Abstract
The article describes a method for deriving the precision of a predicted land uplift value at an arbitrary terrain point which is assumed connected in height to a levelling benchmark using GNSS and a precise geoid model. We derive a statistical model for predicting the uplift rate from the existing point rates along with its empirical signal covariance function. One of our aims is a study on how a land uplift rate model and its empirical covariance function can be determined and then used for calculating changes in height over the time interval between precise levellings or GNSS heightings. Santrauka Aprašomas numatomos Žemės plutos kilimo reikšmės tikslumo pasirinktame taške, susietame su niveliacijos punktu pagal GPNS ir precizinį geoido modelį, nustatymo metodas. Pasiūlytas statistinis modelis kilimo greičiui prognozuoti, turint žinomus taškų greičius, pagal jų empirinę signalo kovariacinę funkciją. Vienas iš tikslų yra ištirti, kaip apibrėžti Žemės plutos kilimo greičių modelį ir jo empirinę kovariacinę funkciją ir kaip toliau ją taikyti aukščių kitimui apskaičiuoti einant laikui tarp precizinių niveliacijų ar GPNS aukščių nustatymo epochų. Резюме В статье описан метод определения точности значения поднятия земной коры в определенной точке, связанной с нивелирным пунктом с применением GPNS измерений и прецизионной модели геоида. Предложена статистическая модель для прогнозирования скорости поднятия земной коры по отношению к точкам с известной скоростью, основанная на применении эмпирической ковариационной функции сигнала. Основной целью работы было исследование возможностей построения модели скорости поднятия земной коры и эмпирической ковариационной функции и применение этой функции для вычисления изменения высот с течением времени между нивелировками или между эпохами определения высот с помощью измерений GPNS.
Highlights
In the future, National Height Systems will likely be maintained by GNSS (Global Navigation Satellite System) technology
The article describes a method for deriving the precision of a predicted land uplift value at an arbitrary terrain point which is assumed connected in height to a levelling benchmark using GNSS and a precise geoid model
One of our aims is a study on how a land uplift rate model and its empirical covariance function can be determined and used for calculating changes in height over the time interval between precise levellings or GNSS heightings
Summary
National Height Systems will likely be maintained by GNSS (Global Navigation Satellite System) technology. Today we have permanent station networks of GNSS operating for more than 15 years This motivates us to study precision that can be obtained determining the postglacial land uplift rate at an arbitrary point within the Fennoscandian area, because we will want to use the already known uplift rates to project geodetic heights forward in time. One should know the general stochastic behaviour of local uplift deviations from this functional uplift model. These deviations can be characterized by a signal covariance function; the estimation technique to be used is least squares collocation. The signal covariance function is to be estimated empirically using a set of real-life uplift values for point pairs at a wide range of inter-point distances
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