Gravity, Geoid and Geodynamics 2000

The interdisciplinary potential of gravity is stressed with special emphasis on the synergistic use of gravity with other data types. Satellite gravity measurements expected from GRACE and CHAMP will provide unprecedented views of the Earth’s gravity field and its changes with time. These measurements will be complementary with those of GOCE, which will provide unprecedented determination of the high-resolution static field. Gravity changes directly reflect changes in the masses of the ocean (thus allowing the separation of steric (heat induced) and non-steric contributions to sea level rise), the Greenland and Antarctic ice sheets, and the water stored in the continents. Not only can measurements of those changes provide a truly global integrated view of the Earth; they have, at the same time, sufficient spatial resolution to aid in the study of individual regions of the Earth. These data should yield information on water cycling previously unobtainable and be useful to both fundamental studies of the hydrologic cycle and practical assessments of water availability and distribution. Together with complementary geophysical data, satellite gravity data represent a new frontier in studies of the Earth and its fluid envelope.

The global phenomenon of glacial isostatic adjustment is one that involves internal Earth System interactions that are recorded in ways that are essentially “geodetic”. This phenomenon, in which changes in the shape of the viscoelastic earth are driven by large scale exchanges of mass between the cryosphere and the oceans, is observable both “paleo-geodetically” and space-geodetically. Examples of paleo-geodetic measurements include 14C dated histories of the changing level of the sea (the geoid) with respect to the surface of the solid earth, as well as measurements of the history of variations in the rate of axial rotation based upon the timing of ancient eclipses of the sun and moon. Examples of space geodetic measurements include joint VLBI, SLR and GPS observations of displacement rate vectors of “points” fixed to the surface of the solid earth, as well as satellite derived measures of the “anomalous” gravitational field. Observations of the time dependence of the gravity field that will be delivered by the GRACE mission are expected to further transform our ability to infer both earth structural properties (e.g. viscosity) and past and present degrees of cryospheric (in)stability. This brief paper reviews the present state of the theory that has been developed in order to exploit the totality of such geodetic observations so as to enable accurate geophysical inferences to be made based upon them.

Two alternative approaches are available for the global unification of height systems. Either one connects the datum points, usually associated to tide gauges, directly by ocean levelling or indirectly by a combination of space positioning, geodetic levelling and the solution of a modified version of the geodetic boundary value problem (GBVP). In both cases a significant improvement will result from the gravity and geoid model produced by the Gravity and steady-state Ocean Circulation Explorer (GOCE) mission of ESA. For the direct method the GOCE-geoid will be combined with satellite altimetry to give a global map of dynamic ocean topography, for the indirect method it serves the computation of reference geoid height differences. In both cases the off-sets between height datums will become estimable with a precision of a few centimetres.

Besides global terrestrial reference systems, such as ITRF (S) WGS 84, as updated in 1997, there exist a variety of continental or regional reference systems basically related to ITRF. With ongoing applications of global vertical positioning a global vertical datum becomes feasible. As systems, such as EUREF etc., are basically three-dimensional, the combination and unification of continental and regional vertical datums can now be implemented. First approaches of that kind, using tide-gauges in combination with repeat GPS-positioning as well as levelling together with satellite altimetry of different kind (TP, ERS-1/2 etc.) are affected by the temporal changes of global heights which are basically different from temporal changes in horizontal systems which are dominated by global plate tectonics in such a way that, at least, large scale behavior can be modelled by NUVEL-1A and similar systems. Moreover, in vertical systems the global geoid in terms of the geopotential W has to be incorporated. Thus an additional parameter which is not very well known globally, even though regional differences were meanwhile quite well explored, plays a significant role. Together with the geoid a Somigliana type normal field is appropriately introduced. In view of ecological and climatological aspects the mass exchange of ocean and atmosphere, its temporal variations in terms of El Nino and climatology, and a variety of dynamic aspects related to oceanic effects become relevant. In SC-3 of IAG all these aspects are presently discussed. New results have been investigated and compared with each other. In that connection the geopotential at the geoid W° plays a significant role and the accuracy of its present determination, problems associated with it, its interrelation with other global parameters and its use as a primary constant were considered. Results are presented in this paper.

The Reference Network Antarctica represents a highly precise densification of the International Terrestrial Reference Frame (ITRF) in the Antarctic region. It was established within two bundle projects sponsored by the Ministery of Science and Research of Germany (BMBF) under the auspices of the Scientific Committee on Antarctic Research (SCAR). Several German scientific institutions including the Geodetic Institute of the University of Karlsruhe contributed to this network. This result is based on simultaneous GPS observations in the Antarctic summers 1994/95 and 1997/98. The ITRF96 has been introduced as datum information via several ITRF sites in Antarctica and on neighbouring continents.For the practical use of the ITRF it is essential to consider the compability of the SCAR98 with the ITRF96 network. Therefore several aspects like, e.g., correlations between the datum parameters or their spectral characteristics according to eigenvalue decompositions will be presented. In addition the difference between the GPS network geometry noise and the Reference Frame Noise will be discussed.

The problem of the optimal definition of a Global Reference Frame based on a geodetic network of continuously observing stations is analyzed from various points of view. The non-linear datum definition problem is extended to the time domain and the optimal reference frame for a de-formable network is obtained as a geodesic line on a curved manifold in the vector space of all network coordinates, which is the union of instantaneous shape manifolds. The original ideas of Meissl are extended from the linear to the non-linear case and from the space to the space-time domain. The resulting definition of a Meissl Reference Frame is shown to be a geodesic frame as well as a Tisser-and-type frame. The difference between the operational Meissl-Tisserand geodetic network frame and the theoretical geophysical Tisserand earth frame is emphasized and it is shown how a connection between the two can be established by incorporating geophysical hypotheses, such as plate tectonics. Finally the stochastic problem of the optimal combination of estimated network frames is examined from both a non-linear and an approximate linearized solution point of view.

The problem of modelling the aliasing error in single-input single-output (SISO) linear systems with gridded input data is studied. First, a general linear estimation framework for SISO systems, based on the use of a multiresolution reference scaling kernel, is established, which includes the usual FFT-based numerical approximation of geodetic convolution integrals as a special case. The output signal error is modelled with the help of a spatio-statistical parameter (sampling phase) that depends on the resolution of the input data grid. A frequency domain algorithm is then developed which computes the decay rate of a certain output error functional with respect to the data resolution level, using the power spectra of the input signal, the chosen scaling estimation kernel, and the theoretic convolution kernel of the linear system. A simple numerical experiment is also included to compare the accuracy of the classic FFT approach in SISO approximation problems against the proposed generalization that utilizes an arbitrary reference scaling kernel.

In this study, we formulate two different approaches that will enable us to detect and control inconsistencies when integrating heterogeneous data sets. Through two numerical examples with simulated and real data, we compared both model solutions with a combination solution in which no attempt has been made to rectify the partial inconsistencies.

Most boundary value problems of the geopotential field have integral and series solutions in terms of Green’s convolution kernels. These solutions are advantageously evaluated using fast spherical harmonic transforms for regular arrays of simulated or observed data. However, the computational complexity and numerical conditioning of spherical harmonic transforms for relatively dense data are quite challenging and recent algorithmic developments warrant further investigations for geodetic and geophysical applications.

The Residual Terrain Correction is a standard step in the local geoid estimation procedure by the remove / restore technique; this computation involves the knowledge of a Digital Terrain Model and it is usually resolved by numerical integration by prisms or FFT integration. The first approach requires a long computation time; the second one, faster, implies significant approximations in areas where topography is rough. To properly exploit the large data sets of nowadays available DTM’s, a new formulation for RTC has been studied and implemented.

A fast computation of terrain corrections requires (1) a quick forward algorithm, and (2) a strategy for organising the data in a computer program. In this paper we present some new ideas on (1). The discussion of (2) is very brief. The proposed method is a space domain method, similar to prism integration, but quicker and more flexible. We show that the method works both in the flat-Earth geometry and in the spherical Earth geometry. The “elementary body” of the mass density model is an infinitely thin, horizontal and homogenous rectangular lamina.The main speedup comes from replacing the exact formulas for the gravitational attraction of a lamina by an approximation, a polynomial model. We argue that such approximation is sufficient to ensure the high accuracy of the approximation. In fact, we have tried it in numerical simulations (not shown here). We chose a polynomial model, because it is straightforward to use it for derivation of similar models for other types of gravity data.In practice, terrain corrections are computed from height data given on a regular grid in either spherical or Cartesian geometry. The regular grid structure of the terrain information is a particular advantage. For a given grid spacing, and prior to terrain correction computations, one can construct a polynomial model for all the geometrical aspects of the gravity station-mass point configuration. This is valid for any type of gravity data. We briefly mention how such general polynomial model can be used for optimizing the computations of the terrain corrections.

In Geodesy, parameter estimation based on the least-squares principle is a common tool for the solution of data analysis problems. It is assumed, at least implicitly, that the unavoidable observation errors are exclusively stochastic with zero expectation. The corresponding variance-covariance matrix (vcm) of the estimated parameters is then computed from the observations’ vcm just by means of variance propagation. However, the complete error budget of the observation process comprises additional, non-stochastic types of observation errors like, e.g., imprecision. Imprecision summarizes effects due to the imperfect knowledge about the observation setup. Fuzzy set theory and fuzzy data analysis supply adequate techniques to model and to handle imprecision. Since in geodetic data analysis both stochasticity and imprecision of the observations may be relevant, approaches for their combination are needed. Techniques from fuzzy-theory are introduced in this paper for the handling of observation imprecision. The joint treatment of observation stochasticity and imprecision is discussed. Numerical examples are given.

Numerically efficient methods for the solution of the Wiener-Kolmogorov equations in collocation always make use of the stationarity of the underlying stochastic process. In many applications the condition of stationarity is violated. The paper aims at a construction of a wavelet-based, numerically efficient method for the solution of non-stationary Wiener-Kolmogorov equations.

This paper describes an earth gravitation model (EGM) in a wavelet basis. The motivation is to provide an EGM that can be updated efficiently when new regional gravity data are available. Current techniques employ high degree and order spherical harmonic expansions that are characterized by global basis functions, thus precluding efficient regional update. In contrast, wavelets exhibit excellent localization properties that facilitate regional update. The approach uses a 2-D extension of the Beylkin-Coifman-Rokhlin (BCR) algorithm for evaluating integral operators. This algorithm is applied to Stokes’ integral to obtain an expression for the geoid undulation in a wavelet basis. An implementation is described and a geoid undulation map is produced. A technique to obtain a local update to both the wavelet EGM and the geoid undulations in regions where new gravity anomalies are available is described.

Dedicated SST- or SGG missions like GRACE and GOCE will provide gravity field information of new quality. But the computation of gravity models from these missions involves the solution of large, dense and ill-conditioned normal equation systems, and therefore fast solvers are needed. One way to deal with the problem is to make use of a hierarchy of lower-dimensional approximations to the unknown gravity anomalies. Such techniques, in numerical analysis well-known as multigrid methods, give rise for fast iterative solvers. We investigate the implementation of multigrid methods to satellite data analysis, including regularized problems. Multigrid algorithms are considered as stand-alone solvers as well as for the construction of preconditioners in the conjugate gradient technique, and numerical results from simulated missions are given. Moreover, an option to accelerate the choice of regularization parameters is shown.

The episode of climate warming during the 20th century is documented by an ablation of the Vatnajökull ice cap, south-eastern Iceland. Due to the small thickness of the elastic lithosphere and the low viscosity of the asthenosphere below Iceland, the ablation resulted in a retarded land uplift of about 3–8 mm/a in the vicinity of the ice cap. This is confirmed by GPS campaigns carried out south of the ice cap in 1992 and 1996 (Sjöberg et al, 1999). Furthermore, a relative uplift of 12.4 cm along Lake Langisjór south-west of the ice cap was observed between 1959 and 1991 (Sigmundsson & Einarsson, 1992). In the present study, we use a compressible, self-gravitating, spherical earth model with Maxwell viscoelasticity and a load model parabolic in cross section and elliptic in plan view to interpret the observations in terms of viscosity stratification. Our results show that the lithosphere is 10 to 20 km in thickness and the asthenosphere is 7 × 1016 to 3 × 1018 Pas in viscosity.

The Gravity Recovery and Climate Experiment (GRACE) is a dedicated spaceborne mission to map the gravity field with unprecedented accuracy. It consists of two satellites co-orbiting in a nearly polar orbit, at approximately 300–500 km altitude, separated by 100–500 km along track. The satellites are to launch in 2001 with a lifetime of approximately 5 years. Primary measurements are the range change between the two satellites using a dual one-way microwave ranging system. These measurements are combined with accelerometer and GPS measurements. Accelerometer measurements are for estimating the non-gravitational acceleration effect on the range changes. The GPS measurements are used for providing satellite orbit and time-tag information.For certain important error sources in these measurements, we describe the error simulation models. Effects of these error sources on gravity estimation are analyzed through a series of numerical simulations.

The Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) mission has been selected by the Earth Sciences Advisory Committee (ESAC) of the European Space Agency (ESA) as the first of two core missions of ESA’s Earth Explorer Programme to be launched in 2004. The main objective of the GOCE mission is to provide a high-accuracy high-resolution global model of the Earth’s static gravity field and the geoid from a combination of spaceborne gravity gradiometry (SGG) and high-low satellite-to-satellite tracking (hl-SST). Of the order of a hundred thousand gravity field parameters have to be estimated from tens of millions measured gravity gradients, which makes a brute force approach in terms of a least-squares solution of the observation equations an enormous numerical task. This huge number of observations and gravity field parameters does not allow to set-up the design matrix and the normal matrix explicitly. In turn this implies that existing software libraries for the platform of choice cannot be used directly. Therefore, we discuss a (parallellized) data processing approach for SGG data on the CRAY T3E supercomputer at Delft University of Technology, which only requires the application of the design matrix or its transposed to some vectors. Moreover, we discuss the performance of the algorithm in terms of degree of parallelism and scalability properties based on simulations.

The determination of the Earth’s gravitational potential from gravity gradients measured at satellite altitude along a non-polar orbit is an ill-posed problem, which lacks stability due to the polar gaps and the downward continuation from satellite altitude to the Earth’s surface. Even in the discrete world of observations the problem is still ill-conditioned, and some kind of regularization is indispensable to provide physically meaningful solutions up to high-degree and order. However, for large-scale problems the determination of the optimal regularization parameter is very expensive in terms of CPU-time, and strategies have to be developed to find this parameter with a minimum number of arithmetic operations. For the pair Tikhonov-Phillips/Morozov discrepancy principle the performance is analyzed for the gravity field recovery from GOCE SGG observations of two methods for accelerating the standard CG-algorithm recently proposed by Frommer & Maass. Moreover, the choice of a number of method-dependent parameters is investigated based on the analysis of several simulations up to degree and order 200 for white noise and colored noise observations and GOCE-like orbits.

A new satellite mission to map the Earth’s gravitational field (GRACE) is based on inter-satellite tracking using micro-wave ranging which can be used to solve for parameters of a global spherical harmonic model of the gravitational field using traditional satellite orbital perturbation analysis. An alternative algorithm has been developed to use the inter-satellite range-rate, supplemented by GPS baseline vector velocities and accelerometer data, to estimate in situ geopotential differences. The collection of these data, treated as a set of boundary values in potential theory, should yield higher geopotential resolution in the polar latitudes than provided by a truncated spherical harmonic model because of the high concentration of data in these areas. On the other hand, in situ data must be downward continued for local geoid determination, whereas this is already incorporated in the spherical harmonic models. Simulations confirm that although spherical harmonic estimations also yield relatively higher accuracy near the poles, local geoid estimation from in situ geopotential difference measurements is even more accurate at the poles, by a factor of two or higher for the case of nineteen days’ worth of GRACE data.

Energy exchange relations of the satellites’ motion within the gravity field of the Earth as well as integrals of motion seem to be useful as basic models for the determination of field parameters of the gravity field as well as for the validation and consistency check of gravity field models. The balance equations are adapted especially to the characteristics of accurate satellite-to-satellite tracking techniques either in the high-low or in the low-low applications. The reason is that these methods are based on local measurement principles while the classical techniques exploit accumulated disturbing effects of the inhomogeneous gravity field onto the satellite’s motion. The energy and motion integrals, respectively, show at every instant the energy of the relative and centre of mass motion while changes of the kinematic observables at subsequent instants are directly related to the changes of the potential energy of the gravity field. Alternative procedures for validation of gravity field recovery results, e.g., based on integration techniques as well as downward continuation procedures, frequently applied for this task are susceptible for numerical errors and instability effects. In the following, the balance equations for the energy exchange as well as motion and energy integrals are derived for the satellite-to-satellite motion within the gravity field of the Earth. The formulation is based in principle on the Hamiltonian formulation of classical mechanics. Only mechanical energy forms are considered, but an extension to other energy forms is basically possible but not presented here. The relations are derived in an quasi-inertial system as well as in an earth-fixed reference system. The energy relations are demonstrated in case of high-low and low-low SST scenarios realised with the gravity field missions CHAMP and GRACE.

Following the time-wise approach in the frequency domain (lumped coefficient approach) any functional of the gravitational potential can be formulated as a linear mapping from spherical harmonic spectrum to Fourier spectrum. This linear mapping is represented by transfer or sensitivity coefficients.The basic Fourier spectrum in dynamical satellite geodesy is 2-dimensional and corresponds to two space domain variables: argument of latitude and longitude of the ascending node. Since both variables are periodic, the corresponding space domain is a torus. Various advantages are associated with a torus-approach to satellite geodesy: (1) no assumption of repeat-orbit is required, (2) it combines the best features of space-wise and time-wise modelling, and (3) ascending and descending tracks are separated naturally. Furthermore, a general feature of the lumped coefficient approach is the fact that linear systems are uncorrected between the orders, leading to block-diagonality.The torus approach yields a fast and powerful data reduction strategy for the gravity field satellite missions CHAMP, GRACE and GOCE. A proof-of-concept of such data reduction is presented, in which the spherical harmonic spectrum is recovered from the GOCE-like second radial derivative V _zz .

We tried to model an artificial geoid signal and than decompose it into its causes. First we modeled the geoid heights changes caused by the hydrosphere and the atmosphere, and composed them to simulate the measurable signals by GRACE. Then, we decomposed the signals by considering the following properties; 1) different ocean responses to atmospheric pressure changes, and 2) different time-frequencies of the variations of the hydrospheric contributors. These tests prove that an appropriate assumption for the ocean response is important to minimize decomposition errors. Since atmospheric errors necessarily affect the recovered hydrospheric signal, minimization of these errors by mathematical tricks is desired.

The new satellite Earth gravity field model GRIM5-S1 was recently prepared in a joint GFZ and GRGS effort. Based on this satellite solution and terrestrial and altimetric gravity anomalies from NMA, a combined model GRIM5-C1, with full variance-covariance matrix up to degree and order 120, was computed. Surface gravity and altimetric gravity data are corrected for several systematic effects, such as ellipsoidal corrections and aliasing. A weighting scheme for gravity anomalies, according to their given standard deviations was developed. From each data set full normal equations were set up and finally combined with the GRM5-S1 normals. To take into account good information from the satellite-only model a procedure was developed to identify such coefficients and appropriately weighed them in the final normal equation system. Internal error propagation and comparisons to external data sets show, that the GRJM5-C1 model represents the best state of long wavelength gravity field models.

High resolution gravity field models currently are computed by a combination of least squares adjustment with the full variance-covariance matrix for the lower degrees and a simplified approach for the higher degrees. Simplification means, that numerical quadrature is applied or that the structure of the covariance matrix is reduced to block-diagonals. Both methods have been used since several years to compute high resolution gravity field models. With recent improvements in algorithms and by the usage of parallel computers the degree and order for full variance-covariance matrices could be increased to 180. Several test solutions with combination of full and block-diagonal normals were computed and compared to independent data sets. Comparisons between the simplified and the rigorous approach show, that especially in the spectral domain better results can be reached with the full variance-covariance matrix.

The angular momentum of the oceans changes as both the distribution of mass within the oceans changes and as the direction and speed of oceanic currents change. Since, in the absence of external torques, the angular momentum of the solid Earth-atmosphere-ocean system is conserved, the changing oceanic angular momentum will cause the solid Earth’s angular momentum to change, or, in other words, will cause the Earth’s rotation to change. The changing distribution of mass within the oceans also causes the Earth’s gravitational field to change, an effect that will soon be measured by the CHAMP and GRACE satellite missions. By measuring changes in the second-degree spherical harmonic coefficients of the Earth’s gravitational field, which are related to the elements of the Earth’s inertia tensor, CHAMP and GRACE will, in effect, be directly measuring changes in the Earth’s rotation caused by mass redistribution.

Initial studies of the effects of ocean tides on the GRACE gravity field are. Based on the predicted accuracy estimates associated with GRACE errors in the ocean tide modeling are evaluated using gravity anomalies filtered at harmonic degrees 50 and 80 respectively. The results of the analysis show that the ocean tides and the ocean tide loading are important to consider in analysis of GRACE data. Furthermore, the loading is important to consider. The current ocean tide models are not accurate enough to correct GRACE data. Furthermore, the atmospheric tides may give significant errors in the ocean tide model if altimetry corrected for inverted barometer effects is used.To study the temporal characteristics of the ocean tidal constituents when sampled by GRACE, preliminary alias frequencies have been derived assuming a sampling of one sidereal day. Those results show that the ocean tide errors will not cancel in the GRACE monthly averaged temporal gravity fields at harmonic degrees 1–50. The S2 and the K1 terms have alias frequencies much longer than 30 days, so that they remain almost unreduced in the monthly averages.

Principal Component Analysis, which can reveal maximum temporal-spatial signal structure with a minimum amount of Principal Components (PCs), is used to investigate the temporal-spatial variations of sea level anomalies over the northwest Pacific. Either in S-mode or in T-mode, the sum of the variances contributed by the first 9 PCs in S-mode and by the first 3 PCs in T-mode exceeds 50% of the total amount of variation, respectively. Therefore, these PCs can reveal most of temporal-spatial pattern of sea level variations. There is a strong relationship between the El Nino and the temporal variations of the first PC either in S-mode or in T-mode, which explains the secular and inter-annual changes over the northwest Pacific. The rate of sea level change over the northwest Pacific, for the period October 1992-December 1999, is found to be negative: -0.55±0.30mm/year while in the Yellow Sea, the East China Sea and the South China Sea it is +3.4410.61 mm/year, +3.12±0.47 mm/year and -1.41±0.48 mm/year, respectively.

This paper discusses contemporary research in GPS-buoy sea level measurements and its application to absolute radar altimeter calibration. Different processing techniques to obtain GPS-buoy water level solutions were studied using differential GPS (DGPS) and using absolute positioning by resolving GPS clock errors. Results of GPS-buoy campaigns in Lake Michigan, USA and near Catalunya, Spain for absolute calibration of the TOPEX/POSEIDON Side B (TSB) radar altimeter are presented. Error analysis indicates that the uncertainty associated with a “single” GPS buoy (water-rider) sea surface height measurement in Lake Michigan is ∼40 mm rms, accounting for a list of estimated fixed and variable errors. The corresponding uncertainty for altimeter bias closure using the “single” measurement is estimated to be ∼62 mm rms. Preliminary studies using altimeter water level measurements and GPS buoy measurements to “translocate” historic TOPEX Side A (TSA) radar altimeter lake level measurements to the Holland West, Lake Michigan tide gauge, to conduct altimeter calibrations indicates that the technique is viable. The resulting TSA bias, based on 112 samples, is estimated to be -122.5±41 mm, including an apparent 100 mm offset. The estimated altimeter drift is 4.4±2.5 mm/yr. The drift estimate and its uncertainty are in reasonable agreement with results obtained at the dedicated T/P absolute calibration site at Harvest Platform, California, USA.

This paper is devoted to the influence of several parameters (modelling of solid and ocean tides, air pressure, vertical gradient, site conditions) affecting the determination of the value of the absolute gravity. The confidence in the results relies on the dependence of the gravity (mean value and time-varying residues) on small changes in these parameters and the way we can constrain our choice of them. With the help of data sets obtained from absolute gravimeter (AG) FG5#206 at different stations, we will thus study the influence of i) the modelling of solid tides by the use of several models based on recent tidal developments, ii) the modelling of the oceanic loading tides including models derived from satellite altimetry, iii) the modelling of the pressure correction by the use of a local barometric admittance value versus a global loading computation, iv) the vertical gradient (do we have to measure it each time or is it better to use always the same value even if it is a theoretical one?). A methodological investigation of the consequences of these corrections will help answering the fundamental question of the duration which is needed in order to achieve convergence in the mean g value. We will also show the impact on the gravity residues of these parameters.

The investigation is concerned with the calculation of the total atmospheric contribution to variations of the gravity field. The relevant components are the free-air, the deformation and the air-mass contributions. The free-air and deformation contributions are calculated by means of a plane, compressible, elastic earth model. For the calculation of the air-mass contribution, a simple atmosphere model developed from the U.S. Standard Atmosphere 1976 (NOAA, 1976) and synoptic meteorological data are used. The objective is the reduction of high-accuracy gravity measurements recorded by the super-conducting gravimeter formerly located at the GeoForschungsZentrum Potsdam. A comparison between the residual after reduction with the theoretical model considered here and the residual after reduction with an alternative method is used for an assessment of the quality of the reduction methods.

Long sea level observation series from tide gauges continue to be an important source of information on vertical land motion. We are currently undertaking a review of Estonian tide gauge data. Sea level observations started in Tallinn in 1842. We have data from 29 locations, 9 of which are today operative, 18 span 40 years and 11 span 50 years or more. Estonia belongs to the margin of the rebound area, vertical rates relative to mean sea level are -2...+2 mm/yr. We describe the review, compare our provisional results with earlier computations, look how they fit into rebound maps of the whole Fennoscandian area, and discuss purely local movements.

This paper deals with the stability of gravity measurements in time of some specific sites in France (J9-Strasbourg, Cerga (Grasse), Brest, Welschbruch (Vosges Mountains)) as observed by regular gravity measurements since February 1997 with the absolute gravimeter FG5#206. The rate of repetition of absolute gravity measurements is variable ranging from one experiment every six weeks at Strasbourg to one per year at Brest. The variations of the gravity value are compared with the variations of the vertical position deduced from different collocation positioning techniques (Global Positioning System, Satellite Laser Ranging, Lunar Laser Ranging). This comparison will be analysed in order to bring new elements to a discussion on the discrimination between the gravity contribution resulting from vertical motion in the Earth’s vertical free air gradient field and the one originating from mass redistribution.

The static displacement field generated by an earthquake redistributes the Earth’s mass and consequently causes the Earth’s rotation and global gravitational field to change. Although the coseismic effect of earthquakes on the Earth’s rotation and global gravitational field has been modeled in the past, no unambiguous observations of this effect have yet been made. However, the Gravity Recovery And Climate Experiment (GRACE) satellite, which is scheduled to be launched in 2001, will measure time variations of the Earth’s gravitational field to high degree and order with unprecedented accuracy. Here, the coseismic effect of earthquakes on the Earth’s global gravitational field will be modeled and compared with the expected accuracy of the GRACE measurements. It is shown that the coseismic effects of great earthquakes such as the 1960 Chilean or 1964 Alaskan events can cause global gravitational field changes that are large enough to be detected by GRACE. However, the coseismic effects of the largest earthquakes that have occurred during the past 35 years cause global gravitational field changes that are probably too small to be detected by GRACE.

The results of the evaluation of a new airborne gravimeter developed by Sander Geophysics Limited (SGL) will be presented. This gravimeter is based on a platform type inertial navigation system, and is optimised for the airborne environment. A general description of the instrument is given.The testing was conducted over a relatively flat area which is well covered with ground gravity values. The upward continuation to flying height of a grid of these values was used as a reference for the data reduction. The gravity anomaly was extracted through application of a series of low-pass filters on the inertial data, after removal of the kinematic accelerations and Coriolis effects using the processed GPS data. The results show an agreement with the ground truth well within 1.0 mGal for a 2km half wavelength spatial resolution. The effects of varying flight conditions are assessed as to their impact on the quality of the data. Flight turbulences appear to have very little effect on determination of the gravity anomaly for half wavelengths as short as 2 km.

Using Interferometric Synthetic Aperture Radar (InSAR) technology, Intermap’s STAR-3i provides a new generation of digital elevation models (DEMs) and orthorectified radar image (ORRI) maps. Because the Global Positioning System (GPS) is used as the position reference for STAR-3i, the terrain data provided by STAR-3i are referenced to an ellipsoid. An accurate geoid is required to create a sea level referenced DEM. For this purpose, Intermap has developed a new airborne gravity system (AGS). It is based on the STAR-3i navigation system consisting of differential GPS (DGPS), the strapdown inertial navigational system (INS), and the STAR-3i acquisition system.One important application of long-range airborne gravimetry is regional geoid mapping. Intermap has developed the software to determine geoid undulation based on airborne gravity and other gravity data. A precise regional geoid is determined by applying downward continuation techniques to airborne gravity measurements.This paper introduces the STAR-3i airborne gravity system and the software STARGRAV for airborne gravity and geoid determination. It describes how the processing algorithm was applied to 30,000 km2 of data from Central America and Washington, DC. They were collected and processed by Intermap in 1998 and 1999 and were used to generate digital elevation, orthorectified image, and geoid products. In the paper the gravity and geoid processing results are analyzed for internal consistency at the crossover points of the lines. Further, the data are analyzed for absolute accuracy by comparison with ground gravity information. The results demonstrate that the STAR-3i AGS system can measure gravity anomalies to an accuracy of 1 – 2 mGal. The geoid determined using the STAR-3/ system has a relative accuracy of 5 – 10 centimeter (1σ) when compared with an independently determined geoid reference.

We present results from a first stage prototype dynamic absolute gravity system. In contrast to relative instruments which measure differential force, absolute instruments directly measure the gravity field by tracking a freely falling object in an evacuated chamber using a laser interferometer. The measurement method is based on precise standards of time and distance providing an absolutely calibrated system that neither drifts nor tares.Traditionally absolute gravimeters have been used only in static applications. Because these types of instruments provide an absolute value rather than a measured difference, it is desirable to investigate the feasibility of acquiring absolute data from a moving platform.The static absolute gravity instruments use a long period isolation device to remove ground and environmental noise from the interferometer. We present here a prototype system that uses an external sensor rather than an isolation device to record the motion of the fixed interferometer, and incorporates these data directly into the equation of motion to determine the absolute value of gravity.Results indicate the strap-down system shows promise for gravity acquisition from a moving platform and may eventually be superior in terms of price and performance with current spring-based measurement systems. This has important implications in terms of field portable static absolute gravity systems and lays the foundation for absolute gravity acquisition in dynamic environments.

There are recognised deficiencies in the gravity data around the Australian coastline, which can best be repaired by the use of airborne gravimetry. The development of an Australian capacity in airborne gravimetry will not only allow improvements in local geoid modelling; but also will enable gravimetric measurements to be undertaken in the Antarctic region, contributing to local and global geoid modelling, and to the international scientific effort in the region.This paper describes the airborne gravimetric mission flown in the Barrier Reef region in October 1999. The mission was flown onboard the survey plane of the Laser Airborne Depth Sounder unit of the Royal Australian Navy during one of its routine bathymetric survey campaigns. The gravity data derived from this mission is used in local geoid determinations, and tested to determine what impact this new data has upon the precision of the derived geoid.The gravimetric and bathymetric data obtained during this mission are used to investigate the validity of models for predicting gravity anomalies from bathymetry. Extensive bathymetric charting exists for the Australian coastline, and if sufficient additional constraints are introduced, this data source may prove useful for predicting gravity anomalies in unsurveyed areas. This paper investigates the feasibility of such an approach.

An airborne gravity survey has been carried out 1998–99 to cover the ice-covered parts of the seas around northern and north-eastern Greenland. The aerogravity survey has been done by a Danish-Norwegian aerogravity system setup, based on a Lacoste and Romberg “S” gravimeter. A Twin-Otter aircraft has been used, capable of low and slow flights, yielding airborne gravity measurements of relatively high accuracy and resolution. Crossover adjustments and comparisons to independent marine gravity data indicate accuracies of 2 mGal r.m.s., at a resolution of 6–7 km. This kind of accuracy level corresponds to relative geoid errors around 10 cm across the coastal region.

During the past five years, gravity measurements from airborne systems have become a viable alternative to terrestrial gravity measurements for applications where local or regional modeling of the gravity field of the Earth is required. One of these applications is local geoid determination where data taken along regular flight profiles can replace the use of point gravity values measured on the ground. Although the importance of this application was realized early in the development of airborne gravimetry, only limited results of comparisons between the local geoid derived from airborne gravity data and the local geoid derived from ground gravity data in the same area have so far been published. This is mainly-due to the fact that airborne gravity surveys are typically done in areas with no or sparse ground gravity, so that a direct comparison cannot be done. It is the objective of this paper to provide such a comparison and to analyze the accuracy and resolution of the geoid, currently achievable by airborne gravimetry. The airborne data used cover a 100 km by 100 km area in the Canadian Rocky Mountains with large changes in topography and gravity. It represents therefore a worst-case scenario in terms of the high-frequency spectrum of the gravity field and the geoid variations resulting from it. Results indicate that even under such extreme conditions, the root-mean-square differences between the two the geoids is at the level of two centimeters for the short-wavelength part of the geoid.

Generous support from Australian Hydrographie Office made it possible to install and operate a gravimeter in the aircraft, a Fokker F-27, carrying their Laser Airborne Depth Sounding (LADS) system. The LADS system operated in the Great Barrier Reef region, northeast Australia, at that time. This shallow water area is a major gravimetric data void, and thus degrades the gravimetric geoid models in and around the area. The aim of the airborne gravity measurements was both to gather new data in the area to improve the geoid and to examine the feasibility of combined airborne bathymetry and gravity surveys. An important consequence of this is that the existing bathymetry may be used to predict the gravity field in areas lacking gravity — thus doing away with the need for direct gravity measurement in offshore areas well mapped with bathymetry.This paper outlines the gravity system setup and the applied sensor modelling. The system performance is validated by internal crossover analysis and comparison to existing data. Special emphasis is put on modelling of non-linear terms in the La Coste & Romberg S gravimeters response to aircraft phugoid motion. The phugoid motion of this specific aircraft generates a noise term in the gravity system output that overlaps more with the gravity signal than experienced in smaller aircraft. A simple lowpass filtering of the noise will result in an unsatisfactory resolution of the final data. It is shown that the phugoid motion induced noise can be sufficiently reduced by including non-linear terms in the modelling of the sensor response.

The gravity field may be determined using different techniques, but airborne gravity surveying is becoming a powerful tool mainly due to its potential in remote areas.In the scope of the AGMASCO (Airborne Geoid MApping System for Coastal Oceanography) project a navigation system has been developed in support of airborne measurements acquired during a gravimetric and altimetric campaign that took place in the Azores region, Portugal, in October 1997. This system was originally developed with the purpose of determining the navigational parameters (attitude, velocity and position) of an aircraft. However, it is also capable of producing estimates of the vertical gravity anomaly. Since this anomaly is an important perturbation to the performance of the navigation system, it had to be estimated together with the inertial sensor biases, in order to improve the final solutions. As a result, one decided to test the ability of a low cost Inertial Measurement Unit (IMU) to work as a gravity measuring device.This paper describes the methodology followed to obtain estimates of the local gravity anomaly by integrating GPS and inertial measurements.The results show that the gravity anomaly measured by the differential GPS/IMU integrated system matches quite well the results obtained with the Lacoste & Romberg (L&R) sea and air gravimeters. The ability of this kind of inertial system to recover gravity anomalies, focused on medium wavelengths perturbation signals, was evaluated. The lack of long term stability of the IMU sensors renders long wavelength gravity anomaly determination impracticable for precise.The DGPS/IMU integrated system can be seen as a complement to a gravimeter, which exhibits long term stability.

The Stokes-Helmert scheme for precise geoid determination requires that Helmert’s gravity anomalies are first evaluated on the earth surface. Subsequently, these anomalies must be continued downward onto the geoid, where they make the boundary values for solving the geodetic boundary value problem. The anomalies are continued downward using the Poisson integral; this can be done because the Helmert disturbing potential is harmonic everywhere above the geoid. Thus, the difference between Helmert’s gravity on the earth surface and on the geoid can be computed and the mean vertical gradient of gravity between the earth surface and the geoid can be obtained.In this contribution we show a map of the mean gravity gradient for one particularly interesting area of the Rocky Mountains. We also point out that these values can be used to make orthometric heights more precise. The experiment presented here is just a first attempt, a pilot study to prove the validity of the physical concept.

A method is proposed for eliminating the error of vertical gravity gradient from absolute measurements of gravity. The method involves precise determination of effective measurement heights for each individual measurement and referring the measured gravity to the arithmetic average of those heights. It is shown that the average effective measurement height for a set of measurements preserves the property of the regular effective measurement height for a single measurement, namely the average gravity value referred to the average effective measurement height does not depend on the gradient value. Precise determination of individual effective measurement heights with absolute gravimeter’s weighting functions is discussed.

The new satellite gravity missions (CHAMP, GRACE and GOCE) will all bring substantial improvements to our knowledge of the gravity field and thereby of the (quasi-) geoid. One of the aims of the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) is to determine the geoid to within 1 cm at wavelengths down to 100 km.When determining local or regional geoids, a large part of the error is due to the error in the spherical harmonic expansion used as a reference field in remove-restore calculations. We have estimated this error for the EGM96 and for the future GOCE based model using the so-called error-degree variances associated with these models. These variances have for GOCE been determined in studies analysing the mission performance.The error-degree variances have been used in a Monte-Carlo like generation of pertubations of the EGM96 and the GOCE gravity field model in various scenarios (moderate topography, medium varying topography and Alpine topography) by scaling the error-degree variances. The error of a derived quantity like a geoid height differences have then been estimated by calculating the root-mean square variation of the results.Based on typically 50 generated models (for EGM96 and GOCE) we have estimated mean errors of geoid height differences between the continents as well as for typical levelling lines on the continents. For geoid height differences between the continents the EGM96 error is found to be between 0.45 m and 0.60 m, while the corresponding error when using GOCE decreased to between 0.05 and 0.10 m. For levelling lines of distances between 25 km and 500 km a similar improvement was found, so that maximal errors decreased from 0.88 m to 0.09 m in Alpine topography and from 0.44 m to 0.03 m in Scandinavian type topography. Obviously the use of local gravity anomalies, gravity disturbances, GPS/levelling geoid height differences as well as topographic information may further improve the results. Consequently 1-cm geoid height differences should easily be obtained in areas where these types of data are available.

The determination of the gravity field of the Earth outside the geoid and the surface of the geoid itself are still important tasks of geodesy. With their knowledge the link between geodetic measurements within the gravity field and a geometrically defined reference ellipsoid can be realised (Heck 1995). Especially the geoid could serve as a uniform global reference surface for height systems (Rapp 1994). By using the GPS-technique a highly accurate geoid with a relative accuracy of ±1 cm or better over several hundred kilometres is becoming more and more important to convert ellipsoidal heights (e.g. derived by GPS) into a conventional height system.

A gravimetric boundary value problem in the determination of the external gravity field of the Earth is discussed. The approach follows the concept of variational methods. The focus is on the construction of the stiffness matrix of Galerkin’s system of linear equations. Elementary potentials are used as a function basis and the elements of the matrix are computed for an ellipsoidal solution domain. Legendre’s functions of the first and the second kind are used as a natural tool in this computation.

New research is discussed that relates to improving techniques of hybrid geoid generation and the use of Helmert condensation of surface free-air gravity anomalies. New approaches are examined for modeling signal remaining between a regional gravimetric geoid, G99SSS, and a database of GPS-derived ellipsoid heights at 6169 spirit-leveled benchmarks. One approach reduced the remaining unmodeled signal by one centimeter or about 20% over the approach used for GEOID99. Helmert condensation also offers a solution to improving regional geoids. This approach models the gravitational effects of the terrain masses using fast Fourier transforms for outer-zone (>4°) contributions and spherical, space-domain calculations for the inner-zone. The effects of the 3D masses are removed from the surface anomalies, which are then downward continued to the geoid where the effects of the 2D masses (condensed onto the geoid) are restored. This approach removes the approximation of Faye gravity anomalies and permits downward continuation in the smoother gravity field where the terrain has been removed. Preliminary investigations have begun on this approach that demonstrate the viability of modeling the 3D and 2D terrain masses as compared to other approaches.

A report on quasi-geoid computations in South America, based on the existing gravity data base collected in the framework of the South America Gravity Project (SAGP) is presented. Two estimation methods will be described. One of these is the standard “remove-restore” technique. The gridding of the residual gravity values (i.e. free air gravity anomalies minus the global geopotential model and the terrain effect) has been performed using, with some Refsinements, the GEOGRID program of the GRAVSOFT package (Tscherning et al, 1994) and the residual quasi-geoid signal has been evaluated through the ID FFT approach (Haagmans et al., 1993) which allows a fast and rigorous computation of this component. The second approach is based on ID FFT method applied on mean Helmert’s gravity anomalies, having removed the low frequency components using EGM96 model up to degree 50.

A set of all currently available free-air gravity anomalies in Egypt represents the gravimetric data set for this investigation. In the framework of the well-known remove-restore technique, a set of 30” x 30” and 3’ × 3’ Digital Height Models are used for computing the effect of the topography and its compensation on the gravity anomalies and on the geoid undulations (the indirect effect). The commonly used Airy-Heiskanen isostatic hypothesis is applied. The EGM96 global geopotential earth model is used for computing the effect of the Refserence field. A gravimetric geoid is computed for Egypt using Stokes’ integral in the frequency domain by the multi-band spherical FFT technique. The computed geoid is compared with the geoid derived from the available GPS and levelling benchmarks in the data window. Removing a Kriging (collocation) trend function from the computed FFT geoid gives very good geoid precision for Egypt (about 2.5 cm). The external accuracy of the geoid in this case would be in the order of three decimetres.

A new methodology for the high-resolution geoid computation without application of the Stokes integral has been developed. This methodology renders simultaneously the observables of the type gravity potential and the modulus of the gravity intensity at the known (i.e. GPS positioned) surface of the earth. The method is comprised of following main steps, (i) Removal of the effect of the reference field of the ellipsoidal harmonic expansion to degree/order 360/360 plus the centrifugal field, (ii) Removal of the residual gravitation field of the terrain masses above the reference ellipsoid in a radius of 50 km around the computational points, (iii) Downward continuation of the harmonic incremental/disturbing observables of the type gravitational potential and gravitational intensity from the surface of the earth to the gravitational potential at the surface of the reference ellipsoid based on the inverse solution of the ellipsoidal Abel-Poisson integral and its gradient, (iv) Restoration of the reference field of ellipsoidal harmonic expansion of the degree/order 360/360 plus the centrifugal field and the effect of residual terrain masses in a radius of 50km around the computational point at the surface of the reference ellipsoid, (v) Conversion of the gravity potential values at the surface of reference ellipsoid to the geoidal undulations via the application of the ellipsoidal Bruns formula. As the case study high-resolution geoid of the state Baden-Württemberg Germany will be presented.

A set of free-air gravity anomalies for Austria and neighbour countries represents the gravitational field data for the current investigation. The depths of the Mohorovičič discontinuity (Moho depths) derived by seismic observations are also available. The computation of the terrain reduction is carried out using the pre-estimated seismic Moho depths. The TC-program (originally written by Forsberg, 1984) has been modified to compute the effect of the compensating masses on the disturbing potential (and hence to other gravitational quantities) using the Digital Moho Models. Both fine (11.25″ x 18.75″) and coarse (90″ x 150″) Digital Height Models are available for this investigation. The gravimetric geoid for Austria has been computed using the seismic Moho depths, representing the compensating masses, by applying Stokes’ integral in the frequency domain using 1D-FFT technique. For the sake of comparison, another gravimetric geoid for Austria has been computed using the Airy-Heiskanen isostatic model, for generating the compensating masses. Both geoids are scaled (fitted) to the geoid derived from GPS and levelling. A broad comparison between both geoids is carried out. Both geoids have nearly the same accuracy. Using seismic Moho depths in the geoid computation gives fitted geoid with less difference range (compared to the GPS-derived geoid) than the geoid computed using Airy-Heiskanen isostatic hypothesis.

The Japanese islands are located in a trench and island arc region and the gravity field shows complicated undulations. The Kuroshio Current, one of the strongest oceanic currents in the world, flows along the south coast of Japan and, therefore, the recovery of the gravity field from al-timetry is difficult for cm-precision geoid determination in this region. This paper deals with an improved approach of gravity field modeling around Japan using marine gravity data and an altimetry-derived global marine gravity anomaly model, KMS99. KMS99 is also used to edit and validate the ship gravity data before it is crossover adjusted. Finally the adjusted ship data are merged with KMS99. Then Stokes integral and the least squares spectral combination method are applied to determine the geoid in this region. The computed geoid models are evaluated by comparisons with GPS/levelling geoid undulations.

In this contribution, first the efficiency of the kernel modification techniques in the Poisson upward and downward continuation of gravity is investigated in light of reducing the far zone contribution. Second, the methods of determining the critical radius of the near zone cap are reviewed and discussed in terms of the convergence and the accuracy of the estimate for the far zone contribution.

A new gravimetric geoid model for Japan is constructed on a 1′ x 1.5′ grid, with newly acquired land gravity data. About 6.5 times as many data as those used for the previous models are collected and merged with marine data. The geoid determination method is based on the remove-restore technique and EGM96 is used as a foundation geopotential model. De-trending is applied to the residual gravity anomalies at sea, for reducing long-wavelength distortion in the local application of Stokes integral. The least squares spectral combination is tested for evaluating the effects of Stokes kernel modification. Comparisons with the nationwide GPS/leveling net reveal substantial improvement over the previous geoid models: a SD about the mean is 21.4 cm, tilt is reduced from 1.42 ppm to 0.40 ppm and a post-fit RMS is 14.3 cm. Effectiveness of the de-trending to marine data is confirmed in the reduction of long wavelength distortion.

Previous Australian gravimetric geoid models have used the approximation of a constant topographic bulk density during their computation. However, this is unrealistic because the Australian continent is host to complicated geological structures, with many large contrasts in topographic density. Therefore, this paper presents the first results of the effect of using topographic bulk density data on gravimetric geoid computations over a well-controlled test area in Western Australia. This area has been chosen because there is a significant change in topographic bulk density along the Darling Fault, which can reach approximately 1,000kgm3.

GPS provides geodesy not only with a need for the “one-centimetre” geoid model but also a very important kind of input data, the gravity disturbance data. The boundary value problem (BVP) based on these data is the second geodetic boundary value problem (GBVP). This paper gives a detailed discussion on the significance and the solutions of the second GBVP.

The Topex/Poseidon (T/P) follow-on mission JASON-1 is planned to be launched by the end of 2000. A new multi-satellite calibration site has been proposed for the isle of Gavdos, south of the island of Crete, Greece. Part of the multi-satellite calibration experiment is the detailed computation of a high resolution geoid. The computed geoid is based on altimeter-derived, surface and shipborne gravity and height data. A currently available multi-satellite-based (GEOSAT-GM, ERS1-GM, ERS1-ERM, ERS2, T/P) altimetric geoid combined with newly available gravity data are used in the final model. New methods for the efficient combination of heterogeneous data are employed and special emphasis is paid to the prediction error estimates. We present the evaluation of the approximated accuracy estimates and the effect of the geoid error on the stability and reliability of the calibration site results. We will also elaborate on the assimilation of future measurements that are planned under the proposed project for the establishment of the calibration site.

Analyses of Satellite Laser Ranging (SLR) tracking data have yielded estimates of rates for the low-degree zonal harmonics of the geopotential up through j ₆ . Combined with observed changes in the Earth’s rotation pole and global sea level rise, these observations provide a powerful constraint on aggregate mass transport within the Earth’s systems. Inverse solutions, where these observed geodetic rates are used to constrain geophysical models, can yield estimates of the mantle viscosity contrast affecting postglacial rebound and ice sheet mass balance rates. In order to obtain the most accurate estimates, such analysis requires accounting for as many geophysical and environmental signals as possible that are contained in these observed trends. Analysis to date indicates that both the Antarctica and Greenland ice sheets are nearly in mass balance when the forward models are used without any accommodation for correction terms. These results are only somewhat dependent on the zonal rate solution used, despite the differences between these solutions. The ice mass balance results benefit from improved rate solutions; in particular, the Antarctic ice mass accumulation rate estimate will benefit from better separation of j ₃ and J ₅ . The secular zonal rate solution can be improved using additional data. SLR and DORIS tracking of TOPEX/POSEIDON have been combined with the SLR tracking of LAGEOS, LAGEOS-2, Starlette, Stella, and Ajisai previously used to estimate the geopotential rates. Estimates of scale corrections to the forward models are also used to gain insight into the relative performance of these models and improve the estimate of the ice balances.

We model the present-day time-dependent gravity field of Antarctica driven by solid earth rebound response to deglaciation of a more extensive continental ice cover at Last Glacial Maximum (22–15 kyr BP). Among the various global components of late-Pleistocene and Holocene eustatic sea level rise, Antarctica’s contribution has been most contentious. Using new geological inferences provided by marine sediment cores and ice-volcanic deposits within the Antarctic continental interior, we compute predictive maps of geoid secular variation and uplift. Competing forward models produce quite distinguishable signatures in terms of the resolution and accuracy of the GRACE and GOCE satellite missions. Both the timing and amplitude of the ice sheet paleotopography and the structure of mantle viscosity are crucial inputs to the predicted temporal gravity field in Antarctica. In general, our new predictions indicate that the rebound component of Antarctica’s secularly varying geoid is at the 0.1 to 0.6 mm/yr level. These estimates may err on the conservative side if the ice sheet has been slowly deglaciating during the last two thousand years.

We use satellite solutions to the low degree zonal coefficients of the Earth’s gravitational potential, J ₂ through J₇, to reveal large scale features of rates of thickness change of the polar ice sheets, and the lower mantle viscosity. The polar ice sheets may each be divided into two regions, whose change in thickness and shape were adjusted to predict gravity that agrees well with observation. If the postglacial rebound model of Han and Wahr [1995] is used, the predicted viscosity is 1 X 1022 Pa-s, predicted sea level rise from Antarctica is 0.1 ±0.8 mm/yr, and the sea level rise from Greenland is 0.4 ± 0.3 mm/yr. The total meltwater from both ice sheets is 0.5 ± 1.1 mm/yr.We also set the thickness change over 63 per cent of the grounded Antarctic ice sheet equal to the ERS satellite altimeter measurements and compute the variation of thickness change for Greenland. This can be done with J ₂ through /₅. The incomplete coverage of Antarctica makes the determination of lower mantle viscosity uncertain, but, if we assume this viscosity 1 X 1022 Pa-s, then the predicted combined sea level rise remains 0.5 ±1.0 mm/yr.

We present the first series of absolute gravity measurements at the French station Dumont d’Urville in Antarctica where GPS, DORIS and tide gauge continuous series are available. These gravity observations have been performed with the absolute gravimeter FG5#206 during one week in February-March 2000. We report on the field conditions of the experiment for which a thermally regulated shelter has been built and discuss the quality of the results. A special attention is paid to the influence of tidal ocean loading and different corrections according to existing models are tested. We also use this opportunity to establish a gravimetric link with the tide gauge of Dumont d’Urville in order to provide a geodetic Refserence. The tide gauge belongs to the ROSAME network and we used a Scintrex CG3-M relative gravimeter to perform this measurement. In the long term, it is essential to be able to distinguish between any vertical motion of tectonic origin and the true sea level changes. Furthermore, we have established a precise gravimetric link between Hobart (Tasmania) and Dumont d’Urville, which will be useful for future marine geophysical campaigns in this region.

During 1999 – 2000 Italian expedition in Antarctica started a new Geodetic Program with the aim to extend Northward and Southward the existing GPS geodetic network for the crustal deformation control of northern Victoria Land. The network is named VLNDEF (Victoria Land Network for DEFormationn control).A network of 20 stations, spanning an area of 700 km northward and 300 km westward, with an average distance of 70–80 km, and covering the area from TNB to Pacific Ocean Oates Coast was established and surveyed. Because of some rather long baselines, the session duration was not less than 40 hours and network stations were connected to the GPS permanent stations of Terra Nova Bay Station (TNB1), McMurdo (MCM4) and Dumont DTJrville (DDU).VLNDEF project was made within the activity of GIANT (Geodetic Infrastructure of Antarctica) SCAR (Scientific Committee on Antarctic Research) Program. GIANT is being developed for several years with the goal to study the infrastructure and the geodynamics of Antarctica continent by the analysis of different geophysical and geodetic data, GPS (SCAR GPS Epoch campaigns) and permanent tracking stations, Gravimetry, VLBI, Remote Sensing and tide gauges. Moreover the geodetic activities are coordinates and finalised within the actions of ANTEC (ANTarctic NeoTECtonics) SCAR Group of Specialists.

In the severe environment of polar regions geophysical and geodetic data are relatively sparse. Although various satellite data are recently available in polar regions, it is extremely important that surface observation data be used as ground truth.This paper presents the result of gravity and GPS observations obtained in Antarctica. The Bouguer gravity anomalies obtained shows the large negative anomaly trending inland toward Dome Fuji of the most southern observation area at about — 200 mgal. It indicates that the observed Bouguer gravity anomalies express the depth of Moho discontinuity, thus indicating a thickening of the crust inland. In addition, GPS observations were carried out several points on the traverse route. The baseline length between Syowa and Dome Fuji was 933133.144 m(rms:0.12m) and height of Dome Fuji point was 3796.779 m(rms:0.27m). The obtained results indicate that the movements of ice sheet are certainly detectable in the inland, Antarctica.

An international, cooperative effort is ongoing to compile and evaluate all available gravity data north of 64N, in order to produce a public-domain 5’ free-air anomaly data grid by 2001. The data will, e.g., be useful for limiting the “polar gap” problem of the upcoming gravity field satellite missions. The data contributed so far includes older and recent airborne, surface, marine and submarine gravity data from US, Canadian, German and Scandinavian contributors, as well as limited grid coverage of parts of Russia and data from satellite altimetry. In the paper the current data and compilation status is outlined, along with some comparison results of different data sources in overlapping regions. A preliminary data grid and associated geoid model is presented, highlighting among other the complex tectonic patterns in the Arctic region.