Using Personal Computers in Spherical Harmonic Synthesis of High Degree Earth Geopotential Models

Abstract. We have created software using Matlab ™ to obtain gravimetric quantities from very high degree Earth Geopotential (EGM) models. This program computes gravitational (V), gravity (W) or disturbing (T) potentials, gravity ( gD) or height ( z) anomalies, the components of the vertical deflection ( , x h) and the undulation of the geoid (N). These gravimetric quantities can be calculated at an isolate point, on an evenly spaced geographical grid (specified by the coordinates of two of its corners) with a certain resolution, or at an arbitrary array of points whose coordinates are given in a pair of vectors containing the latitudes and longitudes of these points. This program was developed using an efficient procedure that overcomes the problems of stability when using geopotential models up to a degree and order of 2700. We have compared the modified recursion techniques of Libbrecht (1985), recently reviewed and generalized by Holmes and Featherstone (2002), and the Clenshaw (1955) summation method (Tscherning and Poder, 1982)