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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Water storage variations in the Poyang Lake Basin estimated from GRACE and satellite altimetry

The Gravity Recovery and Climate Experiment（GRACE） satellite mission provides a unique opportunity to quantitatively study terrestrial water storage（TWS） variations. In this paper,the terrestrial water storage variations in the Poyang Lake Basin are recovered from the GRACE gravity data from January 2003 to March 2014 and compared with the Global Land Data Assimilation System（GLDAS） hydrological models and satellite altimetry. Furthermore, the impact of soil moisture content from GLDAS and rainfall from the Tropical Rainfall Measuring Mission（TRMM） on TWS variations are investigated. Our results indicate that the TWS variations from GRACE, GLDAS and satellite altimetry have a general consistency. The TWS trends in the Poyang Lake Basin determined from GRACE, GLDAS and satellite altimetry are increasing at 0.0141 km^3/a, 0.0328 km^3/a and 0.0238 km^3/a,respectively during the investigated time period. The TWS is governed mainly by the soil moisture content and dominated primarily by the precipitation but also modulated by the flood season of the Yangtze River as well as the lake and river exchange water.

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.

Recent Progress on Hydrogeodesy in China

Modern geodetic technologies,including high-precision ground-based gravity measurements,satellite gravimetry,satellite altimetry,Global Navigation Satellite Systems(GNSS),and Interferometric Synthetic Aperture Radar(InSAR),offer a wealth of observations for monitoring global hydrological processes with exceptional accuracy and spatio-temporal resolutions.Mass redistribution and Earth’s surface deformation over land related to global and regional water cycling can be inferred from modern gravimetry,altimetry,GNSS,and InSAR techniques.Hydrogeodesy becomes an emerging field of geodesy aiming to analyze the changes of water in the Earth system.The paper introduces the China’s advances in hydrogeodesy in recent years.It brings together multiple geodetic teams’work from China,showcasing the application of modern geodetic technologies in the field of hydrology,including research on terrestrial water storage,groundwater storage,glaciers/ice sheets,and reservoir water storage.

Advances, Problems and Prospects of Modern Geodesy Applied in Tibetan Geodynamic Changes

Modern geodetic techniques have developed rapidly in recent years, providing reliable observation data and new effective approaches, and greatly enhancing studies of the Tibetan geodynamics. For instance, the well-known GPS technique has been employed to measure seismic slips for many faults in the Tibetan Plateau. GPS data agree well with the hypothesis of a thickening crust and eastward mass flow. Moreover, absolute gravimetric data have been applied to interpret geophysical phenomena such as crust movement, co-seismic gravity change, GIA, and ground water change. The satellite gravity mission GRACE launched in 2002 provided global gravity models with unprecedentedly high precision and high spatial resolution. It has been used in implementing temporal gravity changes and improving our knowledge of the Earth＇s interior, including lithosphere dynamics, mantle viscosity and rheology, plateau uplift, and subduction processing. It is noteworthy that gravity presents unique advantages for the study of Tibetan geodynamics because of its sensitivity to mass migration and dynamic redistribution. To date, great advances have been made in applying modern geodetic data in studying dynamic changes of Tibetan plateau. For instance, the horizontal displacement field from GPS data revealed dynamical characteristics of the present-day Tibetan plateau. The combination of gravity anomalies and topographic data describe the tectonic characteristics of Tibetan plateau. The combination of gravity data and GPS data show present properties of the Tibetan plateau such as crust thickening, Moho＇s subsidence, and plateau uplift. GRACE data were used to estimate the distribution of ice/snow melting. These results demonstrate that mere application of integrated geodetic data as well as geophysical methods and numerical simulations can enhance our knowledge of Tibetan plateau dynamics. It must be pointed out that GRACE data include various geophysical signals such as crust vertical movement, denudation, ice and snow melting, GIA, ground water change, and permafrost degradation. To separate the tectonic information from other impulses, each physical signal must be evaluated and corrected carefully from the GRACE data. The Tibetan geodynamic problem is a complicated and synthetic issue that must be addressed through collaboration of workers in many fields. Succinctly put, although great achievements have been made in studying Tibetan plateau dynamics from each field, the dynamical process remains unclear. Some fundamental problems remain unresolved. They should be solved with modern geodetic data, such as GRACE, GPS, and absolute gravity data, combined with meteorological and geological data, for quantitative analysis of Tibetan plateau dynamics affected by respective geophysical sources. This review article introduces and discusses the scientific importance, advances, problems, and prospects of modern geodesy applied to the study of geodynamic changes of the Tibetan plateau.

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.