Efficient and rapid accuracy estimation of the Earth's gravitational field from next-generation GOCE Follow-On by the analytical method

Firstly, a new analytical error model of the cumulative geoid height using the three-dimensional diagonal tensors of satellite gravity gradiometry （SGG） is introduced based on the variance-covariance matrix principle. Secondly, a study for the requirements demonstration on the next-generation GOCE Follow-On satellite gravity gradiometry system is developed using different satellite orbital altitudes and measurement accuracies of satellite gravity gradiometer by the new analytical error model of SGG. The research results show that it is preferable to design satellite orbital altitudes of 300 km–400km and choose the measurement accuracies of 10-13/s2 –10-15/s2 from satellite gravity gradiometer. Finally, the complementarity of the four-stage satellite gravity missions, including past CHAMP, current GRACE, and GOCE, and next-generation GOCE Follow-On, is contrastively demonstrated for precisely recovering the Earth’s full-frequency gravitational field with high spatial resolution.

Construction of Earth's gravitational field model from CHAMP,GRACE and GOCE data

The basic principle of spectral combination method is discussed,and the general expressions of the spectral weight and spectral combination of the united-processing of various types of gravimetric data are shown.What＇s more,based on degree error RMS of potential coefficients,the detailed expressions of spectral combination formulae and the corresponding spectral weights in the Earth＇s gravitational field model（EGM） determination using GOCE ＋ GRACE and CHAMP ＋ GRACE ＋ GOCE are derived.The fundamental situation that ulux-champ2013 s,tongji-GRACE01,go-cons-gcf-2-tim-r5 constructed respectively by CHAMP,GRACE,GOCE data and go-cons-gcf-2-dir-r5 constructed by syncretic processing of GRACE,GOCE and LAGEOS data are explained briefly,the degree error RMS,cumulative geoid height error and cumulative gravity anomaly error of these models are calculated.A syncretic model constructed from CHAMP,GRACE and GOCE data,which is expressed by champ ＋ grace ＋ goce,is obtained based on spectral combination method.Experimentation results show that the precision of CHAMP data model is the lowest in satellite-only models,so it is not needed in the determination of syncretic models.The GRACE data model can improve the GOCE data model in medium-long wavelength,so the overall precision of syncretic model can be improved.Consequently,as many types of gravimetric data as possible should be combined together in the data processing in order to strengthen the quality and reliability with widening scope and improve the precision and spatial resolution of the computational results.

A contrastive study on the influences of radial and three-dimensional satellite gravity gradiometry on the accuracy of the Earth's gravitational field recovery

The accuracy of the Earth＇s gravitational field measured from the gravity field and steady-state ocean circulation explorer（GOCE）,up to 250 degrees,influenced by the radial gravity gradient V zz and three-dimensional gravity gradient V ij from the satellite gravity gradiometry（SGG） are contrastively demonstrated based on the analytical error model and numerical simulation,respectively.Firstly,the new analytical error model of the cumulative geoid height,influenced by the radial gravity gradient V zz and three-dimensional gravity gradient V ij are established,respectively.In 250 degrees,the GOCE cumulative geoid height error measured by the radial gravity gradient V zz is about 2 1/2 times higher than that measured by the three-dimensional gravity gradient V ij.Secondly,the Earth＇s gravitational field from GOCE completely up to 250 degrees is recovered using the radial gravity gradient V zz and three-dimensional gravity gradient V ij by numerical simulation,respectively.The study results show that when the measurement error of the gravity gradient is 3×10 12 /s 2,the cumulative geoid height errors using the radial gravity gradient V zz and three-dimensional gravity gradient V ij are 12.319 cm and 9.295 cm at 250 degrees,respectively.The accuracy of the cumulative geoid height using the three-dimensional gravity gradient V ij is improved by 30%-40% on average compared with that using the radial gravity gradient V zz in 250 degrees.Finally,by mutual verification of the analytical error model and numerical simulation,the orders of magnitude from the accuracies of the Earth＇s gravitational field recovery make no substantial differences based on the radial and three-dimensional gravity gradients,respectively.Therefore,it is feasible to develop in advance a radial cold-atom interferometric gradiometer with a measurement accuracy of 10 13 /s 2-10 15 /s 2 for precisely producing the next-generation GOCE Follow-On Earth gravity field model with a high spatial resolution.

Effect of different inter-satellite range on measurement precision of Earth’s gravitational field from GRACE

The precision of Earth＇s gravitational field from GRACE up to degree and order 120 was studied for different inter-satellite ranges using the improved energy conservation principle. Our simulated result shows that： For long wavelength （L≤20） at degree 20, the cumulative geoid-height error gradually decreased with increasing range, from 0. 052 cm for 110 km to 1. 156 times and 1. 209 times as large for 220 km and 330 kin, respectively. For medium-wavelength （ 100 ≤ L ≤ 120） at degree 120, the cumulative geoid-height error de- creased from 13. 052 cm for 110 km, to 1. 327 times and 1. 970 times as large for the ranges of 220 km and 330 km, respectively; By adopting an optimal range of 220 ± 50 km, we can suppress considerably the loss of precision in the measurement of the Earth＇ s long-wavelength and medium-wavelength gravitational field.

Secular Effect of Geomagnetic Field and Gravitational Waves on Earth’s Satellite Orbits

In this work we study the perturbation and the change in the orbital elements due to the earth’s magnetic field and the gravitational waves. The acceleration components are derived in the radial, transverse to it and normal to the orbital plane. The equation for the rates of variation of the elements is formed and solved to find the secular variation in the element for polar and equatorial satellites.

High-precision chaotic radial basis function neural network model:Data forecasting for the Earth electromagnetic signal before a strong earthquake

The Earth’s natural pulse electromagnetic field data consists typically of an underlying variation tendency of intensity and irregularities.The change tendency may be related to the occurrence of earthquake disasters.Forecasting of the underlying intensity trend plays an important role in the analysis of data and disaster monitoring.Combining chaos theory and the radial basis function neural network,this paper proposes a forecasting model of the chaotic radial basis function neural network to conduct underlying intensity trend forecasting by the Earth’s natural pulse electromagnetic field signal.The main strategy of this forecasting model is to obtain parameters as the basis for optimizing the radial basis function neural network and to forecast the reconstructed Earth’s natural pulse electromagnetic field data.In verification experiments,we employ the 3 and 6 days’data of two channels as training samples to forecast the 14 and 21-day Earth’s natural pulse electromagnetic field data respectively.According to the forecasting results and absolute error results,the chaotic radial basis function forecasting model can fit the fluctuation trend of the actual signal strength,effectively reduce the forecasting error compared with the traditional radial basis function model.Hence,this network may be useful for studying the characteristics of the Earth’s natural pulse electromagnetic field signal before a strong earthquake and we hope it can contribute to the electromagnetic anomaly monitoring before the earthquake.

Analysis and Simulation of the Influence of Electromagnetic Fields on Living Beings near HV Power Lines Using the FDTD Method

Recent decades have seen rapid advances in the field of electrical engineering, such that our environment has become a sea of electrical and magnetic signals, raising questions about the possible effects of low-frequency electromagnetic fields on the environment and which are capable of modifying and destroying our ecosystem. Particular interest was given in this article due to a massive influx of population living near high voltage lines. The analysis and simulation of the influence of low frequency electromagnetic fields on living beings in the vicinity of high voltage sources 132 kV and 220 kV in urban areas in DR Congo is the subject of our research with a view to estimating the level of exposure of humans to low frequency electromagnetic fields. To carry out our research, we used the classic method of analyzing the field produced near a high voltage line based on Maxwell’s image theory, the Maxwell-Gauss theorem and Maxwell-Ampère theorem to model and quantify low-frequency electromagnetic fields in the vicinity of high-voltage lines. The 2D FDTD numerical formulation was developed from telegraphers’ equations and allowed us to obtain models of current and voltage induced by electromagnetic fields on living beings below and near HV lines. The different simulations carried out on the proposed models illustrate the effects of the electrical and geometric parameters of the pylons on the distribution of the electromagnetic field in the vicinity of the HV lines. The results obtained were compared to the safety limits recommended by the standards.

A GOCE only gravity model GOSG01S and the validation of GOCE related satellite gravity models

We compile the GOCE-only satellite model GOSG01S complete to spherical harmonic degree of 220 using Satellite Gravity Gradiometry （SGG） data and the Satellite-to-Satellite Tracking （SST） observations along the GOCE orbit based on applying a least-squares analysis. The diagonal components （Vxx, Vyy, Vzz） of the gravitational gradient tensor are used to form the system of observation equations with the band-pass ARMA filter. The point-wise acceleration observations （ax, ay, az） along the orbit are used to form the system of observation equations up to the maximum spherical harmonic degree/order 130. The analysis of spectral accuracy characteristics of the newly derived gravitational model GOSG01S and the existing models GOTIM04S, GODIR04S, GOSPW04S and JYY_GOCE02S based on their comparison with the ultrahigh degree model EIGEN-6C2 reveals a significant consistency at the spectral window approximately between 80 and 190 due to the same period SGG data used to compile these models. The GOCE related satellite gravity models GOSG01S, GOTIM05S, GODIR05S, GOTIM04S, GODIR04S, GOSPW04S, JYY_- GOCE02S, EIGEN-6C2 and EGM2008 are also validated by using GPS-leveling data in China and USA. According to the truncation at degree 200, the statistic results show that all GGMs have very similar differences at GPS-leveling points in USA, and all GOCE related gravity models have better performance than EGM2008 in China. This suggests that all these models provide much more information on the gravity field than EGM2008 in areas with low terrestrial gravity coverage. And STDs of height anomaly differences in China for the selected truncation degrees show that GOCE has improved the accuracy of the global models beyond degree 90 and the accuracies of the models improve from 24 cm to 16 cm. STDs of geoid height differences in USA show that GOSG01S model has best consistency comparing with GPSleveling data for the frequency band of the degree between 20 and 160.

Magnetic Structure of the Earth’s Crust in the White Sea Region

The geological structure of the White Sea area and the surrounding land areas has been well studied in the framework of individual case studies. There are a number of local models of the deep structure of the Earth’s crust available. We propose a uniform assessment of deep crustal bodies responsible for long-period (regional) magnetic anomalies and consider their correlation with surface structures. The aim of the study is to build a three-dimensional magnetic model of the Earth’s crust in the White Sea region using aeromagnetic data and modeling technologies of the Integro software package. The model is formed on the basis of a digital map of the anomalous magnetic field reduced to the pole. The sources of magnetic anomalies are considered to be located in the Earth’s crust. The 3D distribution of the relative magnetic susceptibility of rocks was obtained by solving the inverse problem of the magnetic survey. To separate the magnetic sources by frequency and depth, it was necessary to continue the magnetic field of the model upward and to calculate the TDR derivatives, which determine the lateral boundaries of the sources of positive magnetic field anomalies. 2D distributions of magnetic sources of the model for vertical and horizontal sections with depths of 10, 15 and 20 km are analyzed. The correlation between the surface and deep structures of magnetic sources of the Earth’s crust in the region is shown.

利用GOCE模拟观测反演重力场的Torus法

在介绍Torus方法反演地球重力场模型的基本原理和方法的基础上,基于圆环面上均匀分布的卫星引力梯度模拟观测值解算了200阶次的地球重力场模型,在无误差情况下,Torus方法解算模型的阶误差RMS小于10-16,验证了该方法的严密性。利用61dGOCE卫星轨道上无误差的模拟引力梯度观测值解算了200阶次的地球重力场模型,分析了格网化误差、极空白对解算精度的影响,迭代3次后,在不考虑低次系数情况下,模型的大地水准面阶误差和累积误差均较小,最大值仅为0.022mm和0.099mm。在沿轨卫星引力梯度模拟数据中加入5mE/Hz1/2的白噪声,基于Torus方法和空域最小二乘法解算了200阶次的地球重力场模型,Torus方法的精度略低于空域最小二乘法的精度,在不考虑低次项的情况下,两种方法解算模型的大地水准面阶误差最大值分别为1.58cm和1.45cm,累积误差最大值分别为6.37cm和5.55cm。但由于采用了二维快速傅里叶技术和块对角最小二乘法,极大地提高了计算效率。本文数值结果说明Torus方法是一种独立有效的方法,可用于GOCE任务海量卫星引力梯度观测值反演重力场的快速解算。

基于SFEM的结构元件疲劳可靠性分析

将结构元件的弹性模量、泊松比、几何尺寸定义为随机场,并将随机场离散成随机变量,将抗拉强度定义为随机变量,采用Monte Carlo随机有限元法(MCSFEM),给出了元件危险点应力的随机分布。由危险点应力分布、材料的p-S-N曲线和Miner理论给出了概率名义应力法,计算常幅载荷下元件的寿命分布,并利用剩余寿命模型计算元件的可靠度。给出了两个算例,结果表明:计算结果与试验结果吻合良好。

基于S-A模型的覆冰输电线绕流数值分析

基于Spalart-Allmaras湍流模型(S-A模型)封闭的雷诺平均N-S方程,采用沿均匀流线的三阶Runge-Kutta法和Galerkin法分别进行时间和空间离散,得到了湍流方程的有限元格式。采用自编Matlab程序,数值模拟了不同风攻角下覆冰输电线绕流问题,得到了覆冰输电线绕流瞬态和时均流场、气动力系数时程曲线和平均气动力系数随风攻角的变化关系,并与试验结果进行对比,验证了该算法的有效性。基于流场演化和平均压力分布,分析表明风攻角变化引起的边界层分离点转移是产生升力系数尖峰突跳现象的主要原因。

A rapid compensation method for launch data of long-range rockets under influence of the Earth＇s disturbing gravity field

Regarding the rapid compensation of the influence of the Earth＇ s disturbing gravity field upon trajectory calculation,the key point lies in how to derive the analytical solutions to the partial derivatives of the state of burnout point with respect to the launch data.In view of this,this paper mainly expounds on two issues：one is based on the approximate analytical solution to the motion equation for the vacuum flight section of a long-range rocket,deriving the analytical solutions to the partial derivatives of the state of burnout point with respect to the changing rate of the finalstage pitch program;the other is based on the initial positioning and orientation error propagation mechanism,proposing the analytical calculation formula for the partial derivatives of the state of burnout point with respect to the launch azimuth.The calculation results of correction data are simulated and verified under different circumstances.The simulation results are as follows：（1） the accuracy of approximation between the analytical solutions and the results attained via the difference method is higher than 90%,and the ratio of calculation time between them is lower than 0.2%,thus demonstrating the accuracy of calculation of data corrections and advantages in calculation speed;（2） after the analytical solutions are compensated,the longitudinal landing deviation of the rocket is less than 20 m and the lateral landing deviation of the rocket is less than 10 m,demonstrating that the corrected data can meet the requirements for the hit accuracy of a long-range rocket.

基于地球重力场模型的GNSS高程转换与精度分析

为了解决纯数学模型在进行高程转换时,只能反映测区高程异常的大致趋势,影响高程转换精度的问题,采用地球重力场模型与数学函数相结合的"移去-恢复"法来反映高程异常的细节变化,以达到提高转换精度的目的。以安徽省某输电线路工程部分走向线实验区为例,分别采用数学模型的二次曲面、Kriging插值、多面函数以及与EGM2008、EIGEN-6C4、GOCO05S地球重力场模型结合的"移去-恢复"法等13种方案实现了测区的高程转换。结果表明,多面函数的精度优于Kriging插值法和二次曲面法,地球重力场模型与数学函数相结合的"移去-恢复"法精度较纯数学模型有了大幅提升,GOCO05S、EIGEN-6C4与多面曲面相结合的方案精度最佳,内外符合精度优于10.0 mm,RMS、STD均优于9.2 mm。

基于微波S参数测试的MOSFET小信号参数半分析法提取

基于90 nm金属-氧化物半导体场效应晶体管（metal-oxide-semiconductor field-effect transistor,MOSFET）器件的S参数测试的结果,对测试结构进行去嵌,采用直接提取法提取测试结构的寄生元件参数.在去除寄生元件参数的影响后,以仿真模型的S参数和测量所得的S参数之间的差值作为优化标准,应用半分析法提取小信号模型的各个元件参数.结果表明：在1~40 GHz的频率范围内,模拟的S参数和测试的S参数在史密斯圆图中吻合良好,两者之间的误差均处于较低水平,验证了模型的准确性和参数提取方法的正确性.

From the Beginning of the World to the Beginning of Life on Earth

Hypersphere World-Universe Model (WUM) is, in fact, a Paradigm Shift in Cosmology [1]. In this paper, we provide seven Pillars of WUM: Medium of the World;Inter-Connectivity of Primary Cosmological Parameters;Creation of Matter;Multicomponent Dark Matter;Macroobjects;Volcanic Rotational Fission;Dark Matter Reactors. We describe the evolution of the World from the Beginning up to the birth of the Solar System and discuss the condition of the Early Earth before the beginning of life on it.

两种地球重力场模型在GNSS高程拟合中的适用性分析

为比较XGM2019e与EGM2008两种地球重力场模型在GNSS高程拟合中的适用性,基于“移去-恢复”法,使用平面拟合、二次曲面拟合及多面函数拟合在两个不同地形条件区域开展GNSS高程拟合实验。实验数据表明,在两个区域中,基于XGM2019e模型计算出3种不同拟合方法的外符合精度依次为2.22,1.62,1.85 cm及1.56,3.32,1.17 cm,均高于使用EGM2008模型计算出的外符合精度,表明在实验区域内使用XGM2019e模型进行GNSS高程拟合的效果优于EGM2008模型,将XGM2019e模型与不同GNSS高程拟合方法进行组合,还可进一步提升GNSS高程拟合精度。

基于移除-恢复法的GPS水准高差拟合方法研究

讨论了将GPS所测的大地高差转换为正常高差的基本原理和算法,研究了移除-恢复法在GPS高差转换中的应用。利用该算法对某线路GPS大地高差观测数据进行处理,结果表明:基于移除-恢复法的GPS高差转换方法能改善高差转换精度,具有较好的实用价值。

缔合Legendre函数的快速插值计算及其在六边形网格模型重力异常计算中的应用

鉴于局部区域非等纬度分布点的超高阶次球谐综合计算效率较低,本文深入研究了缔合Legendre函数的插值算法,结合模型重力异常求解的展开式,提出了超高阶模型空间重力异常插值快速计算方法,为了验证本文方法在东西狭长分布的点集更具有应用优势,采用球谐旋转变换技术进一步提升了计算效率。试验结果表明,利用2160阶次EGM2008模型计算日本地区同一高度的30303个非等纬度分布的六边形网格点处模型重力异常,插值快速计算方法相比逐点计算,在误差不超±0.005 mGal水平下,计算耗时从3669.41 s缩减到98.05 s,同时经过球谐旋转变换,将南北狭长的日本区域点集旋转为东西狭长分布,使得上述相应计算内容的耗时进一步由98.05 s缩减到19.06 s,计算效率相比最初方法提速比达到近200倍,有效解决了非等纬度分布点的超高阶模型重力异常快速解算的效率难题,且验证了该方法在东西狭长分布的情况下具有更高的提速比。

地球与行星内源磁场建模研究进展

太阳系绝大多数行星都拥有随星体自转而共转的内源磁场.随着人类不断地进行深空探测,人们已经对所有已知具有内源磁场的太阳系星体建立起了其对应的行星磁场模型.行星磁场建模是深入研究行星内部动力学过程、探究行星演化历史、理解行星磁场与太阳风相互作用、认识行星磁场对高能带电粒子的屏蔽效应等多种研究方向的重要基础.同时,行星磁场建模也是一项多学科交叉的研究工作,其涉及到行星磁场建模理论、内外源磁场场源分离、参数反演方法与方程优化等多方面的研究.本文综述了地球与太阳系其他行星,包括月球以及木卫三两颗卫星在磁场建模方向的研究进展,描述了行星内源磁场的特征,整理了太阳系行星最准确的全球磁场模型.本文首先从行星磁场的数学建模方法开始,梳理了自高斯时代以来磁场建模技术的发展历史,介绍了行星磁场建模研究的热点方法.文章最后展望了未来行星磁场建模研究的发展趋势,以及我国未来的深空探测计划对行星磁场建模研究的可能贡献.