Gravimetric Geoid Determination Research Articles

Analysis of different combinations of gravity data types in gravimetric geoid determination over Bali

Abstract Following the Regulation of the Head of the Geospatial Information Agency (BIG) No. 13 of 2021, geoid is used as the Vertical Geospatial Reference System in Indonesia. Applications using the geoid as an ideal reference require a much higher accuracy and resolution than the geoid obtained from models derived solely from satellite data. The Indonesian Geospatial Information Agency considers the geoid ideal if it has reached an accuracy of better than 15 cm. Recent studies have combined satellite and other gravimetric data to produce a combined geoid model with increased resolution. Gravimetric data obtained from measurements close to the Earth’s surface, such as airborne and terrestrial gravity data, are particularly attractive because the high-frequency portion of the signal is more apparent and can contribute to the medium to high frequencies of the gravity field. This study models the geoid over Bali Island by combining satellite, airborne and terrestrial gravity data. Calculations were performed using Least Square Collocation (LSC) and Remove-Compute-Restore (RCR) techniques. The gravimetric geoid model was tested against the geometric geoid profile calculated from a GNSS/Levelling survey. The geoid, calculated by combining the GOCO06S satellite gravity model, the GGMplus gravity model and airborne gravity data at an average flight altitude of 4100 m produces a standard deviation of 14.46 cm along the 125 km validation path. After also adding terrestrial gravity data, the standard deviation increased to 16.37 cm. By comparison, the results of the validation of the geoid model from GOCO06S and INAGEOIDV2 with geometric geoids have standard deviation values of 79.56 cm and 16.40 cm, respectively. However, the results of the statistical tests are strongly influenced by the data quality used as validation, in this case, GNSS/Levelling. It is shown that the GNSS/Levelling data over Bali contains significant errors, which have been reduced based on an analysis of geometric vertical deflections. A geometric geoid profile with higher accuracy is required to test the accuracy of the gravimetric geoid models more reliably.

Effect of a high-resolution global crustal model on gravimetric geoid determination: a case study in a mountainous region

A precise gravimetric geoid model is determined by using Stokes formula assuming that there is no topography above the geoid. Then, the geoid model is simply corrected by considering the constant crustal density of 2670 kg m−3 for topographical mass. In fact, the actual density of topographical mass differs about ±20% from the constant value. Recently a global crustal density model within 30″ resolution has been released by the University of New Brunswick in Canada. The paper is devoted to the study of the effect of using this model on the accuracy of gravimetric geoid in a mountainous region in Turkey. Numerical results prove that the differences in the geoid height due to this model may reach up to several decimetres, which should not be ignored in a precise geoid modelling with 1-cm geoid. Thus, it is concluded that the effect of topographical density variations, contained in this model, is significant and should be taken into account in precise geoid determination, particularly in mountainous regions.

Refinement of a gravimetric geoid model for Japan using GOCE and an updated regional gravity field model

We developed a refined gravimetric geoid model for Japan on a 1 × 1.5 arc-minute (2 km) grid from a GOCE-based satellite-only global geopotential model and a regional gravity field model updated in this study. First, we have constructed a regional gravity field model for Japan using updated gravity datasets together with a residual terrain model: 323,431 land gravity data, 77,389 shipborne marine gravity data, and Sandwell’s v28.1 altimetry-derived global marine gravity model. Then, the geoid was determined with the gravity field model. The methodology for gravimetric geoid determination was based on the remove–compute–restore technique with Helmert’s second method of condensation of topography (Stokes–Helmert scheme). Here, the hybrid Meissl–Molodensky modified spheroidal Stokes kernel was employed to minimize the truncation error under an appropriate combination of different kinds of gravity data. In addition, a high-resolution GSI-DEM on a 0.4 × 0.4 arc-second (10 m) grid, together with the SRTM-DEM on a 7.5 × 11.25 arc-second (250 m) grid, was utilized for precisely applying terrain correction to the regional gravity field model. Consequently, we created a gravimetric geoid model for Japan, consistent with 971 GNSS/leveling geoid heights distributed over the four main islands of Japan with a standard deviation of 5.7 cm, showing a considerable improvement by 2.3 cm over the previous model (JGEOID2008). However, there remain some areas with large discrepancies between the computed and GNSS/leveling geoid heights in northern Japan (Hokkaido), mountainous areas in central Japan, and some coastal regions. Since terrestrial gravity data are especially sparse in these areas, we speculated that the largeness of the geoid discrepancies there could be partly attributed to the insufficient coverage and accuracy of gravity data. The Geospatial Information Authority of Japan has started airborne gravity surveys to be covered over the Japanese Islands, and in future, we plan to develop a geoid model for Japan further accurately by incorporating airborne gravity data to come.

Accuracy Evaluation of Geoid Heights in the National Control Points of South Korea Using High-Degree Geopotential Model

Precise geoid heights are not as important for understanding Earth’s gravity field, but they are important to geodesy itself, since the vertical datum is defined as geoid in a cm-level accuracy. Several high-degree geopotential models have been derived lately by using satellite tracking data such as those from Gravity Recovery and Climate Experiment (GRACE) and Gravity Field and Steady-State Ocean Circulation Explorer (GOCE), satellite altimeter data, and terrestrial and airborne gravity data. The Korean national geoid (KNGeoid) models of the National Geographic Information Institute (NGII) were developed using the latest global geopotential models (GGMs), which are combinations of gravity data from satellites and land gravity data. In this study, geoid heights calculated from the latest high-degree GGMs were used to evaluate the accuracy of the three GGMs (European Improved Gravity model of Earth by New techniques (EIGEN)-6C4, Earth Gravitational Model 2008 (EGM2008), and GOCE-EGM2008 combined model (GECO)) by comparing them with the geoid heights derived from the Global Navigation Satellite System (GNSS)/leveling of the 1182 unified control points (UCPs) that have been installed by NGII in South Korea since 2008. In addition, the geoid heights derived from the KNGeoid models were compared with the geoid heights derived from the GNSS/leveling of the 1182 UCPs to assess the accuracy of the KNGeoid models in terms of relative geoid heights for further gravimetric geoid determination studies in South Korea. As a result, the EGM2008 model could be selected as the suitable GGM from among the three GGMs for determining a gravimetric geoid model for South Korea.

Gravity for Geodetic Purpose: Geoid-Ellipsoid Separation and Orthometric Height System

Gravity plays very crucial role in geodetic issues as gravity field determines the shape of the earth. This paper reviews – beginning from defining the gravity, various applications of gravity in geodesy and in other fields, nature of gravity field of our terrain, instruments of gravity measurement, and techniques of gravity survey. This paper first gives information about gravity networks in Nepal, presents an equation to compute orthometric correction (OC) from height obtained from levelling. Gravimetric geoid-determination method is explained here with various gravity reduction methods and topographic-isostatic gravity reduction method is recommended for N- separation computation as this method results gravity anomalies near to zero.

Definition of Physical Height Systems for Telluric Planets and Moons

In planetary sciences, the geodetic (geometric) heights defined with respect to the reference surface (the sphere or the ellipsoid) or with respect to the center of the planet/moon are typically used for mapping topographic surface, compilation of global topographic models, detailed mapping of potential landing sites, and other space science and engineering purposes. Nevertheless, certain applications, such as studies of gravity-driven mass movements, require the physical heights to be defined with respect to the equipotential surface. Taking the analogy with terrestrial height systems, the realization of height systems for telluric planets and moons could be done by means of defining the orthometric and geoidal heights. In this case, however, the definition of the orthometric heights in principle differs. Whereas the terrestrial geoid is described as an equipotential surface that best approximates the mean sea level, such a definition for planets/moons is irrelevant in the absence of (liquid) global oceans. A more natural choice for planets and moons is to adopt the geoidal equipotential surface that closely approximates the geometric reference surface (the sphere or the ellipsoid). In this study, we address these aspects by proposing a more accurate approach for defining the orthometric heights for telluric planets and moons from available topographic and gravity models, while adopting the average crustal density in the absence of reliable crustal density models. In particular, we discuss a proper treatment of topographic masses in the context of gravimetric geoid determination. In numerical studies, we investigate differences between the geodetic and orthometric heights, represented by the geoidal heights, on Mercury, Venus, Mars, and Moon. Our results reveal that these differences are significant. The geoidal heights on Mercury vary from − 132 to 166 m. On Venus, the geoidal heights are between − 51 and 137 m with maxima on this planet at Atla Regio and Beta Regio. The largest geoid undulations between − 747 and 1685 m were found on Mars, with the extreme positive geoidal heights under Olympus Mons in Tharsis region. Large variations in the geoidal geometry are also confirmed on the Moon, with the geoidal heights ranging from − 298 to 461 m. For comparison, the terrestrial geoid undulations are mostly within ± 100 m. We also demonstrate that a commonly used method for computing the geoidal heights that disregards the differences between the gravity field outside and inside topographic masses yields relatively large errors. According to our estimates, these errors are − 0.3/+ 3.4 m for Mercury, 0.0/+ 13.3 m for Venus, − 1.4/+ 125.6 m for Mars, and − 5.6/+ 45.2 m for the Moon.

Computation of precise geoid model of Auvergne using current UNB Stokes-Helmert’s approach

AbstractThe aim of this paper is to show a present state-of-the-art precise gravimetric geoid determination using the UNB Stokes-Helmert’s technique in a simple schematic way. A detailed description of a practical application of this technique in the Auvergne test area is also provided. In this paper, we discuss the most problematic parts of the solution: correct application of topographic and atmospheric effects including the lateral topographical density variations, downward continuation of gravity anomalies from the Earth surface to the geoid, and the optimal incorporation of the global gravity field into the final geoid model. The final model is tested on 75 GNSS/levelling points supplied with normal Molodenskij heights, which for this investigation are transformed to rigorous orthometric heights. The standard deviation of the computed geoid model is 3.3 cm without applying any artificial improvement which is the same as that of the most accurate quasigeoid.

Space-Wise approach for airborne gravity data modelling

Regional gravity field modelling by means of remove-compute-restore procedure is nowadays widely applied in different contexts: it is the most used technique for regional gravimetric geoid determination, and it is also used in exploration geophysics to predict grids of gravity anomalies (Bouguer, free-air, isostatic, etc.), which are useful to understand and map geological structures in a specific region. Considering this last application, due to the required accuracy and resolution, airborne gravity observations are usually adopted. However, due to the relatively high acquisition velocity, presence of atmospheric turbulence, aircraft vibration, instrumental drift, etc., airborne data are usually contaminated by a very high observation error. For this reason, a proper procedure to filter the raw observations in both the low and high frequencies should be applied to recover valuable information. In this work, a software to filter and grid raw airborne observations is presented: the proposed solution consists in a combination of an along-track Wiener filter and a classical Least Squares Collocation technique. Basically, the proposed procedure is an adaptation to airborne gravimetry of the Space-Wise approach, developed by Politecnico di Milano to process data coming from the ESA satellite mission GOCE. Among the main differences with respect to the satellite application of this approach, there is the fact that, while in processing GOCE data the stochastic characteristics of the observation error can be considered a-priori well known, in airborne gravimetry, due to the complex environment in which the observations are acquired, these characteristics are unknown and should be retrieved from the dataset itself. The presented solution is suited for airborne data analysis in order to be able to quickly filter and grid gravity observations in an easy way. Some innovative theoretical aspects focusing in particular on the theoretical covariance modelling are presented too. In the end, the goodness of the procedure is evaluated by means of a test on real data retrieving the gravitational signal with a predicted accuracy of about 0.4 mGal.

The Uganda Gravimetric Geoid Model 2014 Computed by The KTH Method

Abstract For many developing countries such as Uganda, precise gravimetric geoid determination is hindered by the low quantity and quality of the terrestrial gravity data. With only one gravity data point per 65 km2, gravimetric geoid determination in Uganda appears an impossible task. However, recent advances in geoid modelling techniques coupled with the gravity-field anomalies from the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) satellite mission have opened new avenues for geoid determination especially for areas with sparse terrestrial gravity. The present study therefore investigates the computation of a gravimetric geoid model overUganda (UGG2014) using the Least Squares Modification of Stokes formula with additive corrections. UGG2014 was derived from sparse terrestrial gravity data from the International Gravimetric Bureau, the 3 arc second SRTM ver4.1 Digital Elevation Model from CGIAR-CSI and the GOCE-only global geopotential model GO_CONS_GCF_2_TIM_R5. To compensate for the missing gravity data in the target area, we used the surface gravity anomalies extracted from the World Gravity Map 2012. Using 10 Global Navigation Satellite System (GNSS)/levelling data points distributed over Uganda, the RMS fit of the gravimetric geoid model before and after a 4-parameter fit is 11 cm and 7 cm respectively. These results show that UGG2014 agrees considerably better with GNSS/levelling than any other recent regional/ global gravimetric geoid model. The results also emphasize the significant contribution of the GOCE satellite mission to the gravity field recovery, especially for areas with very limited terrestrial gravity data.With an RMS of 7 cm, UGG2014 is a significant step forward in the modelling of a “1-cm geoid” over Uganda despite the poor quality and quantity of the terrestrial gravity data used for its computation.

Effect of ASTER DEM on the prediction of mean gravity anomalies: a case study over the Auvergne test region

A precise gravimetric geoid determination requires height information and terrestrial gravity data with high accuracy and resolution. The height data is utilized for predicting mean free-air gravity anomalies as well as computing the topographic, atmospheric and downward continuation effects which are fundamental components of any geoid model. Nowadays the Digital Elevation Model (DEM) obtained from the Shuttle Radar Topography Mission (SRTM) has been widely used when an accurate regional DEM does not exist. In addition the DEM generated from Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) was newly released by researchers from Japan and United States. In this study the effect of ASTER DEM on the estimating mean free-air gravity anomalies in geoid determination were investigated in the Auvergne test area where one of its regions exhibits one of the most rugged topography over the world. The numerical results show that ASTER DEM gives worse statistics than SRTM DEM with respect to the accuracy of the height. Using ASTER DEM introduces discrepancies (compared to SRTM DEM) in the range of \(-\)4 to 10 mGal in the interpolation of free-air gravity anomalies. It is also proven that the geoid differences due to the use of ASTER DEM are a few centimeters, which remain below the accuracy level of the external GPS-levelling data.

A software package for computing a regional gravimetric geoid model by the KTH method

Nowadays, the geodetic community has aimed to determine 1-cm accuracy gravimetric geoid model, which satisfies the demands of most engineering applications. However, the gravimetric geoid determination is a difficult mission which needs an exclusive attention to obtain reliable results for this purpose. Today, Least-Squares Modification of Stokes (LSMS) formula which is so-called the KTH method (Swedish Royal Institute of Technology) has been performed in the regional geoid studies. Based upon the earlier investigations, the KTH method provides more reasonable results than the Remove Compute Restore technique, especially in roughly terrain with sparse terrestrial gravity data. Nevertheless, a compact and practical software package is now not available for users and researchers in geosciences. Thus, in this paper, a scientific software called “LSMSSOFT” is developed and presented by adding a new algorithm which speeds up the evaluation of Stokes’ integral. Afterwards, the LSMSSOFT is applied to a case study for the construction of a geoid model over the Auvergne test area in France. Consequently, the algorithm treated in the software and its results imply that the LSMSSOFT is an alternative software package for modelling the gravimetric geoid by the KTH method.

On the topographic effects by Stokes’ formula

AbstractTraditional gravimetric geoid determination relies on Stokes’ formula with removal and restoration of the topographic effects. It is shown that this solution is in error of the order of the quasigeoid-to-geoid difference, which is mainly due to incomplete downward continuation (dwc) of gravity from the Earth’s surface to the geoid. A slightly improved estimator, based on the surface Bouguer gravity anomaly, is also biased due to the imperfect harmonic dwc the Bouguer anomaly. Only the third estimator,which uses the (harmonic) surface no-topography gravity anomaly, is consistent with the boundary condition and Stokes’ formula, providing a theoretically correct geoid height. The difference between the Bouguer and no-topography gravity anomalies (on the geoid or in space) is the “secondary indirect topographic effect”, which is a necessary correction in removing all topographic signals.

Comparison of the KTH and remove–compute–restore techniques to geoid modelling in a mountainous area

In mountainous regions, a gravimetric geoid determination is a difficult task which needs special attention to obtain reliable results satisfying the demands, e.g. of the engineering infrastructure. The present study compares the KTH (Royal Institute of Technology) method with the remove–compute–restore (RCR) technique to attain a precise geoid model for the Konya Closed Basin (KCB) and thus aims to clarify the theoretical and numerical differences between these techniques. The KCB located in the central part of Turkey is a mountainous area with a very limited amount of the ground gravity data. Various data sources, such as the Turkish Digital Elevation Model with 3″×3″ resolution (TRDEM3), a recently published satellite-only global geopotential model and terrestrial gravity observations are combined in the gravimetric geoid models of the KCB by applying the KTH and RCR techniques, separately. The both gravimetric geoid models (KG-KTH11 and KG-RCR11) are compared with GNSS/levelling data at the control points in the target area, resulting the RMS (Root Mean Square Error) differences of ±6.7cm and ±9.8cm in the absolute sense, respectively. These results show that the KTH method gives more reasonable accuracy than the RCR technique in a mountainous area with scarce terrestrial gravity data.

A precise gravimetric geoid model in a mountainous area with scarce gravity data: a case study in central Turkey

In mountainous regions with scarce gravity data, gravimetric geoid determination is a difficult task that needs special attention to obtain reliable results satisfying the demands, e.g., of engineering applications. The present study investigates a procedure for combining a suitable global geopotential model and available terrestrial data in order to obtain a precise regional geoid model for Konya Closed Basin (KCB). The KCB is located in the central part of Turkey, where a very limited amount of terrestrial gravity data is available. Various data sources, such as the Turkish digital elevation model with 3 ″ × 3″ resolution, a recently published satellite-only global geopotential model from the Gravity Recovery and Climate Experiment satellite (GRACE) and the ground gravity observations, are combined in the least-squares sense by the modified Stokes’ formula. The new gravimetric geoid model is compared with Global Positioning System (GPS)/levelling at the control points, resulting in the Root Mean Square Error (RMS) differences of ±6.4 cm and 1.7 ppm in the absolute and relative senses, respectively. This regional geoid model appears to be more accurate than the Earth Gravitational Model 2008, which is the best global model over the target area, with the RMS differences of ±8.6 cm and 1.8 ppm in the absolute and relative senses, respectively. These results show that the accuracy of a regional gravimetric model can be augmented by the combination of a global geopotential model and local terrestrial data in mountainous areas even though the quality and resolution of the primary terrestrial data are not satisfactory to the geoid modelling procedure.

Mean kernels to improve gravimetric geoid determination based on modified Stokes's integration

Gravimetric geoid computation is often based on modified Stokes's integration, where Stokes's integral is evaluated with some stochastic or deterministic kernel modification. Accurate numerical evaluation of Stokes's integral requires the modified kernel to be integrated across the area of each discretised grid cell (mean kernel). Evaluating the modified kernel at the center of the cell (point kernel) is an approximation, which may result in larger numerical integration errors near the computation point, where the modified kernel exhibits a strongly nonlinear behavior. The present study deals with the computation of whole-of-the-cell mean values of modified kernels, exemplified here with the Featherstone–Evans–Olliver (1998) kernel modification [Featherstone, W.E., Evans, J.D., Olliver, J.G., 1998. A Meissl-modified Vaníček and Kleusberg kernel to reduce the truncation error in gravimetric geoid computations. Journal of Geodesy 72(3), 154–160]. We investigate two approaches (analytical and numerical integration), which are capable of providing accurate mean kernels. The analytical integration approach is based on kernel weighting factors which are used for the conversion of point to mean kernels. For the efficient numerical integration, Gauss–Legendre quadrature is applied. The comparison of mean kernels from both approaches shows a satisfactory mutual agreement at the level of 10 −4 and better, which is considered to be sufficient for practical geoid computation requirements. Closed-loop tests based on the EGM2008 geopotential model demonstrate that using mean instead of point kernels reduces numerical integration errors by ∼65%. The use of mean kernels is recommended in remove–compute–restore geoid determination with the Featherstone–Evans–Olliver (1998) kernel or any other kernel modification under the condition that the kernel changes rapidly across the cells in the neighborhood of the computation point.

Surface Gravity Information of Nepal and its Role in Gravimetric Geoid Determination and Refinement

This paper describes proposed first order gravity network which was almost abandoned and existing gravity database that has to be preserved and advocates about its importance in the determination of regional gravimetric geoid of the country. Since GPS is in full phase operation and adopted as an efficient and accurate method in position and height determination the paper also elaborates how all its three components can be taken into consideration.

Determination of a Gravimetric Geoid Solution for Andalusia (South Spain)

The orthometric heights can be obtained without levelling by means of the ellipsoidal and geoidal heights. For engineering purposes, these orthometric heights must be determined with high accuracy. For this reason, the determination of a high-resolution geoid is necessary. In Andalusia (South Spain) a new geopotential model (EIGEN-GL04C) has been available since the publication of a more recent regional geoid. As a consequence, these new data bring about improvements that ought to be included in a new regional geoid of Andalusia. With this aim in mind, a new gravimetric geoid determination has been carried out, in which these new data have been included. Thus, a new geoid is provided as a data grid distributed for the South Spain area from 36 to 39 degrees of latitude and –7 to –1 degrees of longitude (extending to 3 × 6 degrees), in a 120 × 240 regular grid with a mesh size of 1.5’ × 1.5’ and 28800 points in the GRS80 reference system. This calculated geoid and previous geoids are compared to the geoid undulations obtained for 262 GPS/levelling points, distributed within the study area. The new geoid shows an improvement in accuracy and reliability, fitting the geoidal heights determined for these GPS-levelling points better than any previous geoid.

Impact of the new GRACE Geopotential Model and SRTM data on the geoid modelling in Algeria

Abstract In Algeria and since 2000, two published geoid models have been produced by the Geodetic Laboratory of the National Centre of Space Techniques using different data sets and techniques. Although these results were satisfactory and internally consistent they do not have the required accuracy to be able to transform a GPS ellipsoidal height to an orthometric height. Recently, the quantity and quality of terrestrial gravity data increased slightly and, especially, several new geopotential models from the recent satellite missions (e.g., GRACE) were released. At the same time, the new high-resolution SRTM (Shuttle Radar Topography Mission) global DEM was constructed. The main purpose of this paper is to study the impact of the above new data on geoid heights in Algeria. For this reason, a new gravimetric geoid determination has been carried out including these new data. This solution was based on the land gravity data supplied by the BGI (Bureau Gravimetrique International), Digital Elevation model derived from SRTM for topographic correction and the optimal gravity field model GRACE (EIGEN-GL04C), which were combined using the remove–restore technique in connection with the Fast Fourier transformation technique. This gravimetric geoid and previous geoids existing for this study area are compared to the geoid undulations corresponding to 62 GPS/levelling points located in northern part of Algeria. The study shows that the new gravimetric geoid model agrees considerably better with GPS/levelling than any of the other local geoid models in the tested area. Its standard deviation fit with GPS/levelling data are ±27 and ±25.0 cm before and after fitting using the four-parametric model as corrector surface in minimizing the long-wavelength geoid errors and the datum inconsistencies between our height data and GPS. The new geoid model will be used in low accuracy scientific applications and in low-order levelling network densification with regard to the national levelling network coverage considered as good in the north and becomes poor in the south and west of the country. It is an important contribution to geophysics, because it can provide a constraint for density distribution, thermal state of the lithosphere and viscosity in the mantle.

The high-resolution gravimetric geoid of Morocco: MORGEO

In spite of the difficulty to obtain data for the African continent, the necessary measurements for the determination of a high-resolution geoid for Morocco have been collected. In Morocco, since the publication of most recent geoid (MGG97) a new geopotential model is available (EIGEN-CG01C, released on October 29, 2004) and a new high-resolution digital terrain model (SRTM 90M obtained from the Shuttle Radar Topography Mission), has been developed for the whole earth. Logically, these new data represent improvements that must be included in a new geoid for Morocco. For this reason, a new gravimetric geoid determination has been carried out including these new data. The method used in the computation of the geoid has been the Stokes integral in convolution form, because it is an efficient method to reach the proposal objective. The terrain correction has been applied to the gridded gravity anomalies, to obtain the corresponding reduced anomalies. The indirect effect has been also taken to account. Thus, a new geoid is provided as grid data distributed for Morocco from 27° to 37° of latitude and −14° to 0° of longitude (extending 10 × 14°), on a 401 × 561 regular grid with a mesh size of 1.5′ × 1.5′ and 224961 points in the GRS80 reference system. This calculated geoid and previous geoids existing for this study area (MGG97 and EIGEN-CG01C), are compared to the geoid undulations corresponding to 6 GPS/levelling points on Morocco. The new geoid shows an improvement in precision and reliability, fitting the geoidal heights of these GPS/levelling points with more accuracy than the other previous geoids.

A synthetic Earth Gravity Model Designed Specifically for Testing Regional Gravimetric Geoid Determination Algorithms

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 2,670 kg/m3. 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-arc-min 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 μ Gal and 3 mm, respectively, which reduces to 1 μ Gal 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 to in 3 mm with the AusSEGM geoidal heights, thus offering independent verification of theories and numerical techniques used for regional geoid modelling.