Approximation of harmonic covariance functions on the sphere by non-harmonic locally supported functions

Three methods to construct positive definite functions with compact support for the approximation of general geophysical harmonic covariance functions are presented. The theoretical background is given and simulations carried out, for three types of covariance functions associated with the determina tion of the anomalous gravity potential from gravity anomalies. The results are compared with those of the finite covariance function of Sanso and Sch uh (1987).