Development of a Gravimetric Geoid Model and a Comparative Study

International Journal of Advances in Scientific Research and Engineering (ijasre), August 30, 2018

As the surface adopted for geodetic computation is a adopted as a reference for the vertical coordinate system, the ellipsoidal heights obtained from GPS observation are transfor to practical heights known as orthometric heights the knowledge of the geoid-ellipsoid separation at the point of observation. Since the geometric method requires the computation of geoid heights of points from GPS observation and prone to human errors, the accurate geoid heights of the points should be obtained from gravity measurement and a geometric geoid surface fitted to the gravimetric geoid h gravimetric-geometric geoid model of an area or a region. The detailed procedures which consist of selection of suitable/evenly distributed points, DGPS and gravity observations of selec of gravimetric geoid heights of the points, fitting of geometric geoid surface to the computed gravimetric geoid heights and computation of accuracy of the geoid model are presented in se

International Journal of Advanced Engineering Research and Science (IJAERS), 2019

The conversion of geometric as well as ellipsoidal heights from GNSS observations to practical heights for engineering constructions has necessitated the determination of the local geoid model of areas. Benin City is a developing area which requires a local geoid model for conversion of geometric heights to orthometric heights for physical developments in the area. This paper is on the best local geoid model of Benin City, Nigeria by comparing three gravimetric-geometric geoid models of the study area. GNSS and gravimetric observations were carried out on 49 points to respectively obtain their coordinates and absolute gravity values. The theoretical gravity values of the points were computed on the Clarke 1880 ellipsoid, subtracted from the absolute gravity values and corrected for the air (free air) to obtain the free air gravity anomalies of the points. The computed free air gravity anomalies were applied to compute the geoid heights of the points using the integration of the modified Stokes integral. Three geometric geoid surfaces (plane, second degree and third degree surfaces) were fitted to the computed gravimetric geoid heights using the least squares technique to obtain the gravimetric-geometric geoid models of the study area. The RMSE of the three gravimetric-geometric geoid models were computed to determine their (the models) accuracy. The three gravimetric-geometric geoid models were compared using their accuracy to obtain the most suitable geoid model of the study area. The results of the comparison showed that the third degree gravimetric-geometric geoid model is most suitable for application in the study area. It is recommended that ellipsoidal heights obtained from GNSS observation within Benin City, Nigeria should be converted to orthometric heights using the third degree geoid model.

Geo-spatial Information Science, 2002

2009

The main objective of this study is to compute a new gravimetric geoid model of Sudan using the KTH method based on modification of Stokes' formula for geoid determination.

Computers & Geosciences, 2006

Local gravimetric geoid models from a combination of a global geopotential model and local gravity data generally contain errors of dm-level on the long wavelengths and sometimes they may be significantly higher in areas lacking accurate gravity information like Algeria where only few gravity data from Bureau Gravime´trique International (BGI) have been included in the development of the recent geopotential models. Consequently, these models do not have the required accuracy to transform the GPS ellipsoidal heights to orthometric heights. One of the main causes for this is the limited precision of the global and detailed DTM models. On the other hand, we can now measure by means of the space techniques, on land through a combination of GPS positioning and precise levelling and at sea through satellite altimetry, the geoid on some points on the earth's surface with very high absolute accuracy. These points can be used to correct the systematic effects, the medium and longer wavelength errors in the gravimetric geoid. The main goal of this study is to propose a procedure, for combination of available gravimetric geoid and external data from GPS and levelling in an optimal way and for estimating the gravimetric geoid accuracy using the collocation approach. So, the question is to find what is the adequate functional representation of the correction that should be applied to the gravimetric geoid? Several functions have been tested and the most suitable will be selected in test area from a statistical testing procedure. For this purpose, the improved Algerian gravimetric geoid computed by the Geodetic Laboratory of the National Center of Space Techniques from the gravity data supplied by the Geophysical Exploration Technology Ltd. (GETECH), and the precise GPS data collected from the international TYRhenian GEOdynamical NETwork (TYRGEONET), ALGerian GEOdynamical NETwork (ALGEONET) projects with baseline length ranging from about 1 to 1000 km have been used. The comparisons based on different GPS campaigns provide after fitting a RMS of the differences 71.9 cm and prove that a good fit in experimental area between the gravimetric geoid and GPS/levelling data using the seven-parameter model transformation has been reached. Moreover, the analysis of statistics shows that the residuals in benchmarks are due principally to gravimetric geoid errors. The main outlines of the Algerian geoid computation, the available GPS/levelling data, the developed procedure and the obtained results will be presented.

International Association of Geodesy Symposia

The development of a high-resolution and high accuracy geoid model is becoming nowadays a fundamental component of any modern geodetic infrastructure. The Kingdom of Saudi Arabia (KSA) has devoted the last decade a significant number of resources and manpower to collect high-quality land and airborne gravity data as well as GNSS/Levelling observations to create a state-of-the-art geoid model as a fundamental part of the Saudi Arabia National Spatial Reference System (SANSRS). In that frame, this work focuses on the collected gravity, terrain, and GNSS/Levelling data for the area under study, and their pre-processing in terms of horizontal, vertical and gravity reference system homogenization, blunder detection and removal. Given the availability of these data the latest gravimetric geoid model for the KSA is developed.The gravity data pre-processing relied on the available metadata to collect information about the horizontal, vertical and gravity reference system. Hence, all this in...

Journal of Geophysical Research, 1992

Orthometric height differences obtained from a combination of global positioning system (GPS) ellipsoidal height differences and gravimetric geoid predictions have the potential of replacing costly and time-consuming spirit leveling, especially in rcrnotc unsurveyed areas like the Canadian north. In this paper 88 GPS stations along a 900-kin-long first-order leveling linc around the Great Slave Lake area, Northwest Territories, Canada, are used as control for intercomparison of geoid predictions which used various geopotential models and gravimetric techniques. The global spherical harmonic models tested include satellite-only solutions, such as GEM-9, GEM-L2, GEM-T1 and GEM-T2, as well as combination solutions, such as GEMlOB, RAPP78, RAPP81, GPM2, OSU86F, OSU89A, OSU89B and OSU91A. These models fit the geoid with standard errors of 30 to 50 cm. Local gravimetric geoid predictions based on available gravity data were carried out using various forms of Stokes integration, fast Fourier transform methods and least squares collocation. For the first two methods, gravity data were gridded on a 5 km by 5 km Cartesian grid and on a 5' by 10' geographical grid. No terrain reductions were applied due to the flatness of the topography. Results show that the differences between control and predicted geoid heights have standard deviations at the 20-to 25-cm level, with differences between methods at 2 to 8 cm (lo). By fitting a four-parameter model to the geoid prexlictions (corresponding to a GPS, leveling or geoid datum shift and scale change), long-wavelength errors were significantly reduced, with all methods yielding geoid fits of about 7 cm (1o). The relative accuracies achieved were of the order of 2 ppm for baselines shorter than 200 km, and of the order of I ppm for baselines with lengths between 200 km and 700 km. A discussion of possible error sources concludes the paper. Some errors in the original GPS data were detected in the initial phase of the project, and a GPS resurvey verifyed these errors.

Studia Geophysica et Geodaetica, 2011

Turkish regional geoid models have been developed by employing a reference earth gravitational model, surface gravity observations and digital terrain models. The gravimetric geoid models provide a ready transformation from ellipsoidal heights to the orthometric heights through the use of GPS/leveling geoid heights determined through the national geodetic networks. The recent gravimetric models for Turkish territory were computed depending on OSU91 (TG-91 ) and EGM96 (TG-03 ) earth gravitational models. The release of the Earth Gravitational Model 2008 (EGM08 ), the collection of new surface gravity observations, the advanced satellite altimetry-derived gravity over the sea, and the availability of the high resolution digital terrain model have encouraged us to compute a new geoid model for Turkey. We used the Remove-Restore procedure based on EGM08 and applied Residual Terrain Model (RTM ) reduction of the surface gravity data. Fast Fourier Transformation (FFT ) was then used to obtain the residual quasigeoid from the reduced gravity. We restored the individual contributions of EGM08 and RTM to the whole quasi-geoid height (TQG-09 ). Since the Helmert orthometric height system is adopted in Turkey, the quasi-geoid model was then converted to the geoid model (TG-09 ) by making use of Bouguer gravity anomalies and digital terrain model. After all we combined a gravimetric geoid model with GPS/leveling geoid heights in order to obtain a hybrid geoid model (THG-09 ) (or a transformation surface) to be used in GPS applications. The RMS of the post-fit residuals after the combination was found to be  0.95 cm, which represents the internal precision of the final combination.

Journal of Geodesy, 2006

A Synthetic [simulated] Earth Gravity Model (SEGM) of the geoid, gravity and topography has been constructed over Australia specifically for validating regional gravimetric geoid determination theories, techniques and computer software. This regional high-resolution (1-arc-min by 1-arc-min) Australian SEGM (AusSEGM) is a combined source and effect model. The long-wavelength effect part (up to and including spherical harmonic degree and order 360) is taken from an assumed errorless EGM96 global geopotential model. Using forward modelling via numerical Newtonian integration, the short-wavelength source part is computed from a high-resolution (3-arc-sec by 3-arc-sec) synthetic digital elevation model (SDEM), which is a fractal surface based on the GLOBE v1 DEM. All topographic masses are modelled with a constant mass-density of 2670 kg/m 3. Based on these input data, gravity values on the synthetic topography (on a grid and at arbitrarily distributed discrete points) and consistent geoidal heights at regular 1-arcmin geographical grid nodes have been computed. The precision of the synthetic gravity and geoid data (after a first iteration) is estimated to be better than 30 µGal and 3 mm, respectively, which reduces to 1 µGal and 1 mm after a second iteration. The second iteration accounts for the changes in the geoid due to the superposed synthetic topographic mass distribution. The first iteration of AusSEGM is compared with Australian gravity and GPS-levelling data to verify that it gives a realistic representation of the Earth's gravity field. As a by-product of this comparison, AusSEGM gives further evidence of the north-south-trending error in the Australian Height Datum. The freely available AusSEGM-derived gravity and SDEM data, included as Electronic Supplementary Material (ESM) with this paper, can be used to compute a geoid model that, if correct, will agree exactly with the AusSEGM geoidal heights, thus offering independent verification of theories and numerical techniques used for regional geoid modelling.

Abstract. A new airborne gravity survey was conducted over Taiwan in 2004-2005. The survey results in conjunction with existing terrestrial, marine and satellite altimetry data are used for creating a consistent 2 x2 grid of gravity anomalies referred to the Earth's surface. For this, the gravity anomalies observed at the flight level are downward continued to the topographic surface. After the gridding, to solve the boundary value problem (BVP) by Stokes's formula, the surface gravity anomalies are continued further to the sea level.

FUDMA Journal of Sciences (FJS), 2021

The application of the transformation geoid model in Benin City has necessitated its fitting to the existing gravimetric-geometric geoid model of the study area. The transformation geoid model was determined using the Kotsakis (2008) model for the transformation of global geoid heights to local geoidal undulations. To obtain its accuracy, the root mean square error (RMSE) index was applied. The computed accuracy is 2.0172 m. To apply the determined geoid model in the study area, as well as improving on the computed accuracy, the model was fitted to the gravimetric-geometric geoid model of the study area. The fitting result shows that geoid heights can be computed using the determined geoid model with an accuracy of 1.1041 m in the study area.

Journal of Geodynamics, 2005

The transformation from the gravimetric to the GPS/levelling-derived geoid using additional gravity information for the covariance function of geoid height differences has been investigated in a test area in south-western Canada. A "corrector surface" model, which accounts for datum inconsistencies, long-wavelength geoid errors, vertical network distortions and GPS errors, has been constructed using least-squares collocation. The local covariance function of geoid height differences is usually obtained from residual values between the GPS/levelling and gravimetric geoid heights after the elimination of all known systematic distortions. If additional gravity data (in the form of gravity anomalies) are available, the covariance function of geoid height differences can be determined by the following steps: (1) transforming the GPS/levelling-derived geoid heights into gravity anomalies; (2) forming differences between the computed in step 1 and given gravity anomalies; (3) determining the parameters of the local covariance function of the gravity anomaly differences; (4) constructing an analytical covariance model for the geoid height differences from the covariance function of the gravity anomaly differences using the parameters derived in step 3. The advantage of the proposed method stems from the great number of gravity data used to derive the empirical covariance function. A comparison with the least-squares adjustment shows that the standard deviation of the residuals of the predicted geoid height differences with respect to the control point values decreases by 2.4 cm.

2008

A high-resolution and high-precision detailed gravimetric geoid has been computed for San Juan province in Argentina, ranging from 27o S to 34o S in latitude and 72o'W to 65o W in longitude. The gravimetric geoid was calculated using the RTM method, a multiband spherical Stokes Fast Fourier Transformation, and the remove-restore technique for the spherical harmonic reference field and the terrain. As an external evaluation, the gravimetric quasigeoid/geoid was compared to the geoid heights obtained from 90 GPS/levelling points available for the province. Finally, a GPS-tailored local geoid, which fits the GPS observations, was computed. Keywords: Gravimetric Geoid; RTM Method; High Precision Geoid.

Journal of African Earth Sciences, 2011

Sudan is characterized by vast area with flat terrains in most of the country’s regions and therefore the existence of a high-resolution geoid model is considered very important especially with the widespread of the GPS technology in the country. A few studies were previously conducted to compute a geoid model for Sudan, the current study is the second of its kind to compute the Sudanese geoid model by means of gravimetric method. In this study, a new gravimetric geoid model (KTH-SDG08) is computed for Sudan, we apply the method developed at the Royal Institute of Technology (KTH) Stockholm-Sweden. The method utilizes the least-squares modification (LSM) of Stokes formula providing three stochastic solutions (biased, unbiased and optimum). The three solutions are quite similar however in this study we select the optimum solution which provides the best agreement with GPS-levelling data. The modified Stokes formula combines the regional terrestrial gravity data together with the long-wavelength gravity information from a global gravitational model (GGM). We use two sets of regional gravity data: the first set is provided by the GETECH, the points of this set cover discretely some parts of Sudan while the rest of the country’s area are still not covered, the second set was provided by BGI contains a few points scattered over the neighbouring countries. Both datasets (GETECH and BGI) are unified together into one dataset and evaluated by Cross validation technique. Due to the lack of gravity observations we construct our final grid for geoid computation with spatial resolution of 5 × 5 arc-min. The long-wavelength contribution is donated by two geopotential models, EIGEN-GRACE02S satellite-only model is employed in the modified Stokes formula whereas the EIGEN-GL04C combined model is used to enrich the local gravity coverage over the areas with missing data. The Digital Elevation Model (DEM), SRTM generated by NASA and the National Imagery and Mapping Agency (NIMA) is used to compute topography effects on the geoid. Four additive corrections are computed over the entire target area and applied to the approximate geoid heights obtaining the final geoid solution. The new Sudanese gravimetric geoid model KTH-SDG08 is computed on a 5 × 5 arc-min geographical grid over the computation area bounded by the parallels of 4 and 23 arc-deg northern latitude, and the meridians of 22 and 38 arc-deg of eastern longitude. The gravimetric geoid is validated using GPS-levelling information at 19 points distributed over the whole country. The results show that the standard deviation (STD) of differences between the gravimetric and geometric geoid heights at 19 GPS-levelling points is about 0.3 m.

2006

The present paper examines the accuracy of a local model of quasigeoid QBG01 for Bulgaria, as well as of EGG97 and EGM96 models for the territory of Bulgaria. The models have been compared by means of points in which highly precise GPS and levelling measurements have been performed, their number being totally 165. The working domain is restricted within the boundaries of 41° to 44.5° northern latitude and 22° to 28.5° eastern longitude. Differences between the models and the heights of the quasigeoid from GPS/levelling are within the range from ±1.228 m to ± 0.413 m. Four-parametric transformation was applied for their minimization and the accuracy of the models was respectively increased within the boundaries from ±0.243 m to ± 0.416 m. A restricted region in South-western Bulgaria (latitude of 42.05°–42.55° and longitude of 22.87°-23.7°) was investigated, for which higher data density was available. The mean square error of the deviations between GPS/levelling and QBG01 prior to t...