Showing papers in "Bollettino Di Geofisica Teorica Ed Applicata in 1999"

The CHAMP geopotential mission

Abstract: CHAMP is a German small satellite mission aiming at the simultaneous precise observation of both the gravity and magnetic field from a low altitude orbit. Thanks to the dedicated orbit design, an unprecedented low altitude in a near polar orbit, its continuous undisturbed observation of the magnetic field vector through scalar and vector magnetometers and its continuous GPS satellite-to-satellite tracking capability together with a direct on-board measurement of the non-gravitational orbit perturbations, a dramatic improvement in the global modeling of the magnetic field and also an order of magnitude improvement for the broad to mesoscale structures of the gravity field can be expected. In addition, due to the designed 5 years mission duration, temporal changes in both fields will be detectable with a higher signal/noise ratio and at increased spatial resolution as it is possible now. CHAMP was successfully launched on 15 July 2000.

Accelerometers for CHAMP, GRACE and GOCE space missions: synergy and evolution

Abstract: The STAR ultra-sensitive space accelerometer, based on the accurate electrostatic levitation of a parallelepiped proof-mass, is integrated at the center of the mass of the CHAMP satellite to be launched in 1999. STAR will perform the measurement of the non-gravitational accelerations which perturb the low-altitude orbit to be finely determined from the on-board GPS receiver, aiming at the recovery of the Earth's gravity field. The operation, design and technology of the accelerometer are well suited for optimization of the measurements provided for different mission performance requirements and environments. The Super-STAR instrument is designed keeping in view the two GRACE satellites, with a reduced full-scale range, and a resolution ten times better, leading to 10 -10 ms -2 over an 1 Hz bandwidth. The launching of the GRACE satellites is scheduled for 2001 and the GOCE project is a good candidate for a follow-on mission. The GOCE's on-board gradiometer can be composed of a very stable carbon-carbon structure with similar electrostatic accelerometers: taking advantage of the fine active thermal control of the instrument case and of the drag-free compensation system of the satellite, a few 10 -3 Eotvos can be reached at an altitude as low as 250 km.

A method for estimating gas hydrate and free gas concentrations in marine sediments

Abstract: I propose a method for estimating gas hydrate and free gas concentrations versus depth in marine sediments, using Gassmann's equation. The theory models gas hydrate- and free gas-bearing sediments partially saturated with water. A quali- tative estimate of the concentrations can be obtained by comparing the theoretical velocity for full-water saturation to the experimental velocity, evaluated by a tomo- graphic analysis or available from well logging. Positive anomalies indicate the pre- sence of gas hydrate and negative anomalies indicate the presence of free gas. A quantitative estimate of concentrations is obtained by fitting the theoretical velocity to the experimental velocity. The method has been tested against sonic log and VSP data and indirect estimations of gas hydrate concentration from chloride content in core logs.

CHAMP, GRACE and GOCE: Mission concepts and simulations

Abstract: For the first time in satellite geodesy, three gravity missions have the potential of being realized: (1) CHAMP is a low-cost mission, an intermediate step between our present knowledge and the ambitious goals that are formulated by geodesists, solid Earth geophysicists and oceanographers; (2) GRACE is planned as being a more advanced mission, especially aimed at monitoring long wavelength time variations of the gravity field; (3) GOCE will open a completely new range of spatial scales (in order of 100 km) of the geopotential spectrum to research. The three missions are based on different space segments which have in common the high-low satellite-to-satellite tracking (SST) from GPS; other common parts being the low-low SST in the case of the two co-orbiters of GRACE, and gradiometry on board the GOCE spacecraft. Many new numerical simulations have been conducted in a unified effort in order to: 1. compare the concepts in terms of idealized (e.g. polar) missions using only one technique at a time; 2. estimate the capabilities of more realistic missions, closer to the planned scenarios of GOCE, GRACE and CHAMP with instrument, orbit and mission parameters that will allow an easy scaling to the actual cases. The most significant results are reported in this paper.

Iterative 3D gravity inversion with integration of seismologic data

Abstract: Depending on the a priori knowledge, different methods can be chosen for gravity inversion. The method we propose is suitable for cases in which little is known about the crustal structure, except the presence of a sharp density contrast, as occurs at the Moho or at the base of a sedimentary basin. The method combines the downward continuation with the direct evaluation of the gravity field of the undulations of the boundary surface in an iterative process. The a priori assumption of the reference depth of the boundary and density across the surface is necessary. If the depth of the boundary is known along a profile or in single points from seismologic (or other) investigations, this piece of information is used to anchor the boundary. In lack of such knowledge general geophysical considerations must be used to obtain an estimate of the boundary in the undisturbed state. The method is tested in a 3D synthetic model situation, evaluating the effect of erroneous a priori assumptions and noise.

GRACE: a satellite-to-satellite tracking geopotential mapping mission

Abstract: For a number of applications in oceanography, hydrology, glaciology and the solid Earth sciences, the mapping of the Earth's global gravity field can provide a critical observational and constraint dataset. The GRACE mission, selected under the NASA Earth System Science Pathfinder (ESSP) program for a mid-2001 launch, will provide a major advancement in the mapping of the Earth's gravity field in both the mean sense and for temporal variations on time scales of 30 days and longer. This mission will provide measurements of the range between two low Earth orbiters to submicron precision using dual-one-way, dual frequency microwave tracking. The two orbiters will be placed in near polar, near 500 km altitude orbits, separated from each other by approximately 250 km, over a mission lifespan of 3-5 years. The satellites will also carry GPS receivers and high precision accelerometers to aid the recovery of the gravity field from observational data. In our oral presentation, we provided a summary status of the project to date. Also, we reviewed the science rationale and capabilities of GRACE for the measurement and monitoring of the Earth gravity field changes. The impact of the result from GRACE on our measurement and understanding of global climate change, and its interaction with other space and ground-based geophysical data sets were discussed.

The best isotropic approximation of an anisotropic Hooke's law

Abstract: What is the best isotropic approximation of an anisotropic stiffness tensor? How can we quantify isotropy with a single numerical index? This article gives a precise meaning to these questions by introducing an orthogonal projector from the stiffness tensors space onto the isotropic tensors subspace. Moreover, explicit expressions are derived for the Lame parameters of this approximation, when the data are either in coordinate-free form or in Voigt's notation. Thus it is possible to unravel the effect of anisotropy on time-harmonic plane wave propagation. Detailed computations are shown in the case of ANNIE shales, which are transversely isotropic, by way of example. Finally, the isotropic approximations of 44 shales are computed, with the result that the anisotropy index is less than ten percent for just five of them. Potential applications of this approach to rock physics, seismic exploration, reservoir engineering, and seismology are briefly outlined.

The Grotta Gigante horizontal pendulums -instrumentation and observations

Abstract: The horizontal pendulums of the Grotta Gigante have a long history dating back to 1959. In the past the instruments have been revised several times. The main instrumental characteristics are exposed, including the noise spectrum calculated over about 30 years. A review on the main results obtained with the pendulums is made, results which cover the topics of Earth tides and loading effects, free oscillations of the earth, preseismic effects and regional deformations.

Recent improvement in the KMS global marine gravity field

Abstract: During the first half of 1998, the procedure for deriving the KMS global marine gravity field (Andersen and Knudsen, 1995, 1996) was revised. The resolution was enhanced, and several parameters were tuned to obtain a better gravity field. The updated procedure for the new KMS98 gravity field and their differences with the procedure for deriving the older KMS96 gravity field is presented in this paper. An important tool in the improvement of the KMS gravity field was the use of high quality marine gravity observations to check possible finetuning of parameters. Testing and comparison with other recent global marine gravity fields is carried out in regions of rapid changing gravity signal like over trenches and sea mounts to illustrate the improvement in the new gravity field. The improvements involved a better spatial varying filter for the interpolation of the geoid anomalies depending on the local RMS variability, and an enhanced filtering in the conversion between geoid anomalies and gravity. The KMS98 gravity field is available at the Internet-address: ftp://ftp.kms.dk/pub/GRAVITY, which also contains information on how to use the field.

Climatological analysis of the Adriatic Sea thermohaline characteristics

Abstract: A comprehensive hydrographic data set of the Adriatic Sea, obtained mer- ging the historical ATOS1 data set (Adriatic Temperature Oxygen and Salinity) with data from the MODB (Mediterranean Oceanic Data Base) and CTD data obtained from recent European research projects, is presented. Rigorous quality checks have been applied to eliminate duplicate profiles and obtain a coherent and scientifically validated data set. By including CTD data, a better seasonal coverage of the Southern Adriatic Depression, with continuous measurements down to the bottom has been acquired. This made it possible to supplement existing work with a clima- tological analysis, supported by a good data resolution, of the thermohaline fields along characteristic cross-sections and in the deepest layer of the basin. An interan- nual variability of the Adriatic Deep Water (ADW) that resides in the Southern Adriatic Depression was detected.

Gravity studies on active Italian volcanoes: a comparison between absolute and relative gravimetry

Abstract: Gravity studies aimed at detecting volcanic inputs, precursors to a preeruptive state are in process on active Italian volcanoes. To achieve this goal high precision absolute and relative gravity measurements are carried out to identify time variations of the gravity field caused by the ascent of magmatic masses. Since 1980, gravity surveys have been carried out at Mt. Etna, the Aeolian Islands, Pantelleria, Ischia, Mt. Vesuvius and the Campi Flegrei. Absolute measurements of gravity acceleration date back to 1986 and are carried out on selected stations of the relative networks. The absolute stations work as a reference for the relative networks. Moreover, by periodically surveying them, they provide the long-term components for the temporal trend of gravity changes. Intercalibrated LaCoste & Romberg, model D, gravity meters are employed for relative gravity measurements. Absolute measurements of g are carried out by means of the ballistic Absolute Gravimeter (symmetrical rise and fall method) built at the Istituto di Metrologia G. Colonnetti of the Italian National Research Council. Moreover, constantly recording gravity stations are also working at Mt. Vesuvius and Mt. Etna. Their aim is to keep continuous records of the changes versus the time of the gravity field and tidal parameters, possibly consequence of the variations in the physical state of the volcanoes monitored. The absolute stations have been surveyed more than once at Mt. Vesuvius, at the Island of Vulcano and on Mt. Etna. The ensuing comparison between the gravity changes observed by relative and absolute measurements indicates that a combination of both measurements is the most complete and reliable way of defining the long- and short-term space-time evolution of the gravity field associated to volcanic dynamics. The main results concern Mt. Vesuvius and Mt. Etna, where the gravity changes obtained through absolute, relative and recording gravimetry have been associated, respectively, to an increase in seismic activity and to an eruptive event.

Spectral probabilistic seismic hazard assessment for Italy

Abstract: During the last decade the Italian Gruppo Nazionale per la Difesa dai Terremoti has undertaken a project for assessing seismic hazard on probabilistic bases in the national territory, to be used as scientific background for the revision of the current seismic zonation: the seismic hazard was expressed there in terms of peak ground acceleration and macroseismic intensity. A more detailed analysis is now performed. Probabilistic spectral seismic hazard maps at different frequencies of engineering interest demonstrate that the soil condition is a first order factor influencing the level of the expected shaking, with an average increase of about 0.2 g for the prediction related to a 475-year return period, when passing from rock to soft soil. The attenuation model similarly conditions the results, hut in a more magnitude-dependent fashion. Here, the two relationships selected account for the effects of strong rare seismicity and moderate frequent earthquakes differently: differences going from 20% to 80% of the predicted spectral accelerations are, therefore, model-dependent. The uniform hazard response spectra for some major Italian towns are then compared to the elastic response spectra of the present Italian seismic zonation, indicating that two important towns such as Rome and Naples are not adequately represented by the present code. The effective peak acceleration is considered, finally, a good synthetic parameter for representing seismic hazard in most engineering applications.

A comparative analysis between an absolute gravimeter (FG5-206) and a superconducting gravimeter (GWR C026) in Strasbourg: new results on calibration and long-term gravity changes

Abstract: This paper is devoted to a comparative analysis of gravity changes as observed both by an absolute gravimeter (AG-FG5 model 206) and a superconducting gravimeter (SG-GWR model C026) operating in parallel in Strasbourg in 1997-1998. Two main objectives will be sought: on the one hand, we want to establish the calibration capability of AG/SG parallel registrations, especially with respect to stability in time, duration requirement and precision; on the other hand, the absolute gravity values will be superimposed on the superconducting gravimeter observations in order to estimate long-term gravity changes and to attempt to separate true physical effects from the instrumental drift contribution of the cryogenic meter.

Investigation of the Molodensky series terms for terrain reduced gravity field data

Abstract: Masses associated with the local topography are a dominant source of short wavelength gravity field variations. In the modeling of the gravity field it is thus an advantage to eliminate the effect of the terrain in a remove-restore procedure. In this process, terrain reductions are computed for the observation stations at the Earth's surface, considering either the complete topography, the topography and its isostatic compensation, or the residual topography (RTM technique). Hence, the reduced gravity field observations are referring to the actual ground level. Therefore, Molodensky's theory, considering data on non-level surfaces, should be applied in the traditional gravity field modeling approaches, while in collocation this is handled directly through height dependent covariance functions. In this paper, we provide numerical examples for the computation of the Molodensky series terms associated with the traditionally unreduced observations as well as in connection with various terrain-reduced data. Due to the smoothing, resulting from the terrain reductions, the magnitude of the Molodensky terms is reduced as well and the series convergence is improved. The computations are based on the Fast Fourier Transform (FFT) technique. The numerical tests are done in a mountainous area of the European Alps. The terrain data are on grids with various grid spacings starting at a resolution of 200 m. One of the main goals of this study is to investigate the magnitude of the Molodensky terms with regard to the computation of an improved European quasigeoid model.

Topographic mass density and gravimetric geoid modelling

Abstract: Current geoid modelling procedures assume an average density of 2.67 g/cm 3 , which appears to be inadequate for geoid modelling at the centimetre level of accuracy. We have produced the topographic mass density map of Canada based on the digital geological map of the country and in-situ rock density values from various geological studies and actual rock samples. Representative density values of the rock types in Canada vary by as much as 13% when compared to the mean value of 2.67 g/cm 3 . In the Skeena region of British Columbia, Canada, the effect of the variable density on the terrain corrections to gravity ranges nearly three mGal, while in the rolling hills of Northern New Brunswick, Canada, the range is about 0.5 mGal. Consequently, the effect on the geoid ranges nearly 10 centimetres and seven millimetres respectively for the two test areas.

GOCE mission concept, error derivation and performances

Abstract: GOCE is a gravity-measuring satellite under consideration by the European Space Agency. The satellite carries a gravity gradiometer, a GPS receiver and a system to compensate external - non gravitational - accelerations. The detailed study of the errors affecting the mission needs complex computer simulations, however a simplified logic for error evaluation and for the allocation of derived requirements has been developed. This logic is based in the analysis of the error sources and their classification as either probabilistic or deterministic. A classification of the error sources has been performed. This analysis has been used to derive worst case and most likely performances for the mission. This simple approach avoids over-designing while still providing excellent scientific performances.

Temporal gravity field variations from oceanic, atmospheric and inner core mass redistributions and their sensitivity to new gravity missions CHAMP and GRACE

Abstract: Temporal gravity field variations are caused by mass redistributions in the atmosphere, on the Earth's surface and in the Earth's interior. With the upcoming new gravity missions CHAMP and GRACE, for the first time such variations can be measured from space on a global scale. To estimate the time variable gravity signals and their sensitivity to the new missions, simulation studies for specific gravity variation sources in all three areas are performed. Starting from a long series of monthly mean atmospheric air pressure data from 1900 to 1988, monthly atmospheric density variations with respect to the long-term mean are computed and transformed into monthly gravity coefficients. A similar approach was used to estimate monthly gravity field coefficients from oceanic mass redistributions. For an 8-year period, monthly spherical harmonic series up to degree and order 6 from ocean bottom pressure fields, derived from the POCM ocean circulation model, are estimated. Another method for estimating the impact of ocean mass redistributions on the gravity field is based on three-year monthly residual sea-surface models from altimetry, which are corrected for the thermal water expansion. Attraction of these residual water masses is transformed into monthly gravity field coefficients up to degree and order 100. Finally, gravity changes caused by the precession of the inner with respect to the outer core and their density differences are predicted for a long time series from 1900 to 1991. Half-yearly gravity coefficients are estimated up to degree 2. Time series for all gravity field coefficients from these different sources are then analyzed to detect their amplitudes and phase lags. All calculated gravity signals are compared to the expected sensitivity of the CHAMP and GRACE missions.

Gradiometer calibration and performance verification: GOCE approach

Abstract: The GOCE project aims at measuring the gravity gradient of the Earth with a noise spectral density of 1 to 5 mE/Hz 1/2 , depending on the scenario, in a bandwidth going from 0.005 to 0.1Hz, and at an altitude of 250 km. An Electrostatic Gravity Gradiometer (EGG) is studied at ONERA, and requires (i) ultra-sensitive space accelerometers with a noise of around 4×10 -13 m.s -2 /Hz 1/2 , (ii) a very demanding calibration, and (iii) a very quiet environment inside the satellite (thermal and geometrical stability, fine drag compensation...). These performances cannot all be verified directly, on the ground, with the required level. The main reasons are the presence of 1g, and seismic noise. As a consequence, the EGG calibration, with its performance verification plan, demand a trade-off between the on-ground partial verifications, the in-flight ones, the pure calculations, and the combination of complementary approaches. This approach has been developed at ONERA, in parallel with experimental verifications, under ESA contract.

Ocean loading and crustal deformation in Bretagne (France): an experiment involving differential GPS, gravimetry and tide gauges

Abstract: Brest in west part of France, is a place where the oldest tide gauge data are available. A complete recording since 1807 shows the variations of the sea level height from it can be infered the elevation of the mean sea level. More, with its geographic location, Brest is an ideal place to observe the sea tides (high tidal range). For this reasons, it has appeared very interesting to conduct gravimetric and geodetic measurements. This paper presents the first results on the ocean loading studies.

Further analyses towards the introduction of ocean circulation model information into geopotential solutions

Abstract: Two representation methods for the Dynamic Ocean Topography (DOT) are compared. One uses surface spherical harmonics, the other Proudman functions, which form an ocean domain-specific orthonormal basis. The DOT implied by the temporally averaged output of the POCM―4B ocean circulation model, provided the data for the implementation and testing of the two methods. Using these data a spherical harmonic representation was developed, to degree 30, and a Proudman function decomposition employing 961 basis vectors, so that both representations involve an equal number of parameters. The input DOT field had an rms value of ±66.6 cm. The recovered rms DOT was ±66.1 cm for the spherical harmonic case, ±66.3 cm for the Proudman function case, while the rms difference between the two cases was ±4.2 cm. Although in an overall sense the two representations (with equal number of parameters) yield similar results, in the proximity of the ocean domain boundary the Proudman functions approximate the input DOT field better than the surface spherical harmonics.

Development and evaluation of a new Canadian geoid model

Abstract: The purpose of this paper is to present the development and evaluation of a new gravimetric geoid model (GARR98) for Canada and parts of the U.S., created in the Dept. of Geomatics Engineering at the University of Calgary. The methodology applied for the computation of the new geoid, and the data types that were used, are discussed. GARR98 uses the most current databases available for Canada, namely, new additional surface gravity data, high resolution DEM model, and a more accurate geopotential model (EGM96). Comparisons among the new geoid, geopotential models (OSU91A and EGM96), the latest GSD95 Canadian geoid model, and GPS/levelling data, are also presented. Absolute and relative differences at 1300 GPS benchmarks are computed, on both national and regional scales. These external comparisons reveal interesting information regarding the behavior of the Canadian gravity field, the quality of the geoid models, and the achievable accuracy in view of future GPS/levelling applications.

Intercomparison and evaluation of some contemporary global geopotential models

Abstract: The performance of five global Earth gravitational models, published after 1995, was examined through tests with data (mostly) withheld from the development of these models. We considered the models: JGM-3 (Tapley et al., 1996), GRIM4-C4 (Schwintzer et al., 1997), TEG-3 (Tapley et al., 1997), EGM96 (Lemoine et al., 1998) and GPM98A (Wenzel, 1998). The test data that we used for model evaluations include satellite tracking measurements acquired over several spacecraft at various inclinations and altitudes, geoid undulations (or height anomalies) determined from GPS positioning and leveling observations, Dynamic Ocean Topography (DOT) information implied by an ocean circulation model, as well as hydrographic estimates of (relative) DOT. Over 9307 GPS/leveling geoid undulation values distributed over North America, Europe and Australia, EGM96 (to degree 360) outperforms all other models tested, yielding a standard deviation of the undulation differences of ±37.2 cm. Considering that the available GPS/leveling data are located over some of the best surveyed areas (gravimetrically), this value is consistent with the predicted (commission plus omission) geoid error of EGM96, whose global rms value equals ±45.3 cm. Over the ocean, the performance of EGM96 is superior to that of all other models tested, as judged by the results of comparisons with both the POCM―4B circulation model DOT output and with the hydrographic DOT estimates. GPM98A was found to be inaccurate over medium wavelengths, and is not considered suitable for orbit determination applications.

Combining gravity anomalies and deflections of the vertical for a precise Austrian geoid

Abstract: The combination of a rich geomorphology which includes lowlands as well as high mountains and the high quality of the available source data proves Austria to be an excellent test area for geoid computations. A dense field of gravity anomalies and deflections of the vertical together with a high-resolution height model are the ideal base to study different algorithms and methods for geoid computation. The following case study, within the project of the recomputation of the Austrian GEOID2000, investigates the combination of different data-sources for a high-resolution geoid for areas with rough topography. The computations are performed using Least Squares Collocation (LSC) and the remove-restore technique.

An analysis of geopotential difference determination from satellite-to-satellite tracking

Abstract: The determination of the Earth's gravitational field from a dedicated satellite-to-satellite (SST) tracking mission has been considered for more than two decades. The usual assumed approach to gravitational field modeling from SST data is by spherical harmonic series development. On the other hand, many feasibility studies based on covariance analyses have assumed a direct relationship between geopotential and intersatellite range-rate. The latter would make local gravity field determination possible, without the need for computationally massive global spherical harmonic solutions. However, the relationship between the actual observable and the potential is not as simple as assumed in previous studies. Alternatively, three-dimensional velocity differences may be determined with GPS baseline tracking, and then the relationship to potential is, in fact, straightforward. But the measurement accuracy of the observable is less than with intersatellite ranging. This paper examines in detail the relationship between geopotential differences and the observables in intersatellite ranging and in GPS relative velocity measurements. Error analyses and simulations based on the GRACE mission are presented to show the feasibility for local gravity field determination in either case.

Gravimetric geoid computations in Hungary and the surrounding area

Abstract: Different local gravimetric geoid solutions were carried out in Hungary and the surrounding continental area. These solutions were based on terrestrial gravity data and height data using as a reference surface the EGM96 geopotential model. The gravity data used in the area 45.5° < o < 49°, 16° < λ < 23° were finally gridded on a 1.5 x 2.5' geographical grid. These included more dense gravity data with respect to a previous gravimetric solution for Romania and Yugoslavia. The height data were available on a 1km x 1km grid. The methods used were the spherical 1D Fast Fourier Transform (FFT) method and the Fast Collocation (FCOL) procedure. In order to assess the accuracy of the computed geoid heights we compared them with 43 Hungarian GPS/leveling stations belonging to the EUREF89 network. The statistical results of the derived differences give an accuracy close to 12 cm in terms of standard deviation, which decreases to 8 cm after subtracting a linear trend and bias model. Excluding 14 GPS stations located at the borders of Hungary the aforementioned accuracies reached the level of 7 cm and 6 cm, respectively. Moreover, we have compared our geoid solution in the entire test area with the European geoid EGG97 and found a standard deviation of differences close to 41 cm and 20 cm before and after subtracting a linear trend and bias model. In a last numerical experiment we computed geoid heights by 1D FFT using different cap sizes for the gravity data. The geoid height results were similar and no significant improvement has been achieved.

Difference between geoid undulation and quasigeoid height in Hungary

Abstract: The difference between geoid and quasigeoid in Hungary was estimated by an approximate formula given in Heiskanen and Moritz (1967) using a data set of mean 1.5' x 2.5' gridded Bouguer anomalies and elevations. The results obtained are discussed from the point of view of the precision GPS heighting.

Improvement of Japanese geoid with 1D-FFT method and its comparison with altimetry-derived geoid

Abstract: An improvement of the Japanese gravimetric geoid over a pre-existing model, JGEOID93, is studied with the 1D-FFT method as a strict realization of Stokes' spherical integration in a remove-restore manner and in consideration of possible mean offset errors in the network-adjusted ship gravity data used. Simulation shows that the offset errors of about 4.9 mGal in a limited distribution in space, result in geoid errors of a few meters of amplitude in the medium wavelength, a situation which should not be ignored. The differences between the 1D-FFT and single-band 2D-FFT geoids range from 15 cm to - 25 cm with a 2-3 cm RMS. We prepare an approximated error response function of Stokes' kernel, which well indicates the geographical distribution of the differences. The 1D-FFT geoid obtained, provides better accuracy in magnitude and a slight improvement in precision, in comparison with a nation-wide network and several local networks of GPS at benchmarks. Comparison of the gravity field and geoid with an altimeter-derived global model (Sandwell and Smith, 1997) reveals the existence of significant discrepancies in the southeastern edge of the Sea of Japan, which is attributed to the altimeter model errors.

Shallow water tidal determination from altimetry the M4 constituent

Abstract: With the long duration of accurate satellite altimetric measurements from the TOPEX/POSEIDON and the ERS satellites (ERS-1 and ERS-2) it is interesting to investigate if satellite altimetry can provide more accurate tidal models on continental shelves. The call for increasing accuracy in shelf regions, calls for inclusion of more than just semi-diurnal and diurnal constituents in future global ocean tide models. This is because a considerable part of the tidal variability on the shelves is caused by shallow water constituents. One example is the M 4 constituent, which exceeds 50 centimetres at several locations on the northwest European shelf. So far satellite altimetry has not been considered for resolving these constituents, due to its accuracy and coarse ground-track resolution. Reliable empirical estimates of the major shallow water tide constituent called M 4 , can be obtained from TOPEX/POSEIDON, by combining along-track and crossover observations. Estimates are presented in this study and compared with tide gauges and existing hydrodynamic models.

Improving local gravimetric geoid models with external data

Abstract: Local gravimetric geoid models from a combination of a global geopotential model and local gravity anomalies, usually contain errors of dm-level on wavelengths longer than 50 km. One of the main causes for this is the limited precision of the global models. External geoid information on discrete points, like GPS and levelling sites on land and altimeter tracks, combined with permanent sea surface to-pography at sea, is often available with cm-precision. These points can be used to correct the medium and longer wavelength errors in the gravimetric geoid. The problem is to find an adequate functional representation of the correction surface. The authors have developed a method of investiging the form of this correction, and finding empirical representations depending on area size. Once a class of functions have been selected the most suitable can be found by a statistical testing procedure.