Modelling Gravity and Geoid by Least Squares Collocation with Planar Covariance Models

Abstract Least Squares Collocation is a method frequently used in modelling the Earth gravity field and the geoid. Either global or local approaches of this method have been studied and applied. The collocation estimator for gravity and the geoid depends on selecting appropriate auto- and cross-covariance functions for both the data and the functional of the anomalous potential to be estimated. Usually, these models are given in terms of series expansions depending on the Legendre Polynomials. In this paper, a different class of auto- and cross-covariance functions are studied which can be applied in planar approximation. These functions have been used in estimating the geoid from gravity anomalies using the data of the Colorado test. Results proved that this approach could give estimates that are equivalent to those obtained using the well-known covariance models by Tscherning and Rapp.