Toward a Spherical Pseudo-Wavelet Basis for Geodetic Applications

: 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.