Exact Transformation between Ellipsoidal and Spherical Harmonic Expansions

摘要

The difference between an ellipsoidal and a spherical spectrum of gravimetric data lies with the different surfaces on which the data reside. Therefore, all spherical harmonic coefficient sets determined from terrestrial data should more correctly be called ellipsoidal spectra. A spherical spectrum, on the other hand, is obtained from data provided, for example, by a satellite in a circular polar orbit. This paper derives the exact forward and reverse transformations from ellipsoidal to spherical spectra with practical computations in mind. Keywords: Reprints, Ellipsoidal harmonic expansion, Spherical harmonic expansions.