Geoid Undulations Research Articles

Geoid undulation prediction using Gaussian Processes Regression: A case study in a local region in Turkey

In order to convert ellipsoidal heights obtained by the Global Navigation Satellite System (GNSS) to orthometric heights, it is necessary to know the distance between the ellipsoidal and geoid surface, called the geoid undulation. The geoid undulation can be predicted using emerging mathematics tools and algorithms. The objective of this study was to develop a model for predicting the geoid undulation using Gaussian process regression (GPR), one of the soft machine learning algorithms having different covariance functions. This method was then compared with the radial basis function neural network (RBFNN), generalized regression neural network (GRNN), and the interpolation method of inverse distance to a power (IDP) with the power of 1, 2, 3, 4, and 5. First, 70 % of GNSS/leveling data (422 points) were used in the training phase. The remaining 185 points were used as testing data to check the effectiveness of the constructed model. In the GPR modeling, ten covariance functions (Materniso d= 1, 3, 5; Maternard d= 1, 3, 5; SEiso; SEard; RQiso; and RQard) were tested for prediction on this dataset. The GPR based on the Materniso (d = 1) covariance function model was introduced as an effective method for predicting geoid undulation and provided the best results (RMSE = 8.32 cm, MAE = 5.51 cm, R2 = 0.98968) when compared with the other developed GPR models. In addition, the statistical findings showed that the accuracy of all the GPR models was also better in predicting geoid undulation than the RBFNN, GRNN, and IDP with the power of 1, 2, 3, 4, and 5.

Validation of the GPS leveling method through the gradient analysis of the geoidal wave. Case study of Ecuador

We validated the GPS leveling as an alternative to the traditional geometric leveling method. Validation compares the geometric slopes derived from the GNSS positioning technique, heights resulting from geometric leveling campaigns and geoid undulations extracted from the Global Geopotential Model EGM08. This analysis was performed in the Ecuadorian mainland, where we identified areas in which the gradient of the geoidal undulation is less pronounced. The spatialization of the gradient or variation-based methods allowed to analyze the performance of the GPS leveling method, under the hypothesis that less variability in geoid undulation implies less discrepancies in the GPS unevenness. GNSS observations were determined on the leveling plates belonging to the Basic Vertical Control Network. The results of the study are given based on the relative error resulting from the comparison of the traditional differential leveling method with the corresponding values obtained from the GNSS positioning, considering different distances for the spread of unevenness.

Validation of the GPS leveling method through the gradient analysis of the geoidal wave. Case study of Ecuador.

We validated the GPS leveling as an alternative to the traditional geometric leveling method. Validation compares the geometric slopes derived from the GNSS positioning technique, heights resulting from geometric leveling campaigns and geoid undulations extracted from the Global Geopotential Model EGM08. This analysis was performed in the Ecuadorian mainland, where we identified areas in which the gradient of the geoidal undulation is less pronounced. The spatialization of the gradient or variation-based methods allowed to analyze the performance of the GPS leveling method, under the hypothesis that less variability in geoid undulation implies less discrepancies in the GPS unevenness. GNSS observations were determined on the leveling plates belonging to the Basic Vertical Control Network. The results of the study are given based on the relative error resulting from the comparison of the traditional differential leveling method with the corresponding values obtained from the GNSS positioning, considering different distances for the spread of unevenness.

Topography of the Aleutian Trench south-east off Bowers Ridge, Bering Sea, in the context of the geological development of North Pacific Ocean

The research is focused on the topographic modelling and mapping of the Aleutian Trench. The study area is situated in the Bering Sea, a marginal sea located northernmost of the Pacific Ocean, between Alaska and Kamchatka Peninsula. The geological setting of the region is characterized by the subduction of the oceanic Pacific Plate below the continental North American Plate. Other features include high seismic activity along the Aleutian island arcs bordering the oceanic seafloor. The objective of this paper is to explore the interaction between the geophysical setting affecting the relief of the seafloor by using geoinformation techniques and geological analysis. In the hypothesis of this study, variations in the geophysical fields as independent variables are reflected in the morphology of the seafloor, which can be observed using data visualization by the advanced cartographic scripting solutions. The open source high-resolution topographic map (ETOPO1), marine free-air gravity and Bouguer gravity anomaly data were used and integrated to investigate the potential correlation between the geophysical, geological, tectonic and topographic settings of the Bering Sea. Our main method includes bathymetric mapping of the area with publicly available bathymetric data using GMT. Materials include open source data: ETOPO1 raster grid with 1 arc-minute resolution, EGM96 gravity and vector contour layers of GMT. The research included complex thematic mapping of the region, including topographic, contour, geodetic and geophysical mapping, 3D modelling and geomorphological plotting of the 30 cross-section segments of the trench located SE off the Bowers Ridge. According to the processed ETOPO1 dataset, the minimal depth is -8480 m and the mean is -3089.154 m. The geoid undulations model shows that the majority of the gravity values lie in the interval between -10 and 20 m with the lowest values along the trench. The statistical histogram shows that the most common depth value in the segment of the Aleutian Trench is -4800 m, occurring 1722 times. The profile linear trend modelling was done with four different approaches of the regression model (y = f(x) + e) by weighted least squares (WLS) with arguments: 1) m2t = a + bt (polynomial model degree one); 2) m3t = a + bt + ct2 (polynomial model degree two); 3) m4t = a + bt + ct2 + dcos2π*t + esin2π*t (polynomial model with Fourier series one); and 4) additional plotting residuals. Surface modelling was performed using xyz modelling from the ASCII data enlarging fragment towards SE of the Bowers Ridge. The tested functionality of modules of GMT presented an effective cartographic scripting toolset enabling a precise topographic mapping and 3D modelling. The paper contributes to a more detailed understanding of the Pacific Ocean seafloor bathymetry, more specifically of the selected segment of the Aleutian Trench near Bowers Ridge area.

GRASS GIS Modules for Topographic and Geophysical Analysis of the ETOPO1 DEM and Raster Data: North Fiji Basin, Pacific Ocean

The paper presents topographic analysis based on the raster data (NetCDF and grid formats) and visualization of the geophysical datasets that resembles the topographic surface. Geographically, the research focuses on the region of North Fiji Basin, South Pacific Ocean. North Fiji Basin is one of the marginal basins located at the converging boundary between the Pacific and Australian tectonic plates and is notable for complex geological settings. Methodology is based on GRASS GIS and includes scripting and cartographic visualization. Data include ETOPO1, GEBCO, EGM96 gravity and geoid raster grids imported to GRASS GIS via GDAL library (‘r.in.gdal’ module) from NetCDF and GRD formats, evaluated and visualized. Several GRASS modules were used as a sequential scripting for displaying and modelling data. Geomorphometric analysis (slopes, curvature, aspect, elevation) was performed by module ‘r.slope.aspect’ based on ETOPO1 grid. Statistical data analysis (histograms, polar diagram) for topographic and geoid gravitational fields were visualized by combination of GRASS modules d.rast, g.region, d.polar, d.histogram, d.grid, d.legend, d.text. Topographic analysis reveal that free-air gravity anomaly mark the continental shelf-slope border showing that generally, geophysical settings are dominated by the topographic effect. These observations are consistent with the inferred prominent role of the geophysical settings. The histograms reveal that topography (trenches, abyssal plains, shelf areas) has values between -5,000 and -1,000 m, and a clear peak with major values between 100 and 350 m above sea level. This distribution indicates that dominating depths of the ocean floor in North Fiji Basin are between -1,500 to -3,000 m. The aspect map of the ETOPO1 initial raw raster grid show that the surface has mostly 50°-110° oriented slope followed by data range in 250°-300° oriented slopes which is well correlating with submarine topography and general relief forms. The steepening of the gravity values between 50 and 55 mGal and 58 to 63 mGal indicates geoid undulations suggesting that bathymetry is controlled by the geological settings in the study area. Console- based scripts of GRASS GIS are presented together with cartographic outputs showing its effectiveness for the geographic spatial analysis.

Determination of the Selected Gravity Field Functionals by the GGI Method: A Case Study of the Western Carpathians Area

In this paper, some features of the local disturbing potential model developed by the GGI method (based on Geophysical Gravity Inversion) were analyzed. The model was developed for the area of the Western Carpathians covering the Polish–Slovak border. A detailed assessment of the model’s property was made regarding the accuracy of the disturbing potential values (height anomalies), gravity values, complete Bouguer anomalies (CBA), and differences between geoid undulations and height anomalies (N−ζ). Obtained accuracies of the GGI quasigeoid model (in terms of standard deviation of the residuals to the reference quasigeoid models) were at the level of ±2.2 cm for Poland and ±0.9 cm for the Slovak area. In terms of gravity, there was shown dependence of the accuracy of the GGI model on the digital elevation model (DEM) resolution, the point height, the density of gravity data used, and used reference density of topography model. The best obtained results of gravity prediction were characterized by an error of approximately 1 mGal. The GGI approach were compared with classical gravity prediction methods (using CBA and topographic-isostatic anomalies supported by Kriging prediction), getting very similar results. On the basis of the GGI model, CBA and differences (N−ζ) were also determined. The strong dependence of resolution of the CBA model obtained by GGI approach, on the size of the constant density zones, has been demonstrated. This significantly reduces the quality of such a model. The crucial importance of the topographic masses density model for both determined values (CBA and (N−ζ)) was also indicated. Therefore, for determining these quantities, all available information on topographic mass densities should be used in modelling.

Indoor height determination of the new absolute gravimetric station of L'Aquila

In this paper we describe all the field operations and the robust post-processing proceduresto determine the height of the new absolute gravimetric station purposely selected to belong to a new absolute gravimetric network and located in the Science Faculty of the L’Aquila University. This site has been realized indoor in the Geomagnetism laboratory, so that the height cannot be measured directly, but linking it to the GNSS antenna of AQUI benchmark located on the roof of the same building, by a classical topographic survey. After the topographic survey, the estimated height difference between AQUI and the absolute gravimetric site AQUIgis 14.9700.003 m. At the epoch of the 2018 gravimetric measures, the height of AQUI GNSS station was 712.9740.003 m, therefore the estimated ellipsoidalheight of the gravimetric site at the epoch of gravity measurements is 698.0040.005 m. Absolute gravity measurements are referred to the equipotential surface of gravity field, so that the knowledge of the geoidal undulation at AQUIg allows us to infer the orthometric height as 649.32 m.

COMPARATIVE ANALYSIS OF THREE PLANE GEOMETRIC GEOID SURFACES FOR ORTHOMETRIC HEIGHT MODELLING IN KAMPALA, UGANDA

The conversion of theoretical, as well as geometric heights to practical heights requires the application of geoidal undulations from a geoid model. The various global geopotential models that are readily available for application in any part of the world do not best-fit regions, as well as countries. As a result, there is a need to determine the local geoid models of local areas, regions and countries. This study determines the local geoid model of Kampala in Uganda for orthometric heights computation by comparing three plane geometric geoid surfaces. A total of 19 points were used in the study. The least squares adjustment technique was applied to compute the models’ parameters. Microsoft Excel programs were developed for the application of the models in the study area. The Root Mean Square Index was applied to compute the accuracy of the models. The three geometric geoid models were compared using their accuracy to determine which of them is most suitable for application in the study area. The comparison results show that the three models can be applied in the study area with more reliability, with greater confidence in model 2.

EVALUATION OF THE RECENT HIGH-DEGREE COMBINED GLOBAL GRAVITY-FIELD MODELS FOR GEOID MODELLING OVER KENYA

This study carries out an evaluation of the recent high-degree combined global gravity-field models (EGM2008, EIGEN-6C4, GECO and SGG-UGM-1) over Kenya. The evaluation is conducted using observed geoid undulations (18 data points, mainly in Nairobi area) and free-air gravity anomalies (8,690 data points, covering the whole country). All the four models are applied at full spherical harmonic degree expansion. The standard deviations of the differences between observed and GGMs implied geoid undulations at 18 GPS/levelling points over Nairobi area are ±11.62, ±11.48, ±12.51 and ±11.75 cm for EGM2008, EIGEN-6C4, GECO and SGG-UGM-1, respectively. On the other hand, standard deviations of the differences between observed and GGMs implied free-air gravity anomalies at 8,690 data points over Kenya are ±10.11, ±10.03, ±10.19 and ±10.00 mGal for EGM2008, EIGEN-6C4, GECO and SGG-UGM-1, respectively. These results indicate that the recent high-degree global gravity-field models generally perform at the same level over Kenya. However, EIGEN6C4 performs slightly better than EGM2008, GECO and SGG-UGM-1, considering the independent check provided by GPS/levelling data (admittedly over a small area). These results further indicate a good prospect for the development of a precise gravimetric geoid model over Kenya using EIGEN-6C4 by integrating local terrestrial gravity data in a removecompute-restore scheme.

Centimeter Precision Geoid Model for Jeddah Region (Saudi Arabia)

In 2014, the Jeddah Municipality made a call for an estimate of a centimetric precision geoid model to be used for engineering and surveying applications, because the regional geoid model available at that time did not reach a sufficient precision. A project was set up to this end and dedicated sets of gravity and Global Positioning System (GPS)/levelling data were acquired in the framework of this project. In this paper, a thorough analysis of these newly acquired data and of the last available Global Gravity Field Models (GGMs) has been done in order to obtain a geoid undulation estimate with the prescribed precision. In the framework of the Remove–Compute–Restore (RCR) approach, the collocation method was used to obtain the height anomaly estimation that was then converted to geoid undulation. The remove and restore steps of the RCR approach were based on GGMs, derived from the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) and Gravity Recovery and Climate Experiment (GRACE) dedicated gravity satellite missions, which were used to improve the long wavelength components of the Earth’s gravity field. Furthermore, two different quasi-geoid collocation estimates were computed, based on gravity data only and on gravity plus GPS/levelling data (the so-called hybrid estimate). The best solutions were obtained with the hybrid geoid estimate. This was tested by comparison with an independent set of GPS/levelling geoid undulations that were not included in the computed solutions. By these tests, the precision of the hybrid geoid is estimated to be 3.7 cm. This precision proved to be better, by a factor of two, than the corresponding one estimated from the pure gravimetric geoid. This project has been also useful to verify the importance and reliability of GGMs developed from the last satellite gravity missions (GOCE and GRACE) that have significantly improved our knowledge of the long wavelength components of the Earth’s gravity field, especially in areas with poor coverage of terrestrial gravity data. In fact, the geoid models based on satellite-only GGMs proved to have a better performance, despite the lower spatial resolution with respect to high-resolution models (i.e., Earth Gravitational Model 2008 (EGM2008)).

Pseudo height anomaly over Indonesia in respect of GRACE gravity

This paper presents an overview of the recent height anomaly over Indonesia region in respect of Global Geopotential Model 2008 (EGM2008) which known as the most advance Global Geopotential Model. Recent height anomaly over Indonesia computed from Gravity Recovery and Climate Experiment (GRACE) satellite mission long term static solution using Bruns’ formula with degree and order up to 180. The results indicate that the deviation between geoid undulation with pseudo height anomaly deviation vary up to 12 meters with the largest deviations occur in several zones. Further investigation still needed to deduce the causes of the high height anomaly deviation that occur in several places in Borneo, Celebes and Papua, whether it is caused by a large compression forces or any other.

RETRACTED ARTICLE: A Complete Formula of Ocean Surface Absolute Geostrophic Current

Absolute geostrophic current at the ocean surface (S) contains three components: (1) absolute geostrophic current at the geoid undulation (N), (2) geostrophic shear (between S and N) due to horizontal gradient of dynamic ocean topography, and (3) geostrophic shear (between S and N) due to horizontal gradient of density. However, only the second component is used to represent the surface absolute geostrophic current in physical oceanography and satellite geodesy. Four public datasets are used to calculate each component. Evident difference between the surface absolute geostrophic current and the second component (i.e., geostrophic shear due to horizontal gradient of dynamic ocean topography) was found by the statistical characteristics with the relative root mean square difference of 0.605. It shows that the common practice in physical oceanography and satellite geodesy is not correct. The horizontal gradient of dynamic ocean topography alone cannot be claimed as the surface absolute geostrophic current.

Modelling Orthometric Heights from a Combination of Ellipsoidal Heights and Gravimetric Geoid Model in Rivers State, Nigeria

Many applications in geodesy, hydrography and engineering require geoid-related heights. Spirit leveling which is the traditional means of obtaining geoid- or mean sea level-related heights is slow, time-consuming and costly. Global Navigation Satellite Systems (GNSS) offer faster and relatively cheaper way of obtaining geoid-related heights when geoidal undulation is applied to ellipsoidal heights. However, difficulties involved in determining acceptable geoid height have seriously hampered the application of GNSS for leveling in Rivers State, thus necessitating the need to develop an acceptable geoid model which will serve as a means of conversion of GNSS-delivered ellipsoidal heights to their orthometric heights equivalent. In pursuance of this objective, a detailed gravimetric geoid has been evaluated for Rivers State, Nigeria. The computation of the geoid was carried out by the traditional remove-restore procedure. The Earth Geopotential Model 2008 (EGM08) was applied as the reference field for both the remove and restore parts of the procedures; spherical Fast Fourier Transform (FFT) was employed for the evaluation of the Molodenskii’s integral formula for the height anomaly, (ζ) to yield the quasi-geoid; while the Residual Terrain Modelling (RTM) was done by prism integration. The classical gravimetric geoid over Rivers State was obtained from the rigorously evaluated quasi-geoid by adding the quasi-geoid to geoid (N - ζ) correction it. The minimum and maximum geoid height values are 18.599 m and 20.114 m respectively with standard deviation of 0.345 m across the study area. Comparison of the gravimetric geoidal heights with the GPS/Leveling-derived geoidal heights of 13 stations across Rivers State, Nigeria showed that the absolute agreement with respect to the GPS/leveling datum is generally better than 7 cm root mean squares (r.m.s) error. Results also showed that combining both GPS heights and the computed Rivers State geoid model can give orthometric heights accurate to 3 cm post-fit using a 4-parameter empirical model. The geoid model can thus serve as a good alternative to traditional leveling when used with GPS leveling, particularly for third order leveling in the study area.

A numerical model for the gravimetric recovery of sub-lithospheric mantle structures

It is a well-known fact that the long-wavelength terrestrial geoid undulations are mainly attributed to deep mantle density heterogeneities, while more detailed features in the geoid geometry are associated with the topography and the lithospheric density structure. To enhance a gravitational signature of mantle density heterogeneities below the lithosphere, the gravitational contributions of topography and lithospheric density heterogeneities should be modelled and subsequently removed from Earth's gravity field. The refined gravity field obtained after this numerical procedure is more suitable for a recovery of a mantle density structure (below the lithosphere). Following this idea, methods for a spherical harmonic analysis and synthesis of gravity field and lithospheric density structures are presented, and a theoretical relation between gravity field and mass density structure is formulated. Since a gravimetric recovery of inner density structure has a non-unique solution, we propose an alternative method based on a conversion of seismic velocities to mass densities. A forward modelling approach is then employed to find the mantle density configuration that generates the gravitational field that best approximates the corresponding refined gravitational field obtained from observed gravity field after subtracting the gravitational signal of the lithosphere.

Assessment of ArcGIS based extraction of geoidal undulation compared to National Geospatial Intelligence Agency (NGA) model – A case study

Abstract Global Navigation Satellite System (GNSS) and remote sensing Digital Elevation Models (DEMs) represent earth’s surface elevation with reference to ellipsoid and orthometric heights. Proper estimation of the geoid (difference of ellipsoid and orthometric heights) is necessary before comparing data referenced to the different vertical datum. In this paper, an error in estimating EGM96 orthometric height is highlighted, verified by NGA/NASA developed model and MATLAB®. A significant error was found in the ArcGIS derived EGM96 orthometric heights range between ±6.9 meters. In addition, interpolation of low-resolution geoid data also produces significant biases depending on geographic location and the number of the interpolation data point. The bias was maximum negative in the central part of Tibetan Plateau and Himalaya. Therefore, estimation of orthometric height similar to NGA/NASA model precision is necessary for comparison of DEMs for natural resources management, 3D modelling and glaciers mass balance mainly in the mountainous regions.

Utilization of geographically weighted regression for geoid modelling in Egypt

Abstract Modelling the spatial variations of a specific Global Geopotential Model (GGM) over a spatial area is important to enhance its local performance in Global Navigation Satellite Systems (GNSS) surveying. This study aims to investigate the potential of utilizing some of Geographic Information Systems (GIS) geospatial analysis tools, particularly Geographically Weighted Regression (GWR), in geoid modelling for the first time in Egypt as a case study. Its main target is developing an optimum regression method to be applied in spatial modelling of the deviations of a specific GGM (e. g., PGM17). Using a precise local geodetic dataset of 803 GPS/levelling stations, PGM17 undulation differences have been modelled using different regression techniques to evaluate their precision and accuracy. Based on investigating 13 possible regression formulas of probable combinations of independent variables, results showed that the PGM17 discrepancies over Egypt depend mostly on the terrain heights and geoidal undulations. Over 80 checkpoints, the attained variations between the GWR model and known values varied from −0.574 m to 0.500 m, with a mean of 0.001 m and a standard deviation equals ±0.205 m. Based on available data, it has been found that GWR improved the PGM17 deviations by 9 % in terms of standard deviation and by 98 % in terms of the mean. Additionally, the study generates a reasonably innovative product for the local geodetic community by building an enhanced version of the PGM17. This surface will be a precious resource in GNSS surveying in Egypt for heights conversion, leading to considerable cost reduction in civil engineering works and mapping projects.

GRAVIMETRIC GEOID MODELLING OVER PENINSULAR MALAYSIA USING TWO DIFFERENT GRIDDING APPROACHES FOR COMBINING FREE AIR ANOMALY

Abstract. We investigate the use of the KTH Method to compute gravimetric geoid models of Malaysian Peninsular and the effect of two differing strategies to combine and interpolate terrestrial, marine DTU17 free air gravity anomaly data at regular grid nodes. Gravimetric geoid models were produced for both free air anomaly grids using the GOCE-only geopotential model GGM GO_CONS_GCF_2_SPW_R4 as the long wavelength reference signal and high-resolution TanDEM-X global digital terrain model. The geoid models were analyzed to assess how the different gridding strategies impact the gravimetric geoid over Malaysian Peninsular by comparing themto 172 GNSS-levelling derived geoid undulations. The RMSE of the two sets of gravimetric geoid model / GNSS-levelling residuals differed by approx. 26.2 mm. When a 4-parameter fit is used, the difference between the RMSE of the residuals reduced to 8 mm. The geoid models shown here do not include the latest airborne gravity data used in the computation of the official gravimetric geoid for the Malaysian Peninsular, for this reason they are not as precise.

INFLUENCE OF NON-RADIOGENIC COSMIC HEAT GENERATION IN THE BOWELS OF THE EARTH AND PLANETS ON MUTUAL DISPLACEMENTS OF PLANETARY SHELLS Article 1. The Earth

We considered the influence of supposed planet non-radiogenic energy source of cosmic (galactic) origin on the process of mutual displacements of planetary shells. We found that the convection configuration in the Earth’s bowels has simultaneously three variants of topology of convective flows (single-cell, double-cell of open and closed types), a one-time existence of which is conditioned by nonuniform in space and time heating the bowels by an energy source of cosmic origin. Movement of masses during convection leads to mutual nutation of shells relative to the Earth’s axis of rotation. Such swings are characteristic of both the outer stone shell and the inner core of the planet. The motions of the shells are probably gravitationally synchronized, and certain resonances exist in these motions. Nutations occur in the certain corridor, which lies in the middle between the superplumes (African and Pacific), which are antipodally located on the equator. The axis, around which the shells are displaced, roughly coincides with the axis of equatorial maximum moment of inertia and passes through superplumes and positive geoidal undulations corresponding to them. Its existence is conditioned by general mantle isostatism, which causes the emergence of heated segments of the stone shell, forming the Earth's figure and the distribution of its rotational moment.

Optimizing Local Geoid Undulation Model using GPS/Levelling Measurements and Heuristic Regression Approaches

This study investigates to use GPS/Levelling measurements of Kuwait and four heuristic regression methods including Least Square Support Vector Regression (LSSVR), Gaussian Process Regression (GPR), Kernel Ridge Regression (KRR), and Multivariate Adaptive Regression Splines (MARS) for modelling local geoid undulation. The accuracy of the models was compared by geoid undulation of gravitational observations and Global Geopotential Models (GGMs). The results show that the KRR model is suitable for Kuwait geoid model, its error of percentage is 0.018 and 0.124% relative to gravity and GPS/Levelling geoid undulation models, respectively. Furthermore, the comparison of KRR model with GGMs models signifies its accuracy.

Modelling of Orthometric heights from Multi- Networks of GNSS/Precise Levelling in FCT, Abuja

The geoid is used as a transformation linkage between ellipsoidal heights (h) determined from DGPS observations and orthometric heights (H). Widespread acceptability and adoption of GPS in local geospatial data acquisitions require the development of a local geoid model (N) for use to obtain orthometric heights in the absence of a national geoid model. Geoid model can be developed by gravimetric approach; global geopotential model (GGM); geometric technique among others. The conventional approach to GPS measurements is the use of one base reference station for field measurements. It has several drawbacks e.g. in signal range/coverage, accuracy degradation of results, etc. Based on Grashof's law of stability of triangles, this study was therefore based on dual reference base stations to improve on DGPS signal range and stability of results. Pro-online matrix solver was applied to the least squares observation equations of the two modelled FCT surfaces (multi - quadratic and bicubic) to determine polynomial coefficients. The geoid undulation was computed and orthometric height generated for production of a topographical plan at 1m contour interval for elevation data in surveying, engineering and environmental applications. Skill =1 and bias = 0 were computed to confirm the predictive capability of the models and that no bias/errors were introduced into the respective modelling exercise. Diagnostic test also confirmed the viability and feasibility of providing vertical datum surface for FCT by this approach. Standard deviation (σ) as accuracy indicator was computed and the multi-quadratic model with σ =11cm was the better geoid surface for modelling of orthometric height in the FCT by the geometric method.