Convergence of iterative gravity inversion

Abstract

Oldenburg (1974) presented an iterative inversion procedure based on (a rearrangement of) Parker’s (1973) formula for rapid calculation of the gravity anomaly caused by an uneven layer; the algorithm proved effective in practice (Sprenke and Kanasewich, 1982). Nevertheless, Oldenburg stated that straightforward application of the iterative procedure usually results in a divergent solution characterized by high‐frequency oscillations. Only in special cases (when the gravity anomaly can be accounted for by a layer with sufficiently small relief) is convergence obtained. However, Oldenburg did obtain convergence after suitable low‐pass filtering of the gravity anomaly. A criterion is derived to assure convergence of the iterative procedure. This criterion is concerned with the high‐frequency content of the layer’s topography and explains the results Oldenburg found empirically.