On a Local Representation of the Fine Structure in the Earth’s Gravitational Field

Abstract

This paper introduces a class of nearly harmonic functions useful in analyzing gravity above a limited region of the earth’s surface. These “B functions” constitute a complete orthogonal set of functions over that portion of the surface of a sphere which lies between two latitudes and two longitudes. By an iteration process, the coefficients of a series of B functions can be determined in such a manner as to provide an optimum fit to the difference between the prediction of a global gravity model and gravity actually measured on the earth’s surface, thus bypassing the problem of reducing the data to a reference surface. Representation of local gravity as the sum of a global model in terms of spherical harmonics and a local model in terms of B functions appears to be an effective technique for handling the problem of altitude extension of surface data.