Abstract: In recent years, the ability of GNSS systems to estimate high accuracy 3D positions has greatly contributed to the development of new monitoring techniques aimed at understanding the mechanisms by which the different Earth processes are generated. This paper presents the result of 9 GPS campaigns, between 2014 and 2019 for a group of 29 stations, held in the Guabirotuba urban area, Curitiba, Brazil, intending to estimate local crustal movements. The average magnitude and direction of horizontal velocities obtained for each site, allow demonstrating deformation of the southern zone of the area as a result of a local landslide process. The magnitude of the vectors varies between 1 and 16 mm/a horizontally. All sites had an absolute vertical movement, probably correlated with a local geological pattern or a physical site’s motion driven by environmental mass redistribution. The uncertainties in positions and velocities for a long-term survey (over 5 years), showed good consistency at most sites when compared with the coordinates and velocities precision of the latest SIRGAS solution. The typical precision for the station positions at the reference epoch was ±2 mm horizontally and ±5 mm vertically, and ±0.60 mm/a horizontally and ±1.37 mm/a vertically for the constant velocities.

Resumo É bem conhecido que as estimativas diárias das coordenadas GPS se encontram fortemente correlacionadas temporalmente. O conhecimento e compreensão desta correlação, permite estabelecer em princípio, incertezas mais realistas dos parâmetros estimados a partir dos dados. Apesar disso, atualmente não existem estudos relacionados à análise e cálculo dos sinais de ruído em série temporal de coordenadas GPS no Brasil. Neste sentido, a presente pesquisa visa estudar as propriedades estocásticas de um total de 486 séries temporais compostas de 10 anos de observações de 159 estações GPS pertencentes à Rede Brasileira de Monitoramento Contínuo de GNSS (RBMC) através da implementação do estimador de máxima verossimilhança. Para descrever de forma adequada as series temporais avaliadas, foram avaliados 4 possíveis modelos estocásticos como modelos de cada série temporal, sendo: 3 modelos com índices espectrais inteiros e 1 com índice espectral fracionário. A comparação das variâncias dos sinais de ruído dos modelos permitiu demonstrar um aumento gradual dos mesmos. Sendo que, a combinação de um processo de lei de potências fracionário e de um processo de ruído branco forneceu o modelo com as menores variâncias, e, a combinação de um processo de random-walk com um processo de ruído branco gerou o modelo com as maiores variâncias. A análise da distribuição espacial dos valores de ruído dos processos permitiu demonstrar que as localizações dos pontos GPS com maiores variâncias acumuladas de ruído, coincidem com os pontos localizados em zonas costeiras e bacias hidrográficas e que suas propriedades estocásticas podem ser afetadas pela ocorrência de diferentes sinais físicos típicos deste tipo de zonas, como no caso do efeito de carga hidrológica.

Abstract It is well known that daily estimates of GPS coordinates are highly temporally correlated and that the knowledge and understanding of this correlation allows to establish more realistic uncertainties of the parameters estimated from the data. Despite this, there are currently no studies related to the analysis and calculation of the noise sources in geodetic time series in Brazil. In this context, this paper focuses on the investigation of the stochastic properties of a total of 486 coordinates time series from 159 GPS stations belonging to the Brazilian Network for Continuous Monitoring of GNSS (RBMC) using the maximum likelihood estimation approach. To reliably describe the GPS time series, we evaluate 4 possible stochastic models as models of each time series: 3 models with integer spectral indices (white noise, flicker plus white noise and random-walk plus white noise model) and 1 with fractional spectral index (fractional power-law plus white noise). By comparing the calculated noise content values for each model, it is possible to demonstrate a stepwise increase of the noise content, being the combination of a fractional power-law process and white noise process, the model with smaller values and the combination of random walk process with white noise process, the model with greater values. The analysis of the spatial distribution of the noise values of the processes allow demonstrate that the GPS sites with the highest accumulated noise values, coincide with sites located in coastal zones and river basins and that their stochastic properties can be aliased by the occurrence of different physical signals typical of this type of zones, as the case of the hydrological loading effect.