THE USE OF THE TWO-DIMENSIONAL SPHERICAL FFT FOR QUASI-GEOID MODELLING IN SOUTH AFRICA

Abstract

Quasi-geoids for the south western Cape, a coastal province of South Africa, and the Gauteng area, in the north-east of South Africa, have been computed by the application of the two-dimensional (2D) spherical fast Fourier transform (SFFT) to Molodensky's formula. The gravimetric quasi-geoids for the south western Cape and Gauteng were computed on a grid resolution of one arc-minute. Validation of the gravimetric quasi-geoid models with GPS/levelling-derived geometric quasi-geoids via a simple planar transformation resulted in a root mean square (RMS) discrepancy of about 4cm for the south western Cape area and about 1.3cm for area of Gauteng. The quasi-geoids have also been evaluated using the 2D planar FFT and 2D multi-band SFFT and our results confirm the suitability of using a 2D SFFT's for geoid/quasi-geoid computation in mid-latitude regions.