Fourier transform methods in local gravity modeling

Abstract

New algorithms have been derived for computing terrain connections, all components of the attraction of the topography at the topographic surface and the gradients of these attractions. These algorithms utilize fast Fourier transforms, but, in contrast to methods currently in use, all divergences of the integrals are removed during the analysis. Sequential methods employing a smooth intermediate reference surface have been developed to avoid the very large transforms necessary when making computations at high resolution over a wide area.

A new method for the numerical solution of Molodensky's problem has been developed to mitigate the convergence difficulties that occur at short wavelengths with methods based on a Taylor series expansion. A trial field on a level surface is continued analytically to the topographic surface, and compared with that predicted from gravity observations. The difference is used to compute a correction to the trial field and the process iterated. Special techniques are employed to speed convergence and prevent oscillations.

Three different spectral methods for fitting a point-mass set to a gravity field given on a regular grid at constant elevation are described. Two of the methods differ in the way that the spectrum of the point-mass set, which extends to infinite wave number, is matched to that of the gravity field which is band-limited. The third method is essentially a space-domain technique in which Fourier methods are used to solve a set of simultaneous equations.