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.

GRACE detection of the medium-to far-field coseismic gravity changes caused by the 2004 Mw9.3 Sumatra-Andaman earthquake

Large earthquakes cause observable changes in the Earth’s gravity field, which have been detected by the Gravity Recovery and Climate Experiment (GRACE). Since most previous studies focus on the detection of near-field gravity effects, this study provides the results from the medium- to far-field gravity changes caused by the 2004 Sumatra-Andaman earthquake that are recorded within GRACE monthly solutions. Utilizing a spherical-earth dislocation model we documented that large-scale signals predominate in the global field of the coseismic gravity changes caused by the earthquake. After removing the near-field effects, the coseismic gravity changes show a negative anomaly feature with an average magnitude of -0.18×10-8 m·s-2 in the region ranging ～40° from the epicenter, which is considered as the 'medium ffield' in this study. From the GRACE data released by Center for Space Research from August 2002 to December 2008, we retrieved the large-scale gravity changes smoothed with 3 000 km Gaussian ffilter. The results show that the coseismic gravity changes detected by GRACE in the medium field have an average of (-0.20±0.06)×10-8 m·s-2, which agrees with the model prediction. The detection confirms that GRACE is sensitive to large-scale medium-field coseismic gravitational effects of mega earthquakes, and also validates the spherical-earth dislocation model in the medium field from the perspective of satellite gravimetry.

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.

Dependence of Gravity Induced Absorption Changes on the Earth’s Magnetic Field as Measured during Parabolic Flight Campaigns

Various spectroscopic experiments performed on the AIRBUS ZERO G—located in Bordeaux, France—in the years 2002 to 2012 exhibit minute optical reflection/absorption changes (GIACs) as a result of gravitational changes between 0 and 1.8 g in various biological species such as maize, oats, Arabidopsis and particularly Phycomyces sporangiophores. During a flight day, the AIRBUS ZERO G conducts 31 parabolas, each of which lasts about three minutes including a period of 22 s of weightlessness. So far, we participated in 11 parabolic flight campaigns including more than 1000 parabolas performing various kinds of experiments. During our campaigns, we observed an unexplainable variability of the measuring signals (GIACs). Using GPS-positioning systems and three dimensional magnetic field sensors, these finally were traced back to the changing earth’s magnetic field associated with the various flight directions. This is the first time that the interaction of gravity and the Earth’ magnetic field in the primary induction process in living system has been observed.

Discovering Crustal Deformation Bands by Processing Regional Gravity Field

Objectives： This article presents a new computational procedure to discover scratches buried in the earth＇s crust. We also validate this new interdisciplinary analysis method with regional gravity data located in a well-known Dabie orogenic zone for test. Methods： Based on the scratch analysis method evolved with mathematical morphology of surfaces, we present a procedure that extracts information of the crustal scratches from regional gravity data. Because the crustal scratches are positively and highly correlated to crustal deformation bands, it can be used for delineation of the crustal deformation belts. The scratches can be quantitatively characterized by calculation of the ridge coefficient function, whose high value traces delineate the deformation bands hidden in the regional gravity field. In addition, because the degree of crustal deformation is an important indicator of tectonic unit divisions, so the crust can be further divided according to the degree of crustal deformation into some tectonic units by using the ridge coefficient data, providing an objective base map for earth scientists to build tectonic models with quantitative evidence. Results： After the ridge coefficients are calculated, we can further enhance the boundary of high ridge-coefficient blocks, resulting in the so-called ridge-edge coefficient function. The high-value ridge-edge coefficients are well correlated with the edge faults of tectonic units underlay, providing accurate positioning of the base map for compilation of regional tectonic maps. In order to validate this new interdisciplinary analysis method, we select the Dabie orogenic zone as a pilot area for test, where rock outcrops are well exposed on the surface and detailed geological and geophysical surveys have been carried out. Tests show that the deformation bands and the tectonic units, which are conformed by tectonic scientists based on surface observations, are clearly displayed on the ridge and ridge-edge coefficient images obtained in this article. Moreover, these computer-generated images provide more accurate locations and geometric details. Conclusions： This work demonstrates that application of modern mathematical tools can promote the quantitative degree in research of modern geosciences, helping to open a door to develop a new branch of mathematical tectonics.

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.

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.

An Improved Energy Balance Approach and Its Application in CHAMP Gravity Field Recovery

An efficient method for gravity field determination from CHAMP orbits and accelerometer data is referred to as the energy balance approach. A new CHAMP gravity field recovery strategy based on the improved energy balance approach IS developed in this paper. The method simultaneously solves the spherical harmonic coefficients, daily Integration constant, scale and bias parameters. Two 60 degree and order gravitational potential models, XISM-CHAMPO1S from the classical energy balance approach, and XISM-CHAMPO2S from the improved energy balance, are determined using about one year＇s worth of CHAMP kinematic orbits from TUM and accelerometer data from GFZ. Comparisons among XISM-CHAMPO1S, XISM-CHAMPO2S, EIGEN-CGO3C, EIGEN-CHAMPO3S, EIGEN2, ENIGNIS and EGM96 are made. The results show that the XISM-CHAMPO2S model is more accurate than EGM96, EIGENIS, EIGEN2 and XISM-CHAMPO1S at the same degree and order, and has almost the same accuracy as EIGEN-CHAMPO3S.

Effects of rotation and gravity on an electro-magneto-thermoelastic medium with diffusion and voids by using the Lord-Shulman and dual-phase-lag models

The effects of rotation and gravity on an electro-magneto-thermoelastic medium with diffusion and voids in a generalized thermoplastic half-space are studied by using the Lord-Shulman (L-S) model and the dual-phase-lag (DPL) model. The analytical solutions for the displacements, stresses, temperature, diffusion concentration, and volume fraction field with different values of the magnetic field, the rotation, the gravity, and the initial stress are obtained and portrayed graphically. The results indicate that the effects of gravity, rotation, voids, diffusion, initial stress, and electromagnetic field are very pronounced on the physical properties of the material.

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.

Gravity Field Variations Associated with the Buried Geological Structures: San Marcos Fault (NE Mexico) Case Study

Gravity data are sensitive to local vertical offsets across high-angle faults, where rocks with different densities are juxtaposed. Yet high densities in some Mesozoic sedimentary rocks just above the basement may smear out the subtle gravity signatures of basement faults. At this study the gravity data processing tends to avoid ill-described “black-box” techniques. The study area is situated in the Palomas site, Cuatrociénegas region, Coahuila, NE Mexico. The San Marcos Fault is at least 300 km long and has WNW-ESE trend from the central part of Nuevo León State through Coahuila, and finally to the eastern part of Chihuahua State. Gravimetric data shows that the lowest values of free air and Bouguer anomalies are in the southern part of the area, and the highest values are in the western and central part of the area. Between these parts exists a zone of high horizontal gravity gradient. Configuration of linear elements of gravity field (gradient zones) delimited the San Marcos Fault in the San Marcos valley below thickness of recent sedimentary cover. Two density models were carried out, which showed that the Cretaceous rocks are in discordant contact with the Paleo- zoic rocks that can be related to the San Marcos Fault. The density was determinate using to Nettleton’s method, which results highlight the presence of the San Marcos Fault. Density models showed that the Quaternary sediments are in direct contact with the San Marcos Fault.

EGMTools:重力场模型评估及重力量计算软件

高精度、高分辨率的地球重力场可用于统一全球高程基准及确定大地水准面等,因此全面评估重力场模型精度及其快速导出的各重力量(如高程异常等)具有重要意义。本文利用VS2015+Intel XE 2016平台及OpenMP等并行技术研发一套用于重力场模型评估及相关重力量计算的软件——EGMTools,该软件的主要功能有:1)可实现基于实测点或格网重力异常、高程异常及垂线偏差等数据对重力场模型截断至任意阶次的精度进行评估;2)可实现利用重力场模型计算任意点或格网(SRTM地形表面)重力异常、高程异常及垂线偏差等重力量;3)在全球范围内,可按照一定的格网间隔(如1°×1°)对不同重力场模型所表示的重力量(如高程异常等)按不同的阶次进行比较;4)重力场模型格式转换、阶方差分析及RTM重力量计算的数据预处理等。

GOCE kinematic orbit adjustment for EGM validation and accelerometer calibration

The main principle and mathematical model of GOCE kinematic orbit adjustment for Earth gravity field model （EGM） validation and accelerometer calibration are presented. Based on 60 days GOCE kinematic orbits with 1-2 cm accuracy and accelerometer data from 2009-11-02 to 2009-12-31, the RMS-of-fit （ROF） of them using EGM2008, EIGEN-SC, ITG- GRACE2010S and GOCO01S up to 120, 150 and 180 degree and order （d/o） are evaluated and compared. The scale factors and biases of GOCE accelerometer data are calibrated and the energy balance method （EBM） is performed to test the accuracy of accelerometer calibration. The results show that GOCE orbits are also sensitive to EGM from 120 to 150 d/o. The ROFs of EGMs with 150 and 180 d/o are obviously better than those of EGMs with 120 d/o. The ROFs of GOCO01S and ITG-GRACE2010S are almost the same up to 120 and 150 d/o, which are about 3.3 cm and 1.8 cm, respectively. They are far better than those of EGM2008 and EIGEN-SC with the same d/o. The ROF of GOCO01S with 180 d/o is about 1.6 em, which is the best one among those EGMs. The accelerometer calibration accuracies （ACAs） of ITG-GRACE2010S and GOCO01S are obviously higher that those of EGM2008 and EIGEN-SC. The ACA of GOCO01S with 180 d/o is far higher than that of EGMs with 120 d/o, and a little higher than that of ITG-GRACE2010S with 150 d/o. I t is suggested that the newest released EGM such as GOCO01S or GOCO02S till at least 150 d/o should be chosen in GOCE precise orbit determination （POD） and accelerometer calibration.

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.

Synthetic tidal parameters for gravity over China and its neighbor area

The synthetic tidal parameters with high spatial resolution for gravity over China and its neighbor area are constructed with Earth＇s tidal model and ocean tide loading calculated using TPXO7 global ocean tide model as well as tidal data over China seas. The comparison between synthetic parameters and ones observed by spring gravimeters at some seismic network stations and Hong Kong station and one observed by super-conducting gravimeter at Wuhan station shows that the average differences in amplitude factors and phases are smaller than 0.005 and 0.5° respectively; and that the discrepancies between observational and synthetic parameters are dependent on gravimetric technique in that the synthetic parameters are in well agreement with the superconducting gravimetric observations. This also indicates that the synthetic result is a good estimation for tidal gravity, and the numerical results in the present paper not only can provide ground and space gravimetry such as absolute gravimetry with correction model of tidal gravity, but also provide effective tidal parameters over areas where no observation is carried out.

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.

Gravity gradient distribution in China's Mainland from GOCE satellite gravity gradiometry data

At present, gravity field and steady-state ocean circulation explorer（GOCE） gravity data are always used to compute regional gravity anomaly and geoid height. In this study, the latest GOCE gravity field model data（from Oct. 2009 to Jul. 2010） are used to compute the gravity gradient of China's Mainland according to a rigorous recursion formula（in all the six directions）. The results show that the numerical values of the gravity gradients are larger in the T rr direction than those in the other directions. They reflect the terrain characteristics in detail and correlate with the regional tectonics; however, in the T ql and T r l directions,the numerical values are relatively smaller and the gravity gradients in the T r l direction do not reflect the terrain characteristics in detail.

On the Cosmic Evolution of the Quantum Vacuum Using Two Variable G Models and Winterberg’s Thesis

We work within a Winterberg framework where space, i.e., the vacuum, consists of a two component superfluid/super-solid made up of a vast assembly (sea) of positive and negative mass Planck particles, called planckions. These material particles interact indirectly, and have very strong restoring forces keeping them a finite distance apart from each other within their respective species. Because of their mass compensating effect, the vacuum appears massless, charge-less, without pressure, net energy density or entropy. In addition, we consider two varying G models, where G, is Newton’s constant, and G-1, increases with an increase in cosmological time. We argue that there are at least two competing models for the quantum vacuum within such a framework. The first follows a strict extension of Winterberg’s model. This leads to nonsensible results, if G increases, going back in cosmological time, as the length scale inherent in such a model will not scale properly. The second model introduces a different length scale, which does scale properly, but keeps the mass of the Planck particle as, ± the Planck mass. Moreover we establish a connection between ordinary matter, dark matter, and dark energy, where all three mass densities within the Friedman equation must be interpreted as residual vacuum energies, which only surface, once aggregate matter has formed, at relatively low CMB temperatures. The symmetry of the vacuum will be shown to be broken, because of the different scaling laws, beginning with the formation of elementary particles. Much like waves on an ocean where positive and negative planckion mass densities effectively cancel each other out and form a zero vacuum energy density/zero vacuum pressure surface, these positive mass densities are very small perturbations (anomalies) about the mean. This greatly alleviates, i.e., minimizes the cosmological constant problem, a long standing problem associated with the vacuum.

Modeling of Earth’s Gravity Fields Visualization Based on Quad Tree

The problems of the earth's gravity fields' visualization are both focus and puzzle currently. Aiming at multiresolution rendering, modeling of the Earth's gravity fields' data is discussed in the paper by using LOD algorithm based on Quad Tree. First, this paper employed the method of LOD based on Quad Tree to divide up the regional gravity anomaly data, introduced the combined node evaluation system that was composed of viewpoint related and roughness related systems, and then eliminated the T-cracks that appeared among the gravity anomaly data grids with different resolutions. The test results demonstrated that the gravity anomaly data grids' rendering effects were living, and the computational power was low. Therefore, the proposed algorithm was a suitable method for modeling the gravity anomaly data and has potential applications in visualization of the earth's gravity fields.

Lithospheric Structure in the North China Craton Constrained from Gravity Field Model(EGM 2008)

A detailed knowledge of the thickness of the lithosphere in the North China craton（NCC） is important for understanding the significant tectonic reactivation of the craton in Mesozoic and Ce-nozoic.We achieve this goal by applying the newly proposed continuous wavelet transform theory to the Gravity Field Model（EGM 2008） data in the region.Distinct structural variations are identified in the scalogram image of profile Alxa-Datong（大同）-Qingdao（青岛）-Yellow Sea（profile ABC）,trans-versing the main units of NCC,which we interpret as mainly representing the Moho and lithosphere-asthenosphere boundary（LAB） undulations.The imaged LAB is as shallow as 60-70 km in the south-east basin and coastal areas and deepens to no more than 140 km in the northwest mountain ranges and continental interior.A rapid change of about 30 km in the LAB depth was detected at around the boundary between the Bohai（渤海） Bay basin（BBB） and the Taihang（太行） Mountains（TM）,roughly coincident with the distinct gravity decrease of more than 100 mGal that marks the North-South Grav-ity Lineament（NSGL） in the region.At last we present the gravity modeling work based on the spectral analysis results,incorporating with the observations on high-resolution seismic images and surface to-pography.The observed structural differences between the eastern and western NCC are likely associ-ated with different lithospheric tectonics across the NSGL.Combined with seismic tomography results and geochemical and petrological data,this sug-gests that complex modification of the litho-sphere probably accompanied significant litho-spheric thinning during the tectonic reactivation of the old craton.