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.

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