Transformation from a global spherical to an adjusted local rectangular harmonic model

Abstract

This work presents a technique to transform a global spherical to an adjusted local rectangular harmonic model. First, the mathematical form of a global spherical harmonic model is presented. Second, the necessary conversion from global (geocentric) into local rectangular coordinates is given. Third, Laplace’s equation is solved by the method of separation of variables in local rectangular coordinates and its solutions in different functional forms are presented. Then, the estimation of the coefficients of these mathematical models by a least squares’ adjustment process is described, using as data the values of the disturbing potential of the Earth’s gravity field. The strategy for the selection of the best mathematical model for a successful transformation is described and validated in different case studies. These refer to areas in Greece, China and Germany and include comparisons with other models or methods. The results show the applicability of the presented transformation and confirm its advantages.