Integração de redes GNSS: uma proposta metodológica de densificação da rede SIRGAS na América do Sul

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Modelagem de distorções entre sad 69 e sirgas 2000 pelo método de shepard e grades regulares

Brazil follows the tendency of some countries to update and/or review their fundamental geodetic network. The adoption of geocentric referentials like SIRGAS 2000, the new official reference system of the Geodetic Brazilian System has been an advance. Changes in referential implies in coordinates changes on the network stations as well as the network geometry. To make use of analogical and digital products which are already known in the old referentials are necessary approaches to the coordinate conversion, which minimize the distortions between the used reference frames. This paper presents a distortion modeling approach between reference frames, based on distortion grid generation by using the Shepard's method. To analyze the approach some experiments were performed with the generation of a 1 degrees x1 degrees distortion grid to model the distortions between SAD 69 (1996) and SIRGAS (2000) frames. The results in the test stations were promising, with an average reduction of 50% in the RMS coordinates after the distortions modeling.

Strain rate of the South American lithospheric plate by SIRGAS-CON geodetic observations

A multiyear solution of the SIRGAS-CON network was used to estimate the strain rates of the earth surface from the changing directions of the velocity vectors of 140 geodetic points located in the South American plate. The strain rate was determined by the finite element method using Delaunay triangulation points that formed sub-networks; each sub-network was considered a solid and homogeneous body. The results showed that strain rates vary along the South American plate and are more significant on the western portion of the plate, as expected, since this region is close to the subduction zone of the Nazca plate beneath the South American plate. After using Euler vectors to infer Nazca plate movement and to orient the velocity vectors of the South American plate, it was possible to estimate the convergence and accommodation rates of the Nazca and South American plates, respectively. Strain rate estimates permitted determination of predominant contraction and/or extension regions and to establish that contraction regions coincide with locations with most of the high magnitude seismic events. Some areas with extension and contraction strains were found to the east within the stable South American plate, which may result from different stresses associated with different geological characteristics. These results suggest that major movements detected on the surface near the Nazca plate occur in regions with more heterogeneous geological structures and multiple rupture events. Most seismic events in the South American plate are concentrated in areas with predominant contraction strain rates oriented northeast-southwest; significant amounts of elastic strain can be accumulated on geological structures away from the plate boundary faults; and, behavior of contractions and extensions is similar to what has been found in seismological studies. © 2013 Elsevier Ltd.

Integração de Redes GNSS locais ao SIRGAS

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

SIRGAS reference frame realization SIR11P01

To estimate the kinematics of the SIRGAS reference frame, the Deutsches Geodätisches Forschungsinstitut (DGFI) as the IGS Regional Network Associate Analysis Centre for SIRGAS (IGS RNNAC SIR), yearly computes a cumulative (multi-year) solution containing all available weekly solutions delivered by the SIRGAS analysis centres. These cumulative solutions include those models, standards, and strategies widely applied at the time in which they were computed and cover different time spans depending on the availability of the weekly solutions. This data set corresponds to the multi-year solution SIR11P01. It is based on the combination of the weekly normal equations covering the time span from 2000-01-02 (GPS week 1043) to 2011-04-16 (GPS week 1631), when the IGS08 reference frame was introduced. It refers to ITRF2008, epoch 2005.0 and contains 230 stations with 269 occupations. Its precision was estimated to be ±1.0 mm (horizontal) and ±2.4 mm (vertical) for the station positions, and ±0.7 mm/a (horizontal) and ±1.1 mm/a (vertical) for the constant velocities. Computation strategy and results are in detail described in Sánchez and Seitz (2011). The IGS RNAAC SIR computation of the SIRGAS reference frame is possible thanks to the active participation of many Latin American and Caribbean colleagues, who not only make the measurements of the stations available, but also operate SIRGAS analysis centres processing the observational data on a routine basis (more details in http://www.sirgas.org). The achievements of SIRGAS are a consequence of a successful international geodetic cooperation not only following and meeting concrete objectives, but also becoming a permanent and self-sustaining geodetic community to guarantee quality, reliability, and long-term stability of the SIRGAS reference frame. The SIRGAS activities are strongly supported by the International Association of Geodesy (IAG) and the Pan-American Institute for Geography and History (PAIGH). The IGS RNAAC SIR highly appreciates all this support.

Aplicação das fórmulas de Vincenty nos cálculos das correções dos efeitos do relevo na gravidade e na altura geoidal.

O presente trabalho apresenta a aplicação das fórmulas de Vincenty nos cálculos das correções do terreno e do efeito indireto, que desempenham papel relevante na construção de cartas geoidais. Implementa-se um programa de processamento que realiza a integração numérica sobre o modelo digital do terreno, discretizado em células triangulares de Delaunay. O sistema foi desenvolvido com a linguagem de programação FORTRAN, para a execução de intensos algoritmos numéricos usando compiladores livres e robustos. Para o cálculo do efeito indireto, considera-se a redução gravimétrica efetuada com base no segundo método de condensação de Helmert, face ao pequeno valor de efeito indireto no cálculo do geóide, em função da mudança que este produz no potencial da gravidade devido ao deslocamento da massa topográfica. Utiliza-se, o sistema geodésico SIRGAS 2000 como sistema de referência para o cômputo das correções. Simplificando o exame dos resultados alcançados, distingue-se o processamento e desenvolvimento do trabalho em etapas como a escolha de ferramentas geodésicas para máxima precisão dos resultados, elaboração de subrotinas e comparação de resultados com cálculos anteriores. Os resultados encontrados foram de geração sadia e satisfatória e podem ser perfeitamente empregados no cálculo do geóide em qualquer área do globo.

Fundamentos de cartografia

Apresenta fundamentos de cartografia e sua aplicação no Geoprocessamento. Define os conceitos e aplicações de geóide, elipsóide, datum, sistema de referência, South American Datum (SAD-69), Sistema de Referência Geocêntrico para as Américas (SIRGAS 2000), elipsóide GRS80, elipsóide WGS84. Exemplos de utilização de sistemas de referência distintos e problemas relacionados.

Integration of a regional GPS network within ITRF using precise point positioning

GPS precise point positioning (PPP) can provide high precision 3-D coordinates. Combined pseudorange and carrier phase observables, precise ephemeris and satellite clock corrections, together with data from dual frequency receivers, are the key factors for providing such levels of precision (few centimeters). In general, results obtained from PPP are referenced to an arbitrary reference frame, realized from a previous free network adjustment, in which satellite state vectors, station coordinates and other biases are estimated together. In order to obtain consistent results, the coordinates have to be transformed to the relevant reference frame and the appropriate daily transformation parameters must be available. Furthermore, the coordinates have to be mapped to a chosen reference epoch. If a velocity field is not available, an appropriated model, such as NNR-NUVEL-IA, has to be used. The quality of the results provided by this approach was evaluated using data from the Brazilian Network for Continuous Monitoring of the Global Positioning System (RBMC), which was processed using GIPSY-OASIS 11 software. The results obtained were compared to SIRGAS 1995.4 and ITRF2000, and reached precision better than 2cm. A description of the fundamentals of the PPP approach and its application in the integration of regional GPS networks with ITRF is the main purpose of this paper.

Posicionamento por ponto de alta precisão utilizando o GPS: Uma solução para a geodinâmica

Point positioning from GPS data can provide precision varying from 100 meters to a few millimeters at the level of 95% probability. To reach the best level of accuracy, users need proper equipment and software, as well as access capability to GPS products available at the International GPS Geodynamics Service. In this paper, the theory related to point positioning using GPS is presented as well as the results of an experiment conducted using data from the Brazilian Active Control System. The results show repeatability better than 5mm and 10mm for the N and E baseline components respectively, and 6mm + 4ppb (parts per billion) for the vertical. Comparison with SIRGAS campaign showed results at the same level of uncertainty as that of the stations used to tie the SIRGAS frame to ITRF94. Therefore, precise point positioning is a powerful tool to be used in applications requiring high level of precision, such as Geodynamics.

Modelagem de distorções entre realizações de referenciais geodésicos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Establecimiento de una red local en la zona de Tacurú Pucú (Presa de Itaipu- Paraguay)

Este proyecto se enmarca dentro de los trabajos realizados para el Parque Tecnológico Itaipu. La misión principal, dentro de la beca, fue la realización de un proyecto de ingeniería que ayudase en alguno de sus proyectos al PTI. En este sentido se decidió la realización de este proyecto para el posterior empleo de la red local como apoyo en los trabajo de construcción de la nueva sede del PTI-PY, que actualmente ya se están desarrollando. En Paraguay todos los datos y trabajos astronómicos, geodésicos, topográficos, fotogramétrico y cartográficos los efectúa la Dirección del Servicio Geográfico Militar. Como consecuencia, la realización de cualquier trabajo fuera de esta institución llevaría consigo un proceso de investigación que dificultaría muchísimo la realización de cualquier proyecto topográfico y cartográfico, pues la información no es de carácter público. Trabajando con el sistema de referencia SIRGAS, se facilita muchísimo este problema, pues toda la información geodésica y cartográfica es pública. Aunque durante la primera etapa del proyecto surgieron algunas dificultades en relación a la falta de documentación geodésica del entorno, problemas relacionados con eluso y disponibilidad del instrumental durante la etapa prevista para la observación en campo, y la demora ante trámites burocráticos, los objetivos fijados se cumplieron con éxito. La red que ha sido elaborada ha alcanzado la precisión prevista tal y como y muestra en la presente memoria. Para que el trabajo realizado sea útil y sirva para futuros proyectos se recomienda llevar a cabo la reparación del cercado del recinto y así evitar futuros desperfectos en la monumentación, como ya aconteció. Para finalizar sería interesante que los datos obtenidos en este proyecto se incorporaran a una base de datos que estuviese al alcance de todas las personas que pudiesen estar interesadas en ellos, de forma que sirvieran para dar apoyo geodésico a todos aquellos trabajos que se realicen en la zona y de esa forma contribuir al desarrollo de la misma.

Desarrollo, implementación y análisis de un modelo cinemático local de velocidades para Costa Rica basado en la integración y homogenización de datos de estaciones GNSS continuas

El primer procesamiento estricto realizado con el software científico Bernese y contemplando las más estrictas normas de cálculo recomendadas internacionalmente, permitió obtener un campo puntual de alta exactitud, basado en la integración y estandarización de los datos de una red GPS ubicada en Costa Rica. Este procesamiento contempló un total de 119 semanas de datos diarios, es decir unos 2,3 años, desde enero del año 2009 hasta abril del año 2011, para un total de 30 estaciones GPS, de las cuales 22 están ubicadas en el territorio nacional de Costa Rica y 8 internaciones pertenecientes a la red del Sistema Geocéntrico para las Américas (SIRGAS). Las denominadas soluciones semilibres generaron, semana a semana, una red GPS con una alta exactitud interna definida por medio de los vectores entre las estaciones y las coordenadas finales de la constelación satelital. La evaluación semanal dada por la repetibilidad de las soluciones brindó en promedio errores de 1,7 mm, 1,4 mm y 5,1 mm en las componentes [n e u], confirmando una alta consistencia en estas soluciones. Aunque las soluciones semilibres poseen una alta exactitud interna, las mismas no son utilizables para fines de análisis cinemático, pues carecen de un marco de referencia. En Latinoamérica, la densificación del Marco Internacional Terrestre de Referencia (ITRF), está representado por la red de estaciones de operación continua GNSS de SIRGAS, denominada como SIRGAS-CON. Por medio de las denominadas coordenadas semanales finales de las 8 estaciones consideradas como vínculo, se refirió cada una de las 119 soluciones al marco SIRGAS. La introducción del marco de referencia SIRGAS a las soluciones semilibres produce deformaciones en estas soluciones. Las deformaciones de las soluciones semilibres son producto de las cinemática de cada una de las placas en las que se ubican las estaciones de vínculo. Luego de efectuado el amarre semanal a las coordenadas SIRGAS, se hizo una estimación de los vectores de velocidad de cada una de las estaciones, incluyendo las de amarre, cuyos valores de velocidad se conocen con una alta exactitud. Para la determinación de las velocidades de las estaciones costarricenses, se programó una rutina en ambiente MatLab, basada en una ajuste por mínimos cuadrados. Los valores obtenidos en el marco de este proyecto en comparación con los valores oficiales, brindaron diferencias promedio del orden de los 0,06 cm/a, -0,08 cm/a y -0,10 cm/a respectivamente para las coordenadas [X Y Z]. De esta manera se logró determinar las coordenadas geocéntricas [X Y Z]T y sus variaciones temporales [vX vY vZ]T para el conjunto de 22 estaciones GPS de Costa Rica, dentro del datum IGS05, época de referencia 2010,5. Aunque se logró una alta exactitud en los vectores de coordenadas geocéntricas de las 22 estaciones, para algunas de las estaciones el cálculo de las velocidades no fue representativo debido al relativo corto tiempo (menos de un año) de archivos de datos. Bajo esta premisa, se excluyeron las ocho estaciones ubicadas al sur de país. Esto implicó hacer una estimación del campo local de velocidades con solamente veinte estaciones nacionales más tres estaciones en Panamá y una en Nicaragua. El algoritmo usado fue el denominado Colocación por Mínimos Cuadrados, el cual permite la estimación o interpolación de datos a partir de datos efectivamente conocidos, el cual fue programado mediante una rutina en ambiente MatLab. El campo resultante se estimó con una resolución de 30' X 30' y es altamente constante, con una velocidad resultante promedio de 2,58 cm/a en una dirección de 40,8° en dirección noreste. Este campo fue validado con base en los datos del modelo VEMOS2009, recomendado por SIRGAS. Las diferencias de velocidad promedio para las estaciones usadas como insumo para el cálculo del campo fueron del orden los +0,63 cm/a y +0,22 cm/a para los valores de velocidad en latitud y longitud, lo que supone una buena determinación de los valores de velocidad y de la estimación de la función de covarianza empírica, necesaria para la aplicación del método de colocación. Además, la grilla usada como base para la interpolación brindó diferencias del orden de -0,62 cm/a y -0,12 cm/a para latitud y longitud. Adicionalmente los resultados de este trabajo fueron usados como insumo para hacer una aproximación en la definición del límite del llamado Bloque de Panamá dentro del territorio nacional de Costa Rica. El cálculo de las componentes del Polo de Euler por medio de una rutina programa en ambiente MatLab y aplicado a diferentes combinaciones de puntos no brindó mayores aportes a la definición física de este límite. La estrategia lo que confirmó fue simplemente la diferencia en la dirección de todos los vectores velocidad y no permitió reveló revelar con mayor detalle una ubicación de esta zona dentro del territorio nacional de Costa Rica. ABSTRACT The first strict processing performed with the Bernese scientific software and contemplating the highest standards internationally recommended calculation, yielded a precise field of high accuracy, based on the integration and standardization of data from a GPS network located in Costa Rica. This processing watched a total of 119 weeks of daily data, is about 2.3 years from January 2009 to April 2011, for a total of 30 GPS stations, of which 22 are located in the country of Costa Rica and 8 hospitalizations within the network of Geocentric System for the Americas (SIRGAS). The semi-free solutions generated, every week a GPS network with high internal accuracy defined by vectors between stations and the final coordinates of the satellite constellation. The weekly evaluation given by repeatability of the solutions provided in average errors of 1.7 mm 1.4 mm and 5.1 mm in the components [n e u], confirming a high consistency in these solutions. Although semi-free solutions have a high internal accuracy, they are not used for purposes of kinematic analysis, because they lack a reference frame. In Latin America, the densification of the International Terrestrial Reference Frame (ITRF), is represented by a network of continuously operating GNSS stations SIRGAS, known as SIRGAS-CON. Through weekly final coordinates of the 8 stations considered as a link, described each of the solutions to the frame 119 SIRGAS. The introduction of the frame SIRGAS to semi-free solutions generates deformations. The deformations of the semi-free solutions are products of the kinematics of each of the plates in which link stations are located. After SIRGAS weekly link to SIRGAS frame, an estimate of the velocity vectors of each of the stations was done. The velocity vectors for each SIRGAS stations are known with high accuracy. For this calculation routine in MatLab environment, based on a least squares fit was scheduled. The values obtained compared to the official values, gave average differences of the order of 0.06 cm/yr, -0.08 cm/yr and -0.10 cm/yr respectively for the coordinates [XYZ]. Thus was possible to determine the geocentric coordinates [XYZ]T and its temporal variations [vX vY vZ]T for the set of 22 GPS stations of Costa Rica, within IGS05 datum, reference epoch 2010.5. The high accuracy vector for geocentric coordinates was obtained, however for some stations the velocity vectors was not representative because of the relatively short time (less than one year) of data files. Under this premise, the eight stations located in the south of the country were excluded. This involved an estimate of the local velocity field with only twenty national stations plus three stations in Panama and Nicaragua. The algorithm used was Least Squares Collocation, which allows the estimation and interpolation of data from known data effectively. The algorithm was programmed with MatLab. The resulting field was estimated with a resolution of 30' X 30' and is highly consistent with a resulting average speed of 2.58 cm/y in a direction of 40.8° to the northeast. This field was validated based on the model data VEMOS2009 recommended by SIRGAS. The differences in average velocity for the stations used as input for the calculation of the field were of the order of +0.63 cm/yr, +0.22 cm/yr for the velocity values in latitude and longitude, which is a good determination velocity values and estimating the empirical covariance function necessary for implementing the method of application. Furthermore, the grid used as the basis for interpolation provided differences of about -0.62 cm/yr, -0.12 cm/yr to latitude and longitude. Additionally, the results of this investigation were used as input to an approach in defining the boundary of Panama called block within the country of Costa Rica. The calculation of the components of the Euler pole through a routine program in MatLab and applied to different combinations of points gave no further contributions to the physical definition of this limit. The strategy was simply confirming the difference in the direction of all the velocity vectors and not allowed to reveal more detail revealed a location of this area within the country of Costa Rica.