Topics in Geodetic Algorithm Research

The concept of 'geodetic algorithm' is defined in the context of estimating and computing gravity field quantities of interest from available measured data. Examples of major categories of geodetic algorithms are given. These include classical integral evaluation methods, least-squares collocation, the contractor's GEOFAST technique, and Fourier transform methods. Also summarized and reviewed are algorithms and techniques considered in investigations by an International Association of Geodesy (IAG) Special Study Group. Detailed results are presented for numerical experiments with the GEOFAST algorithm applied to synthetic data, demonstrating the high accuracy and computational efficiency of this method. Various aspects of the treatment of terrain effects are considered, including relevant efforts and results of the IAG Special Study Group as well as new theoretical and experimental contributions by the contractor. Keywords: Geodesy, Gravity anomaly, Deflection of the vertical, Collocation, Terrain reduction, and GEOFAST algorithm.