Fourier Physical Geodesy

Fourier transforms are efficient and convenient for analyzing local gravity data, but the accuracy of Fourier methods is restricted by the flat-earth approximation. In this paper, the theory of matched asymptotic (inner and outer) expansions is used to develop improved flat-earth approximations, determine regions of convergence, and match global (round-earth) and local (flat-earth) gravity models. Accurate solutions in the terms of Fourier transforms are given for the integrals of Poisson, Stokes, and Vening Meinesz. The new theory provides an error analysis of flat-earth algorithms and a systematic procedure for improving their accuracy. (Author)