Observing our Changing Earth

Unambiguous reference systems are a fundamental requirement for accurate and reliable geodetic products. The definition of the reference system, the realization by a reference frame, and the allocation of the geodetic datum have to be strictly coherent. In traditional geodetic reference systems used in triangulation and trilateration networks, the datum was given through independent (astronomic) observations in selected fundamental stations, which fixed the origin and the orientation of the coordinate system. The datum of modern geocentric reference systems must also be determined by independent methods, namely by gravity field parameters and physical models. If it is derived from the reference frame itself, i.e., by coordinate transformations between selected reference stations, the definition of the system will be changed: It does no longer refer to the geo-centre but to the centre of the reference network. Therefore it is indispensable to strictly pay attention that the datum is not affected by the measurements of the frame, and that the realization of the frame does not change the definition of the system

A “dynamic” geodetic datum is a datum that consists of coordinates and velocities of control points, which can provide users with the realistic positions of sites within the network that reflects the result of local or regional motion induced by a number of causes. A new ITRF-linked scheme is proposed and discussed in order to process available geodetic data in real-time to establish a dynamic ITRF-like datum. The authors suggest providing a variety of such datums for different applications. The noise properties of the geodetic coordinate time series are crucial to reliably estimating positions, velocities, and their stability and uncertainties. A ‘db3’ wavelet transform is used to separate the noise of the velocity series and the autocorrelation. The histogram distribution and spectrum features of the residuals indicate that the outliers impact the de-noising effect. A Kalman filter-based model with the outliers being detected and removed online is investigated to obtain the “purified” velocity series for ITRF modeling. For a local scale application, interpolation methods play an important role in improving the accuracy of the datum. Six interpolation methods are investigated using a simulated velocity data set. The “local patch” model is necessary for a local datum in order to handle unexpected events

This paper presents the results of different methods that have been applied to investigate the strength of SLR observations to realize the scale and origin of the terrestrial reference system. In this context the effect of the network geometry and the satellite altitude has been studied by analysing the covariance matrix of the datum parameters. Furthermore, the time series of the scale and translation parameters of weekly SLR network solutions were analysed from 1993 until 2007 and the effect of range bias estimation has been investigated

The study of station non linear motions requires being able to discriminate between the local motion of every station and their global motion (e.g. geocenter motion). A common used approach consists in estimating Helmert parameters with respect to a secular reference frame. But if the network is small or not well distributed, the global parameters, and mainly the translation and scale parameters, will not be rigorously decorrelated from the station displacements. The distribution of the currently operating Satellite Laser Ranging (SLR) stations is one example of such a network. The understanding of the network effect needs an analysis of the station distribution over time. It appears that SLR station distribution on the X positive hemisphere of the Earth varies seasonally. We suggest here that using GPS results to constrain the estimation of SLR station displacements may improve the estimation of the Helmert parameters. These additional constraints as well as stochastic constraints are numerically tested here in a first attempt to limit the impact of the network effect. We show that the X component of the translation and the scale are the two parameters that are the most sensitive to any change in the configuration of the added constraints

The Bavarian Committee for International Geodesy (BEK) has been a Local Analysis Centre (LAC) for the EUREF Permanent Network (EPN) since 1995. The analysed network covers the northern part of the Mediterranean region with its diverse tectonic features. The processing strategies, the realizations of the global reference system and models for correcting different physical effects have been improved and changed during the past 10 years of analysing GPS data. All these modifications had a significant impact on the coordinate estimation. It is therefore not surprising that time series of coordinate changes always reveal such modifications and may hide tectonic events. A group from the Technische Universität München (TU Munich), Technische Universität Dresden (TU Dresden) and the GeoForschungsZentrum Potsdam (GFZ Potsdam) made an effort to reprocess a global GPS network to derive consistent coordinates of stations as well as orbits and earth rotation parameters (ERPs) in the IGb00 applying absolute antenna phase centre variations (PCV) for the antennas. The reprocessed orbits and ERPs have been used at the BEK for a reprocessing of 10 years of GPS data, using a network of roughly 65 sites. This paper will focus on the improvement achieved by applying consistent products, strategies and models

The Brazilian Network for Continuous Monitoring of GPS – RBMC, since its foundation in December of 1996, has been playing an essential role for the maintenance and user access of the fundamental geodetic frame in the country. It provides to users a direct link to the Brazilian Geodetic System. Its role has become more relevant with the increasing use of space navigation technology in the country. Recently, Brazil adopted a new geodetic frame, SIRGAS2000, in February 2005, fully compatible with GNSS technology. The paper provides an overview of the recent modernization phases the RBMC network has undergone highlighting its future steps. From its current post-mission mode, the RBMC will evolve into a real-time network, providing real-time data and real-time correction to users. The network enhanced with modern GPS receivers and the addition of atomic clocks will be used to compute WADGPS-type corrections to be transmitted, in real time, to users in Brazil and surrounding areas. It is estimated that users will be able to achieve a horizontal accuracy around 0.5 m (1 σ) in static and kinematic positioning and better for dual frequency users. The availability of the WADGPS service will allow users to tie to the new SIRGAS2000 frame in a more rapid and transparent way for positioning and navigation applications. It should be emphasized that support to post-mission static positioning, will continue to be provided to users interested in higher accuracy levels. In addition to this, a post-mission Precise Point Positioning (PPP) service will be provided based on the one currently provided by the Geodetic Survey Division of NRCan (CSRS-PPP). The modernization of the RBMC is under development based on a cooperation signed at the end of 2004 with the University of New Brunswick, supported by the Canadian International Development Agency and the Brazilian Cooperation Agency. The Geodetic Survey Division of NRCan is also participating in this modernization effort under the same project

We describe the treatment of the permanent tide in various geodetic quantities with an emphasis on systems of gravity-related heights. We review the historical development leading to the present situation, and discuss possible scenarios for the future, especially in view of the adoption of a World Height System

The combined adjustment between the National Astro-Geodetic Network and the National GPS2000 Geodetic network in China is described. In this paper, measurements of astro-geodetic network had been taken for nearly 60 years from early 1920’ to 1980’. Some astro-geodetic points may have moved during such a long time period, so coordinate analysis for points co-located in the two networks is very important. The factors which influence combined adjustment, such as earth’s crustal movement, the change of astronomic system, geoid improvement, etc., must be analyzed in advance. In this paper, the measurements and their accuracies are also introduced together with mathematical and stochastic model used in the adjustmen. Due to the huge number of unknowns (about 150 thousands), the solution strategy for large scale equation using PC is also described. Satisfied results are obtained after the combined adjustment

The available gravity field models derived from data of the GRACE mission (tapley and Reigber (2001)) have provided us with an unprecedented accuracy in gravity field determination. Nevertheless the projected GRACE baseline accuracy has not been achieved yet. One reason out of many could be the insufficient modelling of the satellite data by a global representation by means of spherical harmonics. To extract the signal information present in the satellite and sensor data to full content, it seems reasonable to improve global solutions by regional recovery strategies. Especially in the higher frequency part of the spectrum the gravity field features differ in different geographical areas. Therefore the recovery procedure should be adapted according to the characteristics in the respective area.In the approach presented here in a first step a global gravity field represented by a spherical harmonic expansion up to a moderate degree has to be derived. It is then refined by regionally adapted high resolution refinements being parameterized by splines as space localizing base functions. In this context a special attention is paid to the signal to noise ratio in different geographical areas.The approach is demonstrated by examples based on the analysis of the original GRACE Level 1B data

Traditionally, in satellite derived static global gravity field models, the total mass of the Earth is considered to be the sum of the solid Earth mass and the water masses in land (hydrology), oceans, ice (continental ice and sea ice) and atmosphere. The total mass is reflected in the GM value (gravity constant times Earth mass), which usually is a parameter of geodetic reference systems. As the whole system Earth is mass conserving in principle GM should be constant over time. Any time dependency of GM could only be caused by wrong estimates for GM (or the corresponding zero degree coefficient of the spherical harmonic series)For analysis of the time variable gravity field the situation is more complex, because masses are fluctuating at various temporal and spatial scales and are exchanged between components of the Earth system. Disregarding mass variations inside the solid Earth (e.g. by earthquakes, mantle convection, etc.) the water cycle represents the major source of mass variations, of which the atmosphere plays the most prominent role (by pressure field variations, by forcing ocean circulation, by precipitation and evaporation). In order to take into account such temporal variations for gravity field analysis the sampling pattern of the satellite mission and its sensors in addition play a crucial role. This means that during gravity field recovery the known part of mass variations with respect to the mean value have to be modelled independently and corrected for in order to avoid aliasing of temporal signals into the resulting fields. In contrast, unknown time variable mass variations have to be estimated. Both approaches are applied nowadays in the GRACE data analysis simultaneouslyThe paper introduces the problem of atmospheric mass variability for gravity field determination with satellite data. In the main part of the paper estimates for the total mass of the atmosphere and its variability in time as well as an analysis of the impact of the vertical structure and of potential errors in the atmospheric fields are provided. Results indicate, that the total atmospheric mass during the last 20 years slightly increased, what could be a hint to global warming. Results of error analysis also show, that for reaching the ultimate performance with GRACE data analysis, the vertical structure of the atmosphere as well as potential errors in the atmospheric fields are crucial

Kinematic positions of individual low Earth orbiting satellites equipped with spaceborne GPS receivers have been used in the past to determine the long wavelength static part of the Earth’s gravity field. In the near future GPS-derived relative kinematic positions of present and upcoming formation flying satellites like COSMIC and SWARM could be used in addition to perform and improve the long wavelength static part of the gravity field also with non-dedicated satellites. Since space baselines between satellites can be determined more precisely from GPS than the individual positions, a corresponding improvement of the estimated gravity field coefficients is commonly expected. We review and extend the principles of gravity field determination from kinematic positions of single satellites and apply them to kinematic baseline data. Simulated as well as real data from the GRACE GPS receivers are used to evaluate our procedures and to assess the impact of different GPS observables and processing strategies on the quality of the estimated gravity field coefficients

Gravimetric geoid NKG04 (Forsberg et al., NKG Geoid Meeting, Copenhagen) is derived by KMS using all available gravimetric data from the region. Some areas, also close to the Estonia are not completely covered by gravity measurements, example the eastern part of the Gulf of Finland. Baltic Sea is measured by airborn gravimetry with accuracy probably 2 mGal. Our idea was to compare the geoid on the sea areas against the independent method like GPS-levelling on the mainland. Main problem have been of course how to remove water tilt during the campaignThe existent GPS device on board a ship stores data every second and determines the heights with an accuracy of a few centimetres (using the kinematic method with post-processing, several base stations close to the ferry line). As a result, it is possible to observe the present relative water level profile in reference to the ellipsoid. If we take into account the tilt of the water level at the moment of measurement, we can observe the relative change of the geoid using independent methodology, which serves as a comparison to the gravimetric geoid solutionWith this method we explored some areas on the Baltic Sea covered with regular ferry lines where the geoid profile changes faster. One such area lies about 30 km north of the island of Hiiumaa, where the geoid has a “lump”: the separation of the geoid from the ellipsoid changes by 1 m over a 70-km distance starting from Paldiski; further towards Sweden the original separation is restored. In addition, we analyzed all the Estonian and Swedish profiles, also using GPS data from Swedish base stationsWe also performed the same kind of measurements on ferries running the regular line Tallinn- St. Petersburg-Helsinki-Tallinn. Those measurements were of particular interest as there was no gravimetric data available for the eastern part of the Gulf of FinlandAs a third track, measurements were performed on liners running between Sillamäe and KotkaThe results show that the 150-km geoid NKG04 profile close to Hiiumaa did not differ any more than 15 cm from the GPS-measured level surface. The influence of the water tilt was more or less eliminated using the available tide gauge data. The profile between Tallinn and St. Petersburg manifested similar difference. Most of the measurements were repeated several times on the same profile

In order to improve the gravity field and geoid modelling in the border area between Germany and Denmark, and over the Baltic Sea, an airborne gravity campaign BalGRACE 2006 (Baltic Airborne GRAvity Campaign and Elevation Estimation) was carried out in October 2006. The area covered was bounded approx. by 53.5–55.5°N, 8–15°E, with about 10,000 km of track data. A main purpose of this endeavour was to improve the gravity data base and geoid modelling in this area, hence, to give a substantial contribution towards comparison, verification and improvement of the vertical referenceUsing the newly obtained airborne data in connection with existing terrestrial and satellite observations, the combined data set allows various methodological investigations into gravity field modelling to be carried out. First numerical results of modelling the gravity field and the regional geoid are presented applying different geoid determination techniques

Airborne gravimetry is capable of filling the gap between the long wavelength parts of the gravity field provided by the satellite missions such as CHAMP or GRACE and the short wavelength parts derived from terrestrial data. Furthermore, airborne gravimetry techniques are not restricted to continental areas and are not subjected to certain limitations in contrast to terrestrial data. Considering optimal conditions the measurement accuracy varies around 1–2 mGal for a spatial resolution of approximately 2 kmIn order to achieve this accuracy the downward continuation process in connection with the representation of the gravity field functionals becomes of special importance. In this paper we would like to present the use of space localizing spline functions and their effect on the downward continuation process. The use of the presented approach is demonstrated on simulated airborne gravimetry data as well as on airborne gradiometry data. After all the spline-method is applied to a real gravity field composed of upward continued terrestrial gravity data

The differences between gravity anomalies and gravity disturbances are numerically investigated in this study. In particular, we demonstrate how the topography, atmosphere and mass irregularities enclosed within the geoid contribute to these differences. The numerical analysis is conducted at the area of study in the Canadian Rocky Mountains. Results reveal that the dominant contributions due to the topography and mass irregularities within the geoid are similar in magnitude but opposite in sign to the extent that their combined contribution is reduced significantly

For the new generation of satellite gravity missions, the observations of the onboard accelerometer can be calibrated by the dynamic method. In this paper, the strategy to calibrate the onboard accelerometer is studied in detail using the simulated precise orbit, and the impacts of the reference earth gravity model on the accelerometer calibration are discussed specifically. To evaluate the impacts of different strategies on the accelerometer calibration, the satellite orbit is integrated again with the calibrated accelerometer observations and the related dynamic models, and compared with the precise orbit. When the reference earth gravity model is fixed in the accelerometer calibration, the standard deviation of the differences between the re-integrated orbit and the simulated may be up to the order of meters, which shows that the reference earth gravity model has a significant effect on the accelerometer calibration. When the geopotential coefficients and the accelerometer calibration parameters are estimated simultaneously (simultaneous solution method in short), the accelerometer calibration parameters are independent of the reference earth gravity model. The results in this paper show that the simultaneous solution method is suitable for the calibration of the onboard accelerometer. It is also illustrated that to determinate the earth gravity model and the calibration parameters more reliably and accurately, we should choose an optimal maximum degree of the recovered earth gravity model

The Fundamental Gravity Network (FGN) is foundation for all national gravity measurements. This network consists of 42 points: 6 absolute gravity points (0. Order Gravity Network) and 36 relative gravity points (I. Order Gravity Network). Further densification of FGN will be carried out by the lower order networks (II. Order Gravity Network). Fundamental gravity points should be homogeneously spaced over the whole state. In some large countries the distance between gravity points can be more than few hundred kilometres. Levelling connection of the absolute and first order gravity points at the national levelling network benchmarks was not performed. Also, the position of gravity points in respect to existing geodetic network stayed unknown. Quality positional and height definition of gravity points is necessary for calculating different corrections, which are needed for processing gravimetric measurements. By implementation of the FGN Finalization Project, along with already finalized projects, the modern gravity foundation for the Republic of Croatia will be established

The European Gravity and Geoid Project (EGGP) is a project within IAG Commission 2, reporting to Sub-commission 2.4. The main goal of the project is to compute an improved European geoid and quasigeoid model based on new and improved data sets which have become available since the last computation in 1997 (EGG97). The improvements include better global geopotential models from the CHAMP and GRACE missions, better digital elevation models (DEMs) in some regions (e.g., new national DEMs, SRTM3, GTOPO30), updated gravity data sets for selected areas, updated ship and altimetric gravity data, improved procedures for the merging of ship and altimetric data, the use of GPS/levelling data, as well as refined computation techniquesThis contribution describes the progress made during the 4-year term from 2003 to 2007, including the development of a new geoid and quasigeoid model EGG07 for entire Europe. First, the status of the gravity and terrain data sets as well as the development of the EGG07 model by the spectral combination approach is described. Then, the EGG07 and other models are evaluated by independent GPS and levelling data, showing that the use of GRACE geopotential models as well as upgraded gravity and terrain data leads to significant improvements compared to EGG97 (in total by 25 – 65%). The results indicate an accuracy potential of the EGG07 model in the order of 0.03 – 0.05 m at continental scales and 0.01 – 0.02 m over shorter distances up to a few 100 km, provided that high quality and resolution input data are available

This paper describes the computation of a geoid model for the Amazon Basin (GEOAMA) limited by 5°N and 10°S in latitude and 70°W and 50°W in longitude. The software package SHGEO developed by the University of New Brunswick, Canada, was used for the calculation. The geoid model was derived by using the following data: digital terrain model SRTM3 (Shuttle Recovery Topography Mission) version 2.0 with 3” grid, the geopotential model EIGEN-GL04S1, degree and order 150, derived from GRACE satellite, and terrestrial gravity data basically observed along the rivers. For GEOAMA validation the longitudinal profiles of some rivers over the basin derived from three geoid models (EGM96, MAPGEO2004 and (EIGEN-GL04C) combined with geodetic heights from 28 GPS stations close to the tide gage stations were used. The results show that GEOAMA is in good agreement with the EGM96, MAPGEO2004 and EIGEN-GL04C profiles and with the average of the main rivers (Solimões and Amazonas) gradient (20 mm/km). MAPGEO2004 has been the official geoid model in Brazil since 2004. It was developed by Brazilian Institute of Geography and Statistics (IBGE) and Surveying and Geodesy Laboratory of the University of São Paulo (LTG/USP)

Local geoid determination is traditionally carried out on land and at sea areas using gravity anomaly and altimetry data. This determination can be aided and improved by the data of missions such as GOCE. In order to assess the performance of the combination of heterogeneous data for local geoid determination, simulated data for the area of the central Mediterranean Sea are analyzed. These data include gravity anomaly, altimetry, and GOCE observations processed with the space-wise approach. The results show that GOCE data improve the results for areas not well covered with other data types, while also accounting for any long wavelength errors of the adopted reference model. Even when the ground gravity data are dense, data from GOCE improve the error standard deviation and eliminate biases. At sea, the altimetry data give the dominant geoid information. However the geoid accuracy is sensitive to orbit calibration errors and the unmodelled mean sea surface topography. If such effects are present the GOCE data can account for them

The optimum combination of gravity field wavelengths in the framework of geoid computation remains always a hot research topic. Different approaches for such a combination of the wavelengths exist. The window technique (Abd-Elmotaal and Kühtreiber, Journal of Geodesy, 77–85) has been suggested to get rid of the double consideration of the topographic-isostatic masses within the data window in the framework of the remove-restore technique. The modified Stokes’ kernel has been suggested to possibly combine the local data signals with the global geopotential earth models. Both techniques have been used in computing a gravimetric geoid for Austria. The available gravity, height and GPS data for the current research are described. The EGM96 geopotential model has been used. A broad comparison between modified Stokes’ kernel and window techniques has been carried out within this investigation in the framework of the geoid computation. The comparison is made on two different levels; the residual gravity anomalies after the remove step and the computed geoid signals before and after scaling to the GPS/levelling geoid. The results proved that the reduced gravity anomalies using the window technique are the smoothest, un-biased and have the smallest range. The modified Stokes’ kernel technique gives the best fit to the GPS/levelling derived geoid. The window technique gives, however, fairly better results than the Stokes’ un-modified kernel technique

The integral of Stokes or similar formulae, used to estimate global models of the gravity fields, are based on the solution of the external boundary value problem (BVP) for the disturbing potential T. This approach presupposes the disturbing potential T to be harmonic on the geoid, which implies that there are no masses outside the geoid vanicek1986

The purpose of this paper is to further develop a method ofcombining terrestrial and satellite gravity field data, which in an optimal way exploits gravity field information contained in the solution of boundary problems in a close neighborhood of the Earth. The method is considerably generalized in this paper. In particular effects caused by the topography of the Earth are taken into account. The starting point is a transformation of the boundary problems considered under a small modification of curvilinear coordinates. In the new coordinates the boundary and also the boundary condition is simpler, but topography dependent coefficients appear in the structure of Laplace’s operator. Effects caused by the topography of the Earth are treated as perturbations and refinements of the solution are expressed as corrections constructed by means of successive approximations. As a consequence of the transformation a spherical mathematical apparatus may be applied at each iteration step. Especially Green’s function is constructed for the problem solved in a domain bounded by two concentric spheres. The structure of an iteration step connects the paper with earlier results. Within the iteration step they provide an applicable treatment. The continuation of the solution is discussed with a particular view to its harmonic branch and regularity at infinity. The reasoning leads to optimization concepts considered in the paper

The subject of the paper is an analysis of an approach for the combination of gravity anomalies and GPS-levelling data for regional gravity field modelling recently proposed (Prutkin and Klees, J Geod 2007). The well-known incompatibility of the two data sets is explained as the effect of non-uniqueness of regional gravity field modelling from a regional set of gravity anomalies. Hence, the proper mathematical formulation for the combination of the two data sets is a Cauchy boundary value problem. The differences between gravimetric quasi-geoid and GPS-levelling data are used as boundary data. We present an alternative interpretation of the approach. Moreover, we analyze the behaviour of the solution of the Cauchy boundary value problem if the size of the target area increases. The solution is expected to converge to zero if the size of the target area increases and in the limit covers the globe. This is confirmed by numerical tests. Finally, we investigate the effect of data noise on the solution. We show that when information about the data noise standard deviation is properly exploited in the course of the numerical solution of the Cauchy boundary value problem, we obtain a stable solution, which outperforms any gravity-only solution. Of particular interest for practical applications is the ability of the approach to correct for any lack of gravity field information inside and outside the target area, which is limited only by the spatial density and quality of the GPS-levelling data

The orthometric height is the distance, measured positive outwards along the plumbline, from the geoid to a point of interest usually situated on the Earth’s topographic surface. According to its “classical definition”, it can be computed from the geopotential number of a point, using the mean value of the Earth’s gravity acceleration along the plumbline within the topography (i.e. between the geoid and the Earth’s surface). Hence, the main problem in the rigorous definition of an orthometric height reduces to the accurate evaluation of the mean value of the Earth’s gravity acceleration along the plumbline. Alternatively, recent efforts concentrate on the determination of orthometric heights from GPS derived geodetic heights (above the ellipsoid) and geoid undulations derived from detailed local geoid models using the familiar Stokes integration or FFT techniquesIn this paper, we seek to determine the orthometric height from the knowledge of the geodetic (ellipsoidal) height and a representation for the gravity field at the surface point and without any information about the topographic mass distribution. We show that an approximate determination of the orthometric height of a point on the Earth’s surface can be made by a methodology which relates the orthometric height with the geopotential number C, the magnitude of the gravity vector g, and the curvature k of the plumbline, all determined at the point of interest on the physical surface. The required geopotential number C is computed through the evaluation of the Earth’s gravity potential W from one of the available Global Geopotential Models (GGMs) in spherical harmonics, while g and k are computed by suitable analytical formulae which use the first and second partial derivatives of the disturbing potential T (Eötvos components) and the normal potential U accordinglyAn overview is given of the steps involved in the computational process and the assumptions made. The proposed approach was tested using different GGMs and an extensive GPS/Leveling dataset on benchmarks in the USA. Results from these comparisons are presented for the larger part of the conterminous United States in non-mountainous areas. They demonstrate that generally the differences between these determined orthometric heights and actual orthometric heights from geodetic leveling typically range from a few centimeters and up to 3 decimeters, thus showing the viability of the methodology and its future promise as new and continually improving geopotential models from the CHAMP/GRACE and GOCE missions become available to be used for this purpose. Plans for future work will also be given

To reduce the absolute gravity measurements onto the geoid, the vertical gravity gradient is usually applied. Alternatively, the reduction can be realized by applying the mean vertical gravity gradient. In this study, the mean gravity gradient along the plumbline within the topography is investigated. We demonstrate how the mean gravity gradient is related with the mass density distribution within the topography, the shape of the Earth and the vertical change of gravity gradient with the depth, whereas the effect of atmosphere is negligible. We also show how the errors due to uncertainties in topographical mass density distribution propagate to the errors in a prediction of the mean gravity gradient. The numerical analysis is conducted at the area of study in the Canadian Rocky Mountains

Three different techniques for quasigeoid modelling from gravity and GPS-levelling data are compared: (i) a penalized least-squares technique using spherical radial basis functions provides a gravimetric quasigeoid solution; the combination with GPS-levelling data is formulated as the solution of a Cauchy boundary-value problem for the Laplace operator. This solution when added to gravimetric solution yields the final quasigeoid; (ii) a direct least-squares solution using gravimetric and GPS-levelling data as observations and point masses as parameterization of the disturbing potential. The inconsistency between GPS-levelling data and gravimetric data is treated assigning high weights to GPS-levelling data in the least-squares adjustment; (iii) a least-squares collocation technique for computing a gravimetric quasigeoid. The combination with GPS-levelling data is realized using a low-degree polynomial corrector surface estimated from the differences between gravimetric height anomalies and height anomalies from GPS-levelling data. The three methods are compared using real data for an area in Germany. The results reveal a very similar performance of these methods if gravity data and GPS-levelling data are combined, whereas gravimetric quasi-geoid solutions differ significantly

A wavelet transform algorithm combined with a conjugate gradient method is used for the inversion of Poisson’s integral (downward continuation), used in airborne gravimetry applications. The wavelet approximation is dependent on orthogonal wavelet base functions. The integrals are approximated in finite multiresolution analysis subspaces. Mallat’s algorithm is used in the multiresolution analysis of the kernel and the data. The full solution with all equations requires large computer memory, therefore, the multiresolution properties of the wavelet transform are used to divide the full solution into parts at different levels of wavelet multiresolution decomposition. Global wavelet thresholding is used for the compression of the kernel and because of the fast decrease of the kernel towards zero, high compression levels are reached without significant loss of accuracy. Hard thresholding is used in the compression of the kernel wavelet coefficients matrices. A new thresholding technique is introduced. A first-order Tikhonov regularization method combined with the L-curve is used for the regularization of this problem. First, Poisson’s integral is inverted numerically with the full matrix without any thresholding. The solution is obtained using the conjugate gradient method after 28 iteration steps with a root mean square error equal to 5.58 mGal in comparison to the reference data. Second, the global hard thresholding solution achieved a 94.5% compression level with less than 0.1 mGal loss in accuracy. These high compression levels lead to large savings in computer memory and the ability to work with sparse matrices, which increases the computational speed

The gravitational condensation problem of infinitely distributed substance is directly connected with gravitational instability problem. The linearized theory of gravitational instability leads to the well-known Jeans’ criterion. The main difficulty of Jeans’ theory is connected with a gravitational paradox: for an infinite homogeneous substance there exists no potential of gravitational field in accord with the Poisson equation. Since the classic gravitational theory did not give good solution of the gravitational condensation problem, the statistical theory for a cosmological body forming (so-called the spheroidal body model) has been proposed. In this model the forming cosmological bodies are shown to have fuzzy contours and are represented by spheroidal forms. This work considers a gas-dust protoplanetary cloud as a rotating and gravitating spheroidal body. The distribution functions and the mass densities for an immovable spheroidal body as well as rotating one have been derived. This work explains a slowly evolving process of gravitational condensation of a spheroidal body from an infinitely distributed substance. The equation for initial evolution of distribution function of a gas-dust protoplanetary cloud is derived. Because of the specific angular momentums are averaged during a conglomeration process, the specific angular momentum for a protoplanet in the protoplanetary cloud is found in this paper. As a result, a new law for planetary distances gives a very good estimation of observable planetary distances for our solar system

The research aims at an investigation of the optimal choice of local base functions, to derive a regional solution of the gravity field. Therefore, the representation of the gravity field is separated into a global and a residual signal, which includes the regional details. To detect these details, a superposition of localizing radial base functions is used. The base functions are developed from one mother function, and modified by four parameters. These arguments can be separated into two coordinates, one scale factor and a shape parameter. The observations of a few residual gravity fields are simulated by orbit integration and the energy-balance technique, in order to test the current approach. After selecting a region of interest, the parameters of the base functions are estimated. In order to get the optimal positions, two searching algorithms are compared. In the first algorithm the scale factors are estimated, while the positions and shape parameters are fixed. This method requires no initial values, because of the linear, but ill-posed and maybe ill-conditioned problem, but usually a regularization is necessary. The second algorithm searches possible positions for one base function in each step, until a termination condition is fulfilled, and improves the positions and scale factors in one adjustment. The results in the second case are better and faster for the test fields, but they depend on the initial values, the number of iterations and an assumption of an approximate constant orbit height

Precise monitoring and a conclusive interpretation of temporal gravity variations at a given station is based upon accurate knowledge about the properties of the used instruments. Only the combination of concurrent sets of superconducting and absolute gravity measurements allow both. Whereas absolute gravimeters provide the scale and reference level, superconducting gravimeters enable to determine gravity variations with high sensitivity and temporal resolution. A method is proposed here to derive the scale factor and zero drift function of the superconducting gravimeter as well as a reliable survey of the instrumental stability of absolute meters with high precision without the need of gravity reductions. In this way it is possible to separate between geophysical signals and instrumental effects in the time series. Results for the stations Bad Homburg, Wettzell in Germany are presented, demonstrating the potential of the technique

A numerical study has been conducted in order to analyze under what conditions temporal variations of the Earth’s gravity field can be recovered from the orbit of a satellite that is not equipped with an accelerometer. In the study, the motion of one of GRACE satellites was reproduced. A variant of the acceleration approach was used to process the simulated data. It turned out that the presence of non-gravitational satellite accelerations does not obscure temporal gravity field variations, provided that the satellite orbit (and, consequently, the set of observed satellite accelerations) is noise-free. Therefore, inaccuracies of the orbit determination is the only reason why a satellite orbit cannot be used to monitor temporal gravity field variations. It is shown that these inaccuracies should be reduced 30–100 times with respect to the level reached currently for the CHAMP and GRACE mission. Of course, a simultaneous utilization of data from several satellites can make this requirement less stringent

The GRACE satellite mission has provided the Earth’s gravity field models for more than four years by the end of October, 2006, which is in form of spherical harmonic coefficients. They are useful to infer variation of continental water storage in large scale. In this paper, the Empirical orthogonal functions (EOF) are used to analyze the time series of J₂ inferred from GRACE and SLR respectively to see the characteristics and the differences between the two time series. With 50 monthly models of the Earth’s gravity field (from August, 2002 to October, 2006) from Center for Space Research, University of Texas at Austin (UTCSR), the variations of continental water storage in China are computed. Meanwhile, EOF is used to analyze the water storage anomalies to get the characteristics of variation. The annual amplitudes in Yangtze River basin and Yellow River basin are derived with EOF reconstruction, respectively

Temporal variations of the Earth’s gravity field are traditionally represented with a set of spherical harmonic coefficients derived once per month. In practice, however, the gravity field changes continuously (e.g. because of on-going hydrological processes). This discrepancy causes temporal aliasing which manifests itself as errors in the obtained gravity field models. The goal of this study is to quantify the influence of temporal aliasing caused by hydrological processes onto the quality of computed monthly gravity field models; the Zambezi river basin is used as the test area. The GRACE observations are simulated along the actual GRACE orbits as gravitational potential differences. The mass variations obtained by the Least Square adjustment are compared with the “true” values used for data simulations. It is shown that the optimal estimation period is determined by the trade-off between the two conflicting effects of ever-decreasing propagated noise and ever-increasing aliasing. Catchments smaller than roughly 2000 km and estimation periods up to a month produce solutions with no noticeable aliasing. A catchment 3300 km wide has an optimal estimation period of 15 days and the one that is 4400 km large is most accurate if estimated for not more than 11 days. This is under the assumption that aliasing does not corrupt the solution significantly if it is less than half the propagated noise

In this paper a new approach is presented for enhancing image super-resolution via a filtered scale integral reconstruction. Based on the concept that any sensed quantity (from an instrumental point of view) must be necessarily considered as an averaged value in a suitable time and space continuum, the local reconstruction approach expects to map a space of average values onto another one (filtered scales) with a reduced extension and possibly, in an asymptotic limit, onto the space of points. The only assumption is that measurements are given in the integral average sense i.e., for some reason, they have to be considered as integral average values for given computational domains or cells. The proposed algorithm can be used to correlate averaged values to point values; yet the most reliable results, in a probabilistic sense, can be obtained if the ratio between input and output scales is not too high. The essential concept of this working methodology is the possibility to correlate average measurements to point-wise measurements upon suitably weighting the contribution of the molecules surrounding the inspected one

The aim of the data analysis of the GOCE satellite mission is to estimate spherical harmonic coefficients of the gravitational potential and the corresponding error covariance matrix. However this error estimation is generally very complicated and computationally demanding because of the large number of observations. In particular, this is true for the space-wise approach, which is a collocation solution implemented by several stepsUp to now the error covariance matrix for this approach has been computed under simplifying hypotheses. In order to get a more realistic assessment of the true estimation error a Monte Carlo method can be applied. This requires the generation of several stochastic simulations and the computation of the corresponding solutions. This procedure is made numerically feasible by storing and not recomputing every time the operators that form the space-wise approach. Tests on realistic scenarios are performed and positive results are achieved

With the upcoming Esa satellite mission Goce, all components of the gravitational tensor (2nd derivatives of the Earth’s gravitational potential) will be measured globally except of the polar gaps. The highest accuracy level within the measurement bandwidth (Mbw, 5–100 mHz) is 11 mE/√Hz for the diagonal components of the tensor (1 mE = 10-121/s^2). To meet this accuracy level, the gradiometer will be calibrated and evaluated internally as well as externally. One strategy of an external evaluation includes the use of a global geopotential model in combination with ground gravity data upward continued to satellite altitudeIn this study an error estimation for the external reference data is carried out (a) statistically by applying least-squares collocation and (b) empirically in a synthetic environment including (correlated and uncorrelated) noise. The use of synthetic data permits a closed-loop validation in all points. The spectral combination method based on integral formulas with a modified kernel function is applied to compute all components of the tensor. The closed-loop differences are analysed in the space and in the frequency domain. The dependency of the prediction error on the characteristics of the input data (noise level, area size and resolution) is shown. An accuracy below the required level of 11 mE/√Hz can be reached combining gravity anomalies with a noise level of 1 mGal and current global geopotential models

We present the gravity field model AIUB-CHAMP01S, which has been generated using the Celestial Mechanics approach. GPS-derived kinematic positions of low Earth orbiters (LEOs) are used as pseudo-observations to solve for the Earth’s gravity field parameters in a generalized orbit determination problem. Apart from normalized spherical harmonic (SH) coefficients, arc-specific parameters (e.g., accelerometer calibration parameters, dynamical parameters, or pseudo-stochastic parameters) are set up and normal equations are written for all daily LEO arcs. The daily normal equations are combined to weekly, monthly, and annual systems before inversion. The parametrization can be modified on the normal equation level without a new time-consuming set up of the daily normal equations. The results based on one year of CHAMP data demonstrate that the Celestial Mechanics approach is comparable in quality with other approaches

Due to their outstanding accuracy and resolution, the innovative satellite gravity gradient (SGG) measurements from the European mission GOCE need dedicated calibration and validation procedures. It has been shown, that comparing the measurements in satellite track cross-overs offer an opportunity to get relative quality information, when applying a straight-forward reduction method. From SGG cross-over differences data sets, calibration parameters can be estimated. Here, the advantage of robust estimation methods over the standard least-squares approach for the analysis of short SGG cross-over data sets is shown. Simulated SGG data with different artificial trends are processed in different subsets. The least-squares approach is feasible to produce trend estimates from the cross-over differences of several days of measurements. Long-term trends can be estimated from cross-overs of a single revolution when applying robust estimation. Anticipating these estimation techniques, cross-over validation offers a fast approach to assess independently the quality of space gradiometry with focus on certain time intervals

After the launch of the CHAMP and GRACE satellite missions, an increasing number of spherical harmonic models have become available for the long-, medium- and short-wavelength mapping of the Earth’s gravitational field. In view of the need for a coherent comparison between such Earth Gravity Models (EGMs) and a detailed evaluation of their accuracy for various gravity field functionals, it is important to investigate the consistency of their inherent reference frames, especially when their use is intended for high precision studies. Following the methodology described in an earlier paper by Kleusberg (Manuse Geod, 5: 241–256) the Helmert transformation parameters among the inherent reference frames for several CHAMP and GRACE models are estimated in this paper. In particular, the differences between the corresponding spherical harmonic coefficients for a given pair of EGMs are parameterized through a 3D similarity transformation model, whose weighted least-squares adjustment yields valuable information for the origin stability, the orientation consistency and the spatial scale variation between their underlying reference frames

The semi-analytical (SA) approach is proposed for the fast determination of gravity field from the GOCE (Gravity Field and steady-state Ocean Circulation Explorer) observations. In this paper, we discuss the principle and the characteristics of the SA approach in detail, and point out that based on the application of FFT and the introduction of the nominal orbit (circular, exact repeat orbit, uninterrupted measurement time series, and constant inclination), the SA approach can effectively recover the potential coefficients from large observations. This method can give a fast diagnosis of the GOCE system performance in parallel to the running of the GOCE mission by comparing the estimated noise characteristics of the SGG (Satellite Gravity Gradiometry) time series with the gradiometer error PSD (Power Spectrum Density) (prior). The performance of this method is evaluated using the simulated observations generated in different cases (ideal and practical). The results in this paper show that this method can be applied to the practical cases of non-circular, non-repeat orbits and non-constant inclination in the time series of observations by the iteration algorithm which can eliminate or weaken the approximate errors in the observation model. The test examples show that to recover the high degree gravity field model, the optimal regularization parameter should be selected in the Kaula regularization technique

Lake Victoria in Africa, the world’s second largest freshwater lake, has been experiencing receding water levels since 2001. As it recedes, more than 30 million people who depend on it for livelihood are facing a disaster. Similarly, Australia is facing its worst drought on record with the livelihoods of a few million people at stake. gravity recovery and climate Experiment (GRACE) data for 45 months (i.e., April 2002–April 2006) are employed to analyze these emerging challenges by measuring variations in the stored water. The results indicate a general decline in the lake Victoria basins water level at a rate of 1.83 km3/month

A new gravimetric geoid (OCTAS07v2) is generated using Stokes’ formula with gravity data as input. As local gravity data, a combination of land gravity data, new and old airborne gravity data, and adjusted marine gravity data has been used. All marine gravity data has been error screened and quality assured by removing dubious data and adjusting the data when necessary. Voids in the gravity data distribution were patched with gravity data from satellite altimetry. The OCTAS07v2 geoid was estimated using the remove-compute-restore technique. The long-wavelength signal of the local gravity data was reduced using a Wong-Gore modified Stokes’ function. The long-wavelength part was represented by a global gravity field model based on GRACE data. The OCTAS07v2 geoid model was combined with the OCTAS07_MSS model to create a synthetic Mean Dynamic Topography (MDT) model. In comparison with the OCCAM MDT, our new synthetic MDT model gave a std. dev. of the residuals of 11 cm. A comparison to the main northern North Atlantic currents show many similar features

A new quasigeoid solution HGTUB2007 was computed for Hungary using least-squares collocation technique for the first time by combining different gravity datasets. More than 300 000 point gravity data were interpolated onto a 1.5′× 1′ geographical grid consisting of 26, 478 values in the IGSN71 gravity system. The selected subset of these gravimetric data were combined with 138 astrogeodetic deflections and gravity gradients available at more than 25, 000 points in the least-squares collocation procedure. Topographic information was provided by SRTM3 data at 3′′× 3′′ resolution. We have used the GPM98CR model and a GRACE GGM02-based combined model as a global geopotential reference to our new solution. Several solutions were produced and compared by combining different datasets. The final solution was chosen to fit to the national GPS/leveling network of Hungary with a very high weighting. As a quick evaluation of the solution with GPS/Leveling data shows, the obtained accuracy is about 2–4 cm in terms of standard deviation of geoid height residuals

In the context of a GOCE regional validation and combination experiment in Germany, a work package within the framework of the GOCE-GRAND II project, gravity observations, vertical deflections and GPS/levelling data are collected as independent data sets. The observation of absolute gravity values is carried out by the Bundesamt für Kartographie und Geodäsie (BKG), while the vertical deflections are observed by the Institut für Erdmessung (IfE) using the Hannover digital transportable zenith camera system TZK2-D. The vertical deflections have an accuracy of approx. 0.1 arc seconds and are arranged along a North–South and East–West profile. The two profiles have a length of about 500 km each with a spacing of 2.5–5 km between adjacent stations. Furthermore, a national GPS and levelling data set of about 900 stations with an accuracy of approx. 1 cm is available for Germany. The analysis of the vertical deflections is carried out by the astronomical levelling method, resulting in two (quasi)geoid profiles. The accuracy of the profiles is expected to be at the cm level. A cross-validation of both the vertical deflection and GPS/levelling data is realised by traversing the profiles through all nearby GPS/levelling stations (approx. 40 in total). In addition, comparisons are performed with the German Combined QuasiGeoid 2005 (GCG05) and the purely gravimetric solution EGG07 (European Gravimetric Quasigeoid 2007)

The precise geoid determination technique from the University of New Brunswick (UNB) was adopted in Mexico to compute the national geoid model GGM05. To generate it, the input data was treated carefully and the theoretical background is well established. However, the final assessment gives unsatisfactory biases at level of metres. Some preliminary results of the corresponding research expose the possible sources for those large errors. The reference geoidal heights are the main suspect. Hence, in order to obtain a reliable assessment for GGM05, the issue of building better references has to be addressed. New developments like recent vertical movements modeling, rigorous orthometric heights estimation and precise positioning shall be combined to help removing uncertainties from the reference data, resulting in a better understanding of the Mexican gravimetric geoid

An improved geoid, called ADBVE2006 (Autorita di Bacino di Venezia 2006), has been calculated for the north-east of Italy using new land and marine gravity data together with new high resolution multibeam bathymetric data. A standard processing procedure has been applied to gravity data in order to compute the Free Air and the Bouguer anomalies. The gravity reference datum is IGSN71. The long wavelenghth part of the gravity field has been modelled by EGM96. The computation has been carried out by the “remove-restore” spectral technique (Stokes’ approach) using the software GRAVSOFT. The goal of the calculated model is to improve the geoid estimation in the coastal areas, where the calculated geoids usually suffer from the lack of gravimetric data as well as a good bathymetry

In order to assess the contribution of non-tidal oceanic mass changes to polar motion, equatorial oceanic excitation functions are determined from combinations of space geodetic techniques and ocean data. Satellite altimetry provides accurate information on sea level anomalies (SLA) which are caused by mass and volume changes of seawater. Since Earth rotation is solely affected by mass variations the volume (steric) effect has to be reduced from the observations in order to infer oceanic contributions to Earth rotation. Oceanic polar motion excitations from reduced SLA are compared with respective results from ocean models. Contributions of ocean currents, atmospheric and hydrological effects are added in order to validate the oceanic excitations from altimetry with independent geodetic observations which reflect the integral effect of a multitude of geophysical processes in the Earth system. This requires an investigation of accuracy and consistency of the combined data sets. The study reveals that model-only combinations of atmospheric, oceanic and hydrological excitations agree better with geodetic observations than combinations which include excitations from altimetry. Possible reasons could be errors in the steric reduction of SLA and/or the compensation of erroneous patterns in atmosphere data by numerical ocean models

This paper focuses on atmospheric wind-driven effects on changes in length-of-day (δLOD). A 20th century simulation has been carried out using the ECHAM5 standalone atmosphere general circulation model (GCM). The spectrum of the resulting time series for δLOD shows typical structure patterns which resemble geodetic observationsFurthermore a future scenario run for the period 2000–2100 driven by SRES A1B forcing scenario shows a strong increase in the axial atmospheric angular momentum (AAM) which implies a lengthening of the LOD. For the scenario runs the coupled atmosphere ocean GCM ECHO-G has been used. The extent of the simulated changes in axial AAM exceeds results from former studies. By 2100 the model shows an increase in axial AAM of about 10 percent compared to present day conditions. The strongest trends in zonal windspeed are detected in the Southern Hemisphere for mid and higher latitudes in the upper troposphere. The reason for this trend can be found in the thermal wind equation. The westerly winds in high levels are directly related to the magnitude of the horizontal, north-south, gradient in temperature averaged from the Earth’s surface to the height of the level. The future scenario runs show significant strengthening in this gradient at higher levels

The tidal potential generated by bodies in the solar system contains Poisson terms, i.e., periodic terms with linearly time-dependent amplitudes. The influence of these terms in the Earth’s rotation, although expected to be small, could be of interest in the present context of high accuracy modelling. We have studied their contribution in the rotation of a non rigid Earth with elastic mantle and liquid core. Starting from the Liouville equations, we computed analytically the contribution in the wobble and showed that the presently-used transfer function must be supplemented by additional terms to be used in convolution with the amplitude of the Poisson terms of the potential and inversely proportional to (σ - σ_n)^2 where σ is the forcing frequency and σ_n are the eigenfrequencies associated with the retrograde free core nutation and the Chandler wobble. These results have been detailed in a paper that we published in Astron. Astrophys. in 2007. In the present paper, we further examine the contribution from the core on the wobble and the nutation. In particular, we examine the contribution on extreme cases such as for wobble frequencies near the Free Core Nutation Frequency (FCN) or for long period nutations. In addition to the analytical computation, we used a time-domain approach through a numerical model to examine the core and mantle motions and discuss the analytical results

Degree-2 spherical harmonic coefficients of the surface mass density determined from independent GRACE, SLR, GPS, and Earth rotation measurements are compared to each other and to a model of the surface mass density obtained by summing the contributions of atmospheric pressure, ocean-bottom pressure, land hydrology, and a mass-conserving term. In general, the independent measurements are found to be quite consistent with each other and with the model, with correlations being as high as 0.87 and with the model explaining as much as 88% of the observed variance. But no measurement technique is found to be best overall. For the different degree-2 coefficients, measurements from different techniques are found to agree best with the model. Thus, each measurement technique contributes to understanding the degree-2 surface mass density of the Earth

The Earth’s mechanical and geometrical parameters were estimated from the simultaneous adjustment of the 2nd-degree harmonic coefficients of six gravity field models and seven values of the dynamical ellipticity H_D all reduced to the common MHB2000 precession constant at epoch J2000. The transformation of 2nd-degree harmonic coefficients in the case of a finite commutative rotation was developed to avoid uncertainty in the deviatoric part of inertia tensor. This transformation and the exact solution of eigenvalue-eigenvector problem are applied to determine (a) the static components and accuracy of the Earth’s tensor of inertia at epoch 2000 and (b) the time-dependent constituents of the inertia tensor. Special attention was given to the computation of temporally varying components of the Earth’s inertia tensor, which are based on the time series of 2nd-degree coefficients through GRACE observations. A remarkable stability in time of the position of the axis Ā of inertia as the parameter of the Earth’s triaxiality is discussed

The Earth’s global density model given by the restricted solution of the 3D Cartesian moments problem inside the ellipsoid of revolution was adopted to preserve in this way the external gravitational potential up to second degree/order, the dynamical ellipticity, the geometrical flattening, and six basic radial jumps of density as sampled for the PREM model. Comparison of lateral density anomalies with estimated accuracy of density leads to the same order values in uncertainties and density heterogeneities. Hence, four radial density models were chosen for the computation of the Earth’s gravitational potential energy E: Legendre- Laplace, Roche, Bullard, and Gauss models. The estimation of E according to these continuous density models leads to the inequality with two limits. The upper limit EH agrees with the homogeneous distribution. The minimum amount E_Gauss corresponds to the Gauss’ radial density. All E-estimates give a perfect agreement between E_Gauss, the value E derived from the piecewise Roche’s density with 7 basic shells, and the values E based on the four simplest models separated additionally into core and mantle only

The temporal variations of the C₂₀ spherical harmonic coefficient of the geopotential are estimated from the length of day (LOD) and compared with the C₂₀ variations due to geophysical contributions. In particular, we analyzed the agreement of the hydrological C₂₀ changes as estimated by the Land Dynamics Model (LaD) model. The computation spans between January 1980 and May 2004 for the hydrological modelThe contribution of atmospheric mass redistributions, along with the oceanic mass terms and solid Earth tides were removed from the geodetic C₂₀ time series for computing residuals. Afterward the hydrological influence was investigatedAfter eliminating seasonal variations, the hydrological excitation seems to be not adequate to explain the inter-annual variations found in the C₂₀ residualsThe luni-solar precession and nutation of the Earth depend on the dynamical flattening (H); which is related to the principal moments of inertia of the whole planet. H is linked to the C₂₀ coefficient of the Earth’s potential, which is regularly determined by space geodetic techniquesIn this work, we also estimate the seasonal variations on H due to geophysical causes. These results should be useful to investigate the geophysical considerations in the computation of the IAU 2000 precesion-nutation model

Since 2002 the Gravity Recovery and Climate Experiment (GRACE) satellite mission is mapping the Earth’s gravity field, showing variations due to the integral effect of mass variations in the atmosphere, hydrosphere and geosphere. After reduction of oceanic and atmospheric contributions as well as tidal effects during the GRACE standard processing, monthly solutions of the gravity field are provided by several institutions. The solutions of the analysis centres differ slightly, which is due the application of different reduction models and centre-specific processing schemes. In addition, residual signals from insufficient pre-processing of the transmitted satellite data may be presentWe present our investigation of mass variations in the areas of glacial isostatic adjustment (GIA) in North America and Northern Europe from GRACE data, especially from the latest release of the GFZ Potsdam. One key issue is the separation of GIA parts and the reduction of the observed quantities by applying dedicated filters and models of hydrological variations. In a further step, we analyse the results of both regions regarding their reliability, and finally a comparison to results from geodynamical modelling is presented. Our results clearly show that the quality of the GRACE-derived gravity change signal benefits from improved reduction models and dedicated analysis techniques. Nevertheless, the comparison to results of geodynamic models still reveals differences, and thus further studies are in progress

The Global Geodynamics Project was renewed for the foreseeable future at the IUGG in Perugia. The second cycle (called GGP2) of operations started in 2003, and followed the initial years of GGP1 (1997–2003). Thus GGP has now completed 10 years of collecting data from all the currently operating superconducting gravimeters (SGs). During the last cycle, GGP operations have gone smoothly for most stations, but with the inevitable instrumental problems. We have lost (at least temporarily) stations Boulder and Bandung, but gained an instrument in MunGyung (S. Korea) and two instruments in Hsinchu (Taiwan). New installations were recently done in Pecny (Czech Republic) and Dehradun (India), and several other locations in the US and Asia are being contemplated in the next cycle of GGP (2007–2011). Over the past two years, we have worked to prepare raw GGP data (at sampling times of 1–5 s) for inclusion into the IRIS data set for the seismologists to use in normal mode studies of the Earth. A successful GGP Workshop was held in Jena, Germany in March 2006, and the first official Asian SG Workshop took place in March 2007 in Taiwan, hosted by our colleagues in Hsinchu. Of continuing interest within GGP is the issue of combining measurements from absolute gravimeters at the SG stations for a variety of long-term studies of the gravity field such as tectonic uplift, subduction zone slip, and determination of the Earth’s centre of mass with respect to the terrestrial reference field. GGP has now become involved with the development of GGOS, a project that intends to coordinate the use of many different geodetic data sets for future ease of access

The data of sixteen West European tidal gravity stations have been reprocessed. The tidal gravity factors have been corrected for ocean loading effect using the mean of 9 different ocean tides models with different grid size (0.5°, 0.25° and 0.125°). For the principal tidal waves O1 and M2 the standard deviation of the corrected amplitude factors δ_c is lower than 0.1%. For O1 the value δ_c = 1.15340 ± 0.00023 lies between the Dehant, Defraigne and Wahr, 1999 (DDW99) elastic model and the Mathews, 2001 (MAT01) inelastic model. For M2 the value δ_c = 1.16211 ± 0.00020 fits very well the DDW99 and the MAT01 inelastic models. For K1 the mean result δ_c = 1.13525 ± 0.00032 (7 Global Geodynamics Project stations and Pecny) fits the MAT01 model to better than 0.05%. We determine the FCN parameters using either generalized least-squares or a Bayesian approach and find values between 428 and 432 sidereal days for the eigenperiod and quality factor Q values around 15,000

New inclinometers devoted to hydrological studies were set up in the Vosges Mountains (France). Two orthogonal 100-m base hydrostatic inclinometers were installed in December 2004 as well as a hydrometeorological monitoring system for the 100-km2 hydrological unit around the inclinometer. As inclinometers are very sensitive to environmental influences, this observatory is a test site to confront hydrological modelling and geodetic observations. Physical modelling to remove hydrological effects without calibrating on geodetic data is tested on these instruments. Specifically, two deformation processes are most important: fluid pressure variations in nearby hydraulically active fractures and surface loading at regional scale

The Tibetan Plateau is the center-piece of the broad India-Eurasia collision zone, and a natural laboratory to study large-scale continental deformation. We analyze Tibet campaign data from 1993 to 2002 and some continuous Global Positioning System (GPS) stations around Tibet using GAMIT/GLOBK software. The data analysis involves two major procedures. The first procedure uses the GAMIT software to estimate parameters such as station position and orbital trajectory on a daily basis from the union of two data sets: (a) the campaign stations, and (b) long-running continuous GPS stations around Tibet. In the second procedure, we combine the daily solutions with global GPS sub-networks (IGS1, IGS2, IGS3), which are provided by Scripps Institute of Oceanography (SIO), using the GLOBK software in a “regional stabilization” approach in order to estimate the positions and velocities. Then we discuss present-day crustal movement of Qinghai-Tibetan Plateau, and determine the strain rate. The conclusion is that the Himalayan block is mainly under compressing strain, and the maximum compressing rate is -98.5 ± 4.2 nstrain/yr and with the extension rate of 26.7 ± 2.8 nstrain/yr in the direction of N127.1 ± 0.7°E; the middle part of the Tibet block is mainly under compressing strain, and the maximum compressing rate is -20.3 ± 1.2 nstrain/yr in the direction of N39.0 ± 2.0°E with the extension rate of 10.8 ± 1.6 nstrain/yr in the direction of N129 ± 2.0°E. Both principal compressing strain rate and extension rate trails off from the Himalayan block to the middle part of the Tibet block. Besides, GPS result shows that Tibet Plateau uplifts with 3–5 mm per year

The DICA (Department of Civil and Environmental Engineering) of Perugia University currently operates two local GNSS permanent stations networks in central Italy. These networks supply various types of positioning services, which are currently being used mostly by surveyors and mapping agencies. This kind of networks also have a strong potential for the monitoring of crustal deformations in local areas. In the specific case, such applications are particularly interesting because the covered region (Umbria and central Italy) is characterized by a relevant seismicityIn the present paper, both networks are described, as for stations location, data availability, and performances in terms of positioning services at different accuracy levels. The possibilities for applications on local geodynamics with different approaches are then discussed, showing the results of a test performed with displacements simulated by means of a mechanical device

Temporal variations in the flow of an active ice stream are analyzed using GPS data collected over a period of two months at six different locations. The diameter of the network is about 60 km. The ice stream moves with a velocity of about one meter per day. The kinematic data are processed using three different strategies: zero-difference network solution, Precise Point Positioning, and double-difference network solution with resolved carrier phase ambiguitiesThe solutions are compared with regard to the quality of the resulting coordinate time series. Special attention is paid to the positional accuracy as a function of temporal frequency for these different analysis methods as the overall aim of the measurements is to estimate temporal variability in ice flow

The geodetic-geodynamic network of Israel, named G1, was constructed in the 1990s, with the aim of understanding recent tectonics and deformation in Israel. The network contains approximately 150 points which were built according to high-standard technical specifications to ensure their high geotechnical stability. In this research we use measurements of 60 points, from the northern part of the G1 network together with five permanent GPS stations to monitor current crustal movements across the Dead Sea Rift (DSR) in the north of Israel. The DSR is the northern part of the Syrian-African Fault. It extends from southern Turkey to the Aqaba Gulf and separates the Arabian plate from the Sinai sub-plate. Recent researches show that the DSR behaves as a locked strike-slip faultThe research makes use of the Two-Step analysis of dynamical networks. This method is based on a first step of independent adjustment of every measurement campaign to a set of network points coordinates, followed by a second step in which we use the coordinates as pseudo-observations for adjusting a set of kinematical or dynamic parameters. The least squares estimation of the second step assumes an ideal mathematical model of the tectonics. While the correlation between the mathematical model and the physical phenomenon is not absolute, the solution is biased due to the correlation. That is the main reason for using prior information for matching of the model to the phenomenonWe use the locked fault model to describe the dynamic behavior of points in the north of Israel. It relies on an arctangent function and depends on four independent parameters. The locked fault model suffers from an instability relationship between its parameters since it deals with extremely different scales of its parametersBy using prior knowledge we evaluate the model parameters by enforcing constraints on the adjusted parameters. A second solution of the model parameters is presented by extended free dynamic network. In this method we adjust the kinematical parameters simultaneously with the dynamical softened parameters. A third solution is achieved by regulation of the normal matrix in certain waysThe paper presents results which based on two GPS measurement campaigns carried out in 1996 and 2002. Applying different solutions strengthens the possibility of correct use of the mathematical model to achieve results in close proximity to the actual physical behavior and enables reaching a reliable solution. The solution indicates a left lateral motion of the DSR in a rate of 2–7 mm/yr. In addition, the system is characterized by a high level of model noise which indicates an unsuitability of the mathematical model to the geophysical reality

Since 29 May 2006, gas and hot mud has been gushing from the ground in Sidoarjo, East Java, Indonesia. As of late September 2006 scientists assume that the eruption may be a mud volcano forming, and may be impossible to stop. Surface displacements of the area, both in the vertical and horizontal directions, are expected due to this massive mud extrusion.GPS observations, both in campaign and continuous modes, were conducted to study this surface displacement phenomenon. GPS surveys were performed on up to about 20 stations using dual-frequency geodetic-type receivers with observation session lengths of about 5–7 h. Nine GPS campaigns have been conducted between June 2006 and June 2007. GPS continuous subsidence monitoring was conducted on five to ten stations, and started on 22 September 2006. A field survey to check the surface representation of the subsidence phenomenon was also conducted.Based on the GPS-derived results it was determined that the area about 3–4 km around the extrusion centre experiences surface displacements. Rates of horizontal displacement are about 0.5–2 cm/day, while vertical displacements are about 1–4 cm/day, with rate increasing towards the extrusion centre. These observed surface displacements might consist of ground relaxation due to mudflow, loading due to the weight of mud causing the area to compact, land settlement and/or reactivation of the geological structures

This paper presents two strategies for improving GPS coordinate solutions using regional ionosphere maps in South America, a region susceptible to strong ionospheric activity.Since 2005, the La Plata Ionospheric Model (LPIM) has been used to routinely generate Vertical Total Electron Content (VTEC) maps at the La Plata Processing Center (CPLAT) using about 50 GPS stations in South America. VTEC is modelled using a linear combination of undifferenced GPS carrier phase observations in modified dip latitude or modip: tan μ = I/√ cos φWhere √ is moddip latitude, I the magnetic dip and φ the geographic latitude. A particular approach is used to solve the hardware related biases.Since 2003, the Instituto Brasileiro de Geografia e Estatistica (IBGE) has collaborated in order to maintain the SIRGAS Reference Frame in South America, delivering weekly coordinate solutions using the same set of permanent stations that the CPLAT uses for computing ionosphere maps.This work examines two possible benefits of VTEC maps in GPS processing, namely, solving ambiguities in differential solutions and mitigating ionospheric biases in undifferenced single-frequency solutions.In differential processing, ionosphere maps are applied in the ambiguity resolution step when using the Bernese GPS processing software. For undifference processing, ionosphere maps are input to mitigate ionospheric biases when using the Precise Point Positioning (PPP) software developed by the Geodetic Survey Division (GSD), Natural Resources Canada (NRCan).In order to validate the authors’ proposal, data from four different periods in 2006 from a network of GPS stations near the ionospheric anomaly region in the South Atlantic and equatorial regions were tested with and without VTEC regional ionosphere maps.

The Precise Point Positioning Working Group within the Next Generation RTK Sub-Commission of IAG Commission 4 has been involved with Precise Point Positioning (PPP) developments for the past few years. The information presented here summarizes the Working Group’s findings concerning the state of PPP technology, and discusses the probable near-term future potential and limitations of the technique. The broad question of the place of PPP within the future spectrum of space geodetic measurement techniques is addressed by investigating specific aspects of the method

Precipitable Water Vapor (PWV) time series acquired using space geodetic techniques such as GPS (Global Positioning System) and VLBI (Very Long Baseline Interferometry) have statistical properties which exhibit spatial-temporal variations. These variations could be seen as manifestation of atmospheric structure and dynamics. Statistically, second-order moments may carry spatial-temporal information. The measures of spatial-temporal information in the PWV time series such Self-Similar (SS) and Long-Range Dependence (LRD) parameters could be utilized for both geodetic applications and meteorology. If the time series is segmented into small windows and local statistical parameters calculated, the second-order quantities derived thereof could be used to describe global and local (non-)stationary processes in the atmosphere. Results from our study show that, the PWV time series reconstructed by Singular Spectrum Analysis (SSA) has features that describe (non-)stationary. The trends, spikes and excursions seen in the power spectra of a non-decimated discrete Haar wavelet transform of the PWV time series is further evidence to (non-)stationarity.Further, a wavelet based joint estimator of SS and LRD shows that the PWV time series has memory and the mean, variance, and the scaling exponents show fluctuations. These fluctuations depict nonstationarity

In conventional differential radar interferometry (DInSAR), the ground surface displacement can be measured along the line-of-sight. In order to measure the vertical and horizontal displacements DInSAR results of the same deformation derived from at least two different look directions are required. This study utilised the DInSAR results generated from ENVISAT data acquired from three different look angles to determine the 3-D displacement vectors resulting from surface deformation due to underground mining. However, The ENVISAT results showed ambiguous phases due to high phase gradients in the differential interferogram. The newly acquired ALOS/PALSAR data is also used here to demonstrate how the high phase gradient problem can be overcome by using interferometric signals with longer wavelength and finer imaging resolution

High precision positioning can be achieved using GPS satellites. However, there exist many error sources. For example, receiver locations have to be chosen on the basis of task requirements rather than by optimality of the environment with respect of GPS signal propagation. Hence the effect of unfavorable error sources on precise GPS positioning is a typical problem. Least squares estimation (LSE) yields results of low accuracy in the presence of outliers in GPS measurements. Different weight models have therefore been suggested in order to account for such errors.In this study the authors use robust estimators which clearly identify outlier observations. They perform significantly better than LSE. Furthermore, GPS observations are fundamentally correlated, hence the robust estimators are applied to eterogeneous and correlated observations. The mean success rate (MSR) statistic is employed as a practical tool for measuring the abilities of different methods. Many different correlated GPS networks based on IGS sites were used and the robust methods were applied to simulated corrupted samples and the degree of corruption is varied. Performance of the estimators was further demonstrated using real GPS data

The paper presents a methodology that combines geometry-based models and geometric constraints for improved three carrier ambiguity resolution (TCAR). First of all, a general modelling strategy using three or more phase-based ranging signals is presented. The strategy can generally identify three best “virtual” signals to allow for more reliable AR under certain observational conditions characterised by ionospheric and tropospheric delay variability, level of phase noise and orbit accuracy. The selected virtual signals often have minimum or comparatively low ionospheric effects, and thus are known as ionosphere- educed virtual signals. As a result, the ionospheric parameters in the geometry-based observation models can be eliminated for long baselines, typically those of length tens to hundreds of kilometres. Secondly, the general formulation of the equation system for the ambiguity resolution problem is examined. This general formulation enables the combination of apriori position and ambiguity and ionosphere information, to achieve reliable integer solutions or high availability of Real-Time Kinematic (RTK) solutions. Thirdly, numerical experiments have been performed and three sets of dual-frequency GPS data have been collected over baselines of length 21, 56 and 74 km and the performance benefits of the proposed algorithms have been investigated. Results confirm that the AR with the ionosphere-reduced NL signals, instead of the original L₁ and L₂ signals, performs better over longer baselines. For instance, the AR success rate for the 74 km data set is improved from 88 to 93%. Introducing geometric constraints, particularly, apriori position and ionospheric corrections predicted from the previous epochs, AR reliability is further improved, to 98% for the above data set

In 2006, OASYS, an EU funded project on a multi-scale monitoring concept for landslides as a basis for an alert system was completed. Twelve institutes from 6 countries tried to merge their multidisciplinary knowledge in the field of landslides and disaster management. The main goal of the research was to develop a cost saving concept for landslide disaster prediction in areas with a higher density of landslides. The present paper reports about the innovative steps and about some highlights of the research, emphasising mainly three tasks:GIS integrated geological evaluations of remote-sensing data to delineate the high-risk areas in regions with a larger number of landslidesgeometrical analysis of the monitoring data by fuzzy techniques as a basis for the design of the sensor network andgeomechanical modelling of the landslide by Finite Difference-methods as a basic information for an alarm system.At the moment the achieved results are separately focussed on the main tasks. A combined solution must be realized in subsequent investigations.

The knowledge of the ionospheric behaviour is an important factor in GPS positioning. Data of five ALGEONET (Algerian GEOdynamical NETwork) and a hundred IGS stations are processed with the Bernese GPS software, which is based on the use of spherical harmonic expansion, to provide an ionospheric mapping of the Total Electronic Content (TEC). The used model supposes that the whole free electrons are concentrated on a thin spherical layer to an altitude varying between 250 and 450 km. Results are obtained for several heights (350, 400 and 450 km) with a 2-hourly resolution. The maximal value of the obtained TEC in the north Algerian area is about 20 (midnight) to 60 (midday) TECU, such values are obtained for the day of April 30, 2001, which refers to a high solar activity period with a sunspot number of 112. Calculated TEC values are thereafter applied to correct the single frequency solution. The comparison between the corrected $L₁$ and ionosphere-free solutions shows that the ionospheric effects involve a network contraction. Also, the corrected $L₁$ solution is close to the ionosphere-free one; for baselines of several hundreds of kilometers, deviations are about 10 cm (in horizontal coordinates), they are reduced by about 50% in vertical component

Precise Point Positioning (PPP) is a technique where observations from a single GNSS receiver are used to estimate coordinates with precision ranging from centimeters to decimeters. PPP does not rely on data from dedicated reference receivers and is logistically a very competitive alternative to differential GNSS methods. In areas with reduced satellite availability the geometrical strength of the solution will be reduced and observations from such periods should be treated with special attention. In marine applications the use of additional information in the form of height constraints will enhance PPP during periods with marginal satellite availability. Additional observations from GLONASS satellites or Inertial Navigation System (INS) will also to a certain degree compensate for reduced availability of GPS satellites. This paper addresses the contribution from height aiding and from current GLONASS satellites. Based on formal precision and reliability as well as accuracy both height aiding and GLONASS improve the quality of estimated coordinates. The contribution to reliability is more significant than the contribution to precision and accuracy. In periods with very weak GPS constellation, height aiding gives the most valuable contribution. The paper verifies that even under marginal satellite availability, PPP processing is capable of producing coordinates with precision and accuracy at the subdecimeter level and with reliability at the one meter level.

PROBRAL - Precise positioning and height determination by means of GPS: Modeling of errors and transformation into physical heights is the name of a joint venture between the Department of Geomatics (DGEOM), Federal University of Paraná (UFPR), Curitiba (Brazil) and the Geodetic Institute (GIK), University Karlsruhe (TH), Karlsruhe (Germany). The aim of this research project, which started in 2006 and is founded by the Brazilian academic exchange service CAPES and the German academic exchange service DAAD, is to validate and to improve the quality of GNSS-based positioning, especially concerning the height component.Therefore, the close cooperation between the DGEOM and the GIK was intensified. One main objective of the first year of this three years lasting cooperation was to establish a receiver antenna calibration field for GNSS instrumentations on the roof top of the so-called LAGE (http://www.lage.ufpr.br/).In the framework of PROBRAL case studies were carried out in close collaboration at the DGEOM as well as at the GIK concerning site-specific effects (e.g. multipath, receiver antenna modeling), especially.The status of the establishment of a GNSS receiver antenna calibration field, called First Baseline Calibration Station for GNSS Antennas in Brazil (1a. BCALBR), is going to be presented within this paper.The very first results derived on 1a. BCALBR showed that the pillar 1000 is affected by carrier phase multipath less than pillar 2000. The IBGE (Brazilian Institute of Geography and Statistics) reference station PARA is slightly affected by carrier phase multipath.

Differential GPS (DGPS) and Real-Time-Kinematic (RTK) solutions are widely accepted methods for accurate positioning and navigation. Initially these methods were based on single reference stations. A big breakthrough in performance and accuracy was achieved by the introduction of network solutions. Today, the use of the Virtual Reference Station method is a standard technology applied in a large number of regional RTK networks all over the world, to provide a positioning service with centimetre accuracy. DGPS techniques are used for marine, airborne and land applications and provide accuracies in the several decimetre range. The DGPS and RTK methods are based on regional reference station networks or nearby single stations. In contrast, the Precise Point Positioning (PPP) method is providing position accuracy of several centimetres to decimetres based on a globall distributed tracking network. Precise satellite orbit and clock information is derived from the network processing. The achievable accuracy with PPP is impressive, but this method suffers from long convergence times of the order of more than 20–30 min to achieve acceptable accuracies and therefore might not be the method of choice for all applications.This paper describes the current state-of-the-art in RTK and DGPS technology and compares it with the performance of PPP applications today. Performance numbers are presented for various baseline lengths and networks including accuracy, convergence, and reliability.

To overcome the limitations of standard real-time kinematic (RTK) GPS systems, a multiple-reference-station network can be used to achieve larger service coverage, increase robustness, and higher positioning accuracy compared with using a single reference station. The virtual reference station (VRS) approach is an efficient method of transmitting corrections through a data link to network users for RTK positioning. The Shanghai Virtual Reference Station (VRS) Network serves as infrastructure for the “Digital Shanghai” information system, and will provide a high precision and fast positioning service. Concerning different applications, a systematic test has been performed at different locations in Shanghai to assess the achievable accuracy and reliability for VRS-RTK positioning. The results indicate that Shanghai VRS Network positioning achieved satisfactory accuracies in both the horizontal and vertical position components, with the corresponding values being within 1.5 and 3 cm respectively. The average reliability was within 3 mm.

In many GNSS software packages a simplified observation weighting model is used which is merely based on the satellite elevation angle and valid under the assumption of azimuthal symmetry. This elevation-dependent weighting model is only suitable for undisturbed GNSS signals based on the existing strong correlation between signal quality and satellite elevation angle. However, for high-precision geodetic applications this geometry-related weighting model becomes obsolete if observations are strongly affected by multipath effects, signal diffraction as well as receiver characteristic under non-ideal observation conditions. An improved observation weighting model based on signal-to noise power ratio measurements has been developed and experimentally implemented in the Bernese GPS software 5.0. Tests indicate that when this weighting model is used for low elevation data additional 10% ambiguities can be resolved and the accuracy of the estimated site-specific neutrosphere parameters can be improved by nearly 25% compared with the standard elevation-dependent weighting model

The integration of the Brazilian Fundamental Vertical Network (BFVN) with satellite altimetry data and multiple tide gauges (TG) is one way for an independent validation of the Brazilian Vertical System. Satellite altimetry (Sat-Alt) gives precise information on the sea surface topography (SSTop) over a great part of the oceans. However, SSTop is characterized by large differences at deep, open sea and at coastal or shallow waters. The evaluation/validation of the studies on BFVN could be achieved through the connection of the reference levels from TGs and Sat-Alt data, allowing SSTop “correction” at some selected TGs along the Brazilian coast. Initial tests were performed with SSTop estimates from the application of a 1D-filter to the EIGEN-GL04C geoid model and to the altimetric data from Jason-1 and TOPEX/Poseidon extended mission (T/P-EM). Tracks of these two satellites over deep, open oceans were taken as reference for connecting three selected TG reference levels. SSTop time series were obtained for Sat-Alt points near those TGs as well as for the crossing points between the reference tracks and those passing the TGs. These time series show good correlation along each TG-track but have low correlation to the ref-tracks. This points out the need for additional ref-tracks in order to improve that correlation

Continued excessive extraction of groundwater may lead to significant land subsidence, which causes economic loss. The aim of this research is to investigate ground subsidence in several Australian capital cities using the Persistent Scatterer Interferometry approach. Such studies may help improve our understanding of the deformation of terrain and built structures, and evaluate the effectiveness of any measures taken to ease the problem. The Persistent Scatterer Radar Interferometry approach is an alternative technique for land subsidence monitoring to conventional surveying methods. The Persistent Scatterer Interferometry approach first identifies all the stable point scatterers and a deformation analysis is then applied to these points. Persistent Scatterer InSAR techniques can generate deformation time-series with an accuracy down to the millimetre level depending on the number and quality of SAR images. The Persistent Scatterer InSAR results are validated with other spatial data such as groundwater extraction bore sites and groundwater level. Six cities are selected for these analyses, and the results show that the deformation rate from cities with groundwater significant levels of water extraction are much larger than for those cities with low levels of groundwater extraction.

While using GPS data to calculate TEC (Total Electron Content), the bias due to GPS hardware errors (including satellite and receiver clocks), tropospheric error and multipath error must be removed, or at least significantly reduced. In this paper the authors use carrier phase smoothed pseudo-range data within a complementary Kalman filter. Under the assumption that there is a linear variation of TEC with respect to geographical latitude and longitude, the Kalman filter has been used to estimate the TEC with less bias. Also an ionospheric electric potential model is used for smoothing the TEC.Taking Australian GPS continuous observation station data as an example, the authors have analysed the ionospheric TEC daily variations in 2006, and hourly variations in a sample day in Spring, Summer, Autumn and Winter. In addition the Australia TEC spatial distribution during a certain time has been determined using the data from 14 Australia GPS continuous observation stations. The result shows that the TEC values in Summer and Spring are higher, and have more obvious variability, than during Autumn and Winter

This paper compares global and regional ionosphere maps in different aspects, from vertical TEC and slant TEC in the range domain to their application in single-frequency Precise Point Positioning. Under quiet ionospheric conditions, the mean of the difference in vertical TEC between the global (GIM) and regional (SWACI) map, in Europe, was found to be less than 1 TECU, and the RMS generally in the order of 1–2 TECU. Both static data and kinematic (flight) data are analysed. Although being limited in its coverage for the moment, the real-time regional map SWACI (from DLR) provides promising results also with highly kinematic data. It is shown that for the dataset under investigation the SWACI map can bring the vertical positioning accuracy to the same level as the horizontal one, at 2–3 km (95% level)

In the past, high-precision online 3D measuring required artificial targets defining the points on the objects to be monitored. For many tasks such as monitoring of displacements of buildings, artificial targets are not desired. Today’s image-assisted measurement systems can perform their measurements even without targeting. Such systems use the texture on the surface of the object to find “interesting points” which can replace the artificial targets. However, well-trained “measurement experts” are required to operate such a measurement system. In order to make such systems easy to use even for non-experts, it can be extended by an appropriate decision system which supports the operator. At the Institute of Geodesy and Geophysics of Vienna University of Technology a new kind of image-based measurement system is being developed (research project “Multi-Sensor Deformation Measurement System Supported by Knowledge-Based and Cognitive Vision Techniques”). This system can be used for measuring, analysing and interpreting deformations for the task of quality control in civil engineering. The work-flow is based on new techniques originally developed in the field of Artificial Intelligence

New solutions are provided to the direct and indirect geodetic problems on the ellipsoid. In addition, the area under the geodesic and the problem of intersection of geodesics are treated.Each solution is composed of a strict solution for the sphere plus a small correction to account for the eccentricity of the ellipsoid. The correction is conveniently determined by numerical integration.

Integer carrier phase ambiguity resolution is the key to fast and high-precision global navigation satellite system (GNSS) positioning and application. Although considerable progress has been made over the years in developing a proper theory for ambiguity resolution, the necessary theory is far from complete.In this contribution we address three topics for which further developments are needed. They are: (1) Ambiguity acceptance testing; (2) Ambiguity subset selection; and (3) Integer-based GNSS model validation. We will address the shortcommings of the present theory and practices, and discuss directions for possible solutions

This contribution extends the previous work of (2005). Using Groebner basis and Dixon resultant as the engine behind Computer Algebra Systems (CAS). The authors demonstrate how 3D GPS positioning, 3D intersection, as well as datum transformation problems are solved ‘live’ in Mathematica, thanks to modernization in CAS. Mathematica notebooks containing these ‘live’ computational models and examples are available at http://library.wolfram.com/infocenter/ MathSource/6654

A comparison of the ability of artificial neural networks and polynomial fitting was carried out in order to model the horizontal deformation field of the Cascadia Subduction Zone, as determined from GPS analyses of the Pacific Northwest Geodetic Array (PANGA).One set of data was used to calculate the unknown parameters of the model (training set 75 {%} of the whole data set) and the other set was used only for testing the accuracy of the derived model (testing set–25 {%} of the whole data set). The testing set has not been used to determine the parameters of the model.The problem of overfitting (see Kecman (2001)) (i.e., the substantial oscillation of the model between the training points, the same problem than polynomial wiggle (Mathews and Fink 2004) can be avoided by restricting the flexibility of the neural model. This can be done using an independent data set, namely the validation data (one third part of the training set). The proposed method is the so-called “stopped search method”, which can be used for obtaining a smooth and precise fitting model. However, when fitting high order polynomials, it is difficult to overcome the negative effect of the overfitting problem.Different order polynomial models and neural network models with different numbers of neurons were calculated. The best fitting polynomial model was 6th order with 28 parameters. The finally used neural network model contained 7 neurons in it’s one hidden layer, with radial basis activation functions, with 31 parameters. These two models, with same order of numbers of parameters, were compared. Calculating the remained errors at the training points the two models had the same fitting precision. However according to the testing point’s results, the neural network model offered more reliable results, with 2–3 times smaller errors.The computations were performed with the Mathematica software, and the results are given in a symbolic form which can be used in the analysis of crustal deformation, e.g. strain analysis

The project on “Next-generation algorithms for navigation, geodesy and earth sciences under modernized Global Navigation Satellite Systems (GNSS)” has been under development within the scope of the Geomatics for Informed Decisions (GEOIDE) Network. The GEOIDE Network is part of the Networks of Centres of Excellence program (NCE) of the government of Canada. Networks of Centres of Excellence are unique partnerships among universities, industries, government and non-profit organizations aimed at turning Canadian research and entrepreneurial talent into economic and social benefits for all Canadians. Among its objectives, the GEOIDE Network intends to drive the research and development of new geomatics technologies and methods via multidisciplinary collaboration in a fully networked environment. The GEOIDE Network, having started operations in 1998, is currently in its Phase III. In this paper the authors will present an overview of the activities which have taken place under this project. They include: (a) Processing and analysis of real modernized GNSS data (L2C) as well as simulated modernized GPS and Galileo data; (b) Performing constellation system performance and augmentation analyses of the modernized GNSS; (c) Designing algorithms for single point and relative positioning using combined signals; and (d) Integrating legacy and modernized GNSS signals.

Synthetic aperture radar interferometry (InSAR) has been widely used over the past two decades for such geodetic applications as topographic mapping and ground deformation monitoring. In particular, in contrast to other geodetic techniques, differential InSAR has the capability of measuring surface deformation with a measurement precision of a few millimetres and a spatial resolution of a few tens of metres or less, over areal extents of thousands of square kilometers.However, the ground surface may deform by a large amount within a small area due to localised effects such as earthquakes, underground mining, groundwater extraction, and others, which may cause severe damage to manmade surface and underground structures. Current satellite radar interferometry, because of its single-frequency signal structure, cannot measure deformations with large horizontal gradients as they produce very dense fringe patterns. The upper limit of the deformation gradient is determined by the signal wavelength and pixel spacing. Although the longer wavelength of the radar signal is less susceptible to high deformation gradients, loss of correlation often still occurs even when L-band imagery is usedIn this paper, the authors propose a method to effectively monitor such large-gradient deformation using differential InSAR by linear combinations of interferograms acquired from dual-frequency sensors. Some simulated interferograms are generated through the combination of the commonly used radar wavelengths, for instance C, L₁, L₂, S and even P-band. Using appropriate linear combinations, the virtual wavelength of the combined interferogram is flexible enough to be used for different applications. From the simulated results, it is found that the linear combination technique is powerful and can improve the correlation, as well as making the phase unwrapping process much easier

From October 2003 to September 2005, the International VLBI Service for Geodesy and Astrometry (IVS) examined current and future requirements for geodetic VLBI, including all components from antennas to analysis. IVS Working Group 3 “VLBI 2010”, which was tasked with this effort, concluded with recommendations for a new generation of VLBI systems. These recommendations were based on the goals of achieving 1 mm measurement accuracy on global baselines, performing continuous measurements for time series of station positions and Earth orientation parameters, and reaching a turnaround time from measurement to initial geodetic results of less than 24 h. To realize these recommendations and goals, along with the need for low cost of construction and operation, requires a complete examination of all aspects of geodetic VLBI including equipment, processes, and observational strategies. Hence, in October 2005, the IVS VLBI2010 Committee (V2C) commenced work on defining the VLBI2010 system specifications. In this paper we give a summary of the recent progress of the VLBI2010 project

The network of more than 24 superconducting gravimeters (SGs) of the Global Geodynamics Project (GGP) is available as a set of reference stations for studies related to time-varying gravimetry. The inherent stability of the SG allows it to detect signals from a sampling time of 1 s up to periods of several years with a time-domain accuracy of 0.1 μGal or better. SGs within the GGP network comprise a valuable set of stations for geodetic and geophysical studies that involve Earth’s surface gravity field. Experience has shown that SGs can be calibrated to an accuracy of 0.01–0.1 {%}, and that most instruments have a low, but well-modeled, drift of a few μGal/yr. For most purposes except the determination of an absolute gravity reference level, the SG is the best observation-style instrument we have today. SG data is now freely available, much of it going back to the early 1990’s, from the GGP database at ICET (International Centre of Earth Tides, in Brussels, Belgium) and GFZ (Potsdam, Germany). Frequently it is combined with other datasets such as atmospheric pressure and hydrology for studies of ground deformation and tectonics. One of the most interesting new ideas within GGOS (Global Geodetic Observing System) is the determination of the geocenter using a combination of satellite and ground-based gravimetry. The GGP network can provide a unique contribution through continuous data at the stations where absolute gravimeters (AGs) will be deployed. The combination of the two instruments is necessary to ensure that AG measurements are referencing the mean station gravity and not short-term gravity perturbations due for example to hydrology or meteorology. Another promising application is the use of SG sub-networks in Europe and Asia to validate time-varying satellite gravity observations (GRACE, GOCE)

The determination of the temporal variations of the Earth orientation parameters (EOP) and spherical harmonic coefficients of the gravity field are geodetic contributions to the analysis of global geodynamic processes. As the Earth’s tensor of inertia is functionally related both to the EOP via the Euler-Liouville equations and directly to the gravity field coefficients of degree 2 it allows the mutual validation of these two sets of parameters.This paper proposes a statistically founded method of combining the temporal variations of the EOP and of the gravity field coefficients of degree 2 by a least-squares estimation based on the Gauss-Helmert model (condition equations with unknowns). Thereby statistically founded values for the unknown parameters can be derived, together with residuals for the observations, checkability and accuracy measures.The EOP and gravity field coefficients of degree 2 are introduced as observations together with correction terms such as excitation functions of atmosphere and ocean. The results of the Gauss-Helmert model computed with gravity field coefficients from GRACE and the C04 series from the International Earth Rotation and Reference Systems Service are shown in this paper. If given standard deviations are taken into account and covariances are neglected the following results are obtained: Δlod is coupled with C₂₀ and vice versa, C₂₁ and S₂₁ are coupled with the polar motion, but the polar motion itself and the gravity field coefficients C₂₂ and S₂₂ are not checked by any other parameter