Determination of Nigerian Geoid Undulations from Spherical Harmonic Analysis
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Geoid undulation has been determined for Nigeria in order to demonstrate its relationship with topography and the dynamic structure of the Earth’s interior. Spherical harmonic expansion using the Earth Gravitational Model 2008 (EGM2008) referenced to the WGS84 (World Geodetic System 1984) with coefficients extending to degree 2190 and order 2159 was found suitable for the determination of geoid undulation. The results from the analysis show that the Nigerian geoid undulations are positive and show overall good correlation with topography. The internal origin of the geoid undulation is attributed to excess mass beneath the ellipsoid. This internal mass distribution extend deep into the mantle. The highest geoid undulations are centered over the North central region of Nigeria with relatively lower values confined to the Nigerian sedimentary basins. The lowest geoid undulation values are within the oceanic areas.A new, high resolution, high precision and accuracy gravimetric geoid of Australia has been produced using updated data, theory and computational methodologies. The fast Fourier transform technique is applied to the computation of the geoid and terrain effects. The long, medium and short wavelength components of the geoid are determined from the OSU91A global geopotential model, 2'x2' (residual gravity anomalies in a 3 degrees cap and 1'x1' digital terrain model (DTM), respectively.Satellite altimeter gravity data have been combined with marine gravity data to improve the coverage of the gravity data, and thus the quality of the geoid. The best gridding procedure for gravity data has been studied and applied to the gravity data gridding. It is found that the gravity field of Australia behaves quite differently. None of the free-air, Bouguer or topographic-isostatic gravity anomalies are consistently the smoothest. The Bouguer anomaly is often rougher than the free-air anomaly and thus should be not used for gravity field gridding. It is also revealed that in some regions the topography often contains longer wavelength features than the gravity anomalies.It is demonstrated that the inclusion of terrain effects is crucial for the determination of an accurate gravimetric geoid. Both the direct and indirect terrain effects need to be taken into account in the precise geoid determination of Australia. The existing AUSGEOID93 could be in error up to 0.7m in terms of the terrain effect only. In addition, a series of formulas have been developed to evaluate the precision of the terrain effects. These formulas allow the effectiveness of the terrain correction and precision requirement for a given DTM to be studied. It is recommended that the newly released 9x9 DTM could be more effectively used if it is based on 15x15 grid.It is estimated from comparisons with Global Positioning System (GPS) and Australian Height Datum Data that the absolute accuracy of the new geoid is better than 33cm and the relative precision of the new geoid is better than 10~20cm. This new geoid can support Australian GPS heighting to third-order specifications.
Anomaly (physics)
Free-air gravity anomaly
Geopotential
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Direct Global Positioning System measurement of geoid undulations on accurately levelled stations, usually tens of kilometres apart, can be interpolated by taking advantage of denser surveys of free-air gravity anomalies covering the same area. Using either a spherical or a planar earth model, a two-layer equivalent source is constructed, with the deepest masses located under the geoid stations and the shallower ones under the gravity stations, in such a way that the effect of the masses fits simultaneously, with different precisions, the anomalous potential related to the geoid and its vertical gradient or gravity anomaly. This poses a linear Bayesian problem, whose associated system of equations can be solved directly or by iterative procedures. The ability of the described method to predict the geoid elevation over the gravity stations is assessed in a synthetic example; and in the application to a real case, a gravity-enhanced geoid is mapped for an area of Buenos Aires province, Argentina, where local features are put in evidence.
Free-air gravity anomaly
Elevation (ballistics)
Anomaly (physics)
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Levelling
Dynamic height
Anomaly (physics)
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A precise orthometric height (H) and orthometric height difference (ΔH) determination is required in many fields like construction, geodesy and geophysics. H is often obtained from an ellipsoidal height (h) and geoid height (N) of a geoid model (GM) because this computation does not have the spirit leveling restrictions on long distances. However, the H accuracy depends on the GM local area adaptation, and current global geoid models (GGMs) have not been yet evaluated for Costa Rica. Therefore, this paper aims to determine which GGM maintains a better fit with a GPS/levelling baseline that contains the gravity full spectrum. A 74 km baseline was measured using GPS, spirit leveling and gravity measurements to validate the N computed from EGM2008, EIGEN-6C4, GECO, EGM96, GGM05C and GOCO05C. First, an absolute N assessment was made, where geoid height from the GGMs (NGGM) were directly compared to the geometric geoid heights (Ngeo) obtained from GPS and spirit levelling. A bias fit (Nbias) of about 2 m was computed from this comparison for most GGMs with respect to the local vertical reference surface (W0). By subtracting the Nbias, a relative geoid height (ΔN) assessment was designed to compare the differences between GGM relative geoid height (ΔNGGM) and geometric relative geoid height (ΔNgeo) on segments along the baseline. The ΔN comparison shows that EGM2008, EIGEN-6C4 and GECO better represent the Costa Rican Central Pacific Coastal Zone and over long distances, ΔH can be computed with a decimeter to centimeter precision.
Levelling
Baseline (sea)
Dynamic height
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The available geoid undulations on the WGS84 ellipsoid at over two hundred GPS stations are interpolated using a least-squares surface fitting technique to determine the geoid of the central highlands in Sri Lanka. However, it is not possible to interpolate these points directly to prepare a detailed map of the geoid surface as the geoid separation varies intense due to the rugged local topography making the interpolation inaccurate. The gravity potential and subsequently the undulation of the local geoid due to the topography have been calculated separately using a topographic model and removed from the available geoid undulations. This model was created using information obtained from 1:50 000 digital topographic maps provided by the Survey department of Sri Lanka. The resulting geoid separations were interpolated and three surface polynomials were employed to determine the geoid using the least-squares surface fitting technique. To avoid possible artefacts in regions without observations, an area including central highlands was selected to determine the geoid. Finally, the geoid undulations due to the topography were added back to the Bouguer co-geoid represented by three mathematical surfaces to create a detailed map of the geoid of Sri Lanka. A local positive geoid surface superimposing a large negative regional surface has been obtained and the local maximum value of the geoid undulation is about –92.05 m in the vicinity of Piduruthalagala peak.
Interpolation
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Abstract In the past, geoid was computed from gravity anomaly data using Stokes or Molodensky approaches. Obtaining gravity anomaly data is difficult because it needs some reductions of gravity from surface of the earth to the geoid using orthometric height from spirit level measurement. In the modern era, gravity anomaly data may be replaced by gravity disturbance data. It only required gravity and GNSS (Global Navigation Satellite System) measurement. This research aimed to determine geoid using Hotine’s approach. Disturbance data were generated from archived free air anomaly of airborne gravimetry in Sulawesi area. South East Sulawesi province was selected as a case study area. In this study, gravity observation was calculated at an altitude of 4000 m above the reference ellipsoid. Gravity estimation at the same height aims to increase the precision of the downward continuation process to the geoid. Hotine integral is calculated above the geoid, so that the gravity disturbance data is downwarded to the geoid. The geoid undulation is graded from north to south. Geoid from airborne gravity around Pegunugan Mekongga in the northern part of Southeast Sulawesi Province has the largest geoid undulation which reaches 63 m, while the geoid in the southern part of Buton Island reaches 52 m. Geoid validation of airborne gravity at 13 test points produces a standard deviation of ± 0.050 m. The standard deviation is much smaller than the results of geoid testing from airborne data in North Sulawesi, Central Sulawesi and Southeast Sulawesi. This fact indicates that the Hotine approach has the potential to produce a precise geoid if used in geoid-based airborne gravity calculations.
Free-air gravity anomaly
Anomaly (physics)
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Abstract A detailed gravimetric geoid around Japan is computed based on 10’ X 10’ block mean gravity anomalies. The block mean gravity anomalies are obtained by the use of the least‐squares collocation technique from point gravity data in a gravity data file compiled by the Hydrographic Department of Japan. The available 1° x 1° block mean gravity anomalies are also used in data‐sparse areas. The GEM 10B earth gravity model is adopted as the global anomaly field. Meissl's modification is used in the performance of Stokes’ integral in order to reduce truncation errors. An integration cap with the radius of 10° is adopted. The computed geoid undulations are compared with the Seasat‐1 altimeter data, and the possibility of the detection of sea‐surface topography corresponding to the Kuro‐shio Current is investigated.
Collocation (remote sensing)
Free-air gravity anomaly
Gravimetry
Ocean surface topography
Anomaly (physics)
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The optimal combination of global positioning system (GPS) geometric heights with gravimetrically derived geoid undulations for the determination of orthometric heights above mean sea level (GPS/geoid leveling), or more precisely with respect to a vertical geodetic datum, requires the incorporation of a parametric corrector surface model. Such a parametric model is needed to absorb the datum inconsistencies and systematic distortions inherent among the different types of height data. An analysis for the achievable accuracy of relative GPS/geoid leveling is performed in this paper, using the covariance (CV) matrix of the estimated parameters in the corrector surface model, the standard measuring accuracy of GPS height differences, and the relative internal accuracy of a gravimetric geoid model. A test network of spirit leveled GPS control points located in the southwestern part of Canada has been used to perform a simulative integrated least-squares adjustment of all three types of height data, and to obtain the CV matrix of the parameters in the corrector surface model. The input CV matrices for the GPS and the orthometric height values at the control network points have been computed through separate simulative adjustments that take into account the measuring accuracy of GPS and spirit leveling. The input accuracy for the geoid undulation differences is based on the performance evaluation of the GSD95 Canadian geoid model in western Canada. The focus is placed on studying the effects of the combined relative accuracy of GPS and geoid data, in conjunction with a number of different parametric corrector surface models, for GPS/geoid leveling on new baselines within the test network area.
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This paper describes the determination of geoid using height data measured by GPS and Spirit Levelling. The GPS data of the 88 stations were used to determine the geoid undulation (N) which can be easily obtained by subtracting the orthometric height(H) from the ellipsoidal height(h). From the geoid undulation (N) calculated at each station mentioned above, geoid plots with a contour interval of 0.25 m were drawn using two interpolation methods. The following interpolation methods were applied and compared with each other: Minimum Curvature Method and Least Squares Fitted Plane. Comparison between geometric geoid and gravimetric geoid undulation by FFT technique was carried out.
Levelling
Interpolation
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