Toward a Spherical Pseudo-Wavelet Basis for Geodetic Applications



Abstract:  In this contribution an investigation is made to exploit the advantages of 2D planar wavelets for the representation of scalar-valued signals on the sphere, with particular emphasis on the local or regional patches as they may originate from the so-called “Igloo” decomposition of the spherical surface. After introducing isometric coordinates on the sphere and applying a suitable map projection (such as “Mercator” along the equator, for instance) a family of basis functions which we called “pseudo-wavelets” can be constructed on the sphere that may be well suited to capture regional phenomena such as the fine structure of the terrestrial gravity field, and its representations toward multi-resolution flexibility. Such wavelet functions, if successful, are critically needed for a number of research topics and applications.