Stable inverse deconvolution of magnetic data

Abstract

The final aim of a magnetic survey is to obtain quantitative information about the geological source generating the observed field. In this paper, I show how the employment of a suitable non-iterative operator in the Fourier domain permits to recover the horizontal magnetization distribution of a plausible equivalent source by a simple deconvolution. The results obtained in the synthetic case show a good agreement with the generating model, and moreover the recovered magnetization map appears more stable concerning high-frequency noise amplifi-cation with respect to other operators previously used in literature. The analytic justification of this stability will be described in detail by comparison with the traditional operators. The extension of this operator to the sector of field transformations, such as Upward Continuation or Reduction to the Pole, is straightforward because it is sufficient to re-calculate the field due to the apparent magnetization distribution. The results obtained by synthetic and real data tests demonstrate that the equivalent-source operator shown in this paper is able to give meaningful answers with a minimum amount of information by the user concerning depth of the source. These parameters as known, when unavailable, can be estimated in a stable way from the power spectrum of the magnetic anomaly, so that in the final analysis only a Fourier transformation of the data is needed to evaluate a realistic magnetization model.