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Über dieses Buch

This volume includes a selection of papers presented at the IAG international symposium "Gravity, Geoid and Height Systems 2012" (GGHS2012), which was organized by IAG Commission 2 “Gravity Field” with the assistance of the International Gravity Field Service (IGFS) and GGOS Theme 1 “Unified Global Height System”. The book summarizes the latest results on gravimetry and gravity networks, global gravity field modeling and applications, future gravity field missions. It provides a detailed compilation on advances in precise local and regional high-resolution geoid modeling, the establishment and unification of vertical reference systems, contributions to gravity field and mass transport modeling as well as articles on the gravity field of planetary bodies.



Gravimetry and Gravity Networks


Towards the Establishment of New Gravity Control in Poland

The existing Polish gravity control (POGK) was established in the last few years of twentieth century (Sas-Uhrynowski et al. (A new national gravity control network—POGK97 (in Polish). Proceedings of the Institute of Geodesy and Cartography, 1999); Sas-Uhrynowski et al. (A new gravimetric control network for Poland. Reports on Geodesy, 2000)) according to the international standards (Boedecker (BGI Bull d’Inf 63:51–56, 1988)). It is based on 12 absolute gravity stations surveyed with four different types of absolute gravimeters. Relative measurements performed by various groups on nearly 350 points with the use of LaCoste & Romberg (LCR) gravimeters were linked to those 12 stations.

The development of absolute gravity survey technologies, in particular instruments for precise field absolute gravity measurements, provides an opportunity to establish a new type of gravity control consisting of stations surveyed with absolute gravimeters. The projects of the densification of the gravity control with absolute gravity measurements using the A10 gravimeter were performed in France (Duquenne et al. (Gravity measurements on the French geodetic network. Symposium of the IAG subcommission for Europe (EUREF), Vienna, 2005)) and in Germany (Falk et al. 2009). The establishment and maintenance of this kind of gravity control is much easier than the one performed with the use of relative gravity measurement technique. It also better fulfills the recent requirements of geodesy and geodynamics in terms of accuracy and efficiency of its re-survey. The two absolute gravimeters: the FG5-230 of the Warsaw University of Technology and the A10-020 of the Institute of Geodesy and Cartography, Warsaw, along with a set of LCR gravimeters are available to be used for the establishment of new gravity control in Poland planned for the years 2012–2014.

New gravity control will consist of 28 fundamental points (surveyed with the FG5 gravimeter), and 169 base points (surveyed with the A10 gravimeter). Base points include chosen existing POGK points, POLREF and EUVN stations, as well as eccentric stations of the Active Geodetic Network (ASG-EUPOS). The fundamental stations are located in thebasements of buildings, 14 of them coincide with those of the existing gravity control, while base stations are well monumented field stations. Methodology and measurement schemes for both gravimeters, as well as the technology for vertical gravity gradient determinations in the new gravity control were developed and tested. Also the way to assure proper gravity reference level with relation to ICAG (International Comparison of Absolute Gravimeters) and ECAG (European Comparison of Absolute Gravimeters) campaigns as well as local absolute gravimeter comparisons are described. As the new gravity control will be based on absolute gravity determinations, metrology plays an especially important part of the whole project. Integral part of the project are proposals of re-computation of old gravity data and their transformation to a new system (as second order network) as well as a definition of gravity system as “zero-tide” system.

J. Krynski, M. Barlik, T. Olszak, P. Dykowski

Testing the Suitability of the A10-020 Absolute Gravimeter for the Establishment of New Gravity Control in Poland

The A10 absolute gravimeter is the first fully operational equipment to perform absolute gravity determinations in field conditions. A long time series of gravity determinations with the A10-020 performed since 2008 on a monthly basis on three stations in Borowa Gora Observatory provides an invaluable data source for quality estimation of the meter and its performance. Data from regular metrological calibrations of both, linear-polarized and stabilized laser and rubidium oscillator of the A10-020 are a complementary material for the analysis of the gravimeter performance. In May 2012 a measurement campaign at nearly 15 points was conducted to test and verify the developed methodology of absolute gravity survey with the A10 for establishing a new gravity control in Poland. Measurements were performed at absolute gravity stations of current Polish gravity control and their eccentric points. The obtained results were analyzed considering different types of station monumentation. At five laboratory stations the A10-020 results were compared with the recent FG5-230 determinations. The comparison included unification of vertical gravity gradient determinations as well as metrological parameters. At all occupied stations the vertical gravity gradient had been determined with two LaCoste & Romberg gravimeters with the use of a special stand made in the Institute of Geodesy and Cartography. The importance of vertical gravity gradient determination for the establishment of the new gravity control is discussed. The experience with the A10-020, including its suitability for modernization and re-measurement of gravity control in Finland, Sweden, Norway, and Denmark proves its high efficiency and accuracy. Furthermore it allows to develop a complete methodology for the establishment of a new type of gravity control.

P. Dykowski, J. Krynski, M. Sekowski

Global Gravity Field Modeling, Assessments and Applications


GOCE Long-Wavelength Gravity Field Recovery from 1s-Sampled Kinematic Orbits Using the Acceleration Approach

The acceleration approach is an efficient and accurate tool for the estimation of the low-frequency part of GOCE (Gravity field and steady-state Ocean Circulation Explorer) gravity fields from GPS-based satellite-to-satellite tracking (SST). This approach is characterized by second-order numerical differentiation of the kinematic orbit. However, the application to GOCE-SST data, given with a 1s-sampling, showed that serious problems arise due to strong amplification of high frequency noise. In order to mitigate this problem, we developed a tailored processing strategy in a recent paper which makes use of an extended differentiation scheme acting as low-pass filter, and empirical covariance functions to account for the different precision of the components and the inter-epoch correlations caused by orbit computation and numerical differentiation. However, also a more “brute-force” strategy can be applied using the standard unextended differentiation scheme and data-weighting by error propagation of the provided orbit variance-covariance matrices (VCMs). It is shown that the direct differentiator shows a better approximation and the exploited method benefits from the stochastic information contained in the VCMs compared to the former strategy. A strong dependence on the maximum resolution, the arc-length and the method for data-weighting is observed, which requires careful selection of these parameters. By comparison with alternative GOCE hl-SST solutions we conclude that the acceleration approach is a competitive method for gravity field recovery from kinematic orbit information.

T. Reubelt, O. Baur, M. Weigelt, M. Roth, N. Sneeuw

Use of High Performance Computing for the Rigorous Estimation of Very High Degree Spherical Harmonic Gravity Field Models

The estimation of the global Earth’s gravity field parameterized as a finite spherical harmonic series is computationally demanding. The computational effort depends on the one hand on the maximal resolution of the spherical harmonic expansion and on the other hand on the number of observations which might be several millions. All global high-resolution Earth’s gravity field models currently available above degree and order 360 were computed introducing approximations, significantly reducing the numerical complexity. For example, the prerequisites for the orthogonality of the spherical harmonic base functions, leading to a block diagonal system of normal equations, are often introduced artificially by working with equally distributed data along parallels assuming constant accuracy. These methods do not allow for a complex modeling of the observation errors, or the inclusion of redundant observations. Within this contribution, we demonstrate how high-performance computers can be used for very high degree gravity field determination without introducing approximations. In addition, complex modeling of the observation errors is made possible within the algorithm to derive consistent error estimates for the spherical harmonic coefficients. Based on the high performance computing library ScaLAPACK, a gravity field solver was implemented which allows for the estimation of high degree gravity fields (e.g. degree and order 720, resulting in more than 500, 000 unknown parameters) from various data sources with the direct solution method using assembly and solution of full normal equations.

Jan Martin Brockmann, Lutz Roese-Koerner, Wolf-Dieter Schuh

Time Variable Gravity: Contributions of GOCE Satellite Data to Monthly and Bi-monthly GRACE Gravity Field Estimates

A feasibility study by Pail et al. (Can GOCE help to improve temporal gravity field estimates? In: Ouwehand L (ed) Proceedings of the 4th International GOCE User Workshop, ESA Publication SP-696, 2011b) shows that GOCE (‘Gravity field and steady-state Ocean Circulation Explorer’) satellite gravity gradiometer (SGG) data in combination with GPS derived orbit data (satellite-to-satellite tracking: SST-hl) can be used to stabilize and reduce the striping pattern of a bi-monthly GRACE (‘Gravity Recovery and Climate Experiment’) gravity field estimate. In this study several monthly (and bi-monthly) combinations of GRACE with GOCE SGG and GOCE SST-hl data on the basis of normal equations are investigated. Our aim is to assess the role of the gradients (solely) in the combination and whether already one month of GOCE observations provides sufficient data for having an impact in the combination. The estimation of clean and stable monthly GOCE SGG normal equations at high resolution ( >  d/o 150) is found to be difficult, and the SGG component, solely, does not show significant added value to monthly and bi-monthly GRACE gravity fields. Comparisons of GRACE-only and combined monthly and bi-monthly solutions show that the striping pattern can only be reduced when using both GOCE observation types (SGG, SST-hl), and mainly between d/o 45 and 60.

Moritz Rexer, Roland Pail, Thomas Fecher, Ulrich Meyer

Application of Wavelets for Along-Track Multi-resolution Analysis of GOCE SGG Data

Due to limitations of the gradiometer the GOCE satellite gravity gradients (SGG) require filtering outside the measurement bandwidth. Several methodologies have been proposed and in use within the GOCE processing centre to filter the along-track data in the frequency domain. In this study we investigate the utilization of the localization properties of wavelets in both the frequency and space domains to decompose, analyze and reconstruct the gravity field signal in the SGG data at the different levels of a Wavelet Multi-resolution Analysis (WMRA). This approach can also be used to identify and eliminate temporally and spatially correlated errors in GOCE SGG data. The WMRA is applied in both the rotation of SGGs from the gradiometer reference frame to a local north orientated frame and in the downward (upward) continuation of the SGG tensor to a mean orbital height. Results presented here show that, at the GOCE mean orbital height, the MWRA has the potential to enhance the short-wavelength gravitational signal content of the along-track GOCE data.

Rossen Grebenitcharsky, Philip Moore

Assessment of High-Resolution Global Gravity Field Models and Their Application in Quasi-geoid Modelling in Finland

The two high-resolution global gravity field models, EGM2008 and EIGEN-6C, are compared with ground truth in Finland and surrounding areas. Thereafter, the models are used as background models in the calculation of a quasi-geoid model for Finland. The differences between height anomalies calculated from the global models and from two GPS-levelling datasets for Finland show standard deviations between 5 and 7 cm. Comparisons with free-air anomalies show small and homogeneously distributed differences over most of the area. In both comparisons the largest discrepancies are found close to the Russian border east of the 29° longitude line. This is most probably due to lower resolution Russian data used in the global models. When the global models are used as background models in the calculation of a quasi-geoid model for Finland, the problems around the 29° longitude line disappear. Comparison between the final quasi-geoid models and GPS-levelling data show an improvement over earlier models for Finland.

Mirjam Bilker-Koivula

Comparison of GOCE Global Gravity Field Models to Test Fields in Southern Norway

Numerous global gravity field models (GGFMs) have resulted from the satellite gradiometry mission GOCE. Validation is indispensable to test the performance of the new-generation models. For this purpose independent datasets of terrestrial data are very often used.

In this study, homogenous datasets of free-air gravity anomalies and GNSS/leveling points have been collected in southern Norway. These datasets have been exploited for validation of four GOCE-derived GGFMs (DIR_r3, GOCO03s, TIM_r3, and DGM-1S) by the spectral enhancement method.

Numerical experiments have proven that the effect of the residual terrain model is important to free-air gravity anomalies but not to height anomalies. Validation of GOCE GGFMs has revealed that performance of these models is very similar. However, in comparison to EGM2008, we have observed 10 % increase of the standard deviation for the GOCE-derived models at d/o 210, 20 % increase at d/o 230, and up to 65 % increase at d/o 250. In addition, validation by GNSS/leveling data suggests significant improvements delivered by the GOCE GGFMs with respect to EGM2008 between d/o 100–200 in our test field.

M. Šprlák, B. R. Pettersen, O. C. D. Omang, D. I. Lysaker, M. Sekowski, P. Dykowski

Evaluation of Recent GRACE and GOCE Satellite Gravity Models and Combined Models Using GPS/Leveling and Gravity Data in China

A total of 649 GPS/Leveling points and 799897 2′ × 2′ gridded mean gravity anomalies in mainland China are used for the evaluation of the recently released Earth Gravitational Models (EGMs) including the GOCE only models (GO_CONS_GCF_2_TIM_R3 (GO_TIM_R3), GRACE only models ITG-Grace2010s, combined satellite gravity field models (GO_CONS_GCF_2_DIR_R3 (GO_DIR_R3), GOCO03S, DGM-1S, EIGEN-5S, EIGEN-6S), and combined gravity field models (EIGEN-51C, EIGEN-6C, GIF48, EGM2008) from satellite observations and ground gravity data sets. The statistical results show that in mainland China the most precise model is EIGEN-6C with the standard deviation (STD) ±0.183 m of the quasi-geoid height differences compared with the GPS/Leveling data and the STD ±22.5 mGal of the gravity anomaly differences compared with the gridded mean gravity anomalies from observations. For EGM2008, they are ±0.240 m and ±24.0 mGal respectively. Among the satellite only gravity models from GRACE, GOCE and LAGEOS observations, GO_TIM_R3 is the best one in mainland China, and the STDs of the corresponding quasi-geoid differences and the gravity anomaly differences are ±0.459 m and ±31.3 mGal respectively, which are nearly at the same levels as the ones for the models EIGEN-6S, GOCO03S and GO_DIR_R3. This shows that the GOCE mission can recover more medium-short wavelength gravity signals in mainland China than former satellite gravity missions.

Jiancheng Li, Weiping Jiang, Xiancai Zou, Xinyu Xu, Wenbin Shen

Evaluation of GOCE/GRACE Derived Global Geopotential Models over Argentina with Collocated GPS/Levelling Observations

This paper presents the results of the evaluation of recent GOCE/GRACE Global Geopotential Models (GGMs) over Argentina. Since the Gravity and steady state Ocean Circulation Explorer (GOCE) dedicated satellite gravity field mission was launched in March 2009, several global geopotential models have been computed and released. GOCE’s mission was designed to provide models of the Earth’s gravity field on a global scale with high-accuracy in the medium wavelength spectral band (maximum degree/order 200–250). Comparisons of geoid heights derived from different GGMs with GPS/Levelling derived geoid heights over Argentina have been carried out in both absolute and relative sense, to assess and validate the accuracy of GGM models over the entire country. The analysis has been carried out with actual GOCE-only, GOCE/GRACE and combined global gravity field models. In all cases, EGM2008 has been used as the baseline model, since it provides the overall best results. From the results, it was concluded that the latest Release 3 GOCE-only, TIM and SPW, GGMs provide improved accuracies by 1–4 cm compared to the Release 1 models. As far as the combined GOCE/GRACE models, GOCO and DIR, are concerned, the overall best results come from the Release 1 of the DIR model, probably due to the a-priori information from EIGEN5C used in its development. The Release 3 version of the GOCO GGMs improves the Release 1 model by 4 cm, while the same level of improvement is found between the Release 3 and Release 2 of the DIR GGMs.

C. Tocho, G. S. Vergos, M. C. Pacino

Evaluation of GOCE/GRACE Global Geopotential Models over Greece with Collocated GPS/Levelling Observations and Local Gravity Data

The advent of the GOCE and GRACE missions during the last decade have brought new insights and promising results both in the static and time-variable representation of the Earth’s gravity field. The focus of this work is directed to the evaluation of most available Global Geopotential Models (GGMs) from GOCE and GRACE, both satellite only as well as combined ones. The evaluation is carried out over an extensive network of collocated GPS/Levelling benchmarks (BMs) which covers the entire part of continental Greece and with respect to the reductions the GGMs provide in existing gravity data in order to assess their performance in a scenario that a remove-compute-restore procedure would be followed for geoid determination. From the evaluation with GPS/Levelling BMs, it was concluded that the GOCE/GRACE GGMs provide an absolute accuracy at the 12–15 cm level, up to degree and order (d/o) 250, when considering the geoid omission error. This is comparable and in some cases better than the performance of EGM2008 in Greece. Moreover, the latest (Release 3) versions of the GGMs provide considerably better results compared to the earlier version by 1–5 cm. In terms of relative errors, GOCE/GRACE GGMs reach the 1 cm level for baselines between 50 and 60 km, while for longer ones, 80–90 km, their performance is analogous to the local geoid model and the ultra-high degree combined GGMs. Finally, GOCE/GRACE GGMs manage to provide the same, as EGM2008, level of reduction to the local gravity anomalies, with a std at the 26.7–27.8 mGal level, when evaluated up to d/o 250.

G. S. Vergos, V. N. Grigoriadis, I. N. Tziavos, C. Kotsakis

Evaluation of the GOCE-Based Gravity Field Models in Turkey

The recent GOCE-based global gravity field models are tested in Turkey and in two sub-regions, the Istanbul and Sakarya territories, by means of geoid undulations. Global gravity field model computed geoid undulations are compared with different sets of GPS/leveling-derived geoid undulations for different spherical harmonic degree expansions. High frequency components of the geoid undulations are estimated from EGM2008 and are removed from the GPS/leveling-derived geoid undulations. Therefore, model-based and GPS/leveling-derived geoid undulations are reduced to about the same gravity spectral band. The comparisons between the two geoid undulations are performed directly on the same benchmark points and also between the benchmark points by means of geoid slope differences. The comparison results suggest that GOCE-based as well as GRACE and GOCE combined satellite-only models provide better agreement with GPS/leveling-derived geoid than EGM2008 by up to a few centimeters for medium wavelength gravity components. Based on the results obtained in this study, current and upcoming satellite-based gravity models are expected to improve the regional geoid, as well as the regional gravity prediction from such models. Turkey is currently discussing the options for height system modernization. The investigations performed in this study will be useful for the height modernization project of Turkey and will help the development of an accurate geoid model and improvement of the current vertical datum in the regions.

E. S. Ince, B. Erol, M. G. Sideris

A Stokesian Approach for the Comparative Analysis of Satellite Gravity Models and Terrestrial Gravity Data

A Stokesian approach is formulated to update the geoid model for a specific spherical harmonic band by spectrally combining a GOCE-based satellite global geopotential model with terrestrial gravity data. A simulation test shows that the GOCE-based model can be combined into a geoid solution with an accuracy better than 3 mm for the band between degrees 90 and 180. A comparison of the GOCE-based model GOCO03S and the Canadian terrestrial gravity data for the spherical harmonic band between degrees 90 and 180 shows that the geoid update by GOCO03S reaches 1.6 cm in RMS in the Yukon Territory, 1.8 cm in northern British Columbia, and 1.6 cm in the Maritimes. This may suggest a slight improvement of the GOCE model over the Canadian gravity data considering the standard deviation of 1.0 cm given by GOCO03S. However the analysis indicates comparable accuracy between the terrestrial gravity data and GOCE models for the rest of Canada where topography is relatively flat. The comparisons at the GPS-levelling points suggest that GOCE has improved our existing knowledge of the Earth’s gravity field for wavelength components longer than 200 km over the Yukon Territory, northern British Columbia, the Maritimes, and Newfoundland.

Jianliang Huang, Marc Véronneau

Future Gravity Field Missions


New Approach to Estimate Time Variable Gravity Fields from High-Low Satellite Tracking Data

Estimating the time-variable gravity field signal has become an important task in climate research. Different scientific communities rely on the produced time series of gravity field information to investigate for example ice melting, changes in water storage or the effects of heavy earthquakes. Today the only measurement system which can provide these gravity field solutions without any constraints is the satellite mission GRACE (Gravity Recovery and Climate Experiment). Therefore it would be of interest to prolong the current time series by another technology. A method to estimate the gravity field is based on the kinematic orbit positions of a satellite. These positions are determined using the Global Positioning System. This method is well known and is widely used as a supplement to other measurement technologies. But present orbit estimates are degraded by systematic effects which affect the long-wavelength components of the gravity field estimation. Especially these frequencies are of concern for investigating variations in the Earth’s gravity field. If these systematic effects are reduced it should be possible to generate a time series of gravity field solutions similar to those available today. To improve the orbit accuracy we introduce a new approach to estimate kinematic orbit positions based on raw observations. This contribution presents this method and first results based on real data.

N. Zehentner, T. Mayer-Gürr

Status of the GRACE Follow-On Mission

The Gravity Recovery and Climate Mission (GRACE) has been so far the only satellite mission capable of monitoring mass variations in the Earth system and has made many breakthroughs in the understanding of Earth system dynamics. The mission has been operating for over 10 years at the time of this paper. Expected end of mission is dependent on future solar activity, instrument conditions and—most likely—on the battery health. Due to the extreme success of GRACE in many Earth science disciplines there was a long-standing strong request by the user community to launch a GRACE Follow-On (GRACE-FO) mission as soon as possible to extend the GRACE mass transport time series with the minimum practical data gap between both missions. GRACE-FO has in fact been approved by the NASA and German ministries BMBF (Federal Ministry of Education and Research) and BMWi (Federal Ministry of Economics and Technology), and will be implemented under US-German partnership. GRACE-FO entered Phase-A in January 2012 and Phase-B in September 2012. The current target launch date is August 2017. This paper summarizes the status of the various mission elements.

Frank Flechtner, Phil Morton, Mike Watkins, Frank Webb

Feasibility Study of a Future Satellite Gravity Mission Using GEO-LEO Line-of-Sight Observations

In this article the feasibility of gravity field determination with very high-low satellite-to-satellite tracking, as intended as part of the GETRIS (“Geodesy and Time Reference in Space”) mission concept, is investigated. For this purpose several geostationary satellites (GEOs) are positioned around the Earth. A microwave system is used to determine the relative position between satellites in low Earth orbits (LEOs) and GEOs with very high accuracy, from which the gravity field of the Earth can be estimated.This concept is simulated to retrieve the time-variable gravity field caused by temporal changes in continental hydrology. The simulation is based on simplified assumptions, taking only errors of the ranging instrument into account. The gravity field is recovered in a closed-loop environment from the simulated observations. Furthermore, the possibility of enhancing GRACE results with GEO-LEO tracking is investigated.Overall the results show that the GEO-LEO concept is very promising, since it possibly reduces some of the weaknesses of the LEO-LEO tracking concept and measures the radial component of the Earth’s gravity field. Due to the option of multi-satellite tracking, the time-variable gravity field might be observed within shorter time periods than with a single GRACE-like mission. However, more detailed simulations are required to draw final conclusions on the exact magnitude of benefit.

Jakob Schlie, Michael Murböck, Roland Pail

Advances in Precise Local and Regional High-Resolution Geoid Modeling


GOCE Data for Local Geoid Enhancement

The GOCE gradients, having a spatially dense data distribution, may potentially provide better predictions of the regional gravity field than those obtained using a spherical harmonic Earth Geopotential Model. The aim of this study is to develop a methodology to improve the use of GOCE gradients and to determine the Earth’s gravity field with better accuracy than by using global models, which have been truncated at a specific harmonic degree and order. The method makes use of all available GOCE gradient data in addition to the global models and aims at improving the determination of Earth’s gravitational field in regional areas. Subsequently, the calculated geoid is used together with measurements of sea surface height in a calculation of the Mean Dynamic Topography.In regional geoid recovery from GOCE gradients, two methods are used, one of them being Least-Squares Collocation (LSC). The second method is developed as a part of this study, and it is based on the Reduced Point Mass (RPM) response. The results show that the RPM method and LSC method give very similar results when using the same data, i.e. the difference is insignificant when compared to the EGM2008 results. However, when all of the available GOCE gradient data are used with the RPM method, an improvement in the gravitational field determination is achieved. The enhanced geoid by the RPM method is then used for the improvement of the MDT in the North Atlantic region.

Matija Herceg, Per Knudsen, Carl Christian Tscherning

Investigation of Gravity Data Requirements for a 5 mm-Quasigeoid Model over Sweden

When GNSS height determination improves in the future, users will ask for increasingly better geoid models. It is not unlikely that a standard error of 5 mm will more or less be required in a couple of years. The main purpose of this paper is to investigate the gravity data requirements to compute a Swedish gravimetric quasigeoid model to that order. The propagation of errors in the terrestrial gravity observations and the Earth Gravitational Model (EGM) are studied using both variance-covariance analysis in the spectral domain and least squares collocation. These errors are also checked by computing a new gravimetric quasigeoid model and comparing it with GNSS/levelling height anomalies. It is concluded that it will be possible to compute a 5 mm model over Sweden in the case that the gravity data set is updated to fulfil the following requirements: the resolution should be at least 5 km and there should be no data gaps nearby. Finally, the standard errors of the uncorrelated and correlated gravity anomaly noises should be below 0.5 and 0.1 mGal, respectively.

Jonas Ågren, Lars E. Sjöberg

Consistent Combination of Satellite and Terrestrial Gravity Field Observations in Regional Geoid Modeling: A Case Study for Austria

In this investigation a consistent combination of the complementary data types of satellite observations and the available terrestrial gravity field measurements in Austria is considered. For this purpose, the well known Remove-Compute-Restore technique is adapted to perform long- and short-wavelength signal reductions. The long-wavelength effect is represented by a global satellite-only model in terms of spherical harmonics. The short-wavelength are modeled by topographic masses in the spatial domain. As the topographic reduction contains also long-wavelength effects a possible double consideration has to be avoided. Alternatively to Least Squares Collocation (LSC) method (Moritz 1980a) a least squares approach with parametrization as Radial Basis Functions (RBF) is applied. The RBF approach has the advantage that an increasing number of observations can be included in the calculations and a downsampling of the available data, as it is required in LSC, will no longer be necessary. Another advantage is that RBF is to able to handle an inhomogeneous input data distribution. The very first outcomes are verified by comparing with independent GPS/leveling observations.

Christian Pock, Torsten Mayer-Guerr, Norbert Kuehtreiber

Modelling the Influence of Terraced Landforms to the Earth’s Gravity Field

Medium resolution (1–3 arc-min) gravity anomaly grids do not reflect reality very accurately over terraced landforms, which in turn may affect the uncertainty of subsequent geoid modelling. This inaccuracy is due to many factors. The gravimetric datasets used in the gridding of gravity field models have a varying accuracy and coverage, especially in terraced and coastal areas. Further, the resolution of the terrain model used in the modelling of anomaly grids is usually too low to capture the complete gravimetric attraction of terraced landforms.

Since the values of free-air anomalies are strongly correlated with terrain heights, it is difficult to model the gridded surface over terraced landforms. Depending on the quality of existing gravity data and terrain height models, different procedures should be used. In the case of a terraced area that is densely covered by gravity data, if an accurate terrain model exists, free-air anomaly grids should be calculated on high resolution (6

× 12

) and using Bouguer anomaly values on grid nodes. If gridding is proceeded without Bouguer anomalies, triangulation based gridding methods should be preferred.

Silja Märdla, Tõnis Oja, Artu Ellmann, Harli Jürgenson

Accurate Geoid Height Differences Computation from GNSS Data and Modern Astrogeodetic Observations

This work presents the revival of the astrogeodetic observation procedure by means of modern instrumentation and processing. The determination of astronomical coordinates Φ, Λ and the components ξ and η of the deflection of the vertical is achieved with an accuracy that reaches ±0.01


The used method brings to the fore the classical geodetic astronomy actually aided by modern technology. The system of NTUA is used [Lambrou (Development of a methodology for astrogeodetic determinations, using digital geodetic instruments. Ph.D. Thesis, 2003)]. This system consists of a first order total station connected with a GNSS receiver in order to register time with 1 ms.

The same method is applied by changing the instrumentation. An advanced “imaging” total station is used, providing a direct connection to the internet, to a world time server, in order to obtain the necessary accurate time information. This total station runs windows CE and moreover it allows carrying out the observations on a digital screen, as the telescope is not deemed essential anymore. The sightings may be also carried out remotely via a PC’s screen situated anywhere and connected to the internet.

Alternatively, in order to bypass the need of accurate time information, the Laplace equation can be used. Thus the determination of η is achieved. As a limitation, this procedure requires visibility between the points.

By using the corresponding geodetic coordinates φ, λ and azimuth, which are all provided by the GNSS measurements, the deflection of the vertical components (ξ and η) are computed. Thereinafter the geoid undulation differences ΔN are calculated, with few mm accuracy.

By following this procedure, the results are independent from the definition of the local height datum. For this reason, it can improve the global geoid models as it enriches their data in areas characterized by large geoid variations due to rough topography. Finally, this procedure could be used for the unification or the definition of a unified height datum, for a country.

Evangelia Lambrou

Improving the Swedish Quasigeoid by Gravity Observations on the Ice of Lake Vänern

One of the key activities in

Geodesy 2010

, the Swedish strategic plan for geodetic activities during the period 2011–2020, is the restoration of the gravity network and data in order to improve the accuracy of the national quasigeoid model. One weak point has been that very few gravity observations have been available over Lake Vänern, Sweden’s largest lake. During the extremely cold winters 2010 and 2011, the ice became sufficiently thick to make ice observation of gravity. The main purpose of this paper is to present the 2011 ice gravity campaign, summarise the experiences made and investigate how much the new ice observations improve the computed quasigeoid model in the area. This is investigated under the assumption that a modern Earth Gravitational Model based on GRACE and GOCE is used. It is found that new ice measurements improve the quasigeoid with a RMS of about 2–3 cm in and around the lake with a maximum improvement of 7 cm.

Jonas Ågren, Lars E. Engberg, Linda Alm, Fredrik Dahlström, Andreas Engfeldt, Martin Lidberg

Geoid Model and Altitude at Mount Aconcagua Region (Argentina) from Airborne Gravity Survey

Aconcagua is part of the Southern Andes in the Argentine Province of Mendoza and it is the highest mountain in the Americas. The Aconcagua region is mostly inaccessible for land surveys. The existing gravity data are sparsely distributed, and mainly along the route currently used to climb the mountain. Gravity data are needed for applications such as geoid modeling, vertical datum determination and geological study. In 2010, a high-altitude survey (between 7,000 and 8,000 m above sea level), covering the entire area of Aconcagua was performed. This survey was done within the framework of IAG Project “Gravity and Geoid in South America”. Free Air anomalies were computed and compared to Earth Gravitational Model 2008 (EGM08), degree 2190 at the flight altitude. The residuals can be attributed to the fact that the airborne data carries a lot of new gravity information not represented in the EGM08 model. A geoid model was computed from those airborne gravity anomalies and land gravimetry data. A remove-restore method was used for terrain and global spherical harmonic reference models, with the residual gravity field signal downward continued by least-squares collocation, and the geoid and quasi-geoid computed by spherical Fourier methods. The N value at Aconcagua’s summit was combined with the ellipsoidal height observed at the summit GPS station to obtain the orthometric height above sea level, confirming the most recent triangulated summit height of 6,960 m.

M. Cristina Pacino, Eric Jäger, René Forsberg, Arne Olesen, Silvia Miranda, Luis Lenzano

HRG2009: New High Resolution Geoid Model for Croatia

Using an updated Earth´s gravity field data set widely available and applying the least square collocation calculation technique, a new Croatian geoid model HRG2009 was calculated. Significant accuracy improvements have been achieved regarding the previous national geoid model HRG2000; four times better resolution and 69 % better absolute accuracy of the model. The following data sets were used: great number of new measured terrestrial gravity data and data obtained from satellite altimetry for the area of the Adriatic Sea, along with geoid undulations at discrete points measured by GNSS/leveling on almost 500 stations all over the mainland, futhermore long and mediumwave field structures taken from the latest detailed global geopotential model EGM2008 and high frequencies field structures modeled with the help of 3


× 3


Shuttle Radar DEM’s. Absolute accuracy assessment made on 59 GNSS/leveling control stations, that were not used in calculations, have resulted with 69 % improvement of new national geoid model regarding the previous one, with standard deviation of 3. 5 cm on overall computation area. It is significantly more reliable surface as compared to the earlier HRG2000 solution with standard deviation of 11.4 cm.The new geoid surface has been used for different purposes, primary in the precise height definition using modern GNSS technology. Therefore, the Croatian Positioning System CROPOS was upgraded in 2011 with the new service which enables the real time transformation of ellipsoidal heights to the (normal) orthometric heights using HRG2009 geoid GRID and Trimble Transformation Generator software for more than 440 surveying and geoinformation companies in Croatia.

Tomislav Bašić, Olga Bjelotomić

Validation of Regional Geoid Models for Saudi Arabia Using GPS/Levelling Data and GOCE Models

To meet increased demands in mapping, surveying, geodesy, and large infrastructure projects, an accurate national geoid model for Saudi Arabia is required to transform ellipsoid heights to orthometric heights. The lack of data and the nature of the topography make the computation of a geoid model in Saudi Arabia a difficult task. Two regional geoids were developed for the Kingdom of Saudi Arabia (KSA): (1) the KSA geoid developed by the General Directorate of Survey (GDS); and (2) a geoid developed by the Ministry of Municipality and Rural Affairs (MOMRA). The KSA model was developed using a remove and restore technique and over 5,000 observations of Global Positioning System (GPS) ellipsoidal heights on leveling benchmarks (GPS/BM). The MOMRA geoid was estimated from 861GPS/Levelling with a kriging approach. A GPS/Levelling test campaign (T campaign) was carried out in 2010 by re-observing about 391 BM stations common to the two geoid models. The two geoid models are first compared against each other and EGM2008 at the 391 BM stations from the T campaign. The absolute differences between models may reach several meters, whereas the standard deviation of the differences ranges between 0.5 and 1.5 m. Analysis revealed that KSA and MOMRA geoids seem not to coincide. Both are biased (means of 0.46 m) and highly scattered (standard deviation is ±0.72 m). Next, geoid models developed using GOCE satellite data are used to validate the T campaign data.

A. Alothman, J. Bouman, T. Gruber, V. Lieb, M. Alsubaei, A. Alomar, M. Fuchs, M. Schmidt

Establishment and Unification of Vertical Reference Systems


W 0 Estimates in the Frame of the GGOS Working Group on Vertical Datum Standardisation

During the 2011 IUGG General Assembly, GGOS, the IAG Commissions 1 (Reference Frames) and 2 (Gravity Field) and the IGFS established a joint working group devoted to the

Vertical Datum Standardisation

. This working group supports the activities of GGOS Theme 1

Unified Height System;

in particular, to recommend a reliable geopotential value



to be introduced as the conventional reference level for the realisation of the GGOS Vertical Reference System. At present, the most commonly accepted



value corresponds to the best estimate available in 2004; however, this value presents discrepancies of about 2 m




with respect to recent computations based on the latest Earth’s surface and gravity field models. According to this, as a first approach, four different teams working on the computation of a global



value were brought together in order to compare methodologies and models, and to establish the reliability of the individual computations. Results of this comparison show that the four individual estimates present a maximum discrepancy of about 0.5 m




. They also confirm that the



value declared as the best estimate in 2004 corresponds to an equipotential surface located about 17 cm beneath the sea surface scanned by satellite altimetry, while the potential value



of the GRS80 ellipsoid realises an equipotential surface located about 67 cm lower. In this context, the need to provide a new better estimate of



is evident.

L. Sánchez, N. Dayoub, R. Čunderlík, Z. Minarechová, K. Mikula, V. Vatrt, M. Vojtíšková, Z. Šíma

Realization of WHS Based on the Static Gravity Field Observed by GOCE

The paper deals with a determination of



as well as testing of geoid candidates for a realization of the World Height System using the GOCO03S satellite-only geopotential model. The



values are estimated for two different altimetric mean sea surface models (DTU10_MSS and MSS_CNES_CLS2011) using four different global geopotential models (GGMs), namely GOCE-DIR2 or GOCO03S satellite-only GGMs, and EGM2008 or EIGEN-6C combined GGMs. In all cases the impact of including polar regions into the integration area is presented.

The second part studies how the high-degree combined GGMs or local gravimetric geoid models correspond to the static gravity field observed by GOCE. The nonlinear diffusion filtering is used to reduce the stripping noise of the geopotential evaluated from the GOCO03S model up to degree 250. On lands, the geopotential is evaluated at 3D positions of the local (national) gravimetric-only geoid models, namely USGG-2012 in USA, CGG-2010 in Canada, AGQG-2009 in Australia, and NZGeoid09 in New Zealand, otherwise at 3D positions of the EIGEN-6C or EGM-2008 geoid models. At oceans, the geopotential is filtered on the DTU10 mean sea surface whose 3D position is precisely provided by satellite altimetry. Apart from high mountainous areas, the smoothed geopotential on the considered geoid models shows good agreement with GOCO03S, i.e. with the low-frequency part of the gravity field precisely observed by GRACE/GOCE. At the same time the filtered satellite-only mean dynamic topography is provided specifying its relation to the geoid models at coastal areas.

Róbert Čunderlík, Zuzana Minarechová, Karol Mikula

First Results on Height System Unification in North America Using GOCE

We study the impact of GOCE on the North American height system unification by assessing different factors: the performance of the GOCE global geopotential models, the models’ omission error and its effect on the computed mean height datum offsets, and the effect of the biased local gravity data. Depending on the distribution of the data points, the omission error of the third release time-wise GOCE model used up to degree and order 180 contributes 13–15 cm to the computed mean offset of CGVD28 in Canada and only 2 cm to the mean offset of NAVD88 in the USA. The effect of the biased local gravity anomalies on the datum offsets is assessed by means of Stokes’s integration with the original and residual kernels in a regional simulation scenario. This effect is found to be negligible when GOCE geopotential models are used in the computation of the geoid heights.

M. G. Sideris, E. Rangelova, B. Amjadiparvar

Using GOCE to Straighten and Sew European Local Geoids: Preliminary Study and First Results

National geoids of neighbouring countries usually do not fit to each other along the borders. This problem is mainly due to inconsistencies between the national reference frames used to estimate local geoids: it is well known that a change in the height datum and in the reference ellipsoid causes systematic effects in terms of geoid undulation. Therefore, before merging national geoids, these effects should be estimated and removed. The availability of a global geoid coming from satellite data, such as one of the GOCE models or a GOCE-GRACE combined model, can be of great importance to solve this problem. In fact, these models are not affected by local biases since they do not make use of any ground gravity data and they are referred to a global geocentric ellipsoid. In the present work a merging strategy based on two steps is proposed. Firstly, the bias and the systematic effect due to an ellipsoidal centre variation are estimated for each national geoid by exploiting GOCE data; particular attention is dedicated to the covariance modelling of all involved quantities. Secondly, these straightened geoids are “sewn” to each other by applying a standard collocation procedure along the borders. In this way the final result is an unbiased geoid, joining in a optimal way the national models. The merging strategy is here applied to create a new geoid model for Spain, Portugal, France, Italy, Switzerland and part of the Mediterranean Sea.

M. Gilardoni, M. Reguzzoni, D. Sampietro

Combination of Geometric and Orthometric Heights in the Presence of Geoid and Quasi-geoid Models

A generalization of the well-known relationship between geometric and orthometric heights is presented in this paper. The advantage of our revised formulation is that, instead of the non-determinable true orthometric heights, it employs the (most commonly used in geodetic practice) Helmert orthometric heights. Based on standard concepts from physical geodesy theory and straightforward analytical derivations, we obtain a set of linearized constraints relating the geometric and Helmert orthometric heights in the presence of a geoid or quasi-geoid model. These constraints should be theoretically satisfied in the case of errorless data and thus they provide a standard framework for the joint analysis and the quality testing of heterogeneous heights in a terrestrial network.

C. Kotsakis, I. Tsalis

Contribution of Tide Gauges for the Determination of W0 in Canada

Canada plans to implement a geoid-based and GNSS-accessible vertical datum in 2013 in order to replace the existing Canadian Geodetic Vertical Datum of 1928, which no longer meets the needs of the modern user in terms of accuracy and accessibility. One of the primary concerns when realizing a geoid-based vertical datum is to determine the



value that will represent the potential of the zero-height surface. Thus, the objective of this study is to determine



by averaging the potential of points on the mean water surface by using Canadian tide gauge records and GOCE-based global geopotential models. The GOCE-based models are extended with the high-resolution gravity field model EGM2008 in order to assess the effect of the omission error on the computation of



. Similarly, the regional gravimetric geoid model CGG2010 is also used for the estimation of



in order to assess the effect of higher frequency contributions of the gravity field, which are missing from the GOCE-based global geopotential models. Additionally, sea surface topography models are utilized in order to validate the



results based on tide gauges and to estimate



values for North America. The



values obtained using Canadian tide gauges and high resolution gravity field and geoid models are not statistically different from the International Earth Rotation and Reference Systems Service 2010 global conventional value of 62,636,856.00 m





T. Hayden, E. Rangelova, M. G. Sideris, M. Véronneau

Estimation of the Reference Geopotential Value for the Local Vertical Datum of Continental Greece Using EGM08 and GPS/Leveling Data

Estimation of the zero-height geopotential level represented by




in a local vertical datum (LVD) is a problem of main importance for a wide range of geodetic applications related to different height frames and plays a fundamental role in the connection of traditional height reference systems into a global height system or even a modern geoid-based vertical datum. This paper aims primarily at the estimation of




for the continental part of Greece, with the use of surface gravity data and geopotential values computed from EGM08 in conjunction with GPS and orthometric heights over an extensive network which covers sufficiently the test area. The method used focuses on the estimation of




from a least squares adjustment scheme that is applied on the Helmert model for orthometric heights, using surface geopotential and gravity values (as obtained from EGM08 and the known 3D geocentric coordinates of each benchmark) along with the local Helmert heights over all network stations. Moreover, an attempt is made towards the modeling and removal of any height correlated errors in the available data according to this adjustment procedure. Different weighting schemes are tested, and, finally, some conclusions are drawn considering the accuracy of the obtained results.

V. N. Grigoriadis, C. Kotsakis, I. N. Tziavos, G. S. Vergos

Tidal Systems and Reductions for Improvement of the Bulgarian National Vertical Reference System

Although discussed worldwide, the application of tidal systems in the Bulgarian National Vertical Reference System is still in its initial steps. The information available in the papers and technical reports concerning the current tidal system and/or tidal reductions applied to different quantities is either vague or missing.

The current paper shows the status of terrestrial gravity and levelling data in Bulgaria with respect to the tidal system. The differences between geopotential numbers and normal heights in mean and zero tidal system are examined. For data source, four levelling lines from the National First Order Levelling Network are used. In addition, a comparison between the calculated normal heights and the official data published in the “Catalogue of the National First Order Levelling Network Benchmarks in European Vertical Reference System 2007” is made. At the end of the paper, proposals for the proper choice of tidal system in the country are given, taking into account future international as well as local precise geodetic applications.

Stanislava Valcheva, Iliya Yovev, Rossen Grebenitcharsky

Gravity Field and Mass Transport Modeling


Consistent Combination of Gravity Field, Altimetry and Hydrographic Data

The ocean’s mean dynamic topography as the difference between the mean sea surface and the geoid reflects many characteristics of the general ocean circulation. Consequently, it provides valuable information for evaluating or tuning ocean circulation models. However, the determination of the mean dynamic topography from satellite based gravity field and altimetric observations as well as in-situ data is not straightforward. We developed a rigorous combination method where both instrumental errors and omission errors are accounted for, including the determination of optimal relative weights between the observation groups. This method allows the direct determination of the normal equations of the mean dynamic topography on arbitrary grids. In this paper we focus on the steps for preprocessing the in-situ data. We show results for the North Atlantic Ocean based on a combined GRACE/GOCE gravity field, altimetric sea surface height observations from Jason-1 and Envisat and in-situ observations of salinity, temperature and pressure from Argo floats.

Silvia Müller, Jan Martin Brockmann, Wolf-Dieter Schuh

Local Hydrological Effects on Gravity at Metsähovi, Finland: Implications for Comparing Observations by the Superconducting Gravimeter with Global Hydrological Models and with GRACE

We construct a model for the influence of variation in local water storage on the observations of the superconducting gravimeter (SG) T020 in Metsähovi, Finland. The following hydrological components are accounted for: (1) soil moisture and groundwater in sediments, (2) groundwater in the fractures of the crystalline bedrock, (3) snow on the ground, and (4) snow on the laboratory roof. We show that due to the geometry of the local storage, its gravity influence at the SG is only a fraction of the influence of the corresponding Bouguer sheet, and discuss the implications for comparing the SG with variation in gravity observed with GRACE. We compare the SG residuals with the variation in gravity predicted from the local model and two models of continental water storage. The general patterns are similar but there are differences in amplitude and phase. Further research is outlined.

Jaakko Mäkinen, Tero Hokkanen, Heikki Virtanen, Arttu Raja-Halli, Risto P. Mäkinen

Global Groundwater Cycles and Extreme Events Responses Observed by Satellite Gravimetry

The groundwater is one of key parameters in water resource management and hydrological cycle. However, the global groundwater and its changes are very difficultly monitored by traditional instruments. The recent Gravity Recovery and Climate Experiment (GRACE) mission launched in 2002 provided an opportunity to measure the global water storage and its changes. Some regional groundwater variations were well estimated and investigated from GRACE, however, global groundwater variations are not clear. In this paper, an approximate decade of the global groundwater is obtained after subtracting the soil moisture, snow, ice and canopy water from the hydrological model GLDAS (Global Land Data Assimilation System). Significant annual variations of global groundwater are found with the mean amplitude of 28.98 mm, while the semi-annual amplitude is almost half of annual amplitude in most parts of the world with the mean of 11.06 mm. The mean trend of global groundwater variations is 1.86 ± 0.36 mm/year. The trend mostly reflects the recent extreme events, e.g. groundwater depletion in Northwest India, California and North China, droughts in La Plata and Southeast USA, and flood in Amazon. In addition, the groundwater has an acceleration change in some areas with up to ±4 mm/year



Shuanggen Jin, Guiping Feng

Modeling and Inversion of Gravity-Solid Earth Coupling


Sensitivity of GOCE Gravity Gradients to Crustal Thickness and Density Variations: Case Study for the Northeast Atlantic Region

We discuss the gravity gradient signal measured at the height of the GOCE satellite and compare it with the gravity gradients related to the density contrast between crust and mantle. The gravity gradients are reduced for the topographic masses to emphasize the lithospheric signal. Comparison with the Moho-related signal shows that with a density contrast of 400 kg/m


, the amplitude of the calculated gradients is almost twice that of the observed field. The differences can only partly be explained by the uncertainty of the crustal thickness, but is clearly related to the applied density contrast. Calculation of the gravity gradients requires a reduced density contrast, which is an important consideration for establishing global models, which might otherwise overestimate crustal thickness.

J. Ebbing, J. Bouman, M. Fuchs, S. Gradmann, R. Haagmans

Detecting the Elevated Crust to Mantle Section in the Kohistan-Ladakh Arc, Himalaya, from GOCE Observations

The Kohistan Ladakh area in northeastern Pakistan is an exposed top to bottom crustal section, implying that high density rocks of the lower crust are at the surface. The new GOCE satellite observations improve the gravity field in this remote area, giving a new dataset for geophysical interpretation. We use the new data to determine the crustal thickness variations and to define the geometry of the overturned crustal columns constituting the base of the former island arc. For the first time the entire extension of the arc is traced with the help of the gravity field observed by GOCE. The entire arc generates a positive gravity signal up to 180 mGal, limited by two geological boundaries, the Main Karakorum Thrust at north, and the Main Mantle Thrust at south. The Main Karakorum thrust marks the transition from the Indian to the Eurasian plate. The crustal thickness varies here between 40 and 70 km. The three geologic units that define the Kohistan arc, the South Plutonic Complex, the Chilas and Gilgit Complexes, occupy the upper crust, with depths increasing northwards between 14 and 44 km. There are not enough constraints to model the eastern part of the arc, the Ladakh, but the similarity of the gravity signal suggests that the thickness of the upper dense crustal units is similar.

Daniele Tenze, Carla Braitenberg, Eva Sincich, Patrizia Mariani

A Grip on Geological Units with GOCE

The scope of this work is to show the observations of satellite GOCE in mapping geological units in a key area for mineral exploration, which is also a key location for understanding the formation of the America and Africa continents from the former western Gondwana. The observations of the satellite GOCE have allowed to achieve a qualitative leap ahead in today’s global gravity. The new global field has an improved resolution of 80 km with precision of 5 mGal; this resolution is sufficient to study crustal thickness variations and the upper crustal structure. Geological macrostructures generating density variations are mapped for the first time by a global satellite derived field in continental areas, which opens a new series of applications in geophysical exploration. The study area is located in and around the Congo craton, which is a part of Africa poorly covered in ground gravity surveys, so that GOCE data are essential there. The GOCE gravity field is reduced by the effect of topography, of the isostatic crustal thickness and by sediments, obtaining the field representative of the geologic lineaments. The foldbelts surrounding the Congo craton are identified well through the field, generating signals near to 50 mGal. Compared to the existing geologic map, along the Kibalien belt, a narrow belt with increased density is distinguished, about 125 km wide, and 800 km long, that must be representative of a major compressive or magmatic geologic event that generated these rocks. The distinction of separate geologic units characterized by density variation is useful for identifying the areas where focused future geophysical and geologic mapping will be effective in the exploration of new mineral resources.

Carla Braitenberg

Basement Structure of the Santos Basin from Gravity Data

The ocean basement represents the tectonic situation of a specific area and its knowledge is crucial in studies aimed at exploring the seabed. Due to the high sedimentation rate, especially in ocean basins, the topography of the basement is masked and its structures can be buried, inaccessible to direct observation. This paper aims to estimate the depth of the basement in the region of the Santos Basin in Brazil from a combined analysis of gravity data obtained from satellite altimetry and marine gravimetry, bathymetric data and sediment thickness. In the first step of the work the gravity effect of sediments in Santos Basin was calculated and the Crustal Mantle Interface (CMI) was modeled from constrained gravity inversion. Next, the reliability of the models so obtained was tested by flexural analysis. The flexural and gravity CMI proved to be in agreement. The gravity effect of the CMI and the gravity effect of the sediments were then calculated and subtracted from the original Bouguer anomaly. The residual field thus obtained, which is assumed to represent the topographical features of the basement, was inverted in the last step of the work, providing information that shows a basement with features of up to 700 m that appear to be in agreement with tectonic features previously discussed, such as the Avedis volcanic chain. The depth of the basement estimated during this study showed values ranging from 1,500 to 10,500 m, and the deepest region is consistent with the Cabo Frio Fault.

Renata Constantino, Eder Cassola Molina

Gravity Field of Planetary Bodies


Observing the Gravity Field of Different Planets and Moons by Space-Borne Techniques: Predictions by Fast Error Propagation Tools

In the first decade of the twenty first century, great strides have been made in observing the Earth’s gravity field by space-borne techniques such as high-low Satellite-to-Satellite tracking by the Global Positioning System (hl-SST, providing 3D information about orbit perturbations), low-low Satellite-to-Satellite tracking (ll-SST) and Satellite Gravity Gradiometry (SGG). In addition, great advances have been made in (preparations for) gravity field recovery for other bodies in the solar system as well, including Mars and the Moon, using tracking from the Deep Space Network (DSN), but also techniques such as hl-SST, ll-SST, Satellite Laser Ranging (SLR) and Delta VLBI.The purpose of the work described in this paper is to gain insight in the possibilities of observing the gravity field of various planetary bodies by space-borne observation techniques. For low-earth orbiting (LEO) satellites, efficient error propagation tools are available that allow an assessment of the gravity field performance as a function of orbital geometry and instrument or observation technique. These tools have been extended for use to other bodies in our solar system, including the Earth’s Moon, Jupiter, Mars, Titan, Enceladus, Europa and Phobos, which are in the scientific spotlight for various reasons. The gravity field performance has been assessed for satellites orbiting these bodies assuming these satellites can make use of DSN tracking or can acquire ll-SST or SGG observations.

P. N. A. M. Visser

Sensitivity of Simulated LRO Tracking Data to the Lunar Gravity Field

The Lunar Reconnaissance Orbiter (LRO) is the first spacecraft in interplanetary space routinely tracked with 1-way optical laser ranges. Therefore, the mission is a suitable testbed to investigate the potential of laser ranging for precise orbit determination and lunar gravity field recovery compared to radiometric observations. As a first step, we simulated laser ranges and range-rates from various ground stations to LRO. The synthetic data were used to retrieve the satellite orbit. Further, we estimated three sets of spherical harmonic coefficients representing the lunar gravity field: one set based on laser ranges, one set based on range-rates, and one set based on laser ranges and range-rates. We found laser ranging to be capable of recovering the coefficients up to degree and order ≈ 12 without applying regularization. From a joint inversion we conclude that laser ranges only slightly improve the findings obtained from range-rates. Preliminary real data results based on twelve days of laser ranging observations show a range residual root mean square (RMS) value of 2.3 m. The RMS value in total position between our solution and a published LRO orbit derived from radiometric data and altimetric crossovers is about 550 m.

Andrea Maier, Oliver Baur


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