Spherical Geodetic Transformations. Volume 2. Catalog of Explicit Representations in the Spatial and Frequency Domains

摘要

This volume is a catalog of the spatial and frequency domain representations of approximately 100 spherical integral transformations, of which about 85 have an explicitly geodetic interpretation. The following information is provided (when known) for each transformation: The input and output quantities of the transformation stated in geodetic nomenclature; An explicit analytic double-integral expression for the transformation written in the generally accepted geodetic symbolism; An explicit expression for the spectrum of the transformation, or equivalently the transfer function or gain function as it would be called in engineering terminology. An explicit Legendre series expansion of the kernel of the transformation, and a closed form expression for the expansion; Detailed references to the geodetic and mathematical literature for statements or proofs of the expressions; Additional remarks concerning the transformation. This catalog assembles a rather comprehensive set of results in a consistent format and notation. Keywords: Geodesy; Stokes integral; Vening meinesz integral; Spherical digital filters. (jhd)