Reilly, W.I. 1979 Mapping the local geometry of the earth's gravity field. [s.l.]: [s.n.]. Report / Geophysics Division 143 56 p.
Abstract: The geometric parameters describing the earth's gravitational field can be divided into extrinsic and intrinsic sets. The extrinsic parameters comprise (a) the height anomaly, or difference in height between an actual and a normal equipotential surface of the same numerical value, and (b) the deviation of the vertical, or angular difference between the actual and the normal vertical at a point. The intrinsic parameters (c) comprise the five independent differential curvature parameters of the gravitational field. Categories (a), (b) and (c) correspond respectively to the zero, first, and second order derivatives of the gravity potential. The problem of mapping the local geometry of the gravity field consists in obtaining a representation of these parameters on a surface (e.g., a surface of constant height). This is achieved by a process of interpolation on the basis of the following data: (i) estimates of the anomalous gravity potential derived from a comparison of levelling with satellite position fixing, (ii) observation of the deflection of the vertical, (iii) gravity anomalies. Interpolation is done by application of the method of least-squares collocation of these data, based on expressing the statistical covariance function for gravity anomalies in a form suitable for local application, using rectangular coordinates in a conformal projection space. The collocation process yields the zero, first and second order derivatives of the anomalous gravity field, from which the desired parameters can be calculated; in the case of the intrinsic curvature parameters by recombination with the second derivatives of the normal gravity field. The normal field is most simply, but not necessarily, that of an ellipsoidal earth model; a field based on an isostatic earth model, by explicitly introducing topographic data, might improve the interpolation of gravity anomalies, at the expense of increasing the complexity of computing the normal field derivatives
