Since 1991, the International Terrestrial Reference Frame (ITRF) includes the global time evolution of station positions (velocities) in addition to the three-dimensional Cartesian station positions at a fixed reference epoch. The orientation of the velocities refers to a kinematic model of rigid tectonic plates derived from geophysical observations over millions of years. For consistency with other geodetic parameters (e.g., Earth orientation), the models must be aligned to actual no-net-rotation of the whole Earth surface. Because of deviations of present-day velocities and neglect of non-rigid surface deformations, e.g., in seismic zones, the geophysical models are not valid for today. This paper describes a further developed method of estimating a non-rotating terrestrial reference frame from space geodetic observations. Different to previous estimations of geodetic no-net-rotation models, regional inter-plate and intra-plate crustal deformations are included, and instead of using the irregularly distributed observed station velocities, an evenly distributed grid throughout the Earth is interpolated by least squares collocation. Due to significant changes of the station velocities from one ITRF to another, NNR models must be computed for each ITRF. Here it is done for the ITRF2020.

In accordance with recent developments of the International Association of Geodesy (IAG) and the policies promoted by the Subcommittee on Geodesy of the United Nations Committee of Experts on Global Geospatial Information Management (UN-GGIM), a main goal of the Geodetic Reference System for the Americas (SIRGAS) is the procurement of an integrated regional reference frame. This frame should support the precise determination of geocentric coordinates and also provide a unified physical reference frame for gravimetry, physical heights, and a geoid. The geometric reference frame is determined by a network of about 500 continuously operating GNSS stations, which are routinely processed by ten analysis centers. The GNSS solutions from the analysis centers are used to generate weekly station positions aligned to the International Terrestrial Reference Frame (ITRF) and multi-year (cumulative) reference frame solutions. This processing is also the basis for the generation of precise tropospheric zenith path delays with an hourly sampling rate over the Americas. The reference frame for the determination of physical heights is a regional densification of the International Height Reference Frame (IHRF). Current efforts focus on the estimation and evaluation of potential values obtained from high resolution gravity field modelling, an activity tightly coupled with geoid determination. The gravity reference frame aims to be a regional densification of the International Terrestrial Gravity Reference Frame (ITGRF). Thus, SIRGAS activities are focused on evaluating the quality of existing absolute gravity stations and to identify regional gaps where additional absolute gravity stations are needed. Another main goal of SIRGAS is to promote the use of its geodetic reference frame at the national level and to support capacity building activities in the region. This paper summarizes key milestones in the establishment and maintenance of the SIRGAS reference frame and discusses current efforts and future challenges.

<p>High-resolution regional applications require regional reference frames with dense networks of reference stations. These regional reference frames can be realised in the form of multi-year reference frames (that can be fixed to a specific tectonic plate like EUREF for Europe) or as epoch reference frames to represent non-linear phenomena such as earthquakes or loading effects (like SIRGAS for Latin America). Common to these realisations is that they are based on GNSS networks with a geodetic datum that is realised by alignment to the global reference frame (ITRF or IGS TRF).</p> <p>In consequence, the origin of these networks reflects the Earth’s centre of figure rather than the Earth’s instantaneous centre of mass. Moreover, the quality of the realised datum decreases over time, as the linearly-parameterised coordinates of the global reference frame have to be extrapolated beyond the observation period. These effects mean a significantly reduced value of station-specific displacement time series for the study of, e.g., local geophysical effects.</p> <p>This study presents an alternative approach for the realisation of a regional epoch reference frame for Latin America. The approach is based on the common weekly solution of global SLR, VLBI and GNSS networks combined at the normal equation level. Thereby, SLR determines the origin, SLR and VLBI jointly determine the scale, and a homogeneously distributed global GNSS network is used to realise the orientation. This GNSS network is densified by the stations of the regional sub-network, namely the stations of the Latin American SIRGAS network. The approach does not necessarily rely on fiducial points in the region of interest, which means that it is conceptually transferrable to other regional networks.</p> <p>In order to cope with system-specific deficiencies of SLR and VLBI, namely data gaps, low station performances and frequently changing observational networks deteriorating the realised datum parameters, we propose a strategy to stabilise the realised datum via filtering the input data of these techniques at the normal equation level before combination with GNSS.</p> <p>We evaluate the realised datum of the epoch-wise weekly solutions by comparison against the ITRF2014 as an independent multi-year realisation of the ITRS and against the JTRF2014 as an independent sub-secular realisation of the ITRS. Moreover, station-specific displacement time series are validated against non-tidal loading displacement time series derived from geophysical fluid models provided by ESMGFZ in order to demonstrate that the displacement time series reflect seasonal geophysical processes in a geocentric frame.</p>

For high‐resolution regional geodetic applications, the International Terrestrial Reference Frame (ITRF) is complemented by regional densifications. These are realized either as multi‐year solutions related to a tectonic plate (e.g., EUREF for Europe) or as epoch reference frames (ERFs) to capture nonlinear geophysical station motions caused by, for example, earthquakes or non‐tidal loading (e.g., SIRGAS for Latin America). These Global Navigation Satellite Systems (GNSS)‐only based regional reference frames have in common that their geodetic datum is aligned with the ITRF datum at a specific epoch. The consequence is that their origin represents the Earth's center of figure and does not coincide with the instantaneous center of mass. Here, we present studies on a direct geocentric realization of regional ERFs. We propose to realize the geodetic datum for each epoch by combining global GNSS, Satellite Laser Ranging, and Very Long Baseline Interferometry networks via measured local ties at co‐located sites. A uniformly distributed global GNSS network is used to realize the orientation via a no‐net‐rotation constraint with respect to the ITRF and is densified by the stations of the regional subnetwork. The developed combination and filtering strategy aims to guarantee a stable datum realization for each epoch‐wise solution. Validating our results against global reference frames and geophysical loading models relating to the Earth's centers of mass and figure, we show that the realized displacement time series are geocentric and reflect seasonal geophysical processes. As the approach does not need to rely on co‐location sites in the region of interest, it is conceptually transferable to other regions on the globe.

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.

The Deutsches Geodätisches Forschungsinstitut (DGFI) has been involved in the research activities of the Latin American Reference Frame SIRGAS since its establishment in 1993. DGFI coordinated the SIRGAS Global Positioning System campaigns of 1995 and 2000 and acted as an analysis centre of both campaigns contributing to the first two SIRGAS realisations known as SIRGAS95 and SIRGAS2000. In 1996, DGFI established the Regional Network Associate Analysis Centre for SIRGAS of the International GNSS (Global Navigation Satellite System) Service (IGS RNAAC SIRGAS) and took on responsibility for processing the SIRGAS continuously operating stations and generating weekly position solutions. Later followed the determination of cumulative (multi-year) solutions, consisting of station positions and constant velocities, providing accurate solutions for the SIRGAS reference frame. DGFI was integrated into the Technical University of Munich (TUM) in 2015, becoming DGFI–TUM, and based on the SIRGAS operational analyses, it continues investigating strategies to guarantee the reliability of the reference frame through time. This includes the estimation of the reference frame kinematics, evaluation, modelling, and reduction of seismic and post-seismic deformations on the reference frame, and modelling crustal kinematics in the SIRGAS region by continuous velocity models. This article summarises analysis strategies and science data products developed by DGFI–TUM as a SIRGAS analysis centre and as the IGS RNAAC SIRGAS. Special care is given to the determination of the most recent SIRGAS reference frame solution called SIRGAS2022, which is based on the second SIRGAS reprocessing campaign performed by DGFI–TUM to obtain homogeneously computed SIRGAS daily and weekly station position solutions referring to the IGS reference frame IGS14/IGb14 since January 2000.

Based on 24 years of high-level GNSS data analysis, we present a sequence of crustal deformation models showing the varying surface kinematics in Latin America. The deformation models are inferred from GNSS station horizontal velocities using a least-squares collocation approach with empirically determined covariance functions. The main innovation of this study is the assumption of continuous surface deformation. We do not introduce rigid microplates, blocks or slivers which enforce constraints on the deformation model. Our results show that the only stable areas in Latin America are the Guiana, Brazilian and Atlantic shields; the other tectonic entities, like the Caribbean plate and the North Andes, Panama and Altiplano blocks are deforming. The present surface deformation is highly influenced by the effects of seven major earthquakes: Arequipa (Mw8.4, Jun 2001), Maule (Mw8.8, Feb 2010), Nicoya (Mw7.6, Sep 2012), Champerico (Mw7.4, Nov 2012), Pisagua (Mw8.2, Apr 2014), Illapel (Mw8.3, Sep 2015), and Pedernales (Mw7.8, Apr 2016). We see very significant kinematic variations: while the earthquakes in Champerico and Nicoya have modified the aseismic deformation regime in Central America by up to 5 and 12 mm/a, respectively, the earthquakes in the Andes have resulted in changes of up to 35 mm/a. Before the earthquakes, the deformation vectors are roughly in the direction of plate subduction. After the earthquakes, the deformation vectors describe a rotation counter-clockwise south of the epicentres and clockwise north of the epicentres. The deformation model series reveals that this kinematic pattern slowly disappears with post-seismic relaxation. The numerical results of this study are available at https://doi.pangaea.de/10.1594/PANGAEA.912349 and https://doi.pangaea.de/10.1594/PANGAEA.912350.

The history of geodesy can be traced back to Thales of Miletus (∼600 BC), who developed the concept of geometry, i.e. the measurement of the Earth. Eratosthenes (276–195 BC) recognized the Earth as a sphere and determined its radius. In the 18th century, Isaac Newton postulated an ellipsoidal figure due to the Earth's rotation, and the French Academy of Sciences organized two expeditions to Lapland and the Viceroyalty of Peru to determine the different curvatures of the Earth at the pole and the Equator. The Prussian General Johann Jacob Baeyer (1794–1885) initiated the international arc measurement to observe the irregular figure of the Earth given by an equipotential surface of the gravity field. This led to the foundation of the International Geodetic Association, which was transferred in 1919 to the Section of Geodesy of the International Union of Geodesy and Geophysics. This paper presents the activities from 1919 to 2019, characterized by a continuous broadening from geometric to gravimetric observations, from exclusive solid Earth parameters to atmospheric and hydrospheric effects, and from static to dynamic models. At present, we identify geodesy as the discipline of quantifying global change by geodetic measurements.

Studying, understanding and modelling global change require geodetic reference frames with an order of accuracy higher than the magnitude of the effects to be actually studied and with high consistency and reliability worldwide. The International Association of Geodesy, taking care of providing a precise geodetic infrastructure for monitoring the Earth system, promotes the implementation of an integrated global geodetic reference frame that provides a reliable frame for consistent analysis and modelling of global phenomena and processes affecting the Earth’s gravity field, the Earth’s surface geometry and the Earth’s rotation. The definition, realization, maintenance and wide utilization of the International Terrestrial Reference System guarantee a globally unified geometric reference frame with an accuracy at the millimetre level. An equivalent high-precision global physical reference frame that supports the reliable description of changes in the Earth’s gravity field (such as sea level variations, mass displacements, processes associated with geophysical fluids) is missing. This paper addresses the theoretical foundations supporting the implementation of such a physical reference surface in terms of an International Height Reference System and provides guidance for the coming activities required for the practical and sustainable realization of this system. Based on conceptual approaches of physical geodesy, the requirements for a unified global height reference system are derived. In accordance with the practice, its realization as the International Height Reference Frame is designed. Further steps for the implementation are also proposed.

Strong earthquakes cause large changes in the station positions and velocities of the geodetic reference stations; i.e., the global ITRF (International Terrestrial Reference Frame) and its regional densifications like SIRGAS (Sistema de Referencia Geocéntrico para Las Américas) in Latin America and the Caribbean. To ensure the long-term stability of the geodetic reference frames, the transformation of station positions between different epochs requires the computation of reliable continuous surface deformation (or velocity) models. This paper presents the computation of a new continental continuous crustal deformation model for Latin America and the Caribbean inferred from GNSS (GPS+GLONASS) measurements gained after the strong earthquakes occurred in 2010 in Chile and Mexico. It is based on a multi-year velocity solution for a network of 456 continuously operating GNSS stations and covering a five years period from March 14, 2010 to April 11, 2015. This new deformation model, called VEMOS2015 (Velocity Model for SIRGAS 2015), is computed using the least square collocation (LSC) approach with empirically determined covariance functions. The result is summarised as follows: While the effects of the Baja California earthquake can be considered as local, the effects of the Maule earthquake changed the surface kinematics of a large area (between the latitudes 30°S–45°S from the Pacific to the Atlantic coasts). Before the Maule earthquake, the strain rate field in this area showed a strong west-east compression with maximum rates of about 0.40μstrain/a between latitudes 38°S and 44°S. In accordance, the deformation vectors were roughly parallel to the plate subduction direction and their magnitudes decreased with the distance from the subduction front. After the earthquake, the largest compression (0.25μstrain/a) occurs between the latitudes 37°S and 40°S with a N30°E direction. The maximum extensional strain rate (0.20–0.35μstrain/a) is observed in the Sub-Andean zone in the Patagonia south of latitude 40°S. The extensional axes rotate from a N30°E direction in the central Araucania zone to a westerly direction of N72°W in the western part of Patagonia. In the northern region of parallel 35°S, the extension is also directed to the Maule zone (S45°W) but with quite smaller rates (<0.06μstrain/a). This complex kinematics causes a large counter clockwise deformation pattern rotating around a point south of the epicentre (35.9°S, 72.7°W). The magnitude of the deformation vectors varies from 1mm/a close to the rotation point up to 22mm/a near the 2010 earthquake epicentre. The direction of the largest deformation vectors points to the epicentre. VEMOS2015 covers the region from 55°S, 110°W to 32°N, 35°W with a spatial resolution of 1°×1°. The average prediction uncertainty is ±0.6mm/a in the north-south direction and ±1.2mm/a in the east-west direction. The maximum is ±9mm/a in the Maule deformation zone while the minimum values of about ±0.1mm/a occur in the stable eastern part of the South American plate.

The main objective of SIRGAS (Sistema de Referencia Geocentrico para las Americas) is to provide an accurate spatial and time-referenced infrastructure as a basis for Earth System research and to support scientific and practical applications based on high-precise positioning. Following this purpose, significant achievements related to the extension, analysis, and maintenance of this reference frame have been reached during the last years. However, there are still unresolved problems hindering the attainment of the best possible precision. In particular, the assimilation of seismic-related deformations and non-lineal station movements is very difficult and its omission considerably reduces the reliability of SIRGAS as a high precision reference frame. To advance in the solution of these inconveniences, this paper presents the first kinematic model of the SIRGAS reference frame computed after the strong earthquake occurred in the Chilean region of Maule in February 2010. This model is based on the combination of weekly free normal equations covering the time span from April 18, 2010 to June 15, 2013. Computed station positions and velocities refer to the IGb08 reference frame (the IGS realisation of the ITRF2008), epoch 2012.0. The averaged rms precision is +/- 1.4 mm horizontally and +/- 2.5 mm vertically for the station positions at the reference epoch, and. 0.8 mm/year horizontally and. 1.2 mm/year vertically for the constant velocities. Comparisons with reference frames based onmeasurements before the earthquake (like ITRF2008 or former SIRGAS solutions) make evident the strong deformation caused by this earthquake and the necessity of updating accordingly the reference frames in the affected region.

Very Long Baseline Interferometry (VLBI) is a primary space-geodetic technique for determining precise coordinates on the Earth, for monitoring the variable Earth rotation and orientation with highest precision, and for deriving many other parameters of the Earth system. The International VLBI Service for Geodesy and Astrometry (IVS, http://ivscc.gsfc.nasa.gov/) is a service of the International Association of Geodesy (IAG) and the International Astronomical Union (IAU). The datasets published here are the results of individual Very Long Baseline Interferometry (VLBI) sessions in the form of normal equations in SINEX 2.0 format (http://www.iers.org/IERS/EN/Organization/AnalysisCoordinator/SinexFormat/sinex.html, the SINEX 2.0 description is attached as pdf) provided by IVS as the input for the next release of the International Terrestrial Reference System (ITRF): ITRF2014. This is a new version of the ITRF2008 release (Bockmann et al., 2009). For each session/ file, the normal equation systems contain elements for the coordinate components of all stations having participated in the respective session as well as for the Earth orientation parameters (x-pole, y-pole, UT1 and its time derivatives plus offset to the IAU2006 precession-nutation components dX, dY (https://www.iau.org/static/resolutions/IAU2006_Resol1.pdf). The terrestrial part is free of datum. The data sets are the result of a weighted combination of the input of several IVS Analysis Centers. The IVS contribution for ITRF2014 is described in Bachmann et al (2015), Schuh and Behrend (2012) provide a general overview on the VLBI method, details on the internal data handling can be found at Behrend (2013).

The western part of the SIRGAS region is an extremely active seismic area because it is located in the plate boundary zone of six tectonic plates, namely the Pacific, Cocos, Nazca, North American, Caribbean, and South American plates. The frequent occurrence of earthquakes causes episodic station movements, which affect the long-term stability of the SIRGAS reference frame. Normally, these episodic events are taken into account in the frame realisation by introducing new position and, optionally, velocity parameters for the affected stations. However, this is not enough to guarantee the high precision required in a reference frame such as SIRGAS. Additional analyses about the post-seismic behaviour of the reference stations are necessary to allow the precise transformation between preseismic and post-seismic (deformed) frames. According to this, the paper presents an evaluation of the long-term stability of the SIRGAS reference frame including the comparison of the different SIRGAS realisations and the analysis of station displacements caused by earthquakes in the SIRGAS region. Special care is given to the events happened in Arequipa (on 2001-06-23, M = 8.4) and Chile (on 2010-02-27, M = 8.8). The analysis is based on the SIRGAS Continuously Operating Network (SIRGAS-CON). Beside analysing the station position time series and estimating the displacement vectors of the SIRGAS reference stations, some recommendations to mitigate the impact of this kind of events in the use of SIRGAS as a reference frame are formulated.