Current estimates of mean Earth ellipsoid parameters

Caliphate Journal of Science & Technology (CaJoST), 2025

The determination of gravimetric geoid models using gravity anomalies requires the computation of normal gravity on specific ellipsoids. For global models, the International Gravity Formula is applied to the WGS 84 ellipsoid, while local models use the ellipsoid adopted for geodetic computation in the region of study. In countries that use the Clarke 1880 ellipsoid, a theoretical gravity model is computed on this surface to establish a precise local geoid model. This paper formulates a local theoretical gravity model for calculation of theoretical gravity values on the Clarke 1880 spheroid using the Somiglinana's closed formula for normal gravity, angular velocity, gravitational constant, and the Clarke 1880 spheroid parameters. The model is presented in two forms (A and B) and compared to ensure accuracy. Both forms of the model are suitable for accurate normal gravity computation on the Clarke 1880 ellipsoid.

Studia Geophysica et Geodaetica, 2011

The estimation of the Earth's gravitational potential energy E was obtained for different density distributions and rests on the expression E =  (W min + W) derived from the conventional relationship for E. The first component W min expresses minimum amount of the work W and the second component W represents a deviation from W min interpreted in terms of Dirichlet's integral applied on the internal potential. Relationships between the internal potential and E were developed for continuous and piecewise continuous density distributions. The global 3D density model inside an ellipsoid of revolution was chosen as a combined solution of the 3D continuous distribution and the reference PREM radial piecewise continuous profile. All the estimates of E were obtained for the spherical Earth since the estimated (from error propagation rule) accuracy  E of the energy E is at least two orders greater than the ellipsoidal reduction and the contribution of lateral density inhomogeneities of the 3D global density model. The energy E contained in the 2nd degree Stokes coefficients was determined. A good agreement between E = E Gauss derived from Gaussian distribution and other E, in particular for E = E PREM based on the PREM piecewise continuous density model and E-estimates derived from simplest Legendre-Laplace, Roche, Bullard and Gauss models separated into core and mantle only, suggests the Gaussian distribution as a basic radial model when information about density jumps is absent or incomplete.

Surveys in Geophysics, 2009

During the General Assembly of the European Geosciences Union in April 2008, the new Earth Gravitational Model 2008 (EGM08) was released with fully-normalized coefficients in the spherical harmonic expansion of the Earth's gravitational potential complete to degree and order 2159 (for selected degrees up to 2190). EGM08 was derived through combination of a satellite-based geopotential model and 5 arcmin mean ground gravity data. Spherical harmonic coefficients of the global height function, that describes the surface of the solid Earth with the same angular resolution as EGM08, became available at the same time. This global topographical model can be used for estimation of selected constituents of EGM08. Namely gravitational potentials of the Earth's atmosphere, ocean water (fluid masses below the geoid) and topographical masses (solid masses above the geoid) can be evaluated numerically through spherical harmonic expansions. Spectral properties of respective potential coefficients are studied in terms of power spectra and their relation to the EGM08 potential coefficients is analyzed by using correlation coefficients. The power spectra of the topographical and sea water potentials exceed the power of the EGM08 potential over substantial parts of the considered spectrum indicating large effects of global isostasy. The correlation analysis reveals significant correlations of all three potentials with the EGM08 potential. The potential constituents (namely their functionals such as directional derivatives) can be used for a step known in geodesy and geophysics as the gravity field reduction or stripping. Removing from EGM08 known constituents will help to analyze the internal structure of the Earth (geophysics) as well as to derive the Earth's gravitational field harmonic outside the geoid (geodesy).

Scientific Research Journal (SCIRJ), 2019

The application of gravity anomalies for gravimetric geoid model determination has necessitated the computation of normal gravity on the WGS 84 ellipsoid using the International Gravity Formula. For local gravimetric geoid model determination, the gravity anomalies are computed on the local ellipsoid adopted for geodetic computation in the area/region of study. To determine precise local gravimetric geoid model in countries where Clarke 1880 ellipsoid is adopted for geodetic computation, the theoretical gravity must be computed on the adopted geodetic computation surface. As a result, this paper derives a local theoretical gravity model on the Clarke 1880 ellipsoid for practical local geoid model determination. The model was derived using the Clarke 1880 ellipsoid parameters, angular velocity, gravitational constant and the Somiglinana's closed formula for normal gravity. The derived model was presented in two forms, model A and model B. The two forms of the derived model were compared to determine their suitability as well as agreement. The comparison results show that the two forms of the model agree. Thus, any of the model forms can be applied for accurate normal gravity computation where Clarke 1880 ellipsoid is adopted as a computation surface.

1998

The Earth is a dynamic system-it has a fluid, mobile atmosphere and oceans, a continually changing distribution of ice, snow, and groundwater, a fluid core undergoing hydromagnetic motion, a mantle under~oing both thermal convection and rebound from glacial loading of the last ice age, and mobile tectonic plates. These processes affect the distribution of mass in the Earth and produce variations in the Earth's gravitational field (Fig. 1) on a variety of spatial and temporal scales (Fig. 2). Highly accurate measurements of the Earth's gravity field made with appropriate

An improved model for the Earth's gravity field, TEG-1, has been determined using data sets from fourteen satellites, spanning the inclination ranges from 15°to 115°, and global surface gravity anomaly data. The satellite measurements include laser ranging data, doppler range-rate data, and satellite-to-ocean radar altimeter data measurements, which include the direct height measurement and the differenced measurements at ground track crossings (crossover measurements). Also determined was another gravity field model, TEG-1S, which included all the data sets in TEG-1 with the exception of direct altimeter data. The effort has included an intense scrutiny of the gravity field solution methodology. The estimated parameters included geopotential coefficients complete to degree and order 50 with selected higher order coefficients, ocean and solid Earth tide parameters, doppler tracking station coordinates and the quasi-stationary sea surface topography. Extensive error analysis and calibration of the formal covariance matrix indicate that the gravity field model is a significant improvement over previous models and can be used for general applications in geodesy.

Journal of Geodesy, 2003

The solutions of four ellipsoidal approximations for the gravimetric geoid are reviewed: those of Molodenskii et al., Moritz, Martinec and Grafarend, and Fei and Sideris. The numerical results from synthetic tests indicate that Martinec and Grafarend's solution is the most accurate, while the other three solutions contain an approximation error which is characterized by the first-degree surface spherical harmonic. Furthermore, the first 20 degrees of the geopotential harmonic series contribute approximately 90% of the ellipsoidal correction. The determination of a geoid model from the generalized Stokes scheme can accurately account for the ellipsoidal effect to overcome the first-degree surface spherical harmonic error regardless of the solution used.