Assessment of the Improved Covariance in Local Geoid Modeling Using Least Squares Collocation-Case study: Tehran Province

Document Type : Research Article


1 M.Sc. Graduated, Department of Surveying and Geomatics Engineering, Faculty of Engineering, University of Tehran, Iran

2 Professor, Department of Surveying and Geomatics Engineering, Faculty of Engineering, University of Tehran, Iran


The idea of using Improved covariance (I_COV) through Least Squares Collocation (LSC) was first introduced and assessed on gravity anomalies (Ramouz et al, 2020) and geoid heights (Heydarizadeh et al, 2020) modeling over four regions with different data distribution and topography patterns in Iran. The results of these two researches showed that using I_COV could enhance gravity field modeling, specifically the medium to short wave-lengths of the signal which are embedded in the local and near-surface masses and surface density anomalies. For instance, implementing I_COV on a region with rough topography is more effective than classic covariance, in comparison with regions with smooth topography.
The gravity and GNSS/Leveling networks of Iran suffer from the lack of sufficient and well distributed observations. Moreover, existence of Alborz and Zagros mountain chains and the rough topography in the North, South and West of Iran, make regional gravity modeling that cover the whole country a difficult task. On the other hand, thanks to the development in satellite gravity technology and observations that have improved the accuracy of long-wavelength modeling of the Earth gravity field. So, quality processing and densifying terrestrial observations, incorporating high resolution Digital Elevation Models (DEM)s and improving geodetic boundary value problems are the available solutions to extract the medium to short-wavelength of the gravity signal to improve the gravity modeling. In this way, investigation of the effect of area size selection of the terrestrial observations, data density and distribution and topography roughness is classified in the spatial localization of the gravity field modeling.
The goal of this research is to analysis the contribution of the observations’ area size, density and distribution parameters on the accuracy of the local geoid height modeling and assess the possibility of model enhancement through execution I_COV procedure via LSC algorithm. As input, EIGEN-6C4 Global Gravity Model (GGM) up to degree/order 360, terrestrial gravimetric observations inside and around Tehran Province (measured by National Cartographic Center of Iran) and SRTM-1arc-min DEM are used via Remote-Compute-Restore technique.
To determine the analytical covariance function in order to applying LSC, first, an empirical covariance is computed from the terrestrial observations. Then, the Tscherning-Rapp 1974 (TR1974) covariance function is fitted to the empirical one and its three parameters are estimated to calculate the auto and cross-covariance of the LSC modeling formula. After LSC, the systematic parts of the signal i.e. global and topographic effects are restored. To implement the I_COV idea in gravity field localization, the value selection of TR1974 parameters are entered in iterative process to enhance the covariance model and improve the accuracy of the local model.
Assessment of the computed local model with the 141 GNSS/Leveling control points (measured by NCC) illustrates that STD of the model is about 8.9 cm inside the case study. Furthermore, if the comparison is limited to 40 control points inside Tehran City, STD of the model will be about 6.1 cm. To draw a comparative picture, the accuracy of this local model is 49% and 51% higher than EGM 2008 model (which has been the most accurate GGM in the region so far) over the same control points.


Main Subjects

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