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.

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.

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.

A three-dimensional Moho depth model beneath the Yemeni highlands and rifted volcanic margins of the Red Sea and Gulf of Aden, Southwest Arabia

Knowing Moho discontinuity undulation is fundamental to understanding mechanisms of lithosphereasthenosphere interaction, extensional tectonism and crustal deformation in volcanic passive margins such as the study area, which is located in the southwestern corner of the Arabian Peninsula bounded by the Red Sea and the Gulf of Aden. In this work, a 3D Moho depth model of the study area is constructed for the first time by inverting gravity data from the Earth Gravitational Model(EGM2008) using the ParkerOldenburg algorithm. This model indicates the shallow zone is situated at depths of 20 km to 24 km beneath coastal plains, whereas the deep zone is located below the plateau at depths of 30 km to 35 km and its deepest part coincides mainly with the Dhamar-Rada ’a Quaternary volcanic field. The results also indicate two channels of hot magmatic materials joining both the Sana’a-Amran Quaternary volcanic field and the Late Miocene Jabal An Nar volcanic area with the Dhamar-Rada’a volcanic field. This conclusion is supported by the widespread geothermal activity(of mantle origin) distributed along these channels,isotopic data, and the upper mantle low velocity zones indicated by earlier studies.

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.

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.

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.

基于Gauss-Listing大地水准面定义的地球重力场模型评价方法

提出一种基于Gauss-Listing大地水准面经典定义的地球重力场模型评价方法。该方法依据经典大地水准面为重力等位面的特性,选取某大地水准面为参考面,计算不同地球重力场模型在该参考面上的重力位标准差,以此作为不同模型相对优劣的评价指标。利用该方法对不同地球重力场模型以及同一重力场模型在不同区域的精度进行评价,结果表明,EGM96模型、OSU91A模型的大地水准面精度分别为±11.1cm、±14.3cm,EGM2008模型、EIGEN-6C4模型分别为±8.8cm、±8.9cm,说明后2个模型的精度相当,且优于前2个模型。该模型评价方法的研究结果显示,对于某全球大地水准面,EGM2008模型和EIGEN-6C4模型的大地水准面精度分别为±11.3cm和±14.1cm,即在cm级精度上EGM2008模型略优。

基于EGM2008的分区拟合在铁路高程中的应用研究

利用精确的高程异常模型,可以实现将GNSS大地高转换为正常高,满足铁路工程勘测的需要。本文基于GNSS/水准测量数据,对EGM2008地球重力场模型在铁路高程拟合中的应用进行拟合研究,得出在地形变化明显的地区,分区拟合较整网拟合精度要高。

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.

The gravitational gradient tensor’s invariants and the related boundary conditions

Here we report new approaches of recovering the Earth gravitational field from GOCE (Gravity field and steady-state Ocean Circulation Explorer) gradiometric data with the help of the gradient tensor’s invariants. Our results only depend on GOCE satellite’s position and gradiometry, in other words, they are completely independent of the satellite attitude. First, starting from the invariants, linearization models are established, which can be referred as the general boundary conditions on the satellite’s orbit. Then, the spherical approximation expressions for the models are derived, and the corresponding solving methods for them are discussed. Furthermore, considering effects of J2-term, the spherical approximation models are improved so that the accuracies of the boundary conditions can be theoretically raised to O ( J 2/2 T), which is approximately equivalent to O(T2). Finally, some arithmetic examples are constructed from EGM96 model based on the derived theories, and the computational results illustrate that the spherical models have accuracies of 10-7 and the order recovering the gravitational field can reach up to 200, and the models with regard to effect of J2-term have accuracies of 10-8 and the order can reach up to 280.

两种GRACE地球重力场精度评定方法的检验

基于改进的能量守恒法,分别利用先验地球重力场模型法(PEM)和最小二乘协方差阵法(LSM)评定了120阶GRACE地球重力场的精度,模拟结果表明:1)基于美国JPL公布的GRACE轨道参数和核心载荷精度指标,在120阶处分别采用PEM和LSM恢复地球引力位系数的精度为5.192×10-10和6.633×10-10;2)分别基于PEM和LSM恢复120阶地球引力位系数的模拟精度和德国GFZ公布的EIGEN-GRACE02S地球重力场模型的实测精度在各阶处符合较好,从而证明了基于PEM和LSM评定地球重力场恢复精度的有效性;3)通过基于PEM和LSM分别恢复地球引力位系数的模拟精度在各阶处的符合性,验证了基于能量守恒法结合预处理共轭梯度迭代法恢复120阶GRACE地球重力场算法的可靠性。

地球重力场模型研究进展和现状

首先回顾自1966年以来国内外基于传统重力测量技术建立的地球重力场模型。其次,介绍国际基于CHAMP实测数据建立的全球重力场模型。在重力场长波部分,EIGEN-CHAMP03S和EIGEN-3P模型符合较好;在中长波部分,EIGEN-1S、EIGEN-2、EIGEN-3P和EIGEN-CHAMP03S模型的符合性趋于一致。最后,介绍国内外已公布的GRACE卫星重力模型。由于GGM02S和WHIGG-GEGM01S模型采用的卫星观测值数量近似相等,因此二者精度符合较好;由于采用CHAMP、GRACE、卫星测高和地面重力的联合观测数据,EIGEN-CG01C、EIGEN-CG03C、EIGEN-GL04S1和EIGEN-5C模型精度均分别高于EIGEN-GRACE01S、EIGEN-GRACE02S、GGM01S、GGM02S、WHIGG-GEGM01S等GRACE-only模型。

插值公式、相关系数和采样间隔对GRACE Follow-On星间加速度精度的影响

本文基于星间加速度法开展了插值公式、相关系数和采样间隔对GRACE Follow-On星间加速度精度影响的研究.模拟结果表明:1)适当增加数值微分公式的插值点数可有效提高插值精度.基于9点Newton插值公式,星间加速度的插值误差为4.401×10-13 m.s-2,分别基于7点、5点和3点插值公式,插值误差增加了1.192倍、6.912倍和274.029倍.2)适当增大相关系数可有效降低星间加速度的误差.基于相关系数0.99,星间加速度方差为3.777×10-24 m2.s-4,分别基于相关系数0.90、0.70、0.50和0.00,方差增加了9.780倍、22.404倍、26.217倍和26.820倍.3)随着采样间隔增大,星间加速度方差逐渐降低,但卫星观测值的空间分辨率也同时降低,因此合理选取采样间隔有利于地球重力场精度的提高.4)基于9点Newton插值公式、相关系数(K波段测量系统星间距离和星间速度0.85、GPS轨道位置和轨道速度0.95、星载加速度计非保守力0.90)和采样间隔10s,利用预处理共轭梯度迭代法,精确和快速反演了120阶GRACE Follow-On地球重力场,在120阶处累计大地水准面精度为4.602×10-4 m.

扰动重力梯度张量单分量和组合分量最小二乘配置法模型的建立

建立了利用扰动重力梯度张量Tzz分量和Txx+Tyy、Tzz-Txx-Tyy组合分量确定地球重力场的调和分析法模型,进一步推导了扰动重力梯度张量对角线三分量的自协方差和互协方差函数的级数展开式,推导了单分量、组合分量与重力位系数之间协方差函数的实用计算公式,给出了利用单分量和组合分量解算地球重力场模型的最小二乘配置法基本原理公式.结果表明,最小二乘配置法具有一定的抗差能力,随着观测数据误差的不断增大,其恢复的重力场模型有效阶次不断降低,精度也不断下降;Tzz-Txx-Tyy组合分量解算重力场模型的精度最高,其次为Tzz分量,Txx+Tyy组合分量最差.

星间距离影响GRACE地球重力场精度研究

利用改进的能量守恒法,基于不同星间距离反演了120阶GRACE地球重力场。模拟结果表明：第一,基于相同的GRACE核心载荷精度指标反演长波（L≤20阶）地球重力场时,随着星间距离逐渐增大（110330 km）,累计大地水准面的精度依次提高。在20阶处,基于110 km星间距离反演精度为0.052 cm,基于220 km和330 km星间距离反演精度分别提高了1.156倍和1.209倍。第二,当反演中波（100≤L≤120阶）地球重力场时,在120阶处,基于110 km星间距离反演精度为13.052 cm,基于220 km和330 km星间距离反演精度分别降低了1.327倍和1.970倍。第三,星间距离设计为220±50 km可有效抑制由于星间距离选取不当而导致的长波和中波地球重力场精度的降低。

高分辨率地球重力场模型DQM99

地球扰动位的球谐展开式表示是地球重力场模型应用最广泛的一种表示方法。目前通用的位系数模型的分辨率是 0 5° ,最高完全阶次为 360。由于全球重力数据覆盖的密度和数据精度差别较大 ,所以已知的重力场模型的实际分辨率及其精度也因地区而异 ,故重力场模型的精化是一个漫长的过程 ,局部积分谱权综合法是改善已知重力场模型的有效而简便的方法。基于重力场模型OSU91A及EGM 96,利用我国 1 5′× 1 5′及 5′× 5′重力异常 ,我们解算了更高阶次的地球重力场模型DQM99A、B、C、D四个模型 。

基于大地水准面经典定义的地球重力场模型评价

提出一种基于Gauss-Listing经典大地水准面定义的地球重力场模型评价方法.该方法依据经典大地水准面为重力等位面的特性,以任一重力大地水准面为参考面,计算不同地球重力场模型在该参考面上的重力位离散度,以此作为不同模型相对优劣的评价指标.利用该方法对不同地球重力场模型以及同一重力场模型在不同区域的理论表达能力进行评价.结果表明:EGM96和OSU91A模型的大地水准面精度分别为±11.1 cm和±14.3 cm,说明EGM96要优于OSU91 A;EGM2008和EIGEN-6 C4模型的大地水准面精度分别为±8.8 cm和±8.9 cm,说明这两个模型的精度相当.这些结果均与已有研究结果一致.该模型评价方法的研究结果显示:对于利用EGM2008确定的全球大地水准面,EGM2008和EIGEN-6 C4模型的全球大地水准面表达精度分别为±11.3 cm和±14.1 cm,即在厘米级精度上EGM2008要优于EIGEN-6C4.