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APPLICATION OF RADIAL BASIS FUNCTIONS IN LOCAL GEOID DETERMINATION
Abstract
The generally accepted representation of global geoid/quasi-geoid models in a series of spherical harmonics expansion turns out to be inappropriate for geoid modelling in relatively small local areas. To obtain a resolution of a few kilometers requires the development of spherical functions to critically high degrees of expansion, which leads to instability of the solution for several reasons, which are discussed in the article. For that reason, to determine precise local model of the geoid, it is necessary to use functions with not only good frequency localization, but also good spatial localization. For that reason, one of the most appropriate and most often used functions in this case are the radial basis functions. The article considers the main characteristics of the radial basis functions and analyses the factors on which their behavior depends - type of kernel function, maximum degree of expansion, position of radial basis functions and other factors. The steps in modelling the geoid using radial basis functions are presented in the form of an algorithm. Several main kernel functions used in local geoid modelling are considered: the Abel-Poisson kernel, the Stokes kernel for gravity anomalies, and the Hotine-Koch kernel for gravity disturbance. Solution with using combination of different data as input (gravity anomaly, gravity disturbance, components of deflection of the vertical, etc.) is considered. Least squares adjustment with use of different kernel function is presented.
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