Abstract
The gravity field is a signature of the mass distribution and interior structure of the Earth, in addition to all its geodetic applications especially geoid determination and vertical datum unification. Determination of a regional gravity field model is an important subject and needs to be investigated and developed. Here, the spherical radial basis functions (SBFs) are applied in two scenarios for this purpose: interpolating the gravity anomalies and solving the fundamental equation of physical geodesy for geoid or disturbing potential determination, which has the possibility of being verified by the Global Navigation Satellite Systems (GNSS)/levelling data. Proper selections of the number of SBFs and optimal location of the applied SBFs are important factors to increase the accuracy of estimation. In this study, the gravity anomaly interpolation based on the SBFs is performed by Gauss-Newton optimisation with truncated singular value decomposition, and a Quasi-Newton method based on line search to solve the minimisation problems with a small number of iterations is developed. In order to solve the fundamental equation of physical geodesy by the SBFs, the truncated Newton optimisation is applied as the Hessian matrix of the objective function is not always positive definite. These two scenarios are applied on the terrestrial free-air gravity anomalies over the topographically rough area of Auvergne. The obtained accuracy for the interpolated gravity anomaly model is 1.7 mGal with the number of point-masses about 30% of the number of observations, and 1.5 mGal in the second scenario where the number of used kernels is also 30%. These accuracies are root mean square errors (RMSE) of the differences between predicted and observed gravity anomalies at check points. Moreover, utilising the optimal constructed model from the second scenario, the RMSE of 9 cm is achieved for the differences between the gravimetric height anomalies derived from the model and the geometric height anomalies from GNSS/levelling points.
Highlights
The gravity field of the Earth represents the mass distribution and structure of the Earth’s interior
Different methods have been developed and applied for regional gravity field modelling in different study areas, and they are in one way or another flavours of interpolation methods, except for the deterministic methods
The classical interpolation that is based on spherical harmonics, which is used in global gravity field modelling (Pavlis et al, 2012)
Summary
The gravity field of the Earth represents the mass distribution and structure of the Earth’s interior. For the purpose of the regional gravity data fitting, local base functions like spherical radial basis functions (SBFs) provide better accuracy. There are several types of SBFs to regionally model the gravity field, such as the pointmass kernel, the radial multipoles, Poisson wavelets, and the Poisson kernel, which are all functions of the inverse Euclidean distance from the data points to the centres of these functions. In addition to the gravity field, Chambodut et al (2005) applied the Poisson wavelets for modelling the magnetic field and proposed it as an efficient SBFs when data do not have global coverage and regular distribution. Spherical wavelets with different scales are suitable tools to represent the gravity field and applied by, e.g., Schmidt et al (2004, 2005). The centres of the SBFs play a significant role in the accuracy of the modelled gravity field and if they are determined optimally, all of the SBFs can be applied well with insignificant changes in accuracy (Tenzer and Klees, 2008)
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