速科学轨道、一组TUM的约化动力法轨道以及一组GFZ的事后科学轨道,计算了星历提供的速度与只有地球引力场对卫星产生作用时的卫星速度的差值,其中参考重力场模型分别采用EGM96、EIGEN2和EIGEN_CG01C. 通过比较得出：轨道数据与EIGEN2地球重力场模型的自恰性优于EGM96和EIGEN_CG01C地球重力场模型. 速度差各分量的变化具有很明显的周期性且与卫星轨道的运行周期相吻合. 当要求在卫星轨迹处获得1m2/s2精度的扰动位时,也即要求位旋转效应公式中卫星速度的近似精度小于2mm/s时,GFZ的快速科学轨道、TUM的约化动力法轨道只需要剔除那些速度精度不满足要求的卫星轨迹点;当要求在卫星轨迹处获得0.5m2/s2精度的扰动位时,应当重新估算上述轨道的速度信息,或采用精度更高的GFZ事后科学轨道.     

On the solution of the Molodenskii boundary value problem using successive approximations

Gravimetric methods of determining the figure of the Earth can be divided into two groups. The first employs an auxiliary surface—the geoid. The second employs the so-called quasigeoid as an auxiliary surface. Its main advantage is in that it only uses surface measurements and that it does not require knowledge of the structure of the Earth's crust. This method was treated in [1]. The results display an accuracy of the order of the Earth's flattening. The purpose of this paper is to show that this method can be applied theoretically to reach an arbitrary accuracy.     

基于球面边值问题的点质量调和分析方法

对全球扰动点质量模型而言,可以假定虚拟扰动质点系位于地球内部同一Bjerhamar球面上,同时把边值界面视为球面.本文针对这一假设下所形成的线性方程组的系数阵,运用快速傅里叶变换的方法,得到了点质量模型解算中利用分块循环矩阵分解大型线性方程组的新方法.全球30′×30′扰动点质量模型259200阶方程组的解算分解为720个360阶方程组的解算,解决了点质量模型构建中大型线性方程组的稳定解算问题.推导了全球点质量模型与球谐位系数模型的转换关系,得到了一种基于球面边值问题的点质量调和分析方法.数值模拟试验表明,在适当选取点质量埋深度的情况下,本文的点质量调和分析方法较传统的调和分析方法精度更高.     

Similarity solutions to the second boundary value problem of unsaturated flow through porous media

Similarity solutions to the second boundary value problem of unsaturated flow are studied in one-dimensional, semi-infinite porous media with the soil-water diffusivity proportional to some power of the water content. The existence and uniqueness of two types of similarity solutions to the problem are investigated and the properties of these solutions are presented. It is shown that these two types of similarity solutions exist and that they may not be unique for every parameter range studied. The use of the similarity solutions is discussed for the experimental determination of soil-water diffusivity.     

孕震过程中重力位、重力、重力梯度变化的数值模拟研究

简要介绍了为探索和解释地震前后重力变化的各种孕震模式,推导了由孕震引起的密度变化和位移与地面重力位、重力、重力梯度之间的变化关系。摸拟计算了孕震位移和密度变化引起的重力位、重力、重力梯度变化的空间分布并分析了重力位、重力、重力梯度变化的空间分布特征。与此同时,采用广义司托克斯云积分和有限差分方法对云南丽江7. 0级地震前重力位、重力、重力水平梯度进行了计算。结果表明,强震前重力位、重力、重力梯度有其自身的变化特征,这对预测强震有实际意义。     

Accuracy of deflections of vertical determined from discrete solution of the geodetic boundary value problem

Summary The general problem of determining the figure of the earth leads to the solution of the geodetic boundary value problem. By its discrete approximation we obtain the discrete disturbing potential that maintains all properties of the original problem. Thus, the discrete approximation of the disturbing potential can be used in studying the behaviour of the earth's gravity field outside the disturbing masses. The deflections of the vertical are one of the quantities describing the behaviour of the earth's gravity field. A method for their computation from the discrete solution of the geodetic boundary value problem is put forth and estimates for its accuracy are given.     

Variational solution about over-determined geodetic boundary value problem and its related theories

A new solving method for Laplace equation with over-determined geodetic boundary conditions is pro- posed in the paper, with the help of minimizing some kinds of quadratic functional in calculus of variation. At first, the so-called variational solution for over-determined geodetic boundary value problem is defined in terms of principles in calculus of variation. Then theoretical properties related with the solution are derived, especially for its existence, uniqueness and optimal approximation. And then the computational method of the solution is discussed, and its expression is exhibited under the case that all boundaries are spheres. Finally an arithmetic example about EGM96 gravity field model is given, and the computational results show that the proposed method can efficiently raise accuracy to deal with gravity data. In all, the variational solution of over-determined geodetic boundary value problem can not only fit to deal with many kinds of gravity data in a united form, but also has strict mathematical basements.     

Flowing partially penetrating well: solution to a mixed-type boundary value problem

A new semi-analytic solution to the mixed-type boundary value problem for a flowing partially penetrating well with infinitesimal skin situated in an anisotropic aquifer is developed. The solution is suited to aquifers having a semi-infinite vertical extent or to packer tests with aquifer horizontal boundaries far enough from the tested area. The problem reduces to a system of dual integral equations (DE) and further to a deconvolution problem. Unlike the analogous Dagan's steady-state solution [Water Resour. Res. 1978; 14:929–34], our DE solution does not suffer from numerical oscillations. The new solution is validated by matching the corresponding finite-difference solution and is computationally much more efficient. An automated (Newton–Raphson) parameter identification algorithm is proposed for field test inversion, utilizing the DE solution for the forward model. The procedure is computationally efficient and converges to correct parameter values. A solution for the partially penetrating flowing well with no skin and a drawdown–drawdown discontinuous boundary condition, analogous to that by Novakowski [Can. Geotech. J. 1993; 30:600–6], is compared to the DE solution. The D–D solution leads to physically inconsistent infinite total flow rate to the well, when no skin effect is considered. The DE solution, on the other hand, produces accurate results.     

重力位场谱分析方法研究综述

利用Fourier变换将空间域位场数据变换到频率域进行谱分析是重力位场数据处理中的一种重要方法．这种方法在位场的延拓及转换、场分离、物性界面的正反演和位场的曲化平处理等方面已得到广泛的应用．本文详细介绍了位场谱分析的基本理论和方法,总结了国内外最近几十年来在这方面取得的主要成果,并提出了未来值得深入研究的方向．     

On one formulation of the frontal wave problem

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Spectral analysis for recovering the Earth's gravity potential by satellite gravity gradients

根据仪器功率谱密度和重力位系数阶方差的定义,本文建立了卫星重力梯度测量噪声功率谱密度与重力场模型的误差阶方差的直接对应关系,并基于此讨论了重力梯度测量精度、卫星轨道高度以及运行时间对地球重力场恢复精度的影响.相比于传统的基于最小二乘法评估卫星载荷噪声对地球重力场恢复精度的影响而言,本文提出的方法简单、直接,有助于快速设计和确定卫星重力测量计划的有关参数.     

A survey of free boundary value problems in the theory of fluid flow through porous media: variational inequality approach — Part II

A survey is presented of work done using variational inequalities in solving free-boundary problems arising in the filtration of liquids through porous materials. In 1971 Baiocchi proposed this new method for solving such problems. This method proved effective not only from the purely theoretical point of view, that is, for proving the existence and uniqueness of a solution, but also from the point of view of yielding new, simple and efficient numerical solution schemes. This new method was systematically and extensively developed by mathematicians at the Laboratory of Numerical Analysis at the National Research Centre in collaboration with the Institute of Hydraulics of the University of Pavia. The aim of this survey is to present the basic ideas of this method, its applications, and other problems to which various researchers have extended the method. Also, the paper is written in such a manner as to be understood by a more general audience other than mathematicians, who are the ones who have done the majority of work in this area.     

A survey of free boundary value problems in the theory of fluid flow through porous media: variational inequality approach — Part I

A survey is presented of work done using variational inequalities in solving free-boundary problems arising in the filtration of liquids through porous materials. In 1971 Baiocchi proposed this new method for solving such problems. This method proved effective not only from the purely theoretical point of view, that is, for proving the existence and uniqueness of a solution, but also from the point of view of yielding new, simple and efficient numerical solution schemes. This new method was systematically and extensively developed by mathematicians at the Laboratory of Numerical Analysis at the National Research Centre in collaboration with the Institute of Hydraulics of the University of Pavia. The aim of this survey is to present the basic ideas of this method, its applications, and other problems to which various researchers have extended the method. Also, the paper is written in such a manner as to be understood by a more general audience other than mathematicians, who are the ones who have done the majority of work in this area.     

Gravitational potential inside 3-D inhomogeneous earth: A boundary — Value problem for the Poisson equation

Summary The problem of determining the gravitational potential inside the Earth is discussed under assumptions that the 3-D density distribution is known, that the external gravity field is described by known Stokes parameters and, finally, that the smoothed Earth surface is defined by a set of topography coefficients. The spectral method was used to separate the angular and radial parts. The solution of Poisson's equation for the internal gravitational potential was reduced to a system of ordinary differential equations with homogeneous boundary conditions and to a system of linear algebraic equations.

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