半参数测量平差模型与系统误差处理

考虑半参数测量模型L=Bx+S+Δ,x$Rd为未知回归参数,S为未知Borel函数。本文首先利用自然样条函数法,找到符合条件的非参数自然插值样条函数。其次利用偏残差法并综合最小二乘法,导出了这种平差方法的解算公式。最后,用一个算例说明了此方法的优越性。     

整体大地测量的理论和实际应用

本文着重介绍整体大地测量确定性参数模型的理论和整体大地测量的误差分析方法，并进一步说明整体大地测量研究的理论意义和实际应用价值。     

半参数平差模型参数的两步估计

考虑半参数平差模型L=Bx+S+Δ,xεRd,S为未知回归参数,为未知Borel函数。本文首先利用自然样条函数法,找到符合条件的非参数自然样条插值函数。其次利用偏残差法并综合最小二乘法,导出了参数和非参数的解算公式,讨论了窗宽参数的选取方法。在本文的最后,将这种估计方法应用到重力场的计算中,说明了利用半参数平差模型估计参数的有效性。     

四维整体大地测量的有限单元法

本文以有限单元法为基础，将四维整体大地测量模型与固体力学方程求解构造应力场结合起来，在四维整体大地测量方程中加入了由地壳构造运动产生的地面点重力变化的观测方程，其中包含测点的位移参数，边界结点上待求以数利用有限单元法在四维整体大地测量平差过程中推估，采用统一的插值函数。     

大地测量反演线弹性构造应力场

本文基于地表大地测量位移观测值，提出用大地测量监测资料反演线弹性构造应力场方法。讨论了大地测量监测点分布式、观测随机误差以及岩体介质参数对边界力系数反演值的影响，为实际应用大地测量资料反演线弹性构造应力场提供了参考依据。     

基于力学模式的大地测量反演理论及应用

本文的研究工作主要集中在大地测量反演的模型建立、求解方法及应用的相关问题的探讨.首先,在综合分析大地测量反演理论与应用现状的基础上,明确了大地测量反演的定义并对反演方法作了分类,提出了深化大地测量反演研究的若干观点. 根据有代表性的准则函数推演出大地测量反演参数可辨识条件,给出其适用范围;概括典型的大地测量力学模型,讨论了其反演参数可辨识性问题.尝试性地提出大地测量反演的模型辨识这样的一个新课题,并初步探讨了大地测量反演模型辨识的定义、原则和方法,基本描绘了现代大地测量反演研究的系统化、模型化和智能化的架构. 探讨了适合于大地测量反演区域变形的位移数据处理方案:①基于相似变换的"特定基准"确定;②基于一种线性模型的"异常位移"定位;③局部构造有限元的处理.方案体现了一种用"拟准检定法"进行"异常位移"定位的新思想.研究了正法反演结果的几种定性检验方案和统计假设检验定量检验方法,引入一种基于概率距离的定量评价新方法. 比较了约束和非约束的各种局部最优化方法(如单纯形法、模式搜索法、鲍威尔法、变量轮换法、混合罚函数法、复合形法等)和全局搜索算法(如蒙特卡罗、遗传算法),通过反演试验,探讨了不同最优化算法在大地测量反演中的有效性.探索了遗传算法在大地测量反演应用研究中的参数设置和算法的实施步骤,反演实例得到了较好的结果. 初步研究了利用包括大地测量位移在内的2种以上的观测物理量进行联合反演的模型和实施步骤,特别提出在联合反演中引入相对权比,并将它作为待反演参数,同其他反演参数一同反演求解的理论和方法.模拟算例结果显示出这种方法具有优越性和合理性. 在阐述了中国大陆及邻域板块边界构造作用力和构造应力场反演研究现状的基础上,本文利用自己开发编制的大地测量反演程序和中国地壳观测网络GPS观测资料和主应力方向数据进行了中国大陆及邻域边界力位移反演和川滇地区边界力的联合反演研究.反演结果表明:①形成现今中国大陆内部位移场和构造应力场的主要力源仍是来自印度板块和欧亚板块的陆-陆碰撞;②太平洋板块和菲律宾海板块作用力虽然比印度板块作用力小,但仍是影响中国大陆东部的重要因素;③日本海弧后盆地现在继续着引张活动,这可能与洋壳后撤所形成的对大陆的拖曳有关;④来自北部的力承载着中国大陆北向运动作用,表现出相当大的阻力;⑤嫩江断裂和西拉木伦河断裂等似有活动迹象,活动方式不能确定;⑥南北构造带在现今构造运动中起着明显的削减作用.     

随机删失下半参数模型的补偿估计方法

考虑半参数测量模型L=Bx+S+Δ,x∈Rd为未知回归参数,S为未知Borel函数。本文首先利用自然样条函数法,找到符合条件的非参数自然插值样条函数。其次利用补偿法并综合最小二乘法,导出了这种平差方法的解算公式。在本文的最后,将这种方法与最小二乘平差方法进行了比较分析,结果说明,半参数测量模型能更接近于真实情况。     

大地测量反演中参数可辨识性问题

大地测量反演是进行大地测量物理解释研究的重要手段。在反演中，参数选择及求解（参数辨识）的正确性必须确保。本文根据有代表性的准则函数推演出大地测量反演参数可辨识条件，给出其适用范围；在概括了典型的大地测量力学模型基础上，讨论了其反演参数可辨识性问题；利用有限元数值反演算例验证了参数可辨识性的结论。表明：大地测量反演参数可辨识条件及其可辨识性的结论，体现了确定大地测量反演参数（种类和个数）理论上的必要性。     

四维整体大地测量实用模型及观测方程

顾及时空几何及物理效应的四维整体大地测量,给大地测量提出了许多新的研究课题,同时也为大地测量开辟了新的应用前景。本文从实用观点出发,建立了四维整体大地测量实用模型,并给出了地面观测值的观测方程。在所有观测方程中,都以点位速率和重力位速率为未知数,以便减少观测值的历元归算;而且随着观测历元的增加,速率参数的精度将不断提高。     

空间VLBI观测量估计大地测量参数的模拟计算

介绍了研究空间VLBI在大地测量等领域应用的意义，探讨了空间VLBI的观测量类型、观测模型及其涉及的大地测量所关心的参数；并采用1980～2004年的VLBI观测数据进行了计算，对大地测量所关心的几种参数的计算结果进行了分析。     

On a four-dimensional integrated geodesy

In contrast to continuous global considerations of time dependent boundary value problems an attempt is made to define4D-linear observation equations in the framework of integrated geodesy for discrete, more or less regional and local applications (deformation analysis) where time variations in position and in the gravity field have to be considered. The derivation is a strict analogue and extension of the3D integrated approach. In addition the construction of time dependent covariance functions is discussed, which are necessary to solve for unknown displacements and changes in the gravity potential in the generalized least squares collocation model.     

四维整体大地测量模型中的重力向量观测方程

本文论述了四维整体大地测量的基本概念。根据Hein和Grafarend等人的基本思想,推导了四维整体大地测量模型中的重力向量观测方程。其中顾及了地球固体潮和地壳形变所引起的观测量的时间相依变量。     

An integrated wavelet concept of physical geodesy

For the determination of the earth's gravity field many types of observations are nowadays available, including terrestrial gravimetry, airborne gravimetry, satellite-to-satellite tracking, satellite gradio-metry, etc. The mathematical connection between these observables on the one hand and gravity field and shape of the earth on the other is called the integrated concept of physical geodesy. In this paper harmonic wavelets are introduced by which the gravitational part of the gravity field can be approximated progressively better and better, reflecting an increasing flow of observations. An integrated concept of physical geodesy in terms of harmonic wavelets is presented. Essential tools for approximation are integration formulas relating an integral over an internal sphere to suitable linear combinations of observation functionals, i.e. linear functionals representing the geodetic observables. A scale discrete version of multiresolution is described for approximating the gravitational potential outside and on the earth's surface. Furthermore, an exact fully discrete wavelet approximation is developed for the case of band-limited wavelets. A method for combined global outer harmonic and local harmonic wavelet modelling is proposed corresponding to realistic earth's models. As examples, the role of wavelets is discussed for the classical Stokes problem, the oblique derivative problem, satellite-to-satellite tracking, satellite gravity gradiometry and combined satellite-to-satellite tracking and gradiometry. Received: 28 February 1997 / Accepted: 17 November 1997     

多种跟踪组合卫星重力场恢复方法初探

将卫星地面跟踪、高低卫星跟踪和低低卫星跟踪恢复重力场的原理进行统一 ,导出了两种能充分综合多种跟踪观测的卫星重力场恢复基本观测方程。在建立基本观测量与重力场参数的函数传输关系的基础上 ,对目前存在的重力场恢复算法给出了直观的解释 ,并以距离二次变率为重力场恢复的基本观测量 ,提出了一种能组合各种卫星跟踪观测量的动态 /动力组合定轨和重力场恢复方法。     

Space-wise approach to satellite gravity field determination in the presence of coloured noise

For many years, the gravity field of the Earth was only seen by satellite geodesy as the main factor affecting the orbit and consequently it was retrieved together with a number of other orbital perturbations. Since the advent of a new generation of accelerometers, non-gravitational perturbations can be separated from the gravity effects and a new era of gravity field estimates from space has been born. During preparatory data analysis for new missions performed by the geodetic community, three approaches have been proposed and numerically tested: the brute force method (direct approach), the semi-analytical (time-wise) method and the space-wise method. In particular, the time-wise method takes advantage of the incoming time flow of data and, after performing a Fourier transform of the observation equations, exploits the prevailing block diagonal structure of the normal equations to estimate the spherical harmonic coefficients of the gravity field. Complementary to this is the space-wise approach, which goes back to the traditional computation of the harmonic coefficients by an integration technique or by least-squares collocation. Some advantages and disadvantages are peculiar to both methods, particularly the space-wise approach, which has for a long time ignored the marked signature of the noise spectrum due to the specific measuring conditions of space-borne accelerometers. The application of a proper Wiener filter, exploiting the correlation along the orbit, embedded into an iterative scheme, seems to be the answer. The solution to this major problem of the space-wise approach is illustrated and simulation results are discussed.     

The new gravity base net 1976 of the Federal Republic of Germany (DSGN 76)

A new gravity base net (“Schweregrundnetz 1976 der Bundesrepublik Deutschland”, DSGN 76) has been established in the Federal Republic of Germany, to meet the increased requirements of geophysics, geology, metrology and geodesy. The net comprises 21 stations with three excenters each. The gravity values were determined using 4 absolute stations, 11 IGSN71-stations and about 3000 relative gravity meter observations with 4 gravity meters. Instrumental investigations and special treatment of local tidal and atmospheric effects improved the data for the least squares adjustment, which was performed by the method of observation equations following the use of condition equations. The final adjustment showed a point r.m.s. error of about 10μGal[10^?8 ms^?2]. Detailed results will be published in the ”Veröffentlichungen der Deutschen Geodätischen Kommission”.     

大地测量联合反演理论和方法研究进展

综述了10多年来国内外大地测量反演问题研究的成果及最新进展，特别是大地测量联合反演模型、大地测量联合反演算法以及大地测量联合反演理论和方法在研究地壳运动、地球构造等中的应用成果，讨论了联合卫星测高、声纳测深及海洋激光雷达遥感信息反演海洋环境参量，联合INSAR、GPS和水准资料反演研究地壳运动和联合各种观测数据反演研究地球内部构造问题。随着科学技术的发展，大地测量联合反演理论和方法研究将在监测全球变化、防灾减灾、发展地球科学理论方面取得更大进展。     

关于勒让德函数的一组特殊定积分递推公式

根据勒让德函数理论的基本递推公式和基本性质 ,详细推导了在重力梯度调和分析中出现的一组特殊定积分的递推公式 ;并且指出 ,这组递推公式对于物理大地测量的调和分析理论也具有一定的价值。