Gravity Data Coverage Research Articles

Validation of a tailored gravity field model for precise quasigeoid modelling over selected sites in Cameroon and South Africa

Abstract In this study, a tailored gravity-field model is developed to fit and recover local terrestrial gravity data by integrating gravity from global gravity-field models, residual gravity derived from topographic data and observed terrestrial gravity over two study sites in Africa (Cameroon and South Africa). During the modelling phase, two-thirds of the terrestrial gravity data is utilised, reserving the remaining one-third for validation purposes. Additionally, an independent validation is conducted by comparing computed quasigeoid models (derived from tailored gravity data) with height anomalies from GPS/levelling data over the two study sites. The accuracy of the tailored gravity model in reproducing observed gravity data is noteworthy, with a ±8.9 mGal accuracy for the study site in South Africa at 2867 test points and a ±10.4 mGal accuracy for the study site in Cameroon at 637 test points. Comparing height anomalies from GPS/levelling with the SATGQG quasigeoid model (developed from tailored gravity data) and the recent CDSM09A quasigeoid model at 11 GPS/levelling data points reveals comparable accuracies of ±0.10 m and ±0.05 m, for SATGQG and CDSM09A, respectively for the site in South Africa. For the Cameroon site, the differences between height anomalies from GPS/levelling and the CTGQG quasigeoid model (developed from tailored gravity data), along with the recent CGM20 quasigeoid model at 38 GPS/levelling data points, show practically equal accuracies of ±0.15 m for CTGQG and ±0.11 m for CGM20. These findings underscore the potential of tailored gravity-field model in developing accurate quasigeoid models, particularly in regions with limited gravity data coverage. This approach holds promise for gravity recovery and precise geoid modelling in developing countries and regions with insufficient coverage of terrestrial gravity data.

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.

The seismically active Andean and Central American margins: Can satellite gravity map lithospheric structures?

The spatial resolution and quality of geopotential models (EGM2008, EIGEN-5C, ITG-GRACE03s, and GOCO-01s) have been assessed as applied to lithospheric structure of the Andean and Central American subduction zones. For the validation, we compared the geopotential models with existing terrestrial gravity data and density models as constrained by seismic and geological data. The quality and resolution of the downward continued geopotential models in the Andes and Central America decrease with increasing topography and depend on the availability of terrestrial gravity data. High resolution of downward continued gravity data has been obtained over the Southern Andes where elevations are lower than 3000m and sufficient terrestrial gravity data are available. The resolution decreases with an increase in elevation over the north Chilean Andes and Central America. The low resolution in Central America is mainly attributed to limited surface gravity data coverage of the region.To determine the minimum spatial dimension of a causative body that could be resolved using gravity gradient data, a synthetic gravity gradient response of a spherical anomalous mass has been computed at GOCE orbit height (254.9km). It is shown that the minimum diameter of such a structure with density contrast of 240kgm−3 should be at least ∼45km to generate signal detectable at orbit height. The batholithic structure in Northern Chile, which is assumed to be associated with plate coupling and asperity generation, is about 60–120km wide and could be traceable in GOCE data. Short wavelength anomalous structures are more pronounced in the components of the gravity gradient tensor and invariants than in the gravity field.As the ultimate objective of this study is to understand the state of stress along plate interface, the geometry of the density model, as constrained by combined gravity models and seismic data, has been used to develop dynamic model of the Andean margin. The results show that the stress regime in the fore-arc (high and low) tends to follow the trend of the earthquake distributions.

Combining EGM2008 and SRTM/DTM2006.0 residual terrain model data to improve quasigeoid computations in mountainous areas devoid of gravity data

A global geopotential model, like EGM2008, is not capable of representing the high-frequency components of Earth’s gravity field. This is known as the omission error. In mountainous terrain, omission errors in EGM2008, even when expanded to degree 2,190, may reach amplitudes of 10 cm and more for height anomalies. The present paper proposes the utilisation of high-resolution residual terrain model (RTM) data for computing estimates of the omission error in rugged terrain. RTM elevations may be constructed as the difference between the SRTM (Shuttle Radar Topography Mission) elevation model and the DTM2006.0 spherical harmonic topographic expansion. Numerical tests, carried out in the German Alps with a precise gravimetric quasigeoid model (GCG05) and GPS/levelling data as references, demonstrate that RTM-based omission error estimates improve EGM2008 height anomaly differences by 10 cm in many cases. The comparisons of EGM2008-only height anomalies and the GCG05 model showed 3.7 cm standard deviation after a bias-fit. Applying RTM omission error estimates to EGM2008 reduces the standard deviation to 1.9 cm which equates to a significant improvement rate of 47%. Using GPS/levelling data strongly corroborates these findings with an improvement rate of 49%. The proposed RTM approach may be of practical value to improve quasigeoid determination in mountainous areas without sufficient regional gravity data coverage, e.g., in parts of Asia, South America or Africa. As a further application, RTM omission error estimates will allow refined validation of global gravity field models like EGM2008 from GPS/levelling data.

An optimum way to determine a precise gravimetric geoid model based on the least-squares modification of Stokes’ formula — A case study of Sweden

The modification of Stokes’ formula allows the user to compensate the lack of a global coverage of gravity data by a combination of terrestrial gravity and a global geopotential model. The minimization of the errors of truncation gravity data and potential coefficients could be treated in a least-squares sense as is the basic ingredient in the Royal Institute of Technology (KTH) approach as proposed by Sjöberg in 1984. This article presents the results from a joint project between KTH and the National Land Survey of Sweden, whose main purpose is to evaluate the KTH approach numerically and to compute a gravimetric geoid model for Sweden. The new geoid model (KTH06) was computed based on the least-squares modification of Stokes’ formula, the GRACE global geopotential model, a high-resolution digital terrain model and the NKG gravity anomaly database. The KTH06 was fitted to 1162 GPS/levelling points by a 7-parameter transformation, yielding an all-over fit of 19 mm and 0.17 ppm. The fit is even smaller than the estimated internal accuracy for the geoid model (28 mm). If we assume that the accuracy of the GPS and levelling heights are 10 mm and 5 mm, respectively, it follows that the accuracy of the expected gravimetric geoid heights are of the order of 11 mm. Also, we found a significant expected difference between the KTH06 and NKG2004 models in rough topographic areas (up to 36 cm). As the major ground data and global geopotential model were almost same in the two models, we believe that there are different reasons that come into play for interpreting the discrepancies between them, as the method for eliminating outliers from the gravity database, the interpolated denser gravity observations using the high-resolution digital elevation model before Stokes’ integration, the potential of the LSM kernel, which matches the errors of the terrestrial gravity data, GGM and the truncation error in an optimum way, and the effect of applying more precise correction terms in the KTH approach compared to the remove-compute-restore method. It is concluded that the least-squares modification method with additive corrections is a very promising alternative for geoid computation.

Asthenospheric imprints on the lithosphere in Central Mongolia and Southern Siberia from a joint inversion of gravity and seismology (MOBAL experiment)

We present a joint inversion of gravity and teleseismic data to enlighten the lithospheric structures of the Baikal–Mongolia region, an area characterized by high topographic contrasts, sporadic Cenozoic volcanism, extension and large transcurrent faulting in the vicinity of the Baikal Rift, Central Asia. The study uses a 1000 km long seismic transect that cross-cuts the main tectonic structures from north to south (namely, the Siberian platform, Tunka basin, Hangay Dome and Gobi-Altai belt). The Siberian platform depicts a high-velocity lithosphere down to about 150 km. We evidence strong velocity contrasts within the crust below the Hangay Dome and the Tunka depression, interpreted as a thickened crust. A low-velocity/density region is located at various depths below the Hangay Dome. Thanks to the dense spatial coverage of gravity data, we are able to define the 3-D geometry of this particular low-velocity/density anomaly. The Hangay Dome anomalous body extends from 60 to 225 km depth at his largest point and slightly thins to no more than 40 km at its easternmost end. A deep low-velocity zone (below 150 km) with only a weak negative density contrast is observed on the eastern part of the transect. We propose that the late Cenozoic uplift of the whole Mongolian Plateau and associated rifting, magmatism, high heat flow and lithospheric thinning are not externally driven by the India–Asia collision, but results from the interaction of two mantle plumes with the overlying lithosphere. Conversely, recent faulting may be the major expression of the India–Asia collision in this region, as well as N–S striking rift basins that connect and interact with major strike-slip faults, such as the Bolnai fault. The comparison between time residuals of this experiment and the Baikal Rift seismic data shows an undeniable disproportion for the Hangay anomaly. The Hangay time residuals are far more positive than through the Baikal, arguing for an asthenospheric signature that is not seen beneath the Baikal Rift. Furthermore, the southern edge of the thick Siberian cratonic lithosphere may favour the rise of a sublithospheric mantle flow at the contact with the Baikal–Mongolia lithosphere.

Gravity Anomalies from Retracked ERS and Geosat Altimetry over the Great Lakes: Accuracy Assessment and Problems

Lake waters are a useful area for investigating the response of the Earth's gravity field to topographical density variations, since lake beds represent large density contrasts between water and rock. However, our ability to investigate relations between lake bathymetry and gravity field effects is limited because of relatively sparse gravity data coverage over most lake surfaces, and the inability of satellite-derived gravity fields to capture the high frequency response to density effects. Satellite altimetry may provide an alternate method to determine a dense gravity field at surfaces of large inland lakes. We calculate satellite altimetry derived free-air (FA) anomalies over the Great Lakes in Canada, and evaluate them in terms of resolution and accuracy. The anomalies are compared to those calculated from the GRACE-derived EIGEN-GL04C gravity field to test for bias, and from shipborne or airborne results (where available) to test the accuracy of their determination of the high frequency component of the gravity field. Our results show that accuracies may reach less than 10 mgal, both in terms of bias and higher frequency effects, but are often tens of milligals. Furthermore, we find that altimetry does provide a higher resolution gravity field than satellite-derived gravity fields, and so if the accuracy can be improved in later efforts, it will be a useful tool for investigations of topographical density effects of lake waters.

Regional geoid determination in Antarctica utilizing airborne gravity and topography data

Antarctica is the only continent that suffers major gaps in terrestrial gravity data coverage. To overcome this problem and to close these gaps as well as to densify the global satellite gravity field solutions, the International Association of Geodesy (IAG) Commission Project 2.4 “Antarctic Geoid” was set into action. This paper reviews the current situation concerning the gravity field in Antarctica. It is shown that airborne geophysical surveys are the most promising tools to gain new gravity data in Antarctica. In this context, a number of projects to be carried out during the International Polar Year 2007/2008 will contribute to this goal. To demonstrate the feasibility of the regional geoid improvement in Antarctica, we present a case study using gravity and topography data of the southern Prince Charles Mountains, East Antarctica. During the processing, the remove–compute– restore (RCR) technique and least-squares collocation (LSC) were applied. Adding signal parts of up to 6 m to the global gravity field model that was used as a basis, the calculated regional quasigeoid reveals the dominant features of bedrock topography in that region, namely the graben structure of the Lambert glacier system. The accuracy of the improved regional quasigeoid is estimated to be at the level of 15 cm.

Une carte gravimétrique haute résolution du massif du Mont-Blanc : implications structurales

Abstract We performed a gravity survey in the Mont-Blanc and Aiguilles Rouges ranges in order to improve the gravity data coverage of the Alpine crystalline external ranges, and to constrain the deep geometry of a crustal scale thrust. Preliminary results allow us to propose a geometry for the deep structure of the ranges, taking into account a major reverse fault that bounds the Mont-Blanc range: the Mont-Blanc shear zone. To cite this article: F. Masson et al., C. R. Geoscience 334 (2002) 1011–1019.

Tidal gravity anomalies as a tool to measure rheological properties of the continental lithosphere: application to the South American Plate

Characterization of the bulk physical properties of individual tectonic units is important for understanding the dynamics of continental evolution. One important parameter is effective elastic thickness (Te), a measurement of the flexural strength of the lithosphere. Te is traditionally estimated by examination of the transfer function between gravity and topography. Sparse gravity data coverage limits the application of this method in South America. Instead, we use an empirical correlation (as defined by data from Australia and by the world databank) between tidal gravity anomalies and Te to estimate Te for tectonic units of South America. Our results are consistent with independent determinations of Te in several sub-regions of South America. Although the empirical correlation appears to be quite strong, further research needs to be done to develop a physical theory for the connection between gravity tide anomalies (which sample an essentially instantaneous rheological response of the Earth) and Te (which measures the rheological response of the Earth at geological time scales).

THE USE OF GPS DATA FOR IMPROVING LOCAL GEOID DETERMINATION

AbstractThe ellipsoidal heights of selected stations at Port Island in Japan were determined using Global Positioning System (GPS). By using geoidal height values derived both from the GPS ellipsoid heights h GPS and orthometric height of the levelling h levelling, and from gravimetry we have tested the capacity of GPS and gravimetry to derive orthometric heights at the sites to evaluate sea surface topography later. The gravimetric solution over the region covered 6241 of 0.1° × 0.1° point free-air gravity anomalies, ∆g and have been collected from the Japan Gravity Data Base, selected within the region 34.651° ≤ ϕ ≤ 34.661°, 135.212° ≤ λ ≤ 135.227°, where sufficient data existed to evaluate ΔN. The poor gravity data coverage in parts of Port Island produced results of ≤ 10 p.p.m. accuracy, but they are not sufficient for high precision applications, such as sea surface topography determinations.Comparisons of the full gravimetric determinations using different geopotential models of OSU89A, OSU89B and G...

A new, high-resolution geoid for Canada and part of the U.S. by the 1D-FFT method

A new, high-resolution and high-precision geoid has been computed for the whole of Canada and part of the U.S., ranging from 35°N to about 90°N in latitude and 210°E to 320°E in longitude. The OSU91A geopotential model complete to degree and order 360 was combined with a 5′ × 5′ mean gravity anomaly grid and 1km × 1km topographical information to generate the geoid file. The remove-restore technique was adopted for the computation of terrain effects by Helmert's condensation reduction. The contribution of the local gravity data to the geoid was computed strictly by the 1D-FFT technique, which allows for the evaluation of the discrete spherical Stokes integral without any approximation, parallel by parallel. The indirect effects of up to second order were considered. The internal precision of the geoid, i.e. the contribution of the gravity data and the model coefficients noise, was also evaluated through error propagation by FFT. In a relative sense, these errors seem to agree quite well with the external errors and show clearly the weak areas of the geoid which are mostly due to insufficient gravity data coverage. Comparison of the gravimetric geoid with the GPS/levelling-derived geoidal heights of eight local GPS networks with a total of about 900 stations shows that the absolute agreement with respect to the GPS/levelling datum is generally better than 10 cm RMS and the relative agreement ranges, in most cases, from 4 to 1 ppm over short distances of about 20 to 100km, 1 to 0.5 ppm over distances of about 100 to 200 km, and 0.5 to 0.1 ppm for baselines of 200 to over 1000 km. Other existing geoids, such as UNB90, GEOID90 and GSD91, were also included in the comparison, showing that the new geoid achieves the best agreement with the GPS/levelling data.

Modelling the fine-structure of the geoid: Methods, data requirements and some results

The requirements for precise geoid models on local and regional scales have increased in recent years, primarily due to the ongoing developments in height determination by GPS on land, but also due to oceanographic requirements in using satellite altimetry for recovering dynamic sea-surface topography. Suitable methods for geoid computations from gravity data include Stokes integration, FFT methods, and least-squares collocation. Especially the FFT methods are efficient in handling large amounts of gravity data, and new variants of the methods taking earth curvature rigorously into account provide attractive methods for obtaining continental-scale, high-resolution geoid models. The accuracy of such models may be from 2–5 cm locally, to 50–100 cm on regional scales, depending on gravity data coverage, long wave-length gravity field errors, and datum problems. When approaching the cm-level geoid basic geoid definition questions (geoid or quasigeoid?) become very significant, especially in rugged areas. In the paper the geoid modelling methods and problems are reviewed, and some investigations on local data requirements for cm-level geoid prediction are presented. Some actual results are presented from Scandinavia, where a recent regional high-resolution geoid model yields apparent accuracies of 2–10 cm over GPS baselines of 50 to 2000 km.

On Derivations and Properties of Stokes' Gravity Formula

Several independent derivations of Stokes' gravity formula have been critically analysed. It is shown that a ‘revised’ Stokes formula derived by R. A. Hirvonen is not valid for gravity data given on an arbitrary surface as claimed, but only for data given on a sphere as in the original Stokes formula. This demonstration invalidates the entire foundation of Hirvonen's New Theory of Gravimetric Geodesy. In derivations based on Poisson's integral theorem a more rigorous treatment of the elimination of zeroth and first order terms of anomalous gravity has been presented. The influence of remote zones in the applications of Stokes' formula has been evaluated by numerical integration. It is shown that tremendous truncation errors occur unless the integration is extended over the entire globe. The differences in truncation error behaviour for different geographical locations are so large that data representing world-wide average behaviour may be very misleading when applied to individual locations. The lack of gravity data coverage over very large parts of the globe causes significant errors in geoidal height determinations and vertical extensions of anomalous gravity by Stokes' formula. In most cases these errors are so large as to render the results virtually meaningless. It is shown that similar drawbacks exist for the calculation of deflexions of the vertical from formulae derived as partial derivatives of the Stokes expression. Significant reduction in the truncation errors is obtained if, following A. H. Cook, a reliable third or higher order spherical harmonic reference model is used in the definition of Δg.