International Association Of Geodesy Research Articles

Unifying the Nepal height system and China height system based on gravity frequency shift approach

Highly accurate international height reference frames with long-term stability, global consistency, and homogeneity are crucial for monitoring sea level variations, understanding climate change, managing disasters, and supporting other applications that benefit scientific research and societal well-being. Currently, there are over 100 local height reference systems worldwide. Unifying these systems is a pivotal step toward constructing international height reference frames. The method introduced in this study—the gravity frequency shift via Satellite Frequency Signal Transfer (SFST)—represents a groundbreaking relativistic geodetic approach, demonstrating its potential to surpass the constraints of conventional techniques. The advent of high-precision optical atomic clocks (OAC) with an accuracy level of has facilitated this method's implementation. The International Association of Geodesy (IAG) has established the International Height Reference System (IHRS) and its practical realization, the International Height Reference Frame (IHRF). Our study focuses on two neighbouring height systems: the China Height System (CHS) and the Nepal Height System (NHS), separated by the Himalayas and the Tibetan plateau. We aim to unify these two systems by determining the geopotential and orthometric height differences between their respective height datum stations: the Qingdao Height Datum Station (QHDS) and the Madar Height Datum Station (MHDS) using a simulation experiment with the method mentioned above. Using an OAC with an accuracy of , we identified a geopotential difference of and an orthometric height difference of m between QHDS and MHDS. These results suggest that the introduced method could unify any two height systems with few-centimeter-level precision, emphasizing its significance in contributing to the construction of the IHRS/IHRF with today's required precision. In summary, the SFST technique is a novel geodetic method that offers an alternative for height system unification, delivering centimeter-level precision, surpassing traditional methods, and supporting the development of the IHRF.

A Atmospheric Correction of FG5 Absolute Gravimetry Data using Measured Air Pressure

Changes in atmospheric density affect atmospheric pressure, which is a key factor affecting high-precision gravity measurement. Currently, atmospheric correction of absolute gravity measurements uses the empirical admittance value recommended by the International Association of Geodesy (−0.3 μGal/mbar); however, the actual admittance value changes with atmospheric mass and time. In this study, we determine the effect of using measured admittance values for absolute gravity correction. First, high-precision relative gravimeters (GWR OSG-057, Scintrex CG5) are used for continuous gravity measurements. Then, air pressure measured by the pressure sensor equipped by FG5 absolute gravimeter is used to obtain the atmospheric admittance using the iterative least squares method, which is compared with the theoretical atmospheric admittance. Taking FG5-257 as an example, we use the measured admittance for atmospheric correction of absolute gravity at four different elevations (Lhasa, Nagqu, Gar, and Suining, China). The results are as follows: 1) According to co-location measurements in Lhasa, CG5 and OSG gravimeter measured admittance values exhibit comparable precision (–0.332 ± 0.003 μGal/mbar and –0.332 ± 0.001 μGal/mbar, respectively), though the CG5 has larger standard deviation. 2) After correction using the measured admittance, changes in set standard deviation and measurement precision are approximately 0.01 μGal; however, the effect on the measurement results does not exceed 1 μGal, which is equivalent to the measurement precision of FG5. Therefore, measured admittance values are only recommended for atmospheric correction of high-precision absolute gravity measurements.

A first step towards a national realisation of the international height reference system in Sweden with a comparison to RH 2000

Abstract The International Height Reference System (IHRS) was defined by the International Association of Geodesy in 2015. Since then, the international geodetic community has been working on the specification and establishment of its realisation, the International Height Reference Frame (IHRF). This frame will primarily be realised by geopotential numbers (or physical heights) in a sparse global reference network. In Sweden, only one such global station is planned. Regional and national realisations (or densifications) computed in accordance with the IHRS definition are needed to enable the best possible unification of height datums. The main purpose of this article is to make a case study for Sweden regarding the national realisation of IHRS and to investigate in what way preliminary IHRF differs from the current Swedish levelling-based realisation of the European Vertical Reference System, RH 2000. The two different quasigeoid models that we consider best over Sweden at the present time are used to compute the preliminary IHRS realisations in the study. The realisations are compared to each other and to RH 2000. It is shown that a very significant part of the difference to RH 2000 is due to the different postglacial land uplift epochs, permanent tide concepts, and zero levels. The standard deviation for the difference between one of the preliminary national IHRS realisations and RH 2000 is reduced from 75.5 to 19.2 mm after correction of the postglacial land uplift and permanent tide effects. The corresponding mean differences are –208.5 and –454.7 mm, respectively. The magnitude of the mean difference thus increases when the corrections in question are applied.

Unification of a Global Height System at the Centimeter-Level Using Precise Clock Frequency Signal Links

The International Association of Geodesy (IAG) aims to establish the International Height Reference System (IHRS) as one of its primary scientific objectives. Central to the realization of the IHRS is global vertical datum unification, which requires the connection of existing local vertical height reference systems (VHS) robustly and consistently. However, conventional methods are not suitable for estimating the offsets between two distant local height systems. In this paper, we propose a framework for connecting two local VHSs using ultraprecise clock frequency signal links between satellites and ground stations, referred to as the satellite frequency signal transmission (SFST) approach. The SFST approach allows for the direct determination of the geopotential and height differences between two ground datum stations without any location restrictions between the two VHSs. The simulation results show that the VHSs of China and the US can be unified with an accuracy of several centimeters, provided that the stability of atomic clocks used on-board the satellite and at on-ground datum locations reaches 4.8×10−17τ−1/2 for an averaging time τ (in seconds). We conclude that the SFST approach shows promise for achieving centimeter-level accuracy in unifying the global vertical height datum and represents a new paradigm for the realization of the IHRS.

GENESIS: co-location of geodetic techniques in space

Improving and homogenizing time and space reference systems on Earth and, more specifically, realizing the Terrestrial Reference Frame (TRF) with an accuracy of 1 mm and a long-term stability of 0.1 mm/year are relevant for many scientific and societal endeavors. The knowledge of the TRF is fundamental for Earth and navigation sciences. For instance, quantifying sea level change strongly depends on an accurate determination of the geocenter motion but also of the positions of continental and island reference stations, such as those located at tide gauges, as well as the ground stations of tracking networks. Also, numerous applications in geophysics require absolute millimeter precision from the reference frame, as for example monitoring tectonic motion or crustal deformation, contributing to a better understanding of natural hazards. The TRF accuracy to be achieved represents the consensus of various authorities, including the International Association of Geodesy (IAG), which has enunciated geodesy requirements for Earth sciences. Moreover, the United Nations Resolution 69/266 states that the full societal benefits in developing satellite missions for positioning and Remote Sensing of the Earth are realized only if they are referenced to a common global geodetic reference frame at the national, regional and global levels. Today we are still far from these ambitious accuracy and stability goals for the realization of the TRF. However, a combination and co-location of all four space geodetic techniques on one satellite platform can significantly contribute to achieving these goals. This is the purpose of the GENESIS mission, a component of the FutureNAV program of the European Space Agency. The GENESIS platform will be a dynamic space geodetic observatory carrying all the geodetic instruments referenced to one another through carefully calibrated space ties. The co-location of the techniques in space will solve the inconsistencies and biases between the different geodetic techniques in order to reach the TRF accuracy and stability goals endorsed by the various international authorities and the scientific community. The purpose of this paper is to review the state-of-the-art and explain the benefits of the GENESIS mission in Earth sciences, navigation sciences and metrology. This paper has been written and supported by a large community of scientists from many countries and working in several different fields of science, ranging from geophysics and geodesy to time and frequency metrology, navigation and positioning. As it is explained throughout this paper, there is a very high scientific consensus that the GENESIS mission would deliver exemplary science and societal benefits across a multidisciplinary range of Navigation and Earth sciences applications, constituting a global infrastructure that is internationally agreed to be strongly desirable.Graphical

Utilización de los valores absolutos de la aceleración de la gravedad para obtener el factor de escala de los gravímetros Lacoste&Romberg Modelo G.

The Military Geographic Institute (IGM) is the institution responsible for maintaining and updating the official geodesic reference system of Chile put into effect through the National Geodesic Network (RGN), which consists of the Horizontal and Vertical RGNs. This latter element is made up of the leveling network, constituted by altitude points referenced to the Mean Sea Level (M.S.L.) and the Gravimetric Network, consisting of absolute and relative stations, with gravity acceleration values (g), referenced to the International Gravity Standardization Network 1971 (IGSN-71). The IGSN-71 was adopted as the world reference for gravimetric measurement at the 25th General Assembly of the International Union of Geodesy and Geophysics (IUGG) in 1971 with a precisión of ± 0,1 mGal. This current research work is mainly focused on making known the chief features of the operation and correct use of the instrument measuring the gravity acceleration (g) that the IGM uses for its gravimetric projects. The instrumental calibration procedure is made known here, obtaining the “scale” (adjustment) factor for each Lacoste&Romberg model G gravimeter in orderto obtain more accurate gravity values.The above is sustained in relation to the requirements suggested by international organisations in the area of geodesy, such as the International Association of Geodesy (IAG) and SIRGAS, which encourage all nations to implement homogeneous and precise global vertical reference systems, in which gravimetry is an essential factor in setting up a new vertical reference frame for the whole country, adopting physical heights.

Uso de valores absolutos de aceleración de gravedad para el factor de escala de gravímetros Lacoste&Romberg Modelo G.

The Military Geographic Institute (IGM) is the institution responsible for maintaining and updating the official geodesic reference system of Chile put into effect through the National Geodesic Network (RGN), which consists of the Horizontal and Vertical RGNs. This latter element is made up of the leveling network, constituted by altitude points referenced to the Mean Sea Level (M.S.L.) and the Gravimetric Network, consisting of absolute and relative stations, with gravity acceleration values (g), referenced to the International Gravity Standardization Network 1971 (IGSN-71). The IGSN-71 was adopted as the world reference for gravimetric measurement at the 25th General Assembly of the International Union of Geodesy and Geophysics (IUGG) in 1971 with a precisión of ± 0,1 mGal. This current research work is mainly focused on making known the chief features of the operation and correct use of the instrument measuring the gravity acceleration (g) that the IGM uses for its gravimetric projects. The instrumental calibration procedure is made known here, obtaining the “scale” (adjustment) factor for each Lacoste&Romberg model G gravimeter in orderto obtain more accurate gravity values.The above is sustained in relation to the requirements suggested by international organisations in the area of geodesy, such as the International Association of Geodesy (IAG) and SIRGAS, which encourage all nations to implement homogeneous and precise global vertical reference systems, in which gravimetry is an essential factor in setting up a new vertical reference frame for the whole country, adopting physical heights.

Historical development of SIRGAS

Abstract The Geodetic Reference System for the Americas (Sistema de Referencia Geodésico para las Américas, SIRGAS) was initiated in 1993 for South America at an international conference organised by the International Association of Geodesy (IAG), the Pan-American Institute for Geography and History (PAIGH), the Deutsches Geodätisches Forschungsinstitut (DGFI), and the U.S. Defense Mapping Agency (DMA) in Asunción, Paraguay. The corresponding South American reference network was observed in 1995 by a ten-day GPS campaign at 58 stations. The network was extended to Central and North America in 2000 and immediately afterwards converted to a frame of continuously observing GNSS stations instead of short-term campaigns. The linear station position changes (velocities) were estimated by a multi-year least squares adjustment of weekly solutions, the first being published in 2002. The total set of station velocities served for the computation of continuous surface deformation models, the first over South America was published in 2005. Today, SIRGAS is accepted by most of the American states as the official geodetic reference frame. Besides the product generation (station positions, velocities, and surface deformation), SIRGAS is active in education and training offering schools and workshops for students, surveyors, and other stakeholders.

Towards Understanding the Interconnection between Celestial Pole Motion and Earth's Magnetic Field Using Space Geodetic Techniques.

The understanding of forced temporal variations in celestial pole motion (CPM) could bring us significantly closer to meeting the accuracy goals pursued by the Global Geodetic Observing System (GGOS) of the International Association of Geodesy (IAG), i.e., 1 mm accuracy and 0.1 mm/year stability on global scales in terms of the Earth orientation parameters. Besides astronomical forcing, CPM excitation depends on the processes in the fluid core and the core–mantle boundary. The same processes are responsible for the variations in the geomagnetic field (GMF). Several investigations were conducted during the last decade to find a possible interconnection of GMF changes with the length of day (LOD) variations. However, less attention was paid to the interdependence of the GMF changes and the CPM variations. This study uses the celestial pole offsets (CPO) time series obtained from very long baseline interferometry (VLBI) observations and data such as spherical harmonic coefficients, geomagnetic jerk, and magnetic field dipole moment from a state-of-the-art geomagnetic field model to explore the correlation between them. In this study, we use wavelet coherence analysis to compute the correspondence between the two non-stationary time series in the time–frequency domain. Our preliminary results reveal interesting common features in the CPM and GMF variations, which show the potential to improve the understanding of the GMF’s contribution to the Earth’s rotation. Special attention is given to the corresponding signal between FCN and GMF and potential time lags between geomagnetic jerks and rotational variations.

The permanent tide and the International Height Reference Frame IHRF

The International Height Reference System (IHRS), adopted by International Association of Geodesy (IAG) in its Resolution No. 1 at the XXVI General Assembly of the International Union of Geodesy and Geophysics (IUGG) in Prague in 2015, contains two novelties. Firstly, the mean-tide concept is adopted for handling the permanent tide. While many national height systems continue to apply the mean-tide concept, this was the first time that the IAG officially introduced it for a potential field quantity. Secondly, the reference level of the height system is defined by the equipotential surface where the geopotential has a conventional value W0 = 62,636,853.4 m2 s–2. This value was first determined empirically to provide a good approximation to the global mean sea level and then adopted as a reference value by convention. I analyse the tidal aspects of the reference level based on W0. By definition, W0 is independent of the tidal concept that was adopted for the equipotential surface, but for different concepts, different functions are involved in the W of the equation W = W0. I find that, in the empirical determination of the adopted estimate W0, the permanent tide is treated inconsistently. However, the consistent estimate from the same data rounds off to the same value. I discuss the tidal conventions and formulas for the International Height Reference Frame (IHRF) and the realisation of the IHRS. I propose a simplified definition of IHRF geopotential numbers that would make it possible to transform between the IHRF and zero-tide geopotential numbers using a simple datum-difference surface. Such a transformation would not be adequate if rigorous mean-tide formulas were imposed. The IHRF should adopt a conventional (best) estimate of the permanent tide-generating potential, such as that which is contained in the International Earth Rotation and Reference Systems Service Conventions, and use it as a basis for other conventional formulas. The tide-free coordinates of the International Terrestrial Reference Frame and tide-free Global Geopotential Models are central in the modelling of geopotential for the purposes of the IHRF. I present a set of correction formulas that can be used to move to the zero-tide model before, during, or after the processing, and finally to the mean-tide IHRF. To reduce the confusion around the multitude of tidal concepts, I propose that modelling should primarily be done using the zero-tide concept, with the mean-tide potential as an add-on. The widespread use of the expression “systems of permanent tide” may also have contributed to the confusion, as such “systems” do not have the properties that are generally associated with other “systems” in geodesy. Hence, this paper mostly uses “concept” instead of “system” when referring to the permanent tide.

Contribution to the Establishment of the IHRF in the State of São Paulo

This letter describes a practical computation to determine the potential values, following the International Association of Geodesy (IAG) recommendations, at Presidente Prudente (PPTE) and Cananeia (NEIA) stations, which are part of the Brazilian Global Navigation Satellite System (GNSS) network, and the first one belongs to the International Height Reference Frame (IHRF) Brazilian network. For the computation, Global Geopotential Models (GGMs) such as EIGEN-6C4, GECO, GOCO05c, and XGM2016 were applied for degree and order 100 and 200. The Least Squares Collocation (LSC), Stokes’ Integral, and Hotine’s Integral were the methodologies selected in this study. The results were validated in terms of geopotential values, normal heights, and height anomalies. The values obtained present more consistence for the integration radius up to 2 degrees. Moreover, LSC and Hotine’s integral showed convergence in the results.

Open access to regional geoid models: the International Service for the Geoid

Abstract. The International Service for the Geoid (ISG, https://www.isgeoid.polimi.it/, last access: 31 March 2021) provides free access to a dedicated and comprehensive repository of geoid models through its website. In the archive, both the latest releases of the most important and well-known geoid models, as well as less recent or less known ones, are freely available, giving to the users a wide range of possible applications to perform analyses on the evolution of the geoid computation research field. The ISG is an official service of the International Association of Geodesy (IAG), under the umbrella of the International Gravity Field Service (IGFS). Its main tasks are collecting, analysing, and redistributing local, regional, and continental geoid models and providing technical support to people involved in geoid-related topics for both educational and research purposes. In the framework of its activities, the ISG performs research taking advantage of its archive and organizes seminars and specific training courses on geoid determination, supporting students and researchers in geodesy as well as distributing training material on the use of the most common algorithms for geoid estimation. This paper aims at describing the data and services, including the newly implemented DOI Service for geoid models (https://dataservices.gfz-potsdam.de/portal/?fq=subject:isg, last access: 31 March 2021), and showing the added value of the ISG archive of geoid models for the scientific community and technicians, like engineers and surveyors (https://www.isgeoid.polimi.it/Geoid/reg_list.html, last access: 31 March 2021).

Determination of the geopotential value on the permanent GNSS stations in Vietnam based on the Geodetic Boundary Value Problem approach

SUMMARY In the realisation of the International Height Reference System, the determination of the geopotential value and its variations in time plays an important role. In this study, the geodetic boundary value problem approach is applied for direct determination of the gravity potential value using a GOCE global gravity field model enhanced with terrestrial gravity data. This determination is carried out on the Global Navigation Satellite System-Continuously Operating Reference Stations (GNSS-CORS) stations towards the realisation of the International Height Reference System in Vietnam. First, the effects of the GOCE global gravity field model omission error, the indirect bias term on the disturbing potential and the systematic cumulative errors in levelling data are estimated. These errors affect the estimated geopotential value. The results calculated on the GNSS/levelling points show that the effect of the GOCE DIR-R5 (up to degree/order 260) omission error on the offset potential value is quite significant. This effect was eliminated using high-resolution terrestrial gravity data using the remove-compute-restore technique. The indirect bias term on the disturbing potential can be safely neglected by using a GOCE global gravity field model for degrees higher than 60 for this study region. The systematic cumulative errors in levelling data can be modelled and removed using a third-order polynomial model. Then, the mean zero-height gravity potential of the Vietnam local vertical datum is estimated equal to ${\rm{W}}_0^{{\rm{LVD}}}$ = 62 636 846.69 m2 s–2 with standard deviation of 0.70 m2 s–2 based on the proposed approach. Finally, the geodetic boundary value problem approach was used to determine the geopotential on the surface of three GNSS-CORS stations in Vietnam. Based on time-series of the vertical component derived from the GNSS observations as well as InSAR data, temporal variations in geopotential are also estimated on these permanent GNSS stations. The purpose is to monitor deformation of the vertical datum. The results indicate that the geopotential value needs to be monitored and determined with the time-dependent component on the three Vietnamese permanent GNSS stations for a vertical datum. These stations may contribute to increase the density of reference points in the International Terrestrial Reference Frame, which is being researched and implemented by the International Association of Geodesy.

High-resolution geoid modeling using least squares modification of Stokes and Hotine formulas in Colorado

The Colorado geoid experiment was initiated and organized as a joint study by the Joint Working Group (JWG) 2.2.2 (1-cm geoid experiment) of the International Association of Geodesy (IAG) in 2017, and different institutions and research groups contributed to this study. The aim of this experiment was to clarify the repeatability of gravity potential values as International Height Reference System (IHRS) coordinates from different geoid determination approaches carried out with the same input dataset. The dataset included the terrestrial and airborne gravity observations, a digital terrain model, the XGM2016 global geopotential model and GPS/leveling data for model validations belonging to a mountainous area of approximately 550 km × 730 km in Colorado, US. The dataset was provided by National Geodetic Survey (NGS) department. In this frame, this article aims providing a discussion on Colorado geoid modeling through individual experimental results obtained by Istanbul Technical University-Gravity Research Group (ITU-GRG). This contribution mainly focused on modeling the Colorado geoid using the least squares modifications of Stokes and Hotine integral formulas with additive corrections. The computations using each formula were carried out using ITU-GRG software, including the solution variants based on terrestrial-only, airborne-only and combined gravity datasets. Then, the calculated experimental geoid models were validated using historical and recently measured profile-based GPS/leveling datasets, and they were also compared with the official solutions submitted by different institutions for the “1-cm geoid experiment” of IAG JWG 2.2.2. For all validation results, the Hotine and Stokes integral formulas yielded similar performances in terms of geoid accuracy; however, the models computed using the combined data had better accuracy than those using the terrestrial-only and airborne-only solutions. The geoid model solutions using the combined data had an accuracy of 2.69 cm for the Hotine method and 2.87 cm for the Stokes method in the test results using GPS/leveling data of the GSVS17 (Geoid Slope Validation Survey 2017) profile. Airborne data from the Gravity for the Redefinition of the American Vertical Datum (GRAV-D) project contributed significantly towards improving the geoid model, especially in the mountainous parts of the area.

Status of the International Gravity Reference System and Frame

The increasing importance of terrestrial gravimetry in monitoring global change processes, in providing a reference for satellite measurements and in applications in metrology necessitates a stable reference system reflecting the measurement accuracy achievable by modern gravimeters. Therefore, over the last decade, the International Association of Geodesy (IAG) has developed a system to achieve accurate, homogeneous, long-term global recording of Earth’s gravity, while taking advantage of the potential of today’s absolute gravity measurements. The current status of the International Gravity Reference System and Frame is presented as worked out by the IAG Joint Working Group 2.1.1 “Establishment of a global absolute gravity reference system” during the period 2015–2019. Here, the system is defined by the instantaneous acceleration of free-fall, expressed in the International System of Units (SI) and a set of conventional corrections for the time-independent components of gravity effects. The frame as the systems realization includes a set of conventional temporal gravity corrections which represent a uniform set of minimum requirements. Measurements with absolute gravimeters, the traceability of which is ensured by comparisons and monitoring at reference stations, provide the basis of the frame. A global set of such stations providing absolute gravity values at the microgal level is the backbone of the frame. Core stations with at least one available space geodetic technique will provide a link to the terrestrial reference frame. Expanded facilities enabling instrumental verification as well as repeated regional and additional comparisons will complement key comparisons at the level of the International Committee for Weights and Measures (CIPM) and ensure a common reference and the traceability to the SI. To make the gravity reference system accessible to any user and to replace the previous IGSN71 network, an infrastructure based on absolute gravity observations needs to be built up. This requires the support of national agencies, which are encouraged to establish compatible first order gravity networks and to provide information about existing absolute gravity observations.

Forced nutations of a two-layer Earth in canonical formulation with dissipative Hori-like kernel

In this research, a modification of the Lie-Hori perturbation method developed by the authors in a recent investigation is used to compute the forced nutations of a non-rigid Earth model, including dissipative processes at the core-mantle boundary. The study is tackled within the Hamiltonian formalism of a two-layer Earth, where the viscous and electromagnetic couplings between mantle and core are introduced via generalized forces. The modified Lie-Hori method is introduced within the framework of the generalized Hamiltonian formalism. It, therefore, allows for calculating first-order perturbations in both conservative and non-conservative systems, while the classical Lie-Hori procedure is not designed to include generalized forces in the kernel to account for dissipative processes. Unlike other methods, this one presents the advantage of keeping the same dimensionality of the original problem, avoiding the doubling of the dimension of the phase space. With this mathematical refinement, differences in the derived nutation amplitudes at the microarcsecond level have been found when compared with the former, first approximation for dissipative systems based on damped oscillators —the only existing previous solution. Those figures are of relevance according to recent recommendations of the International Astronomical Union (IAU) and the International Association of Geodesy (IAG) based on the final report of the Joint Working Group on Theory of Earth rotation and validation.

The worldwide physical height datum project

The definition of a common global vertical coordinate system is nowadays one of the key points in Geodesy. With the advent of GNSS, a coherent global height has been made available to users. The ellipsoidal height can be obtained with respect to a given geocentric ellipsoid in a fast and precise way using GNSS techniques. On the other hand, the traditional orthometric height is not coherent at global scale. Spirit levelling allows the estimation of height increments so that orthometric heights of surveyed points can be obtained starting from a benchmark of known orthometric heights. As it is well known, this vertical coordinate refers to the geoid, which is assumed to be coincident to the mean sea level. By means of a tide gauge, the mean sea level is estimated and thus a point of known orthometric height is defined. This assumption, which was acceptable in the past, became obsolete given the level of precision which is now required. Based on the altimetry observation, one can precisely quantify the existing discrepancy between geoid and mean sea level that can amount to 1 ÷ 2 m at global scale. Therefore, different tide gauges provide biased estimates of the geoid, given the discrepancy between this equipotential surface and the mean sea level. Also, in the last years, another vertical coordinate was used, the normal height that was introduced in the context of the Molodensky theory. In this paper, a review of the existing different height systems is given and the relationships among them are revised. Furthermore, an approach for unifying normal height referring to different tide gauges is presented and applied to the Italian test case. Finally, a method for defining a physical height system that is globally coherent is discussed in the context of the definition of the International Height Reference System/Frame, a project supported by the Global Geodetic Observing System of the International Association of Geodesy (IAG). This project was established in 2015 during the XXVI IAG General Assembly in Prague as described in IAG Resolution no. 1 that was presented and adopted there.

SIRGAS-WGIII activities for unifying height systems in Latin America

Since 1997 SIRGAS (Geocentric Reference System for the Americas) is acting for establishing a unified SIRGAS Vertical Reference System (SVRS) in Latin Ameri- ca and the Caribbean. The standards, procedures and activities aiming the definition and realization of the SVRS are now directed to meet the modern international requirements of integration into a Global Vertical Reference System (GVRS) to support the needs for Earth Observation Systems. These statements imply in a uni- fication of the existing National Vertical Reference Systems (NVRS), each one with its respective Frame (NVRF) and Vertical Datum (NVD) realized in the geopoten- tial space. The study of new possibilities for connecting NVRS in a global basis is in the context of the International Association of Geodesy (IAG) main activities. However, most of modern requirements are not immediately applicable for building the SVRS because the differences in the conception and realization of each NVRS in the SIRGAS region. In this work an overview about the status of NVRS, NVR Fand NVD in South America is presented. The most important characteristics for unifying NVRS in a global context as well as the main related problems are pre- sented. Some emphasis is given on the activities of SIRGAS-Working Group III directed for facing the integration problems in South America. The poor data availability, unknown discrepancies among NVRS, different data collecting and processing strategies for establishing the networks, and other error sources are discussed. The possibilities coming from new strategies and modern tools are dis- cussed mainly by considering new missions and global data basis of Geodesy.

Surface volume and gravity changes due to significant earthquakes occurred in central Italy from 2009 to 2016

We have modelled the surface volume and gravity changes caused by four seismic events: three mainshocks (moment magnitude Mw 6.0, 5.9, 6.5) occurred during the last seismic period started on 2016, August 24 in central Italy, and the 2009, April 6 L’Aquila Earthquake (Mw 6.3). Our calculations start from the source parameters estimated by the inversion of the largest dataset of Interferometric Synthetic Aperture Radar (InSAR) and global positioning system observations ever managed in Italy after earthquake occurrences, based on the half-space elastic dislocation theory. The vertical displacements modelled after the 2016 events allow to infer a substantial unbalance between the subsided and uplifted volumes. In particular, we detected ~ 106 × 106 m3 of hangingwall subsidence against ~ 37 × 106 m3 of footwall uplift, that accounts for ~ 74% of the total volume mobilization. From the ratio between the footwall and total deformed volumes, we have computed an average fault dip of ~ 47°, in line with the values retrieved by seismological methods. The total gravity variations which affected the study area are of the order of ~ 1 μGal (1 μGal = 10−8 ms−2) in the far field, and ~ 170 μGal in the near field. The area affected within a gravity change of 1 μGal is ~ 140 km long and ~ 57 km wide, parallel to the Apennines mountain chain. The larger contribution is given by positive variations which account for the tensional style of deformation and larger subsided area. The significant gravity variations modelled from the coseismic deformations point out the need to update our knowledge about the absolute gravity field in Italy carrying out extensive measurements, and to align Italy to the recent international standards about national gravity and height networks (International Association of Geodesy, IAG Report, Commission 2—gravity field, http://www.iag-commission2.ch , 2015).

The gravity database for Belgium

AbstractData and metadata products based on intensive terrestrial gravity measurements covering the Belgian territory have been established compliant to the new ISO19115‐1 profile for gravity‐related data. A short historical introduction on gravity measurements on the Belgian territory is presented, starting with the first gravity measurement in 1892. This paper focuses on gravity data acquired after 1971, which marks the adoption of IGSN71 as a reference for the world network by the International Association of Geodesy (IAG). Next to a complete dataset containing all Belgian gravity data, the available gravity data were reduced to the corresponding measurement campaign, enabling determination of specific metadata (e.g. used gravimeter, tide system parameters, time of acquisition, etc.). New gravity and spirit levelling measurements were executed by the Royal Observatory Belgium and the National Geographic Institute (Federal Mapping Agency) to validate the g‐value at the historical reference base station ‘Carte du Ciel’ in Brussels. Taking into account the instrumental errors and the varying ground water content, the retrieved data are validated and approved for use in further research.