Refining geoid and vertical gradient of gravity anomaly

We have derived and tested several relations between geoid （N） and quasi-geoid （~） with model validation. The elevation correction consists of the first-term （Bouguer anomaly） and second-term （vertical gradient of gravity anomaly）. The vertical gradient was obtained from direct measurement and terrain calcula- tion. The test results demonstrated that the precision of geoid can reach centimeter-level in mountains less than 5000 meters high.

Calculation of geoid undulations and gravity anomaliesin the Northwest Pacific by using the Topex/Poseidonand Geosat altimeter data

The geoid undulations in the Northwest Pacific were calculated by usingtheTopex/Poseidon and Geosataltimeter data. Firstly the bias between two types of the altimeter data was removed and the geoid undulations in theNorthwest Pacific were acquired by a long wave bias diminishing model with a resolution of 30 km and precision of 14cm. Then an algorithm of inversion of gravity anomalies was derived , and the gravity anomalies in the East China Seawere calculated by using the algorithm and the geoid undulations. The rms of difference between the in situ measure-ments the gravity anomalies from altimeter data was 3 .8× 10-5 m/s2. A method to colculate the gravity anomaliesin a larger area was developed which combined gravity anomalies in four subregions overlapping each other into one data set in a larger region. The error analysys shaws that the model and result of the inversion of gravity anomalies were reliable.

Determination of Antarctic geoid by using global gravity field

With Chinese latest global gravity field model WDM94, the authors provide the geoid height and mean free air gravity anomaly of Antarctica (The range of latitude is from -60° to -90°). In order to conclude and analyze the characters of Antarctic geoid roundly, the authors collect the latest oversea global gravity field model OSU91 (to degree and order 360) and JGMOSU (to degree and order 360), get the corresponding geoid height and mean free air gravity anomaly. The results are compared with the results got from WDM94, thus we get the difference. The standard deviation of geoid height between WDM94 and OSU91 is ±1.90 m;the deviation of geoid between WDM94 and JGMOSU is ±2.09 m. The standard deviation of mean gravity anomaly are ±8.97 mGal and ±9.32 mGal respectively. [WT9.HZ]

Analysis of the merged quasi-geoid of neighbouring areas

Employing the merged quasi-geoid, we analyses the causes of systematic errors in modelling of quasigeoid of neighbouring areas in the paper, and the efficient method is introduced to improve the accuracy of quasi-geoid. First, the systematic error is weakened with the moving window method applied to established quasi-geoids in two adjacent regions, and the accuracy of the merged quasi-geoid in the stitching region is checked using the measured GPS benchmark data; Second, the whole quasi-geoid is recomputed with data obtained from two adjacent regions if the accuracy of the quasi-geoid obtained from the first step in the stitching region is low; Finally, the quasi-geoids in two adjacent regions are recomputed respectively using GPS benchmark data of own region and adjacent region with the same solution if the accuracy of whole quasi-geoid obtained from the second step also is low. Actual data sets from Sichuan Province and Chongqing City are employed to test the moving window method. It is shown that the quasi-geoid models with high resolution and accuracy were obtained.

Methodology for local correction of the heights of global geoid models to improve the accuracy of GNSS leveling

At present,one of the methods used to determine the height of points on the Earth’s surface is Global Navigation Satellite System(GNSS)leveling.It is possible to determine the orthometric or normal height by this method only if there is a geoid or quasi-geoid height model available.This paper proposes the methodology for local correction of the heights of high-order global geoid models such as EGM08,EIGEN-6C4,GECO,and XGM2019e_2159.This methodology was tested in different areas of the research field,covering various relief forms.The dependence of the change in corrected height accuracy on the input data was analyzed,and the correction was also conducted for model heights in three tidal systems:"tide free","mean tide",and"zero tide".The results show that the heights of EIGEN-6C4 model can be corrected with an accuracy of up to 1 cm for flat and foothill terrains with the dimensionality of 1°×1°,2°×2°,and 3°×3°.The EGM08 model presents an almost identical result.The EIGEN-6C4 model is best suited for mountainous relief and provides an accuracy of 1.5 cm on the 1°×1°area.The height correction accuracy of GECO and XGM2019e_2159 models is slightly poor,which has fuzziness in terms of numerical fluctuation.

Modeling a Local Geoid: Application in Thies, Senegal

Many applications in geodesy, hydrography and engineering require determining heights linked to the geoid. Direct leveling, which is the traditional method of obtaining these elevations, is slow, time consuming and expensive. The contribution of space techniques can make it possible to overcome these constraints provided that we have a precision geoid model compatible with that obtained by the GNSS method. There are today relatively precise regional geoid models, at least outside of mountain ranges, in all developed countries, which is not yet the case in developing countries like Senegal. An alternative is to use local models restricted to a small area. Thus, this study aims to produce a geoid model by combining multi-source data for the city of Thies intended mainly to support leveling operations by GNSS. To achieve this objective, direct precision leveling and GNSS leveling (static mode) were carried out covering the study area. The reference points used are, among others, those of the RRS04 (Reference Network of Senegal 2004) and the NGAO53 (General Leveling of West Africa 1953). Additionally, gravimetric measurements were conducted using the Sensor Play-Data Recorder application. The calculation of the model was carried out by the SRBF (Spherical Radial Basis Function) method using the PAGravf4.5 software. The SRBF method uses EGM08 to first calculate height and gravity anomalies. These are then compared with the raw data in order to determine the residuals which will allow the model to be refined. In order to validate our model, control points (GNSS/leveled) were chosen based on a homogeneous geographical distribution in the area in order to evaluate their altitude. An accuracy of less than 2 cm was obtained. Comparing our model with the existing local model GGSV12v1 shows that our model is more accurate.

Direct regional quasi-geoid determination using EGM2008 and DEM:A case study for China's Mainland and its vicinity areas

Earth＇s gravity model（EGM） helps people better determine the figure of Earth, which is generally represented by a global geoid. For a considerable amount of practical applications, people use quasi-geoid to approximate the geoid, thus the quasi-geoid is also treated as an important height datum. In this study we revisit the method to directly determine regional quasi-geoid using EGM and digital elevation model（DEM）, on the basis of Molodensky theory. According to the method we obtain a 50 50quasi-geoid for China's Mainland and its vicinity areas, based on the EGM2008 gravitational potential model and the Shuttle Radar Topography Mission（SRTM） DEM model. By comparing height anomalies derived from EGM2008 with observations at 70 GPS/leveling points in areas including northwest,mid-west, mid-east and southeast of China, we find that the 50 50EGM2008 quasi-geoid well fits the GPS/leveling results, with average deviations less than 10 cm for the selected areas in east China（with mainly plain topography） and ~20 cm for the selected areas in west China（highland or mountainous areas）. We also discuss a few technical issues for directly determining height anomalies based on EGM and DEM, under the frame of Molodensky theory.

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.

Coseismic gravity and displacement changes of Japan Tohoku earthquake(Mw 9.0)

The greatest earthquake in the modern history of Japan and probably the fourth greatest in the last 100 years in the world occurred on March 11, 2011 off the Pacific coast of Tohoku.Large tsunami and ground motions caused severe damage in wide areas, particularly many towns along the Pacific coast. So far, gravity change caused by such a great earthquake has been reported for the 1964 Alaska and the 2010 Maule events. However, the spatial-temporal resolution of the gravity data for these cases is insufficient to depict a co-seismic gravity field variation in a spatial scale of a plate subduction zone. Here, we report an unequivocal co-seismic gravity change over the Japanese Island, obtained from a hybrid gravity observation（combined absolute and relative gravity measurements）. The time interval of the observation before and after the earthquake is within 1 year at almost all the observed sites, including 13 absolute and 16 relative measurement sites, which deduced tectonic and environmental contributions to the gravity change. The observed gravity agrees well with the result calculated by a dislocation theory based on a self-gravitating and layered spherical earth model. In this computation, a co-seismic slip distribution is determined by an inversion of Global Positioning System（GPS） data. Of particular interest is that the observed gravity change in some area is negative where a remarkable subsidence is observed by GPS, which can not be explained by simple vertical movement of the crust. This indicated that the mass redistribution in the underground affects the gravity change. This result supports the result that Gravity Recovery and Climate Experiment（GRACE） satellites detected a crustal dilatation due to the 2004 Sumatra earthquake by the terrestrial observation with a higher spatial and temporal resolution.

Monthly gravity field recovery from GRACE orbits and K-band measurements using variational equations approach

The Gravity Recovery and Climate Experiment（GRACE） mission can significantly improve our knowledge of the temporal variability of the Earth＇s gravity field.We obtained monthly gravity field solutions based on variational equations approach from GPS-derived positions of GRACE satellites and K-band range-rate measurements.The impact of different fixed data weighting ratios in temporal gravity field recovery while combining the two types of data was investigated for the purpose of deriving the best combined solution.The monthly gravity field solution obtained through above procedures was named as the Institute of Geodesy and Geophysics（IGG） temporal gravity field models.IGG temporal gravity field models were compared with GRACE Release05（RL05） products in following aspects：（i） the trend of the mass anomaly in China and its nearby regions within 2005-2010; （ii） the root mean squares of the global mass anomaly during 2005-2010; （iii） time-series changes in the mean water storage in the region of the Amazon Basin and the Sahara Desert between 2005 and 2010.The results showed that IGG solutions were almost consistent with GRACE RL05 products in above aspects（i）-（iii）.Changes in the annual amplitude of mean water storage in the Amazon Basin were 14.7 ± 1.2 cm for IGG,17.1 ± 1.3 cm for the Centre for Space Research（CSR）,16.4 ± 0.9 cm for the GeoForschungsZentrum（GFZ） and 16.9 ± 1.2 cm for the Jet Propulsion Laboratory（JPL） in terms of equivalent water height（EWH）,respectively.The root mean squares of the mean mass anomaly in Sahara were 1.2 cm,0.9 cm,0.9 cm and 1.2 cm for temporal gravity field models of IGG,CSR,GFZ and JPL,respectively.Comparison suggested that IGG temporal gravity field solutions were at the same accuracy level with the latest temporal gravity field solutions published by CSR,GFZ and JPL.

Application of Geoid Anomalies to the Tectonic Research in the East Asian Continental Margin

In this paper, we calculated multi-scale residual geoid anomalies with the method of geoid separation processing, according to EGM2008 ultra-high order gravity field model, remove-restore technique and Stokes integral. The East Asian continental margin was selected as the study area. The residual geoid anomalies have been calculated by programming. On the basis of residual geoid anomalies at various orders, the interlayer geoid anomalies at different depths were calculated to depict the spatial distribution characteristics of the residual geoid. Finally, we conducted a detailed geophysical interpretation for the study area according to the geoid anomalies in combination with other geophysical datasets. Four conclusions can be outlined as follows: 1) it is impracticable that geoid anomalies are used in the interpretation of the shallow objects due to the influence of the terrain; 2) the anomalies of residual geoid can reflect the intensity of small-scale mantle convection in the asthenosphere; 3) the interlayer geoid anomalies can reflect the magmatic activities associated with the mantle convection and mantle plume in different scales; 4) the study of the geoid may provide an approach for the research of the subduction zone, mantle convection and mantle plume.

Development of Precise Geoid Model for the Establishment of Consistent Height System in Geoga Grand Bridge Construction Area

The national benchmarks on islands were mostly established by trigonometric leveling in Korea. This method results in inaccuracy, which is a serious problem in Geoga Grand Bridge construction work that tried to link the mainland and the islands. The Geoga Grand Bridge （Pusan-Geoje fixed link project） was selected as the study area, a huge construction work in Korea that will connect the mainland （Pnsan） and an island （Gecje island）. However, the orthometric heights issued at benchmarks （JINH and GOFJ） were not consistent, because they did not refer to the same zero point, which would make the linking of the sections problematic. This paper introduces the precise local geoidas a vertical datum for the construction area in order to establish a consistent height system. To determine the precise local geoid for the construction area, we firstly developed a precise gravimetric geoid for Korea and its adjoining seas as a whole. This gravimetric geoid was developed by use of all available gravity data, including surface and satellite data on land and on the ocean. The gravimetrie gecid was computed by spherical fast fourier transform with modified Stokes＇ kernels. The remove-restore technique was used to eliminate the terrain effects by use of the RTM reduction and to determine the residual geoid by combining the GGM02S/EGM96 geopotential model, free-air gravity anomalies and high-resolutinn DEM data. Finally, the gravimetric model was fitted to the geoid heights obtained from GPS and tide observations （Ncps/Tiae） by least square coUocatian, to provide the final GPS-consistent local precise geoid model. The post-fit error （std. dev. ） of the final geoid to the NetS/Tide derived from GPS and tide observations was ± 2.2 cm for the construction area. We solved the height inconsistency problem by calculating the orthometric height of the benchmarks and the cnntrol points using the final geoid model. Also, the highly accurate orthometric height was estimated through the GPS/leveling technique by applying the developed local precise geoid. Therefore, the precise local geoid is expected to improve the quality of the construction procedure of the Geoga Grand Bridge.

Using satellite altimetry leveling to assess the marine geoid

Based on the concept of Global Position System(GPS)/leveling,the satellite altimetry leveling(SAL) is first proposed to evaluate the marine geoid.SAL is derived by the difference among the mean sea surface(MSS),mean dynamic ocean topography(MDT),and leveling origin.In this study,(1) the original satellite altimetry data are processed to infer the vertical deflection and gravity anomaly,(2) the Chinese coastal marine geoids(CMG) are determined by using the differe nt methods(including Molodensky,least square collocation,Stokes formula,and two-dimensional fast Fourier transformation(FFT) with the vertical deflection and gravity anomaly data),(3) CMG are evaluated by using the results from above different methods,the Gravity field and steady-state Ocean Circulation Explorer(GOCE) gravity potential model(GGPM),and SAL.The results show that(1) CMG from the Molodensky method has the highest precision by using vertical de flection data,(2) the accuracy of CMG indicate good consistency between the SAL and GGPM,(3) SAL can be used as a new method for assessing marine geoid.

Kriging of Airborne Gravity Data in the Coastal Areas of the Gulf of Mexico

This paper deals with the application of kriging technique to find the continuous map of gravity on the geoid in the coastal areas and to evaluate its precision.

Determination of a Gravimetric Geoid Solution for Andalusia (South Spain)

The orthometric heights can be obtained without levelling by means of the ellipsoidal and geoidal heights. For engineering purposes, these orthometric heights must be determined with high accuracy. For this reason, the determination of a high-resolution geoid is necessary. In Andalusia (South Spain) a new geopotential model (EIGEN-GL04C) has been available since the publication of a more recent regional geoid. As a consequence, these new data bring about improvements that ought to be included in a new regional geoid of Andalusia. With this aim in mind, a new gravimetric geoid determination has been carried out, in which these new data have been included. Thus, a new geoid is provided as a data grid distributed for the South Spain area from 36 to 39 degrees of latitude and –7 to –1 degrees of longitude (extending to 3 × 6 degrees), in a 120 × 240 regular grid with a mesh size of 1.5’ × 1.5’ and 28800 points in the GRS80 reference system. This calculated geoid and previous geoids are compared to the geoid undulations obtained for 262 GPS/levelling points, distributed within the study area. The new geoid shows an improvement in accuracy and reliability, fitting the geoidal heights determined for these GPS-levelling points better than any previous geoid.

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.

基于准零刚度机构与间接力控制的恒拉力系统设计与分析

现有的悬吊式微低重力模拟恒拉力系统常采用力传感器数值作为反馈直接控制系统,但实际情况下力作为反馈信号常会产生突变,影响系统控制精度。为了改进刚性控制策略下系统稳定性差与大冲击条件下力误差大的状况,文中设计了包含准零刚度机构的恒拉力系统,通过控制准零刚度机构长度间接对恒拉力系统输出拉力进行控制。对准零刚度机构进行受力分析,明确影响准零刚度机构性能的关键指标和准零刚度机构的工作行程区间,建立恒拉力系统动力学模型,设计控制系统。为了验证系统控制精度与系统抗干扰性能,进行了动力学联合仿真对设计进行验证,仿真结果表明:该恒拉力系统拉力的控制误差可控制在2%以内,且具有较好的鲁棒性。

湖南省似大地水准面模型对比研究

正常高系统是以似大地水准面为基准的高程系统,也是中国目前采用的高程系统。随着GNSS定位技术的广泛应用,已能在10-7~10-9的精度量级上获得测量点的平面位置,但是却一直未能以相应的精度求解点的高程值。因此,通过建立高精度、高分辨率的区域似大地水准面模型提升高程测量的精度,成为重要的技术手段。该文通过对湖南省2007似大地水准面模型后期各似大地水准面模型的对比研究,找到模型的差异,并对差异较大的地区进行特征分析,查找形成差异的原因,可为全省二、三等水准网测量和大地水准面再精化工作提供参考。

EGM2008模型计算重力扰动位及相关量的方法研究

地球重力场模型EGM2008提供了计算全球高分辨率和高精度重力场相关参量的可能。本文采用球谐综合的方法,对重力扰动位、重力异常、大地水准面高等物理量的计算步骤和方法进行了研究和分析,并编制了相应的计算程序基于EGM2008无潮模型和零潮模型对以上参量进行了计算,同NGA发布的计算程序计算的结果进行了比对,验证了计算的方法正确性和可靠性。