Transformation of global spherical harmonic models of the gravity field to a local adjusted spherical cap harmonic model

Abstract

The new global gravity models represented by global spherical harmonics like EGM2008 require a high degree and order in their coefficients to resolve the gravity field in local areas; therefore, there are interests to represent the regional or local field by less parameters and to develop a parameter transformation from the global model to a local kind of spherical harmonic model. The authors use local spherical cap harmonics for the regional gravity potential representation related to a local pole and a local spherical coordinate system. This allows to model regional gravity potential with less parameters and less memory requirements in computation and storage. From different kinds of representations of spherical cap harmonics, we have selected the so-called adjusted spherical cap harmonics (ASCH). This is the most appropriate for the presented mathematical model of deriving its coefficients from global gravity models. In that way, the global gravity models can fully be exploited and mapped to regional ASCH, in particular with respect to the computation of regional geoid models with improved solution.