基于GRACE卫星重力数据确定地球重力场模型WHU-GM-05

基于卫星轨道运动的能量积分方程,可导出利用卫星跟踪卫星数据求解地球重力场的实用公式.本文在Jekeli给出的公式基础上导出了基于能量守恒方程利用两颗低-低卫星跟踪的扰动位差求解重力位系数的严密关系式.基于两颗GRACE卫星的观测数据,采用本文导出的严密能量积分方法求解得到120阶的GRACE地球重力场模型,命名为WHU-GM-05;将WHU-GM-05模型与国际上同类重力场模型EIGEN-GRACE系列和GGM02S分别在阶方差和大地水准面高等方面作了比较,并与美国和中国的部分地区GPS水准观测值进行了精度分析.结果表明基于本文推导的严密双星能量守恒方程得到的WHU-GM-05重力场模型精度与国际上同类重力场模型的精度相当.     

新一代GRACE重力卫星反演地球重力场的预期精度

基于低低卫卫跟踪模式,本文主要探讨利用动力学法融合精密轨道数据和星间测距或距离变率数据求解地球重力场的基本原理与方法,该方法既可对两颗低低跟踪卫星的初始状态误差进行有效校正,也可充分利用低轨卫星轨道所包含的低频重力场信息.为探讨适合我国国情的低低跟踪模式下的重力卫星指标,本文以不同星载设备精度指标的组合进行模拟计算,模拟结果显示:(1)把GRACE卫星的星间距离变率指标提高一个量级,其余指标保持与GRACE卫星设计指标一致时,可使地球重力场的精度获得同量级的提高;(2)若星间距离变率为1.0×10^-8 m·s^-1,轨道高度为300 km,加速度计精度为3.0×10^-10 m·s^-2,轨道精度为0.03 m, 星间距离100 km,与利用GRACE的设计指标反演出的重力场精度相比,可提高约121倍,并建议我国未来低低跟踪重力卫星计划参考此指标.     

新一代GRACE重力卫星反演地球重力场的预期精度

基于低低卫卫跟踪模式,本文主要探讨利用动力学法融合精密轨道数据和星间测距或距离变率数据求解地球重力场的基本原理与方法,该方法既可对两颗低低跟踪卫星的初始状态误差进行有效校正,也可充分利用低轨卫星轨道所包含的低频重力场信息.为探讨适合我国国情的低低跟踪模式下的重力卫星指标,本文以不同星载设备精度指标的组合进行模拟计算,模拟结果显示:(1)把GRACE卫星的星间距离变率指标提高一个量级,其余指标保持与GRACE卫星设计指标一致时,可使地球重力场的精度获得同量级的提高;(2)若星间距离变率为1.0×10-8 m·s-1,轨道高度为300 km,加速度计精度为3.0×10-10 m·s-2,轨道精度为0.03 m, 星间距离100 km,与利用GRACE的设计指标反演出的重力场精度相比,可提高约121倍,并建议我国未来低低跟踪重力卫星计划参考此指标.     

Expansions of the double product of the global gravity field

Summary Four fundamental forms of expansion of the double product of the gravity function into an infinite series are derived. Two isotropic parts are separated, one is expressed by Legendre polynomials and the other by invariants of Wigner's D-matrices.

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¶rt; m n¶rt;mau ¶rt; au ¶rt; nu¶rt;uaumau uu ¶rt;. ¶rt; ¶rt; umn amu, na aam n nu a¶rt;a u ma n uauam amu ua.

     

重力聚点的地球重力学性质与J2项的关系

重力聚点的概念是基于匀质椭球、水准椭球以及参数椭球各自表面重力随纬度的变化曲线在同一个纬度出现相聚的现象于2000年提出,并且当时给出了地球整体密度变化与重力聚点的关系,但是对于三种椭球表面重力曲线为什么在同一纬度相聚的原因、实际地球是否存在重力聚点以及重力聚点的地球动力学性质的阐述等方面都存在不完备性,使得重力聚点这一概念从提出至今仅停留在几何意义或数学性质上.本文将地球动力形状因子J2项作为变量,研究了地球表面重力随J2的变化规律.研究表明:该规律与“重力聚点定理”所述内容一致,从而将重力聚点与J2联系起来.由于J2的增加或减小,会导致地球表面重力在全球范围内以重力聚点(地心纬度φ=±35.264°)为分界线从北极向南极呈现出“负-正-负”或“正-负-正”的变化规律,全球地震的总体分布以及某些大地震的发生可能与此现象有关.     

Analytical solutions to global and local problems of electromagnetic induction in the earth

This review of analytic solutions is divided into two parts. The first part reviews electromagnetic induction in radially symmetric distributions of conductivity, and is appropriate to the study of global problems. In the second part, local problems of a specific nature are considered, the model being a half-space conductor with at least one lateral discontinuity separating regions of different uniform conductivities. In some problems, an approximate surface-boundary condition is used, and it is shown that the accuracy of the solutions has yet to be determined satisfactorily.     

一种新型重力测量卫星系统确定全球重力场的性能分析

本文设计了一种高-低卫星跟踪卫星、低-低卫星跟踪卫星和卫星重力梯度测量相结合的新型重力测量卫星系统,其可在一定程度上发挥卫星重力梯度和低低卫星跟踪卫星两种测量模式各自的优势.基于重力卫星系统指标设计的半解析法,深入分析了不同重力测量卫星系统配置和不同观测量及其不同白噪声水平情况下,新型卫星重力测量模式反演重力场模型的能力.数值模拟分析结果表明：在观测值精度和星间距离相同的条件下,轨道高度是影响重力场反演精度的关键因素;随着星间距离的增大,高频重力场信号反演精度会先提高后降低,轨道高度在200~350 km之间时,星间距离在150~180 km之间时反演精度最优;星间距离变率和卫星重力梯度两类观测值仅在某些精度配置时可达到优势互补,如果某一类观测值精度很高,则另一类观测值在联合解算时贡献非常小或者没有贡献.在300 km轨道高度,若以GRACE和GOCE任务的设计指标1 μm·s-1/和5 mE/来配置新型重力测量卫星系统中星间距离变率和引力梯度观测值的精度,联合两类观测值解算200阶次模型大地水准面的精度比独立解算分别提高1.2倍和2.8倍.如果以实现100 km空间分辨率1~2 cm精度大地水准面为科学目标,考虑卫星在轨寿命,建议轨道高度选择300 km,星间距离变率和卫星重力梯度的精度分别为0.1 μm·s-1/和1 mE/.本文的研究成果可为中国研制自主的重力测量卫星系统提供参考依据.     

On the estimation of accuracy for global models of gravitational field of the earth

The methods and techniques for estimating the accuracy of global models of the Earth’s gravity field in the form of spherical harmonic expansion of the geopotential are analyzed. Various methods for obtaining the a priori and a posteriori estimates for the accuracy are considered and classified. The application of different approaches is illustrated by numerical examples for nine models, including those recently developed using the modern methods of space geodesy. The basic requirements for the database and software for estimating the accuracy are formulated.     

Derivation of the CHAMP-only global gravity field model TUG-CHAMP04 applying the energy integral approach

A global gravity field model TUG-CHAMP04, derived from CHAMP (CHAllenging Minisatellite Payload) satellite-to-satellite GPS tracking observations in the high-low mode (SST-hl) in combination with CHAMP accelerometry, is presented and described in detail in this paper. For this purpose the energy integral approach was applied to precise kinematic orbits and accelerometer data. The advantage of these kinds of orbits is that they are derived from purely geometrical information, hence no external gravity field information is used for the determination of the positions. The disadvantage of precise kinematic orbit information is, that no velocities are delivered and hence a procedure has to be elaborated to deduce the velocities from kinematic positions. This work is done in preparation for ESA’s GOCE (Gravity field and steady state Ocean Circulation Explorer) satellite mission (scheduled launch November 2006), aiming at a high precision and high-resolution gravity field model on a global scale. This paper concentrates on the CHAMP data processing, where, in contrast to the usual standard method (processing in the Earth fixed frame), an approach in the inertial frame is chosen. Focus is taken on the data preprocessing of both accelerometer and orbit data, emphasising on the correct treatment of data-gaps and outlier detection. Furthermore an arc-wise weighting strategy is introduced and the advantages/disadvantages of this approach are discussed. Finally, the TUG-CHAMP04 model, calculated from one year of CHAMP data is compared with the official CHAMP gravity field model EIGEN-3p and terrestrial data (GPS levelling data).     

The differences in structure of the gravity field and the figure of the earth in the northern and southern hemispheres

Summary It was shown in [5] that the flattening of parallel sections of the geoid (ϕ=const.) differs in the northern and southern hemispheres. This leads up to the idea of studying further the size and shape of the Earth and the structure of the gravity field separately for the northern and for the southern hemispheres. In this paper attention is devoted especially to the mean values of the radius-vectors, to the best fitting ellipsoid parameters and to the mean values of gravity for the whole hemispheres, on the one hand, and for their ϕ=const. sections, on the other. The symbols used are the same as in [5,6]. Address: Politickych vězňů 12, Praha 1-Nové Město.     

Highly-reduced dynamic orbits and their use for global gravity field recovery: A simulation study for GOCE

The so-called highly reduced-dynamic (HRD) orbit determination strategy and its use for the determination of the Earth’s gravitational field are analyzed. We discuss the functional model for the generation of HRD orbits, which are a compromise of the two extreme cases of dynamic and purely geometrically determined kinematic orbits. For gravity field recovery the energy integral approach is applied, which is based on the law of energy conservation in a closed system. The potential of HRD orbits for gravity field determination is studied in the frame of a simulated test environment based on a realistic GOCE orbit configuration. The results are analyzed, assessed, and compared with the respective reference solutions based on a kinematic orbit scenario. The main advantage of HRD orbits is the fact that they contain orbit velocity information, thus avoiding numerical differentiation on the orbit positions. The error characteristics are usually much smoother, and the computation of gravity field solutions is more efficient, because less densely sampled orbit information is sufficient. On the other hand, the main drawback of HRD orbits is that they contain external gravity field information, and thus yield the danger to obtain gravity field results which are biased towards this prior information.     

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.     

基于EGM2008重力场模型的GPS高程转换方法及精度分析

研究利用重力场模型直接进行GPS高程转换的方法,即模型高程异常法和模型重力位法.根据误差传播定律,导出了由重力场模型位系数方差计算模型高程异常以及模型正常高的误差公式,并对影响两种GPS高程转换方法精度的因素进行分析.利用具有代表性的EGM96、EIGEN-51C和EGM2008重力场模型及某线路GPS/水准数据对两种方法进行实验研究与精度分析,结果表明:理论公式及实验结果都显示两种高程转换方法是等价的,转换精度相当;两种方法使用过程中,均可能需要系统偏差校正;EGM2008重力场模型具有非常好的分辨率及精度,在局部区域,基于EGM2008模型的GPS高程转换精度有望达到cm级.     

小行星引力场综述

近年来小行星探测已成为各航天大国的热点,小行星引力场对研究其内部结构、组成成分、早期演化和探测器轨道设计、着陆等方面有着极其重要的作用.随着小行星探测数据的不断更新、探测任务的增多和观测技术改进,针对小行星引力场的研究也在不断增多并产生新的进展.目前获取小行星引力场的方法主要为利用探测器飞掠过程中得到的轨道跟踪数据反演...     

Topography of the Moho and earth crust structure beneath the East Vietnam Sea from 3D inversion of gravity field data

The Moho depth, crustal thickness and fault systems of the East Vietnam Sea (EVS) are determined by 3D interpretation of satellite gravity. The Moho depth is calculated by 3D Parker inversion from residual gravity anomaly that is obtained by removing the gravity effects of seafloor and Pre-Cenozoic sediment basement topographies from the free air anomaly. The 3D inversion solution is constrained by power density spectrum of gravity anomaly and seismic data. The calculated Moho depths in the EVS vary from 30–31 km near the coast to 9 km in the Central Basin. A map of the lithosphere extension factor in the Cenozoic is constructed from Moho and Pre-Cenozoic sediment basement depths. The fault systems constructed by the maximum horizontal gradient approach include NE-SW, NW-SE, and N-S oriented faults. Based on the interpretation results, the EVS is sub-divided into five structural zones which demonstrated the different characteristics of the crustal structure.     

Dynamic pattern characteristics of fault deformation and gravity field in the development process of Yongdeng M S =5.8 earth quake

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