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.

Outlier detection algorithm for satellite gravity gradiometry data using wavelet shrinkage de-noising

On the： basis of wavelet theory, we propose an outlier-detection algorithm for satellite gravity ometry by applying a wavelet-shrinkage-de-noising method to some simulation data with white noise and ers. The result Shows that this novel algorithm has a 97% success rate in outlier identification and that be efficiently used for pre-processing real satellite gravity gradiometry data.

Solving Three Types of Satellite Gravity Gradient Boundary Value Problems by Least-Squares

The principle and method for solving three types of satellite gravity gradient boundary value problems by least-squares are discussed in detail. Also, kernel function expressions of the least-squares solution of three geodetic boundary value problems with the observations {Γ zz },{Γ xz , Γ yz} and {Γ xx -Γ yy ,2 Γxy}are presented. From the results of recovering gravity field using simulated gravity gradient tensor data, we can draw a conclusion that satellite gravity gradient integral formulas derived from least-squares are valid and rigorous for recovering the gravity field.

On Numerical methods for determination of Earth gravity field model using mass satellite gravity gradiometry data

On the basis of Space-Wise Least Square method, three numerical methods including Cholesky de- composition, pre-conditioned conjugate gradient and Open Multi-Processing parallel algorithm are applied into the determination of gravity field with satellite gravity gradiometry data. The results show that, Cholesky de- composition method has been unable to meet the requirements of computation efficiency when the computer hardware is limited. Pre-conditioned conjugate gradient method can improve the computation efficiency of huge matrix inversion, but it also brings a certain loss of precision. The application of Open Multi-Processing parallel algorithm could achieve a good compromise between accuracy and computation efficiency.

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.

Geophysical Modeling with Satellite Gravity Data: Eigen-6C4 vs. GGM Plus

Satellite data sets are an asset in global gravity collections;their characteristics vary in coverage and resolution. New collections appear often, and the user must adapt fast to their characteristics. Their use in geophysical modeling is rapidly increasing;with this in mind we compare two of the most densely populated sets: EIGEN-6C4 and GGMplus. We characterize them in terms of their frequency histograms, Free Air anomalies, power spectrum, and simple Bouguer anomalies. The nature of the digital elevation models used for data reduction is discussed. We conclude that the GGMplus data set offers a better spatial resolution. To evaluate their effect in geophysical modelling, we chose an inland region with a prominent volcanic structure in which we perform 3D inversions of the respective Bouguer anomalies, obtaining density variations that in principle can be associated with the geologic materials and the structure of the volcanic edifice. Model results are analyzed along sections of the inverted data;we conclude that the GGMplus data set offers higher resolution in the cases analyzed.

Structural features in the mid-southern section of the Kyushu–Palau Ridge based on satellite altimetry gravity anomaly

The Kyushu–Palau Ridge(KPR),an anti-S-shaped submarine highland at the center of the Philippine Sea Plate(PSP),is considered the residual arc of the Izu–Bonin–Mariana Island Arc,which retains key information about the cessation of the Western Philippine Basin(WPB)expansion and the Parece Vela Basin(PVB)breakup.Herein,using the new generation of satellite altimetry gravity data,high-precision seafloor topography data,and newly acquired ship-borne gravity data,the topographic and gravity characteristics of the KPR mid-southern section and adjacent region are depicted.The distribution characteristics of the faults were delineated using the normalized vertical derivative–total horizontal derivative method(NVDR-THDR)and the minimum curvature potential field separation method.The Moho depth and crustal thickness were inverted using the rapid inversion method for a double-interface model with depth constraints.Based on these results,the crust structure features in the KPR mid-southern section,and the“triangular”structure geological significance where the KPR and Central Basin Rift(CBR)of the WPB intersect are interpreted.The KPR crustal thickness is approximately 6–16 km,with a distinct discontinuity that is slightly thicker than the normal oceanic crust.The KPR mid-southern section crust structure was divided into four segments(S1–S4)from north to south,formed by the CBR eastward extension joint action and clockwise rotation of the PVB expansion axis and the Mindanao fault zone blocking effect.

Structural characteristics and tectonic division of the Zambezi Delta basin in the offshore East Africa:evidences from gravity and seismic data

The Zambezi Delta basin is a passive marginal basin located on the East African coast that has good oil and gas exploration potential.Due to the special geological evolutionary background of the Beira High in the Zambezi Delta basin,it has a low gravity anomaly,and the existing seismic survey lines do not cover the whole basin;therefore,it is difficult to interpret the structural characteristics of the whole basin based solely on gravity or seismic data.Based on satellite altimetry gravity anomaly data,this study infers the distribution characteristics of faults in the Zambezi Delta basin by using the normalized vertical derivative of the total horizontal derivative(NVDR-THDR)technique.Then,constrained by seismic data,the gravity anomaly at the Moho interface is extracted by using the fast forward method of the double-interface model of the gravity anomaly,and this anomaly is then removed from the Bouguer gravity anomaly to obtain the sedimentary layer gravity anomaly.The thickness of the sedimentary strata is obtained by inversing the sedimentary basement depth of the whole basin.Then,uplifts and depressions are divided based on a sedimentary layer thickness of 3 km.This research demonstrates that the Zambezi Delta basin mainly features nearly SN-trending and NE-trending faults and that these faults exhibit east-west partitioning.The nearly SN-trending strike-slip faults controlled the sedimentary development of the basin,and the NE-trending tensile faults may have acted as migration channels for oil,gas and magma.The“overcompensation”effect of the Moho interface gravity anomaly on the gravity anomaly of the sedimentary layer is caused by the depression of the Moho interface beneath the Beira High,which results in a low gravity anomaly value for the Beira High.The pattern of uplifts and depressions trends NE and has the structural characteristics of east-west blocks.

Physical analysis on improving the recovery accuracy of the Earth's gravity field by a combination of satellite observations in along-track and cross-track directions

The physical investigations on the accuracy improvement to the measurement of the Earth＇s gravity field recovery are carried out based on the next-generation Pendulum-A/B out-of-plane twin-satellite formation in this paper. Firstly, the Earth＇s gravity field complete up to degree and order 100 is, respectively, recovered by the collinear and pendulum satellite formations using the orbital parameters of the satellite and the matching accuracies of key payloads from the twin GRACE satellites. The research results show that the accuracy of the Earth＇s gravity field model from the Pendulum-A/B satellite formation is about two times higher than from the collinear satellite formation, and the further improvement of the determination accuracy of the Earth＇s gravity field model is feasible by the next-generation Pendulum-A/B out-of-plane twin-satellite formation. Secondly, the Earth＇s gravity field from Pendulum-A/B complete up to degree and order 100 is accurately recovered based on the orbital parameters of the satellite （e.g., an orbital altitude of 400 km, an intersatellite range of 100 km, an orbital inclination of 89° and an orbital eccentricity of 0.001）, the matching accuracies of space- borne instruments （e.g. 10-6 m in the intersatellite range, 10-3 m in the orbital position, 10-6 m/s in orbital velocity, and 10-11 m/s2 in non-conservative force）, an observation time of 30 days and a sampling interval of 10 s. The measurement accuracy of the Earth＇s gravity field from the next-generation Pendulum-A/B out-of-plane twin-satellite formation is full of promise for being improved by about l0 times compared with that from the current GRACE satellite formation. Finally, the physical requirements for the next-generation Pendulum-A/B out-of-plane twin-satellite formation are analyzed, and it is proposed that the satellite orbital altitude be preferably designed to be close to 400±50 km and the matching precision of key sensors from the Pendulum-A/B mission be about one order of magnitude higher than from the GRACE program.

Theories and applications of earthquake-induced gravity variation:Advances and perspectives

Earthquake-induced gravity variation refers to changes in the earth’s gravity field associated with seismic activities.In recent years,development in the theories has greatly promoted seismic deformation research,laying a solid theoretical foundation for the interpretation and application of seismological gravity monitoring.Traditional terrestrial gravity measurements continue to play a significant role in studies of interseismic,co-seismic,and post-seismic gravity field variations.For instance,superconducting gravimeter networks can detect co-seismic gravity change at the sub-micro Gal level.At the same time,the successful launch of satellite gravity missions(e.g.,the Gravity Recovery and Climate Experiment or GRACE)has also facilitated applied studies of the gravity variation associated with large earthquakes,and several remarkable breakthroughs have been achieved.The progress in gravity observation technologies(e.g.,GRACE and superconducting gravimetry)and advances in the theories have jointly promoted seismic deformation studies and raised many new research topics.For example,superconducting gravimetry has played an important role in analyses of episodic tremor,slow-slip events,and interseismic strain patterns;the monitoring of transient gravity signals and related theories have provided a new perspective on earthquake early warning systems;the mass transport detected by the GRACE satellites several months before an earthquake has brought new insights into earthquake prediction methods;the use of artificial intelligence to automatically identify tiny gravity change signals is a new approach to accurate and rapid determination of earthquake magnitude and location.Overall,many significant breakthroughs have been made in recent years,in terms of the theory,application,and observation measures.This article summarizes the progress,with the aim of providing a reference for seismologists and geodetic researchers studying the phenomenon of gravity variation,advances in related theories and applications,and future research directions in this discipline.

Characteristics of satellite-gravity variations in the North-South Seismic Belt before the 2013 Lushan earthquake

To study the characteristics of gravity variations in and near the North-South Seismic Belt before the 2013 Lushan earthquake,we used the geopotential-field models based on monthly data of the RI.~5 GRACE satellite to calculate the gravity changes. Here we present the patterns of annually cumulative variation, differentiatial variation and secular trend, as well as the continuous time-series at 4 characteristic sites during 2004 -2012. The result shows that the anomalous positive-to-negative transition zone, in which the epicenter of the 2008 Wenchuan earthquake was located, did not show any new gravity change before the Lushan earthquake, though located in the same zone.

Development of Integrated and Intelligent Geodetic and Photogrammetry Satellites with Corresponding Key Technologies

Aerospace surveying and mapping has become the main method of global earth observation.It can be divided into the geodetic observation satellites and the topographic surveying satellites according to the disciplines.In this paper,the geodetic satellites and photographic satellites are introduced respectively.Then,the existing problems in Chinese earth observation satellites are analyzed,and the comprehensive satellite with integrated payloads,the intensive microsatellite constellation and the intelligent observation satellite are proposed as three different development ideas for the future earth observation satellites.The possibility of the three ideas is discussed in detail,as well as the related key technologies.

An estimation of groundwater storage variations from GRACE gravity satellites in the Heihe River Basin, northwestern China

There are only limited surface water resources available in the Heihe River Basin （HRB）, a typical inland river basin in the arid region of northwestern China, where groundwater overexploitation is a serious problem. Groundwater has become one of main resources of fresh water in the HRB. In this paper, temporal and spatial variations of groundwater in the HRB are estimated by the Gravity Recovery and Climate Experiment （GRACE） satellites. Our analysis shows that groundwater storage in the HRB reaches its highest in the summer of 2005, and then begins to decline in the following years and reaches steady status in 2008. Spatially, groundwater shows a decline in the upper HRB in the first two years and a slight increase in the following years, while this phenomenon is reversed in the middle HRB where groundwater slightly increases in 2005 and then declines in the following three years. In the lower HRB, GRACE detects a continual increase in the full six-year period. This approach is proven successful when employed in the HRB and thus offers a new insight into monitoring groundwater variations in a river basin with limited or even without any observed data.

Progress on the use of satellite technology for gravity exploration

In this paper, the technological progress on Chinese gravity exploration satellites is presented. Novel features such as ultra-stable structure, high accurate thermal control, drag-free and attitude control, micro-thrusters, aerodynamic configuration, the ability to perform micro-vibration analyses, microwave ranging system and mass center trimmer are described.

Study on crustal thickness and the prediction of prolific depressions:the Bohai Basin as an example

The deep crustal structure is closely related to oil and gas reserves.Predicting the oil and gas enrichment of depressions based on the Moho depth and crustal thickness is a promising research topic with significant implications for guiding exploration in petroliferous basins.In this study,seismic data were used as a constraint on the use of satellite gravity anomaly inversion to obtain the distribution of Moho depth and crustal thickness in the Bohai Basin.Stretching factors were calculated to analyze the differential distribution of deep crustal structural activity.Four indicators,including the minimum Moho depth,minimum crustal thickness,sum of Moho stretching factors,and sum of crustal stretching factors,were selected.Principal component analysis was applied to reduce the dimensionality of the multi-indicator system and obtain an oil and gas enrichment score for quantitative prediction of favorable prolific depressions.The deviation between the inverted Moho depth and seismic constraints was small;thus,the data effectively reflect the variations in the characteristics of each depression.The analysis revealed significant statistical features related to the minimum Moho depth/crustal thickness and the sum of Moho/crustal stretching factors associated with prolific depressions.Based on the oil and gas enrichment score,the depressions were classified into four categories related to their different deep crustal structural characteristics.Highly active ClassⅠ,ClassⅡ,and ClassⅢdepressions are predicted to be favorable prolific depressions.This study expands the research on quantitatively predicting favorable prolific depressions in the Bohai Basin using the deep crustal structure and can contribute to reducing production costs and improving exploration efficiency in future explorations.

Construction of nonsingular formulae of variance and covariance function of disturbing gravity gradient tensors

When the computational point is approaching the poles, the variance and covariance formulae of the disturbing gravity gradient tensors tend to be infinite, and this is a singular problem. In order to solve the problem, the authors deduced the practical non-singular computational formulae of the first- and second-order derivatives of the Legendre functions and two kinds of spherical harmonic functions, and then constructed the nonsingular formulae of variance and eovarianee function of disturbing gravity gradient tensors.

Monthly gravity field solution from GRACE range measurements using modified short arc approach

In this paper we present a series of monthly gravity field solutions from Gravity Recovery and Climate Experiment（GRACE） range measurements using modified short arc approach,in which the ambiguity of range measurements is eliminated via differentiating two adjacent range measurements.The data used for developing our monthly gravity field model are same as Tongji-GRACEOl model except that the range measurements are used to replace the range rate measurements,and our model is truncated to degree and order 60,spanning Jan.2004 to Dec.2010 also same as Tongji-GRACE01 model.Based on the comparison results of the C_（2,0）,C_（2,1）,S_（2,1）,and C_（15,15）,S_（15,15）,time series and the global mass change signals as well as the mass change time series in Amazon area of our model with those of Tongji-GRACE01 model,we can conclude that our monthly gravity field model is comparable with Tongji-GRACE01 monthly model.

WHU-Grace01s:A new temporal gravity field model recovered from GRACE KBRR data alone

A new temporal gravity field model called WHU-Grace01s solely recovered from Gravity Recovery and Climate Experiment （GRACE） K-Band Range Rate （KBRR） data based on dynamic integral approach is presented in this paper. After meticulously preprocessing of the GRACE KBRR data, the root mean square of its post residuals is about 0.2 micrometers per second, and seventy-two monthly temporal solutions truncated to degree and order 60 are computed for the period from January 2003 to December 2008. After applying the combi- nation filter in WHU-Grace01s, the global temporal signals show obvious periodical change rules in the large-scale fiver basins. In terms of the degree variance, our solution is smaller at high degrees, and shows a good consistency at the rest of degrees with the Release 05 models from Center for Space Research （CSR）, GeoForschungsZentrum Potsdam （GFZ） and Jet Pro- pulsion Laboratory 0PL）. Compared with other published models in terms of equivalent water height distribution, our solution is consistent with those published by CSR, GFZ, JPL, Delft institute of Earth Observation and Space system （DEOS）, Tongji University （Tongji）, Institute of Theoretical Geodesy （ITG）, Astronomical Institute in University of Bern （AIUB） and Groupe de Recherche de Geodesie Spatiale （GRGS}, which indicates that the accuracy of WHU-Grace01s has a good consistency with the previously published GRACE solutions.

External calibration of GOCE data using regional terrestrial gravity data

This paper reports on a study of the methodology of external calibration of GOCE data, using regional terrestrial-gravity data. Three regions around the world are selected in the numerical experiments. The result indicates that this calibration method is feasible. The effect is best with an accuracy of scale factor at 10 -2 level, in Australia, where the area is smooth and the gravity data points are dense. The accuracy is one order of magnitude lower in both Canada, where the area is smooth but the data points are sparse, and Norway, where the area is rather tough and the data points are sparse.

Periodic orbits around areostationary points in the Martian gravity field

This study investigates the problem of areostationary orbits around Mars in three-dimensional space. Areostationary orbits are expected to be used to establish a future telecommunication network for the exploration of Mars. However, no artificial satellites have been placed in these orbits thus far. The characteristics of the Martian gravity field are presented, and areostationary points and their linear stability are cal- culated. By taking linearized solutions in the planar case as the initial guesses and utilizing the Levenberg-Marquardt method, families of periodic orbits around areo- stationary points are shown to exist. Short-period orbits and long-period orbits are found around linearly stable areostationary points, but only short-period orbits are found around unstable areostationary points. Vertical periodic orbits around both lin- early stable and unstable areostationary points are also examined. Satellites in these periodic orbits could depart from areostationary points by a few degrees in longitude, which would facilitate observation of the Martian topography. Based on the eigenval- ues of the monodromy matrix, the evolution of the stability index of periodic orbits is determined. Finally, heteroclinic orbits connecting the two unstable areostationary points are found, providing the possibility for orbital transfer with minimal energy consumption.