Earth Gravity Model Research Articles

Resolution evaluation of the satellite altimetric gravity anomaly models with shipborne gravity data over the Cosmonaut Sea, East Antarctica (44–52° E)

AbstractSeveral satellite gravity anomaly models are freely available to calculate the free‐air gravity anomaly in areas where shipborne gravity measurements are scarce. Two models produced by the Technical University of Denmark (DTU17) and the Scripps Institution of Oceanography (SIOv32.1), respectively, were selected to compute the free‐air anomalies over the Cosmonaut Sea, East Antarctica. A statistical comparison analysis was performed to evaluate the resolution of satellite gravity anomaly models by comparing them with the shipborne surveying date. The radially averaged energy spectra of free‐air anomaly from different sources were calculated and compared over two selected regions to further evaluate the reliability of the data derived from satellite gravity anomaly models. The satellite gravity anomaly models have a better resolution in the ocean basin than in the area near the continental shelf. The comparison analysis revealed that the precision of both DTU17 and SIOv32.1 is close to the shipborne gravity data, but on average, SIOv32.1 is a little bit better than DTU17. The spectral analysis showed that the shipborne measurements may provide higher resolution than the satellite gravity anomaly model at wavelengths shorter than 20 km, and the free‐air data derived from SIOv32.1 have better resolution than the one from DTU17. These shipborne datasets will provide contributions for the updates of the Antarctic gravity anomaly and enable new high‐resolution combined Earth gravity models to be derived in Antarctica.

Development of Earth Gravity Models in A Sustainable Environment: An Overview of Nigeria’s Ecosystem

The evolution of Earth gravity models in Nigeria's ecological context is essential for advancing sustainable environmental stewardship. These models serve as crucial tools to understand the geological intricacies and environmental dynamics across Nigeria's diverse ecosystems. This article obtained data from previous existing data to emphasizes the significance of sustainable development, technological innovation, and the integration of sustainability principles into Earth gravity modeling efforts. The gravitational variations observed across Nigeria's ecosystems highlight the diverse geological features influencing gravitational anomalies. For instance, forests with dense vegetation exhibit gravitational variations ranging from -5.2 to -2.8 mGal, while coastal areas experiencing erosion and sea level rise show variations from -1.8 to 1.0 mGal. The article explores both advancements and challenges in developing Earth gravity models within Nigeria's unique environmental landscape, emphasizing the intersection of technology and sustainability. By leveraging advanced technologies and interdisciplinary methodologies, Earth gravity models contribute significantly to understanding the gravitational forces shaping the planet's surface and subsurface. Understanding the methodology behind Earth gravity models in a sustainable environment is crucial for effective environmental management and resource conservation, providing valuable tools for preserving Nigeria's diverse ecosystems for future generations. Through this integrated approach, Earth gravity models pave the way for enhanced environmental monitoring, land-use planning, and conservation strategies tailored to Nigeria's specific ecological challenges and opportunities.

MEASUREMENT AND ENHANCEMENT OF GRAVITY DATA FOR GEOPHYSICAL INVESTIGATIONS IN ABUJA, NIGERIA

The availability of gravity data is useful to individuals, governments and organizations that wish to carry out a geophysical investigation in Abuja. The data provides an accurate model for environmental monitoring and disaster studies. This research was aimed at measurement and prediction of gravity data in Abuja, Nigeria. The aim was achieved by observation of terrestrial gravity data at forty (40) gravity stations around the federal capital territory Abuja, prediction of the gravity data at other points and the evaluation of the predicted data. Gravity reduction was carried out on the measured data to account for drift correction, free air correction, bouguer correction latitude correction and terrain correction. The data was further enhanced by interpolation using the Kriging method. A total of 59 points were predicted from the 40 measured stations. The predicted gravity anomalies were validated by comparing with their corresponding gravity anomalies obtained from the Earth Gravity Model 2008 (EGM08) because of their well-established reliability. For the number of observations, n = 59, the RMSE and SE were computed as 4.797mGal (4.787x10-5 ms-2) and 4.880mGal (4.880 x10-5 ms-2) respectively. Also, the correlation value obtained was 0.991 which is significant at 0.01 level. This shows a strong relationship signifying a perfect possible agreement in the values obtained. It was therefore concluded that Kriging is a good interpolator that provides an estimate with high reliability and dependency. In this regard, considering the high cost of geophysical data collection, gravity prediction can make geophysical data collection more efficient and cost-effective.

ESTABLISHMENT OF ORTHOMETRIC HEIGHT CONTROLS IN THE EASTERN PART OF KOGI STATE USING GNSS AND EGM 2008

The aim of this study was to model the orthometric heights in parts of Kogi East, Kogi State using GNSS and EGM 2008 with the objectives of establishing the best geoid undulation for height determination. The Hardwares used for this study include; Hi target V.30 dual frequency GNSS receiver and its accessories, Data logger, Computer hardware and software and Computer – HP Laptop and internet facilities. Softwares used included; Arc GIS, Google map, microsoft word, Microsoft excel, Hi target Geomatic offices, CSRS – PPP website andGeoid Eval Calculator. GNSS observations were conducted on 6 station monument. The dual frequency v30 Hi target instrument was used in the static mode to make observations on all the established points at an epoch rate of 30 seconds; for a period of one hour to one hour thirty minutes (session) per station. The secondary data were the EGM 2008, obtained from Geoid eval platform in https://www.geographiclib.sourceforge.ion/cgi-bin/GeoidEval. Geoid Eval platform makes provision for the geographical coordinates to be inputed before the geoidal-ellipsoidal separation values can be provided. Geoid Eval computes the height of the geoid above the WGS 84 ellipsoid using interpolation in a grid of values for the earth gravity models. To obtain the orthometric height, the geoid value is subtracted from the ellipsoidal height obtained from the GNSS-PPP observation. The accuracy of the geoid value is 1mm and that of the GNSS-PPP was adjudged to be 3cm respectively. It was recommended that, more orthometric heights be distributed for monitoring of the earth’s dynamisms.

A Method for the Precise Coordinate Determination of an Inaccessible Location.

Surveyors are occasionally tasked to with determining the coordinates of inaccessible locations or points in civil engineering applications, ground control points for photogrammetry or LiDAR data acquisition, among others. The present work outlines and investigates a novel method for estimating the GNSS coordinates of an inaccessible location where a surveying instrument cannot be set up. The procedure is based on the well-known surveying intersection method and data extracted from an Earth Gravity Model (e.g., EGM 2008). The location's coordinates are obtained from the least-squares adjustment of the angles and distances measured from at least two sites to the unknown point using a total station, within the framework of the Gauss-Helmert method. Field tests confirmed that the accuracy of the determined coordinates of the inaccessible point is at the level of 1 cm. The proposed method bypasses standard coordinate transformation steps performed with the traditional approach, directly producing geocentric coordinates of the unknown points.

Real-Time Adjustment and Spatial Data Integration Algorithms Combining Total Station and GNSS Surveys with an Earth Gravity Model

During the dynamic development of modern technologies based on advanced algorithmic and instrumental solutions, it is essential to integrate geospatial data efficiently. Such an approach is applied in all geo-information services, especially mobile ones, and is helpful in, for example, precise navigation or effective risk management. One leading application is deformation monitoring (structural monitoring) and displacement control surveying. In addition, spatial data integration methods are used in modern accessibility analysis, Smart City ideas, tracing utility networks, and building information modelling (BIM). The last aforementioned technology plays a crucial role in architectural design and construction. In this context, it is crucial to develop efficient and accurate algorithms supporting data fusion, which do not strain the computing resources and operate efficiently online. This paper proposes an algorithm for real-time adjustment of integrated satellite GNSS (global navigation satellite system), total station, and Earth Gravitational Model (EGM) vertical direction data in a geocentric coordinate system based on a statistical general linear mixed model. A numerical example shows that the proposed algorithm of the online adjustment works correctly. The results of the online adjustment are the same as those of the offline adjustment. It is also shown that the GNSS measurements are necessary only at the total station points in the spatial total station traverse. There is no need to add additional merging points of the total station positions because the differences between the results of the online adjustment, including and excluding the merging points, are very small (around 1–2 mm in standard deviation).

Measuring the gravity potential between two remote sites with CVSTT technique using two hydrogen clocks

ABSTRACT According to General Relativity Theory (GRT), by comparing the frequencies between two precise clocks at two different stations, the gravity potential (geopotential) difference between the two stations can be determined due to the gravity frequency shift effect. Here, we conduct a clock-transportation experiment for measuring geopotential differences based on frequency comparisons via satellite links between two remote hydrogen atomic clocks. Based on the net frequency shift between the two clocks in two different periods, the geopotential difference between stations of the Beijing 203 Institute Laboratory (BIL) and Luojiashan Time-frequency Station (LTS) is determined. Comparisons show that the experimental result deviated from the reference of Earth gravity model EGM2008 result by (38.545.9) m in Orthometric Height (OH). The results are consistent with the frequency stabilities of the hydrogen clocks (at the level of ) used in the experiment. With the rapid development of time and frequency science and technology, the approach discussed in this study for measuring the geopotential is prospective and thus, could have broad applications.

A new method for accurate alignment and calibration of strapdown INS

A new method is proposed for the coarse and fine alignments of the strapdown inertial navigation system (INS) along with the estimation of the INS systematic errors. This is achieved by utilizing an accurate external positioning system such as the global positioning system (GPS) and external gravity disturbances obtained from the Earth gravity models (EGMs) during the INS initialization time. First, a new method for the transformation of the INS acceleration from the sensor frame to the inertial frame using gyro output data is disclosed. Then, using the new method of the transformation, new techniques are developed for the alignment and calibration of the INS using minimizing the variations of the residuals of the gravity disturbances during the back-and-forth rotational motions. The common and conventional initializations cannot be started from any initial orientation, and cannot yield the accurate and actual INS errors. In contrast, under the alignment condition, the accurate and actual estimation of all the INS systematic errors is possible using the developed fine alignment and calibration which can guarantee the accurate autonomous strapdown INS positioning for a long period of time even during high dynamic motions. This is while the estimated error values of the INS by the conventional Kalman filter is unrealistic. In the field of autonomous positioning, a horizontal position with an error less than 200 m and 500 m was achieved during low and high dynamic motions, respectively, after the fine alignment and calibration, for the two hours of the INS positioning for a flight distance about 880 km. The employed INS was a high-performance strapdown INS, the Honeywell LASEREF III.

Effect of the low-order coefficients of the Earth gravity model in calculating the satellite orbit

The Earth's gravity model is a crucial factor in determining satellite orbits. Scientific organizations such as GFZ Potsdam in Germany, GRGS Toulouse in France, and AIUB in Switzerland have established Earth gravity models with increasing precision of spherical harmonic coefficients. Low-order coefficients, including C ̅_21,( S) ̅_21, C ̅_10,C ̅_11,( S) ̅_11and C ̅_20, play a vital role in describing changes in the Earth's poles, geometric center, and flattening. To evaluate the impact of these coefficients and understand altimeter satellite orbital error, the Propagerror program was developed. This program calculates satellite orbital error from the differential components of Earth gravity model spherical harmonic coefficients (dC/Slm), which can be obtained from the difference between two gravity models or from seasonal and annual components of spherical harmonics. By separating appropriate low-order components in the Earth gravity models, the Propagerror program enables the estimation of satellite orbital error. In this study, we isolate C ̅_10,C ̅_11,( S) ̅_11, and C ̅_21,( S) ̅_21 coefficients in the EIGEN-GRGS.RL02bis.MF and EIGEN-6S gravity models to assess the geophysical impact on satellite orbits. The influence of the geometry center elements results in a 2 cm error in the Jason-2 satellite, while the rotational axis elements have no effect. The C ̅_31,( S) ̅_31 coefficient has a 6-7 mm impact on the accuracy of the Jason-2 satellite, as demonstrated by the satellite error map in two situations with and without the C ̅_31,( S) ̅_31 harmonic coefficient. This study highlights the significance of regulating function coefficients in satellite orbit determination, particularly the low-level harmonic parameters. The Propagerror program provides insights into the impact of each spherical harmonic parameter on satellite orbits, contributing to the improvement of orbit accuracy and the understanding of the Earth's gravity model.

Height connection across sea by using satellite altimetry data sets, ellipsoidal heights, astrogeodetic deflections of the vertical, and an Earth Gravity Model

Islands and the mainland are separated by seas, and the distances between them might be so long that the height on the mainland cannot be exactly translated to the islands, resulting in different height systems on the mainland and the islands. In this study, we used astrogeodetic deflections of the vertical and ellipsoidal heights of points on the mainland and island near their coastlines to implement height connection across sea areas. First, the modeled gravity and modeled astrogeodetic vertical deflections of segmentation points along connecting routes over the sea between the mainland and the island were determined by Earth Gravity Model (EGM), and the ellipsoidal heights of segmentation points were determined by the satellite altimetry data sets. Second, we used a linear interpolation model to increase the precision of the vertical deflections of segmentation points. Third, we computed the geopotential difference of points between the mainland and the island using a method derived from geopotential theory and the astronomical leveling principle. Finally, we estimated the normal height of the point on the island using the geopotential-difference iterative computation approach. Using observed data of normal heights, ellipsoidal heights, and astrogeodetic vertical deflections referring to height sites in Qingdao, Shandong Province, we conducted a numerical experiment involving the normal height connection across sea regions. We determined the data of the ellipsoidal heights and gravity of segmentation points along the connecting route across the water in the numerical experiment using DTU10. The distance of the height connection across the sea was approximately 10.5 km. According to China's official leveling specifications, the experimental results met the criterion of third-class leveling precision.

Lithospheric Stress Due to Mantle Convection and Mantle Plume over East Africa from GOCE and Seismic Data

The Afar and Ethiopian plateaus are in a dynamic uplift due to the mantle plume, therefore, considering the plume effect is necessary for any geophysical investigation including the estimation of lithospheric stress in this area. The Earth gravity models of the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) and lithospheric structure models can be applied to estimate the stress tensor inside the Ethiopian lithosphere. To do so, the boundary-value problem of elasticity is solved to derive a general solution for the displacement field in a thin elastic spherical shell representing the lithosphere. After that, general solutions for the elements of the strain tensor are derived from the displacement field, and finally the stress tensor from the strain tensor. The horizontal shear stresses due to mantle convection and the vertical stress due to the mantle plume are taken as the lower boundary value at the base of the lithosphere, and no stress at the upper boundary value of the lithospheric shell. The stress tensor and maximum stress directions are computed at the Moho boundary in three scenarios: considering horizontal shear stresses due to mantle convection, vertical stresses due to mantle plume, and their combination. The estimated maximum horizontal shear stresses’ locations are consistent with tectonics and seismic activities in the study area. In addition, the maximum shear stress directions are highly correlated with the World Stress Map 2016, especially when the effect of the mantle plume is solely considered, indicating the stress in the study area mainly comes from the plume.

Calculation method for deflection of the vertical based on path gravity anomaly compensation

To solverole inefficiency and complete autonomy issues for deflection of the vertical (DOV) determination in geomatics, navigation, and military weapon launching fields, a calculation method based on path compensation has been proposed. After conducting the discretization of the Vening-Meinesz formula in the spherical surface, a novel path gravity anomaly compensation based on the ‘remove–restore’ algorithm was formulated to satisfy the requirement of regional high-precision gravity anomaly data. Meanwhile, utilizing the European Improved Gravity model of Earth by New techniques (EIGEN-6c4), the DOV was calculated using the Vening-Meinesz formula based on the ‘remove–restore’ method, unlike the previous regional direct integral calculations. Finally, to verify the reliability and feasibility of the algorithm, the gravity measurement system, consisting of the high-precision gravimeter and strapdown inertial navigation system, was constructed to conduct the simulation and shipborne experiments. The simulation and experiment results of the proposed method show that the root mean squares, relative to the real values, of DOV calculation components, are 0.89″ and 1.67″, while standard deviation values of the DOV components are the same within 2″ in experiments, which satisfies the precision requirement of the DOV.

A study of the EGM2008 model of Earth's gravitational field

AbstractThe Earth Gravity Model 2008 (EGM2008) is now some years old, and yet information on how to use it to calculate Earth's gravity remains obscure outside the field of geodesy. We describe the mathematics necessary to implement EGM2008, and use this to discuss several points of the model: its sensitivity to the number of spherical harmonics being summed, nuances and a trap for physicists and mathematicians in the normalisation it uses, and a comparison with other work. We conclude that one must not overestimate the precision shown by a global-fit model such as EGM2008.

Investigation of lineaments in the mid-Black arc region using Bouguer gravity data

The gravity data used in this study were taken from the Earth Gravity Model (EGM08) to investigate the crustal structure in the mid-Black arc region. In this study, geological structure boundaries that offer differences in density were tried to determine in the mid-Black arc region. For this purpose, the possible geological structure limits at the basement levels were especially focused on. For this reason, horizontal gradient and tilt angle techniques were practiced to find possible geological structure limits using first vertical derivative data of the regional gravity data of the region. The soft-hard sediment, basement, Conrad and Moho interfaces have been determined using the radial mean amplitude spectrum of Bouguer data of study region. The topographies of these interfaces were also presented utilizing the Parker-Oldenburg algorithm. Depth values found by inversion calculations for soft-hard sediment, basement, Conrad and Moho interface topographies are changed as 0.7-3.5, 2.1-7.4, 9.1-14.2, and 35.1- 42.5 km, respectively. The linearities determined in the study were matched against to substantial faults of region. It has been observed that there is a qualitative relationship between the faults, ore deposit and earthquake epicenters in the region. The results of this practice were based on studies such as exploring the ore deposits and investigating the risks of earthquakes in the future.

Data processing of shipborne absolute gravity measurement based on extended Kalman filter algorithm

The precision dynamic measurement of absolute gravity based on the cold atom interferometer can provide a new method for marine gravimetry, so that it has attracted more attention. Based on the homemade shipborne cold atom interferometric absolute gravity measurement system, we carry out a series of measurement experiments in a certain area of the South China Sea. Under dynamic conditions, the suppression of measurement noise is essential for the improvement of the measurement performance. According to the physical model of the measurement system, in this paper a data processing method is proposed based on the extended Kalman filter algorithm for the absolute gravity dynamic measurement. The observed atomic interference fringe data are filtered in the time domain to estimate the absolute gravity value. Based on this processing method, the sensitivity of absolute gravity measurement under the condition of ship speed less than 2.1 km/h is improved from 300.2 mGal/Hz<sup>1/2</sup> to 136.8 mGal/Hz<sup>1/2</sup> (<i>T</i> = 4 ms). Comparing the processed data with the data calculated from the earth gravity model (XGM2019), it is found that both of the data are in good agreement. These results confirm the effectiveness of the data processing method proposed in this paper, and provide a new processing method of suppressing the measurement noise of shipborne cold atom interferometric absolute gravity measurement system.

New insights into the structural and tectonic settings of the Bay of Bengal using high-resolution earth gravity model data

New insights into the structural and tectonic settings of the Bay of Bengal using high-resolution earth gravity model data

Scientific Comment on Klokočník et al. “Support for two subglacial impact craters in northwest Greenland from Earth gravity model EIGEN 6C4 and other data”, Tectonophysics 780 (2020), 228396

• Hiawatha and Paterson structure in Greenland do not represent confirmed impact structures. • The geophysical findings by Klokočník et al. do not represent supporting evidence for an impact origin of these structures. • Definitive shock metamorphic and/or geochemical evidence is still required for both these structures.

Interpolation and Statistical Analysis for Evaluation of Global Earth Gravity Models Based on GPS and Orthometric Heights in the Middle of Iraq

The regions around the world need to perform their results based on the local geoid. However, each region has different ground topography based on the amount of gravity in this region. Nowadays, the recent global Earth's gravity model of 2008 is successfully used for different purposes in geosciences research. This research presents an overview of the preliminary evaluation results of the new Earth Gravitation Model (EGM08) in the middle of Iraq. For completeness, the evaluation tests were also performed for EGM96 by examining 31 stations distributed over four Iraqi provinces. The national orthometric heights were compared with the GPS /leveling data obtained from these stations. This study illustrated that the GPS /leveling based on EGM08 data was better than that based on EGM96 data in terms of reducing the root mean square error (RMSE) of the differences between the orthometric heights and GPS/leveling data. The standard deviation (SD) values for the national orthometric heights and GPS heights were about 4 and 26cm, respectively. The results also show that there is a small difference in hight ranged (0.0013 - 0.1333 m) in Karbala, (0.0023 – 0.0062 m), in Najaf and (0.0173 – 0.0703 m), in Babylon. Due to the flat area, better results were obtained in Karbala and Najaf than Babylon. The EGM08 geoid method has shown to yield very close results to reality for various projects, thus its accuracy is acceptable.

Gravity aspects from recent Earth gravity model EIGEN 6C4 for geoscience and archaeology in Sahara, Egypt

A new method to detect paleolakes via their gravity signal is presented (here with implications for geoscience and archaeology). The gravity aspects or descriptors (gravity anomalies/disturbances, second radial derivatives, strike angles and virtual deformations) were applied. They were computed from the gravity field model EIGEN 6C4 (European Improved Gravity model of the Earth by New techniques). The model consists of the best now available satellite and terrestrial data, including gradiometry from the GOCE (Gravity field and steady-state Ocean Circulation Explorer) satellite mission. EIGEN 6C4 has the ground resolution ~10 km. From archaeological sources, the positions of archaeological sites of the Holocene occupations between 8500 and 5300 BCE (8.5–5.3 ky BC) in the Eastern Sahara, Western Desert, Egypt were taken. They were correlated with the features found from the gravity data; the correlation is good, assuming that the sites were mostly at paleolake borders or at rivers. Based on this finding, we suggest position, extent and shape of paleolake(s). We also reconsider the origin of Libyan Desert glass in the Great Sand Sea and support hypothesis about an older impact structure created there, repeatedly filled by water, which might be a part of some of the possible paleolake(s).

Support for two subglacial impact craters in northwest Greenland from Earth gravity model EIGEN 6C4 and other data

We support the very recent discovery of two impact craters under the ice of northwest Greenland (Hiawatha Glacier and Paterson). These discoveries are based mainly on geology and bedrock topography. We added an analysis of gravity field aspects (descriptors) in addition to the traditional gravity and magnetic anomalies. The gravity aspects (the Marussi tensor of the second derivatives, the gravity invariants and their special ratio, strike angles and virtual deformations) provide more complex and comprehensive information about the underground density variations due to a causative body than ordinary gravity anomalies. They show signals typical for the individual geological features like a mountain/volcano, fault, (river)valley, (paleo)lake, (ground)water, hydrocarbon/mineral deposits, etc., as well as for the targets known as impact craters. Our method has been tested on various geological features on the Earth and the Moon. The gravity aspects are, in our case, derived from the recent global static combined Earth gravity field model EIGEN 6C4 with a ground resolution ~9 km and a precision ~10 mGal. A further data come from the digital magnetic field database EMAG 2 with resolution ~5 km. Our method is novel and independent of anything which led to discoveries of these craters in Greenland.