Terrestrial Gravity Anomalies Research Articles

Assessments of Gravity Data Gridding Using Various Interpolation Approaches for High-Resolution Geoid Computations

This article investigates the role of different approaches and interpolation methods in gridding terrestrial gravity anomalies. In this regard, first of all, simple and complete Bouguer anomalies are considered in gravity data gridding. In the comparison results of gridding these two Bouguer anomaly datasets, the effect of the high-frequency contribution of topographic gravitation (by means of the terrain correction) is clarified. After that, the role of the used interpolation algorithm on the resulting grid of mean gravity anomalies and hence on the geoid modeling accuracy is inspected. For this purpose, four different interpolation methods including geostatistical Kriging, nearest neighbor, inverse distance to a power (IDP), and artificial neural networks (ANNs) are applied. Here, the IDP and nearest neighbor methods represent simple-structured algorithms among the interpolation methods tested in this study. The ANN method, on the other hand, is preferred as a complex, optimization-based soft computing method that has been applied in recent years. In addition, the geostatistical Kriging method is one of the conventional methods that is mostly applied for gridding gravity data in geodesy and geophysics. The calculated gravity anomalies in grids are employed in high-resolution geoid model computations using the least squares modifications of Stokes formula with additive corrections (LSMSA) technique. The investigations are carried out using the test datasets of Auvergne, France that are provided by the International Service for the Geoid for scientific research. It is concluded that the interpolation algorithms affect the gravity gridding results and hence the geoid model determination. The ANN method does not provide superior results compared to the conventional algorithms in gravity gridding. The geoid model with 4.1 cm accuracy is computed in the test area.

Evaluating the Impact of the Recent Combined and Satellite-Only Global Geopotential Model on the Gravimetric Geoid Model

Geoid represents Earth’s surface, ocean, and gravitational field, which influence the elevations, shape, and mass distribution of the geopotential surface, a hypothetical surface that is perpendicular to the direction of gravity at every point. This geopotential surface serves as a reference for measuring elevations and is used as a fundamental reference surface for geodetic and surveying purposes. In this study, the Least Squares Modification of Stokes Formula (LSMS) with Additive Corrections (AC), also known as the KTH method, is used to generate a new gravimetric geoid model for Peninsular Malaysia. The KTH method was developed at the Royal Institute of Technology (KTH) in Stockholm-Sweden. The dataset used is the most recent global digital elevation model, Shuttle Radar Topography Mission (SRTM) 1 Arc-Second Global, generated by the National Aeronautics and Space Administration (NASA) and the National Imagery and Mapping Agency (NIMA). In addition to this elevation data, the dataset includes the Global Geopotential Model (GGM), which is composed of the XGM2016, XGM2019e, Tongji_GGMG2021S, and Tongji-Grace02k models. Furthermore, it incorporates sets of regional gravity data, including terrestrial gravity, airborne gravity, and marine gravity anomalies, all of which are derived from the Technical University of Denmark (DTU 21). The actual 45 Global Navigation Satellite System (GNSS)-levelling points data have been compared to the gravimetric geoid model developed in this study and the geoid acquired from Department of Survey and Mapping Malaysia (DSMM). According to the statistical results, NXGM2019e provides better accuracy, with the Root Mean Square Error (RMSE) geoid model errors of ±0.033 m, compared to the deviations in free-air anomalies, XGM2019e, which has the minimum RMSE of 10.291 mGal. Meanwhile, Tongji-GMMG2021S has the maximum RMSE of 14.792 mGal. The geoid is derived from the XGM2019e model and has maximum and minimum values of 0.032 m and 0.147 m, respectively, with mean residuals of 0.089 m. In conclusion, the XGM2019e has the potential to determine a precise local geoid model for Peninsular Malaysia

Analysis of a Relative Offset between the North American and the Global Vertical Datum in Gravity Potential Space

The accurate estimation of the zero-height geopotential level in a local vertical datum (LVD) is critical for linking traditional height reference systems to a global height system. In this paper, we investigate the theoretical and practical challenges involved in determining the offset between the North American vertical datum (NAVD) and the global vertical datum (GVD). Drawing on the classical theory of the vertical system in physical geodesy, we define the vertical datum offset and derive rigorous formulas for its calculation. We examine various factors that affect the determination of the offset, including the global gravitational models (GGMs), geodetic reference system, tide system, tilt error, and omission error. Using terrestrial gravity data and gravity anomalies from multiple GGMs in conjunction with Global Navigation Satellite System (GNSS) and orthometric heights, we estimate the vertical offset between the NAVD and GVD. Our results indicate that the geopotential difference approach and the geodetic boundary value problem (GBVP) approach yield consistent results. When the normal gravity geopotential of the geodetic reference system is selected as the gravity geopotential of the global height datum, the NAVD is approximately 0.04 m higher than the GVD relative to the GRS80 ellipsoid, and 0.97 cm higher than the GVD relative to the WGS84 ellipsoid. When the Gauss–Listing geopotential value is chosen as the gravity geopotential of the global height datum, the NAVD is roughly 1.45 m higher than the GVD relative to the GRS80 ellipsoid, and approximately 0.52 m higher than the GVD relative to the WGS84 ellipsoid.

Resolution enhancement of airborne gravity data based on remove–compute–restore scheme (RCR) and downward continuation (DWC) technique

SUMMARY This study aims to present a strategy to enhance the short wavelengths of airborne gravity signal, which attenuate due to the altitude and low-pass filtering based on remove–compute–restore (RCR) scheme and downward continuation (DWC) technique using fast Fourier transform (FFT). The airborne gravity data are measured at an altitude 1 km above the geoid using a GT-1A gravimeter. The enhancement strategy was applied in four cases. In case 1, the original airborne gravity anomaly was downward continued from 1 km to terrain level directly without applying the RCR scheme. In case 2, the XGM2019_2190 was removed from the original airborne gravity anomaly at flight level and back substituted at terrain level after applying the DWC technique. In case 3, the residual terrain model (RTM) was used instead of the XGM2019_2190 model, following the same sequence. Finally, in case 4, both regional and terrain signals were used in the same manner as applied in cases 2 and 3. The downward continued gravity anomalies were compared to the terrestrial gravity anomalies. The statistical results show that the most significant improvement was related to cases 3 and 4 in terms of the mean difference, which reveals 0.48 and 0.36 mGal, respectively. In conclusion, removing the terrain signal before applying the DWC process and back substituting it at terrain level plays a significant role in improving the resolution of the gravity signal-based airborne approach.

Application of the nonlinear optimisation in regional gravity field modelling using spherical radial base functions

The gravity field is a signature of the mass distribution and interior structure of the Earth, in addition to all its geodetic applications especially geoid determination and vertical datum unification. Determination of a regional gravity field model is an important subject and needs to be investigated and developed. Here, the spherical radial basis functions (SBFs) are applied in two scenarios for this purpose: interpolating the gravity anomalies and solving the fundamental equation of physical geodesy for geoid or disturbing potential determination, which has the possibility of being verified by the Global Navigation Satellite Systems (GNSS)/levelling data. Proper selections of the number of SBFs and optimal location of the applied SBFs are important factors to increase the accuracy of estimation. In this study, the gravity anomaly interpolation based on the SBFs is performed by Gauss-Newton optimisation with truncated singular value decomposition, and a Quasi-Newton method based on line search to solve the minimisation problems with a small number of iterations is developed. In order to solve the fundamental equation of physical geodesy by the SBFs, the truncated Newton optimisation is applied as the Hessian matrix of the objective function is not always positive definite. These two scenarios are applied on the terrestrial free-air gravity anomalies over the topographically rough area of Auvergne. The obtained accuracy for the interpolated gravity anomaly model is 1.7 mGal with the number of point-masses about 30% of the number of observations, and 1.5 mGal in the second scenario where the number of used kernels is also 30%. These accuracies are root mean square errors (RMSE) of the differences between predicted and observed gravity anomalies at check points. Moreover, utilising the optimal constructed model from the second scenario, the RMSE of 9 cm is achieved for the differences between the gravimetric height anomalies derived from the model and the geometric height anomalies from GNSS/levelling points.

Comparison of Gravity Anomalies from Recent Global Geopotential Models with Terrestrial Gravity and Airborne Gravity over Johor Region

Gravity anomalies can yield an indirect but extremely useful picture of lateral changes in rock composition and structural patterns especially for rapid development area such as Johor region. The gravity anomalies can be derived from Global Geopotential Model (GGM) which is one of special product from the satellite technology that able to determine high accuracy of the earth’s gravity field. In this study, the gravity anomalies derived from recent GGM published by International Global Geopotential Model were compared with five other GGMs model that compromised either terrestrial or airborne or both to derive the gravity anomalies. In order to identify the best gravity model over the Johor region, two types of GGM class model has been selected for the comparisons which known as satellite only and combined class model. The result shows that the gravity anomalies de-rived from satellite only class model with up 300 spherical harmonic coefficients is the best fit model and can be used as a reference for the Johor region. The RSME for the recent GGM via satellite only were +/- 5.865 and +/- 3.347 mGal for terrestrial and airborne gravity anomalies respectively compared to other GGM.

An assessment of spatial methods for merging terrestrial with GGM-derived gravity anomaly data

The practice of merging terrestrial gravity anomalies with Global Geopotential Model (GGM) derived quantities has become popular in geodetic applications. That notwithstanding, GGM-derived gravity anomalies are mostly not consistent with their terrestrial counterparts. This study presents a method for reducing the inconsistencies between both datasets by the application of atmospheric correction, omission and commission errors to GGM-derived data. Furthermore, the study offers a comparison of the padding, kriging and least-squares collocation (LSC) methods for merging terrestrial and GGM-derived gravity anomalies. The three models were assessed by Leave Out (LO) validation method using 15 terrestrial data points that are well distributed across the study area (Nigeria). Three GGM's (EGM96, EGM2008 and SPW 5) were evaluated, and EGM2008 was selected as being optimal within the study area. The EGM2008-derived data were then merged with 1800 terrestrial FA anomaly data covering the area. Results obtained indicate the relevance of applying the atmospheric correction, omission error and commission errors to GGM-derived data before merging them with terrestrial data. Within the test region, the omission error had the largest contribution to the GGM-data inconsistency with values ranging from −72.18 to 43.98mgals. Also, the LSC technique produced the best result for the data merging with a standard deviation of residuals of ±5.77mgals, followed by the padding method with a standard deviation of residuals of ±6.35mgals.

Refinement of Bouguer anomalies derived from the EGM2008 model, impact on gravimetric signatures in mountainous region: Case of Cameroon Volcanic Line, Central Africa

Global geopotential models have not included the very high frequencies of the Earth’s external gravity field. This is called omission error. This omission error becomes more important in mountainous areas (areas with highly variable topography). The work reported here consists in reducing the omission error in measurements of Bouguer gravity anomalies, by refining the global geopotential model EGM2008 using the spectral enhancement method. This method consists in computing the residual terrain effects and then coupling them to the gravimetric signal of the global geopotential model. To compute the residual terrain effects, we used the Residual Terrain Model (RTM) technique. To refine it required a reference surface (ETOPO1) developed up to degree 2190 (the maximum degree of the EGM2008 model) and a detailed elevation model (AW3D30). Computation was performed with the TC program of the GRAVSOFT package. The topography of the study area was assumed to have a constant density of 2670 kg/m3. For the inner and outer zones, the respective integration radii of 10 km and 200 km have been chosen. We obtained very important RTM values ranging from −53.59 to 34.79 mGal. These values were added to the gravity anomalies grid of the EGM2008 model to improve accuracy at high frequencies. On a part of the Cameroon Volcanic Line and its surroundings (mountainous area), we made a comparison between the residual Bouguer anomalies before and after refinement. We report differences ranging from −37.40 to 26.40 mGal. We conclude that the impact of omission error on gravimetric signatures is observed especially in areas with high variable topography, such as on the Cameroon Volcanic Line and around the localities of Takamanda, Essu, Dumbo, and Ngambe. This finding illustrates the great influence that topography has on accurate measurement of these gravity anomalies, and thus why topography must be taken into account. We can conclude that in preparing a global geopotential model, a high resolution DTM must be used to decrease the omission error: the degree of expansion has to increase in order to take the higher frequencies into account. The refined Bouguer anomalies grid presented here can be used in addition to terrestrial gravity anomalies in the study area, especially in mountainous areas where gravimetric data are very sparse or non-existent.

Coastal gravity field refinement by combining airborne and ground-based data

Gravity field modelling in coastal region faces challenges due to the degradation of the quality of altimeter data and poor coverage of gravimetric measurements. Airborne gravimetry can provide seamless measurements both onshore and offshore with uniform accuracies, which may alleviate the coastal zone problem. We study the role of airborne data for gravity field recovery in a coastal region and the possibility to validate coastal gravity field model against recent altimetry data (CryoSat-2, Jason-1, and SARAL/Altika). Moreover, we combine airborne and ground-based gravity data for regional refinement and quantify and validate the contribution introduced by airborne data. Numerical experiments in the Gippsland Basin over the south-eastern coast of Australia show that the effects introduced by airborne gravity data appear as small-scale patterns on the centimetre scale in terms of quasi-geoid heights. Numerical results demonstrate that the combination of airborne data improves the coastal gravity field, and the recent altimetry data can be potentially used to validate the high-frequency signals introduced by airborne data. The validation against recent altimetry data demonstrates that the combination of airborne measurements improves the coastal quasi-geoid, by ~ 5 mm, compared with a model computed from terrestrial and altimetry-derived gravity anomalies alone. These results show that the recently released altimetry data with relatively denser spatial resolutions and higher accuracies than older altimeter data may be beneficial for gravity field model assessment in coastal areas.

The 5 mm geoid model for Estonia computed by the least squares modified Stokes’s formula

Computational stages of a new high-resolution 5 mm quasigeoid model for Estonia are explained. Certain requirements for the quality and coverage of gravity data in the context of 5 mm geoid modelling were fulfilled. The present gravity data coverage over the target area is 1 point per 10 km2, less dense in adjacent land and marine areas. The average uncertainty estimate of gravity data within the target area is about 0.5 … 0.75 mGal. The gravity data were merged, cleaned, analysed, reduced and gridded to yield a seamless gravity anomaly field. A least squares modified Stokes formula (Sjöberg, L.E., 1991. Refined Least Squares Modification of Stokes Formula”. Manuscripta Geodaetica, 16, 367–375.) that combines local terrestrial gravity anomalies and the global geopotential model derived long-wavelength component in a truncated Stokes’s integral yielded the best gravimetric geoid modelling results. The combined uncertainty for most of the Estonian GNSS-levelling points is not exceeding 5 mm, allowing an adequate verification of the geoid modelling quality. Inter-comparison of the geoid model, GNSS-derived and spirit-levelled heights at discrete points was conducted for geoid modelling assessment. A two stage stochastic spatial prediction was applied to obtain an optimal fit between precise GNSS-levelling data and the geoid model. The location-specific post-fitting uncertainties of the resulting model EST-GEOID2017 revealed standard deviation of 4.2 mm, i.e. the same level as the accuracy of the used GNSS-levelling control points.

Application of Radial Basis Functions for Height Datum Unification

Local gravity field modelling demands high-quality gravity data as well as an appropriate mathematical model. Particularly in coastal areas, there may be different types of gravity observations available, for instance, terrestrial, aerial, marine gravity, and satellite altimetry data. Thus, it is important to develop a proper tool to merge the different data types for local gravity field modelling and determination of the geoid. In this study, radial basis functions, as a commonly useful tool for gravity data integration, are employed to model the gravity potential field of the southern part of Iran using terrestrial gravity anomalies, gravity anomalies derived from re-tracked satellite altimetry, marine gravity anomalies, and gravity anomalies synthesized from an Earth gravity model. Reference GNSS/levelling (geometric) geoidal heights are used to evaluate the accuracy of the estimated local gravity field model. The gravimetric geoidal heights are in acceptable agreement with the geometric ones in terms of the standard deviation and the mean value which are 4.1 and 12 cm, respectively. Besides, the reference benchmark of the national first-order levelling network of Iran is located in the study area. The derived gravity model was used to compute the gravity potential difference at this point and then transformed into a height difference which results in the value of the shift of this benchmark with respect to the geoid. The estimated shift shows a good agreement with previously published studies.

Towards the Selection of an Optimal Global Geopotential Model for the Computation of the Long-Wavelength Contribution: A Case Study of Ghana

The selection of a global geopotential model (GGM) for modeling the long-wavelength for geoid computation is imperative not only because of the plethora of GGMs available but more importantly because it influences the accuracy of a geoid model. In this study, we propose using the Gaussian averaging function for selecting an optimal GGM and degree and order (d/o) for the remove-compute-restore technique as a replacement for the direct comparison of terrestrial gravity anomalies and GGM anomalies, because ground data and GGM have different frequencies. Overall, EGM2008 performed better than all the tested GGMs and at an optimal d/o of 222. We verified the results by computing geoid models using Heck and Grüninger’s modification and validated them against GPS/trigonometric data. The results of the validation were consistent with those of the averaging process with EGM2008 giving the smallest standard deviation of 0.457 m at d/o 222, resulting in an 8% improvement over the previous geoid model. In addition, this geoid model, the Ghanaian Gravimetric Geoid 2017 (GGG 2017) may be used to replace second-order class II leveling, with an expected error of 6.8 mm/km for baselines ranging from 20 to 225 km.

LOCAL EVALUATION OF EARTH GRAVITATIONAL MODELS, CASE STUDY: IRAN

Global gravity models are being developed according to new data sets available from satellite gravity missions and terrestrial/marine gravity data which are provided by different countries. Some countries do not provide all their available data and the global gravity models have many vague computational methods. Therefore, the models need to be evaluated locally before using. It is generally understood that the accuracy of global gravity models is enough for local (civil, mining, construction, etc.) projects, however, our results in Iran show that the differences between synthesized values and observation data reach up to ∼300 mGal for gravity anomalies and ∼2 m for geoid heights. Even by applying the residual topographical correction to synthetized gravity anomalies, the differences are still notable. The accuracy of global gravity models for predicting marine gravity anomalies is also investigated in Persian Gulf and the results show differences of ∼140 mGal in coastal areas. The results of evaluating selected global gravity models in Iran indicate that the EIGEN-6C4 achieves the lowest RMS for estimating the geoid heights. EGM08 predicts the closest results to terrestrial gravity anomalies. DIR-R5 GOCE satellite-only model estimates the low-frequency part of gravity field more accurately. The best prediction of marine gravity anomalies is also achieved by EGM08.

EVALUATION OF RECENT GLOBAL GEOPOTENTIAL MODELS BY GNSS/LEVELLING DATA: INTERNAL AEGEAN REGION

Global geopotential models of spherical harmonic coefficients are used to determine the external gravitational field of the Earth. These coefficients are derived from satellite orbit perturbations, terrestrial gravity anomalies and altimeter data. Hundreds of thousands of coefficients and standard deviation values for these coefficients are estimated from millions of observation. Measurement amount, homogenous distribution of the measurements of global scale, different measurement types reflecting the different frequencies of the gravity signal and measuring-assessment techniques affect the model accuracy directly. Starting from 1960’s and lasts to the present day and also gaining new acceleration with the satellite gravity field missions, every outcome of the studies related to the determination of the global Geopotential model is experienced by a series of validation tests. Accuracy of the model can either be determined from the estimated error degree variances concerning the coefficients (interior validation) or comparison of geoid heights, gravity anomalies, gravity disturbances and components of vertical deflection calculated from the model with terrestrial measurements directly (outer validation). In this paper, recent global geopotential models are primarily explained. Global geopotential models are compared with GNSS/levelling data of the study area. The objective of this comparison is to determine the best fit global geopotential model which will contribute to the study of Turkish geoid determination.

Geoid determination for the area of Poland by the least squares modification of Stokes_s formula

Previous geoid/quasigeoid models calculated for the area of Poland were based on the traditional “remove-compute-restore” procedure. One of the modifications of this method is the least squares modification of Stokes’ formula with additive corrections method (LSMSA), which was developed at the Royal Institute of Technology (KTH) in Stockholm in Sweden. The modified Stokes integral combines the regional terrestrial gravity data with a global geopotential model (GGM) giving the approximate geoid heights. To obtain the gravimetric geoid, four additive corrections, topographic, downward continuation, atmospheric and ellipsoidal, are calculated and applied. This paper presents the results of computation of a new gravimetric geoid model for Poland using the KTH method. In computations terrestrial gravity anomalies derived from nine different gravimetric data sets, global geopotential model EGM2008 and global elevation data SRTM v. 4.1 were used. The determined gravimetric geoid model was evaluated with GPS/levelling points of the Polish ASG-EUPOS network. After fitting the geoid model to the GPS/levelling data using a 7-parameter model, the standard deviation of differences was estimated to 2 cm. ARTICLE INFO

Comparison of GGMs based on one year GOCE observations with the EGM08 and terrestrial data over the area of Sudan

Since 2010, a series of Global Geopotential Models (GGMs) based on Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) satellite gravimetry mission have been released. In this study, the GGMs based on approximately 12 months of GOCE satellite gravity gradiometry (SGG) data have been compared over the area of Sudan with the EGM08 and terrestrial data. Geoid heights and free-air gravity anomalies from four GOCE/GRACE satellite-only GGMs, and one GOCE/GRACE GGM combined with terrestrial/altimetric gravity data were compared with the corresponding ones obtained from the EGM08, terrestrial free-air gravity anomalies and GNSS/levelling data.The results reveal that geoid heights and free-air gravity anomalies obtained from the GOCE-based GGMs agree with the corresponding ones from the EGM08 truncated to d/o 200 with standard deviation of 18–20cm, and 3.4–4.2mGal, respectively. Their agreement with the terrestrial free-air gravity anomalies and the GNSS/levelling geoid heights, in terms of standard deviation is about 5.5mGal, and about 50cm, respectively.

Height unification using GOCE

AbstractWith the gravity field and steady-state ocean circulation explorer (GOCE) (preferably combined with the gravity field and climate experiment (GRACE)) a new generation of geoid models will become available for use in height determination. These models will be globally consistent, accurate (<3 cm) and with a spatial resolution up to degree and order 200, when expressed in terms of a spherical harmonic expansion. GOCE is a mission of the European Space Agency (ESA). It is the first satellite equipped with a gravitational gradiometer, in the case of GOCE it measures the gradient components Vxx , Vyy, Vzzand Vxz. The GOCE gravitational sensor system comprises also a geodetic global positioning system (GPS)-receiver, three star sensors and ion-thrusters for drag compensation in flight direction. GOCE was launched in March 2009 and will fly till the end of 2013. Several gravity models have been derived from its data, their maximum degree is typically between 240 and 250. In summer 2012 a first re-processing of all level-1b data took place. One of the science objectives of GOCE is the unification of height systems. The existing height offsets among the datum zones can be determined by least-squares adjustment. This requires several precise geodetic reference points available in each height datum zone, physical heights from spirit levelling (plus gravimetry), the GOCE geoid and, in addition, short wavelength geoid refinement from terrestrial gravity anomalies. GOCE allows for important simplifications of the functional and stochastic part of the adjustment model. The future trend will be the direct determination of physical heights (orthometric as well as normal) from precise global navigation satellite system (GNSS)-positioning in combination with a next generation combined satellite-terrestrial high-resolution geoid model.

Compilation of the regional quasigeoid model for New Zealand using the discretised integral-equation approach

AbstractWe evaluate the new regional quasigeoid model (OTG12) for New Zealand using the method which utilises the discretised integral equation approach for computing the near-zone contribution. The far-zone contribution is computed by modified spherical harmonics of the geopotential. Adopting the remove-compute-restore computation scheme, the near- and far-zone contributions are computed for the residual height anomalies, while the reference height anomalies are evaluated using a global gravitational model. For the numerical realisation, the GOCO-02S coefficients complete to degree 55 of spherical harmonics are used to generate the reference gravity field. The 1×1 arc-min grid data of terrestrial gravity anomalies are used to compute the near-zone contribution. The far-zone contribution is evaluated using the EGM2008 coefficients at the frequency bound between degrees 56 and 2160 of spherical harmonics. The newly-adjusted levelling data are used to validate the available regional geoid/quasigeoid models. The accuracy assessment of gravimetric solutions at GNSS-levelling testing network reveals that the accuracy of OTG12 is compatible with the existing regional geoid/quasigeoid models; the standard deviation (STD) of residuals between the geometric and gravimetric height anomalies is 13 cm (after applying the 3-parameter correction model).

Quality assessment for terrestrial gravity anomalies by variance component estimation using GOCE gradiometric data and Earth’s gravity models

The satellite gravity gradiometry (SGG) data of the recent European satellite mission, the Gravity field and steady-state Ocean Circulation Explorer (GOCE), can be used as an external source for quality description of terrestrial gravity anomalies and the Earth’s gravity models (EGMs). In this study integral estimators are provided and modified in a least-squares sense to regenerate the SGG data of GOCE from terrestrial gravity anomalies and an existing EGM. Based on the differences between the generated and real GOCE SGG data, condition adjustment models are constructed and variance component estimation (VCE) is applied for balancing the a priori errors of data with these differences. Here, a 1-month orbit of GOCE is considered over Iran and the condition adjustment models and VCE process are used to calibrate the errors of the GOCE data, terrestrial gravity anomalies of the area and the EGM. Numerical studies over Iran show that the a priori errors of the GOCE data and the EGM were properly presented. Also the average error of the terrestrial gravity anomalies, with a resolution of 0.5° × 0.5°, after condition adjustment and VCE process using Tzz, Tx, Tyz and −Txx −Tyy is about 30 mGal.

A strategy towards an EGM08-based Fennoscandian geoid model

Today, the recent global Earth's gravity model, EGM08, is successfully utilised for different purposes in geosciences. Here, EGM08 is used to compute a geoid model for Fennoscandia and since it is restricted to degree and order 2160, the higher frequencies of the geoid, or the truncation bias, is recovered directly from terrestrial gravity anomalies using a simple formula. The total topographic and atmospheric effects are computed and added to the derived geoid as well. A very simple EGM08-based non-integral geoid estimator is developed and applied for computing the geoid of Fennoscandia. The outcome of the estimator is compared with the Global Positioning System (GPS)/levelling data of Sweden, Denmark, Finland and Norway. Numerical results show the successful performance of the presented estimator as the geoid become closer to GPS/levelling data than the one computed solely with EGM08. This study will show that considering the truncation bias of EGM08 will reduce the root mean square error (RMSE) of the differences between the geoid and GPS/levelling data by about 1.3 cm and the additive topographic and atmospheric corrections by 1 cm further. It is shown that the correlations among the data have no significant influence on the estimated geoid.