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.

Earth Gravity Field Recovered from CHAMP Science Orbit and Accelerometer Data

The earth gravity field model CDS01S of degree and order 36 has been recovered from the post processed Science Orbits and on-board accelerometer data of GFZ’s CHAMP satellite. The model resolves the geoid with an accuracy of better than 4 cm at a resolution of 700 km half-wavelength. By using the degree difference variances of geopotential coefficients to compare the model CDS01S with EIGEN3P, EIGEN1S and EGM96, the result indicates that the coefficients of CDS01S are most close to those of EIGEN3P. The result of the comparison between the accuracies of geopotential coefficients in the above models, indicates that the accuracy of coefficients in CDS01S is higher than that in EGM96.The geoid undulations of CDS01S and GGM01C up to 30 degrees are calculated and the standard deviation is 4.7 cm between them.

Review of the Research Progress on Static Earth Gravity Field and Vertical Datum in China during 2019—2023

The contribution presents the representative research progress on global static gravity field modeling,regional geoid/quasigeoid determination,vertical datum study,as well as the theory,algorithm and software for gravity field study in China from 2019 to 2023,which are the highlights of the chapter 6“Progress in Earth Gravity Model and Vertical Datum”in the“2019—2023 China National Report on Geodesy”that submitted to the International Association of Geodesy(IAG).In addition,suggestions are proposed to promote the research in the fields of earth gravity field,geoid/quasigeoid and vertical datumin China according to trends of international geodesy and related disciplines.

A High-Resolution Earth’s Gravity Field Model SGG-UGM-2 from GOCE,GRACE,Satellite Altimetry,and EGM2008

This paper focuses on estimating a new high-resolution Earth’s gravity field model named SGG-UGM-2 from satellite gravimetry,satellite altimetry,and Earth Gravitational Model 2008(EGM2008)-derived gravity data based on the theory of the ellipsoidal harmonic analysis and coefficient transformation(EHA-CT).We first derive the related formulas of the EHA-CT method,which is used for computing the spherical harmonic coefficients from grid area-mean and point gravity anomalies on the ellipsoid.The derived formulas are successfully evaluated based on numerical experiments.Then,based on the derived least-squares formulas of the EHA-CT method,we develop the new model SGG-UGM-2 up to degree 2190 and order 2159 by combining the observations of the Gravity Field and Steady-State Ocean Circulation Explorer(GOCE),the normal equation of the Gravity Recovery and Climate Experiment(GRACE),marine gravity data derived from satellite altimetry data,and EGM2008-derived continental gravity data.The coefficients of degrees 251–2159 are estimated by solving the block-diagonal form normal equations of surface gravity anomalies(including the marine gravity data).The coefficients of degrees 2–250 are determined by combining the normal equations of satellite observations and surface gravity anomalies.The variance component estimation technique is used to estimate the relative weights of different observations.Finally,global positioning system(GPS)/leveling data in the mainland of China and the United States are used to validate SGG-UGM-2 together with other models,such as European improved gravity model of the earth by new techniques(EIGEN)-6C4,GECO,EGM2008,and SGG-UGM-1(the predecessor of SGG-UGM-2).Compared to other models,the model SGG-UGM-2 shows a promising performance in the GPS/leveling validation.All GOCE-related models have similar performances both in the mainland of China and the United States,and better performances than that of EGM2008 in the mainland of China.Due to the contribution of GRACE data and the new marine gravity anomalies,SGG-UGM-2 is slightly better than SGG-UGM-1 both in the mainland of China and the United States.

Characteristics of gravity fields in the Jinggu M6. 6 earthquake

Based on the study of high-precision gravity data obtained from recent studies and the regional gravi- ty network for Yunnan province, a variation in the regional gravity field was identified before the occurrence of the Yunnan Jinggu M6.6 earthquake.

Probing signals of atmospheric gravity waves excited by the July 29,2021 M_(W)8.2 Alaska earthquake

It is commonly believed that the atmosphere is decoupled from the solid Earth.Thus,it is difficult for the seismic wave energy inside the Earth to propagate into the atmosphere,and atmospheric pressure wave signals excited by earthquakes are unlikely to exist in atmospheric observations.An increasing number of studies have shown that earthquakes,volcanoes,and tsunamis can perturb the Earth's atmosphere due to various coupling effects.However,the observations mainly focus on acoustic waves with periods of less than 10 min and inertial gravity waves with periods of greater than 1 h.There are almost no clear observations of gravity waves that coincide with observations of low-frequency signals of the Earth's free oscillation frequency band within 1 h.This paper investigates atmospheric gravity wave signals within1 h of surface-atmosphere observations using the periodogram method based on seismometer and microbarometer observations from the global seismic network before and after the July 29,2021 M_(w)8.2 Alaska earthquake in the United States.The numerical results show that the atmospheric gravity wave signals with frequencies similar to those of the Earth's free oscillations _(0)S_(2) and _(0)T_(2) can be detected in the microbaro meter observations.The results con firm the existence of atmospheric gravity waves,indicating that the atmosphere and the solid Earth are not decoupled within this frequency band and that seismic wave energy excited by earthquakes can propagate from the interior of the Earth to the atmosphere and enhance the atmospheric gravity wave signals within 1 h.

Dynamic pattern characteristics of fault deformation and gravity field in the development process of Yongdeng M_S=5.8 earthquake

In this paper, the fault deformation abnormality, dynamic evolution features of gravity and vertical deformation field in the seismogenic process of the Yongdeng, Gansu Province earthquake on July 22, 1995 are studied primarily. There appeared α β γ tri stage anomaly at three sites near the epicenter, and there appeared anomalies of step and sudden jump at more than 10 sites in outer region since 1993. The high value area before shock, coseismic effect and process of recovery aftershock were monitored by portable gravity data. Data reflects the changing process of fault movement from the quasi linear to the nonlinear in the near source region during seismogenic development of the Yongdeng earthquake and evolution of gravity field from heterogeneity of seismogenic term to quasi homogeneity of postseismic term. There exists close relationship between strong earthquake and dynamic evolution of regional stress strain field. Considering all above, the experience and lessons in this medium short term prediction test are summarized.

Study on Evolution of Gravity Fieldand Earthquake Prediction in theNorth-south Seismic Belt and theEastern Qinghai-Xizang Block

The relation between the dynamic evolution feature of gravity field and strong seismicity is studied. The result shows that the regional gravity field variation enjoys inhomogeneity of spatial and temporal distribution and gravity change in different regions. It may be resulted from active faults and seismogenic process, and may be due to microdynamic activity of regional strain energy, which might be accumulated or released in different stages, and there exists transformation process of stress.

Dynamic changes of gravity fields before and after the 2008 Wenchuan earthquake(Ms8.0)

The pattern evolution and dynamic mechanism of the dynamic changes of regional gravity fields occurring before and after the Wenchuan Ms8.0 earthquake are analyzed, based on five epochs of 1998 -2007 mobile gravity data from the middle-south section of the north-south seismic belt, and two epochs of field research data collected after the 2008 Wenchuan earthquake in combination with GPS data, leveling observations, and geotectonic environment data. The regional dynamic gravity changes demonstrate the effects of the eastward flow of solid matter in the Qinghai-Tibetan plateau and the preparation of the 2008 Wenchuan earthquake （2- 10 yr）. The two most meaningful gravity indicators of the Wcnchuan earthquake preparation are the positive （increasing） gravity changes occurring over many years in the southwest epicenter and the largescale gradient zone of gravity variation, with the cumulative difference between the two sides of the gradient zone of gravity exceeding 200 μGal. The positive gravity changes may facilitate a constant energy accumulation and the gradient belt may support seismic shear breakage. Overall, the gravity changes associated with the earthquake preparation indicate a pattern of accelerating increase-decelerating increase-earthquake occurrence. The Songpan-Ganzi block generally displays a negative gravity change, providing evidence for a local upwarp- ing of the deep crust-mantle and an interior expansion of the deep crust attributable to high temperatures. The viewpoint is consistent with the dilatant mechanism for earthquake preparation.

Simulation of earth gravity field using satellite constellation with variable inclination configuration

Based on a satellite constellation composed of two GRACE-type satellite formations with different inclinations(near polar orbit + low inclination) and the theory of repeat orbit cycle, we discuss the methods for selecting medium-low inclinations for global and local gravity fields. The effects of this constellation configuration on gravity field inversion are comparatively analyzed using a whole-course dynamics simulation. The results show that compared with the single GRACE-type satellite formation,the use of satellite constellations with different inclination configurations improves the gravity solution precision by 34%. The inclusion of multi-directional observations can improve the spatio-temporal resolution of the satellite missions, and yield gravity field solutions with higher isotropic sensitivity.Furthermore, it is necessary to select the optimal low inclination according to the study area, which will have a significant influence on the gravity field solution.

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.

SATELLITE GRAVITY SURVEYING TECHNOLOGY AND RESEARCH OF EARTH’S GRAVITY FIELD

This is a summarized paper. Two topics are discussed: Firstly, the concept, development and application of four kinds of satellite gravity surveying technology are introduced; Secondly, some problems of theory and method, which must be considered in the study of the \{Earth’s\} gravity field based on satellite gravity data, are expounded.

Field source characteristic of gravity variation in Hexi region before Menyuan Ms6.4 earthquake based on the Euler deconvolution

This study adopted the Euler deconvolution method to conduct an inversion and interpretation of the depth and spatial distribution pattern of field source that lead to gravity variation. For this purpose, mobile gravity data from four periods in the Hexi region between 2011 and 2015 were obtained from an observation network. With a newly established theoretical model, we acquired the optimum inversion parameters and conducted calculation and analysis with the actual data. The results indicate that one is the appropriate value of the structure index for the inversion of the mobile gravity data. The inversion results of the actual data showed a comparable spatial distribution of the field source and a consistent structural trend with observations from the Qilian-Haiyuan Fault zone between 2011 and 2015. The distribution was in a blocking state at the epicenter of the Menyuan earthquake in 2016. Our quantitative study of the field source provides new insights into the inversion and interpretation of signals of mobile gravity variation.

Spatio-Temporal Polar-Inclined Space Mission Architecture for a Refined Retrieve of the Earth’s Gravity Field

Future satellite gravity missions (FGMs) have been intensively studied during the last recent years for the era beyond the successful previous GRACE and current GRACE Follow-on satellite missions. Previous studies have investigated the gravity field recovery derived from combined two satellite-pairs (referred here as PI-FGM, a single polar satellite-pair like the GRACE mission combined with another inclined satellite-pair) with different orbital heights of few kilometers and different repeat orbital periods. In this contribution, new innovative idea is introduced by designing the inclined satellite-pair of the FGM at the same orbital height of the polar-type with shifted spatio-temporal (ST-FGM) orbital parameters to avoid any possible collision risk between the two satellite-pairs, polar and inclined, of the FGM architecture. The repeat orbits issue will be taken into consideration through the manuscript and will be set as identical as possible for a fair comparison. The findings through a full-scale simulation analysis show that the new design of shifted spatio-temporal polar-inclined (ST-FGM) mission architecture basically outperforms the two satellite-pairs having different orbital heights (i.e. the PI-FGM mission configuration). Regarding the gravity field recovery, the ST-FGM architecture retrieves the geoid heights with standard deviations of about 17.0 mm providing more isotropic error distribution. An overall improvement by a factor of about 80 and 60 is provided by the ST-FGM and PI-FGM mission architectures, respectively, with respect to the GRACE-like formation and a factor of about 2.4 and 1.8, respectively, with respect to the smoothed gravity solution using the Gaussian filter at radius 400 km. Therefore, the shifted spatio-temporal polar-inclined (ST-FGM) is worthy recommended as stable mission architecture and would be considered as one of the future gravity missions.

Earth gravity field solution with combining CHAMP and GRACE data

Satellite gravity data fusion with multi-type and huge-amount is one of the hot topics in physical geodesy. After a brief review of dynamic approach, the CHAMP-only and GRACE-only gravity fields by using HL-SST and LL-SST data from 2003 to 2009 are recovered respectively. An combination strategy of CHAMP and GRACE data by using Helmert variance component estimation （VCE） is proposed based on normal equation level fusion. Three gravity field models with 150° and order by CHAMP-only data, GRACE-only data and combining CHAMP and GRACE data from 2003 to 2009 are recovered. The comparisons between our recovered models and those latest released models were performed. The external accuracy validations using marine gravity anomalies from DTU13 products and height anomalies from GPS/leveling data are also conducted in this paper. The results show that long-term CHAMP data do contribute to the accuracy improvement of gravity field solution. The accuracy of the combined model using CHAMP and GRACE data is better than those of the individuals and comparative to the models published by international groups.

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.

Gravity and magnetic anomalies field characteristics in the South China Sea and its application for interpretation of igneous rocks

Igneous rocks in the South China Sea have broad prospects for oil and gas exploration.Integrated geophysical methods are important approaches to study the distribution of igneous rocks and to determine and identify igneous rock bodies.Aimed at the characteristics of gravity and magnetic fields in the South China Sea,several potential field processing methods are preferentially selected.Reduction to the pole by variable inclinations in the area of low magnetic latitudes is used to perform reduction processing on magnetic anomalies.The preferential continuation method is used to separate gravity and magnetic anomalies and extract the gravity and magnetic anomaly information of igneous rocks in the shallow part of the South China Sea.The 3D spatial equivalent distribution of igneous rocks in South China Sea is illustrated by the 3 D correlation imaging of magnetic anomalies.Since the local anomaly boundaries are highlighted gravity and magnetic gradients,the distribution characters of different igneous rocks are roughly outlined by gravity and magnetic correlation analysis weighted by gradient.The results show the distribution of igneous rocks is controlled and influenced by deep crustal structure and faulting.

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.

Preparation of electrolytic copper powders with high current efficiency enhanced by super gravity field and its mechanism

Super gravity field was employed to enhance electrolytic reaction for the preparation of copper powders.The morphology, microstructure and size of copper powders were characterized by scanning electron microscopy,X-ray diffractometry and laser particle analysis.The results indicated that current efficiencies of electrolytic copper powders under super gravity field increased by more than 20% compared with that under normal gravity condition.Cell voltage under super gravity field was also much lower.The size of copper powders decreased with the increase of gravity coefficient(G).The increase of current efficiency can be contributed to the disturbance of electrode/electrolyte interface and enhanced mass transfer of Cu2+ in super gravity field.Meanwhile,the huge gravity acceleration would promote the detachment of copper powders from electrode surface during electrolytic process,which can prevent the growth of copper powders.