Sílvio Rogério Correia de Freitas

Geopotential numbers from GPS satellite surveying and disturbing potential model: a case study of Parana, Brazil

Abstract This article deals with the approach to determining the geopotential numbers from Global Positioning System (GPS) satellite surveying and disturbing potential at a point on the Earths surface. The disturbing potential was solved by the Brovar-type solution of Molodenskiis boundary value problem but in the context of the fixed problem. The solution is compatible with the techniques for smoothing of external field: removerestore techniques, residual terrain model, and use of high-resolution global geopotential models. This method provides an absolute geopotential numbers related to the so-called world height system. As an example, we calculate the disturbing potential model in Southern Brazil. The general condition of the sparse and absent gravity values is the main point to be solved. The absolute and relative accuracies of the quasigeoid model were tested vs. GPS/leveling data. Based on 99 GPS/leveling points, the mean value of fitting for the quasigeoid model was estimated near 0.032 m in the absolute view and 0.2 ppm in the relative view.

Tectonic pattern of South America inferred from tidal gravity anomalies

Abstract The knowledge of several physical parameters that characterize a tectonic unit is important to evaluate its dynamic evolution and, therefore, its role in the continental evolution. Several methodologies have been used to measure the elastic properties of tectonic units using: seismic waves, the level of coherence between the wavelength pattern of the topography and gravity fields, borehole deformation rate, mineral fabric, etc. In this study, the Earths dynamic elastic response to gravity tides is applied for measuring the lithosphere effective elastic thickness. This methodology proved to be a good alternative to the conventional coherence method. It was applied over the continent, taking into account the poor gravity coverage in South America and the restricted area of some tectonic units. Results are presented as lateral distribution of the effective elastic thickness in South America.

Challenges and First Results Towards the Realization of a Consistent Height System in Brazil

Few benchmarks of the Brazilian Fundamental Vertical Network (BFVN) have measured gravity values. While its leveling lines have been established since 1945 with approximately the same technical specifications, different institutions performed gravity surveys with different standards. To improve the BFVN aiming its connection with a “world height system”, studies were started in 1995 focusing on the area of the Brazilian Vertical Datum. Since 2004 the lack of gravity data and other particular aspects of BFVN were included in those investigations, as well as the integration of satellite altimetry data as a way to evaluate the BFVN at some selected tide gauges. The first step of the work was the definition of procedures for integrating gravity values into the BFVN. This led to selecting a test area where recent leveling lines are entirely covered by fairly homogeneous gravity surveys from the same institution, allowing for investigations on methods for gravity interpolation, and the resulting error propagation from leveling and gravity data into geopotential numbers. Parallel efforts were performed to collect and analyse gravity data from other institutions, resulting in the detection of some systematic discrepancies.

Strategies for Connecting Imbituba and Santana Brazilian Datums Based on Satellite Gravimetry and Residual Terrain Model

Due to the challenge that the Amazon Basin imposes for traditional geodetic surveys, the Brazilian Fundamental Vertical Network (BFVN) is materialized in two independent parts: the southern segment is linked to the Imbituba tide gauge and the northern part is linked to the Santana tide gauge. The mouth of the Amazon River and its surrounding wetlands generate a large area without access for spirit levelling and conventional gravimetry. There is a minimum distance of about 330 km between the nearest bench marks of the two above mentioned vertical networks. Nowadays, satellite gravity missions such as CHAMP, GRACE and GOCE make it possible to explore new solutions based on Global Geopotential Models (GGMs) obtained from satellite data only. Digital Elevation Models (DEMs) allow an improvement in the spectral resolution of the GGMs based on Residual Terrain Modelling (RTM). Such an approach is an alternative to filling the information gaps in the GGMs by reducing omission errors. The spectral improvement of the GGMs allows us to integrate the vertical datums in a more realistic way, and with a reduction of terrestrial gravity dependency. In this study, two alternatives to the indirect connection of the BFVN are analyzed. A solution is based on a combination of GGM satellite-only data from the GOCE mission and the spectral contribution of the RTM. The other solution is based on the integration of information from GOCE GGM, EGM2008 and the RTM effect. The offset obtained shows that the Imbituba datum is located 1.32 and 1.43 m below the Santana datum for the solutions GGMGOCE+RTM and GGMGOCE+EGM2008+RTM respectively.

A study of the chilean vertical network through global geopotential models and the cnes cls 2011 global mean sea surface

Most aspects related to the horizontal component of the Geocentric Reference System for the Americas (SIRGAS) have been solved. However, in the case of the vertical component there are still aspects of definition, national realizations and continental unification still not accomplished. Chile is no exception; due to its particular geographic characteristics, a number of tide gauges (TG) had to be installed in the coast from which the leveling lines that compose the Chilean Vertical Network (CHVN) were established. This study explored the offsets of the CHVN by two different approaches; one geodetic and one oceanographic. In the first approach, the offsets were obtained in relation to the following Global Geopotential Models (GGM): the satellite-only model (unbiased) GO_CONS_gcf_2_tim_r3 derived from GOCE satellite mission; EGM2008 (combined-biased); and GOEGM08, combining information from the GO_CONS_gcf_2_tim_r3 in long wavelengths (n max ~200) with the mean/short wavelengths of EGM2008 (n>200). In the oceanographic method, we used the CNES CLS 2011 Global Mean Sea surface and EIGEN_GRACE_5C GGM to obtain the values of MDT at the different TG. We also evaluated the CHVN in relation to different GGMs. The results showed consistency between the values obtained by the two methods at the TG of Valparaiso and Puerto Chacabuco. In terms of the evaluation of the GGM, GOEGM08 produced the best results.

Analysis of the Discrepancies Between the Brazilian Vertical Reference Frame and GOCE-Based Geopotential Model

In this study we estimate the discrepancies between the Brazilian vertical network, realized in the system of normal-orthometric heights, and a global quasi-geoid model. We consider the GNSS-leveling and a global quasi-geoid model derived from the Gravity field and steady-state Ocean Circulation Explorer (GOCE) mission enhanced by high degree components of the Earth Gravitational Model 2008 (EGM2008). The results indicate that the enhanced geopotential model fits the GNSS-leveling with a root mean square error of 20.2 cm. The estimated bias of − 0. 4 ± 0.6 cm (w.r.t. the centroid of the network) implies that any future changes to the geopotential value W0 (62636856.0 m2 s−2) should be minor for the Brazilian Height System (BHS). However, since the GNSS-leveling based “height anomalies” refer to the Brazilian Vertical Datum at Imbituba harbor (BVD-I), Southern Brazil, the results of the comparisons may be an indicator of the mean bias of the national leveling network due to the effect of Mean Dynamic Topography (MDT) at the BVD-I.

Vertical deformation and sea level changes in the coast of Chile by satellite altimetry and tide gauges

ABSTRACT Located at the intersection of the triple junction between the Nazca, South American, and Antarctic plates, the Chilean territory is subject to active lithospheric deformations and seismicity. Taking the difference between the satellite altimetry (ALT) data that give the absolute sea level variation and the tide gauge (TG) observations that record the relative sea level variation, we computed the absolute vertical crustal motion of the TG sites. We used 11 TG stations along the Chilean coast and altimeter measurements from multi-satellite missions (Topex, Jason-1 (A), and Jason-2) in nearby waters. The ALT-TG vertical deformations were compared with trends obtained from GPS measurements, which showed good consistency in terms of a correlation coefficient of about 0.9 (in 8 of 11 stations). Our results reveal that the behaviour of the long-term vertical deformations along the Chilean coast presented an important spatial variability. We also estimated the sea level change (SLC) through a multivariate model involving linear trend and decadal and inter-decadal climatic influence; in addition, the glacial isostatic adjustment effect was also removed. Our estimation of the SLC in the Chilean coast revealed an overall increase in sea level. The sea level in Chile does not strictly follow the global trend of the past two decades (~3 mm year−1), but rather a slight agreement (from 1.2 to 0.6 mm year−1) from Arica up to Puerto Montt approximately, with the exception of PTAR and PWIL TGs, where we found a decrease of −0.9 and −0.8 mm year−1, respectively.

CONEXÃO DE SISTEMAS VERTICAIS DE REFERÊNCIA LOCAIS AO SISTEMA GEODÉSICO BRASILEIRO COM BASE EM UM SISTEMA VERTICAL DE REFERÊNCIA GLOBAL

Os Modelos Globais do Geopotencial (MGGs), em especial os oriundos da missao GOCE, associados a Modelos Digitais de Altitude (MDAs) com resolucoes cada vez melhores, tem possibilitado novas alternativas para a obtencao de altitudes com significado fisico. Neste trabalho, propoe-se a realizacao de um sistema local de altitudes, em uma area onde o Sistema Geodesico Brasileiro (SGB) e deficiente, e vincula-lo a um Sistema Vertical de Referencia Global (SVRG) e ao SGB. Os MGGs foram validados utilizando Referencias de Nivel associadas com posicionamento GPS. Para modelar o erro de omissao dos MGGs, foi utilizada a tecnica Residual Terrain Model (RTM). Os numeros geopotenciais foram obtidos com a resolucao simplificada do Problema do Valor de Contorno da Geodesia (PVCG) na forma fixada. A area de estudos e o Estado do Amapa, que utiliza o Datum Vertical Brasileiro de Santana (DVB-S), e para validacao dos MGGs foram utilizadas estacoes do Estado do Para, vinculadas ao Datum Vertical Brasileiro de Imbituba (DVB-I). Como resultados, obteve-se numeros geopotenciais e altitudes fisicas consistentes. Na validacao dos modelos, o RTM nao teve influencia significativa. Utilizando o MGG do GOCE, GO_CONS_SPW_R4, obteve-se que o segmento da rede vinculado ao DVB-S esta 1,30m acima do segmento vinculado ao DVB-I.

ESTUDO DO SISTEMA VERTICAL DE REFERÊNCIA DO EQUADOR NO CONTEXTO DA UNIFICAÇÃO DO DATUM VERTICAL

O Equador e em geral os demais paises da America do Sul, nao dispoem de uma referencia unica para as altitudes. Cada pais tem o Datum Vertical (DV) associado a uma superficie de nivel obtida dos registros de um ou varios maregrafos. A relacao entre os diferentes data verticais locais e condicionada, idealmente, pelas variacoes espaco-temporais da superficie do oceano. O conhecimento das discrepâncias entre data verticais e um elemento fundamental na realizacao de um Sistema Vertical de Referencia (SVR) com caracteristicas globais (SVRG) que permita a determinacao de altitudes fisicas e contribua ao monitoramento de parâmetros fisicos do Sistema Terra. O pressente estudo do SVR equatoriano (SVRE) e apresentado em termos de tipo de altitude, consistencia com Modelos Globais de Geopotencial (MGGs) e a sua relacao com um SVRG. Tambem, explorou-se a tecnica da modelagem residual do terreno com proposito de complementar a informacao espectral da alta frequencia nos MGGs, os Modelos Digitais de Elevacao (MDE) empregados foram o Global Multi-Resolution Topography (GMRT) e o ETOPO1 - Global Relief Model. Como uma solucao alternativa, uma abordagem oceanografica baseada no modelo MSS CLS011 e o modelo GOCONS-TIM-R5 foi utilizada para estimativa da Sea Surface Topography (SSTop) no maregrafo fundamental do Equador.

Towards a Vertical Reference Frame for South America in View of the GGOS Specifications

One of the objectives of the Geocentric Reference System for the Americas (SIRGAS) is to establish a unified Earth’s gravity field-related vertical reference system that meets the Global Geodetic Observing System (GGOS)’s requirements. This statement implies the homogenization and unification of the National Vertical Reference Systems (NVRS) existing in the SIRGAS and their integration into a International Height Reference System (IHRS). At present, different strategies based on the combination of local (e.g. levelling, terrestrial gravity data) and global observations (e.g. global models, GNSS positioning) are under consideration. However, most of them are not immediately applicable in South America due to the differences in the definition and realization of the local height systems. In this work, it is proposed an inventory of the available data and the implementation of a common metadata base in order to provide sufficient information for a consistent characterization of each NVRS. This structure must allow the identification of the different standards and specifications applied for the establishment of those systems and the needs of complementary actions for connecting them, including the standardization of the existing height data. The main goal of this approach is however the minimization of those inconsistencies produced by data unavailability, unknown discrepancies, different data collecting and processing strategies, accuracy, and other non-evaluated errors. Based on results for a case study (or test country) in South America, it is proposed a road map for the inventory of vertical systems established with metadata.