A STABLE TRUNCATED SERIES APPROXIMATION OF THE REDUCTION-TO-THE-POLE OPERATOR

We combine a stabilized reduction-to-the-pole and an upward continuation filter to produce meaningful reduced-to-the-pole fields at low magnetic latitudes. The stabilizing procedure is based on the development, in Taylor's series, of the theoretical expression for the reduction-to-the-pole filter in the wavenumber domain. The filter instability is caused by the huge filter amplitudes along the magnetization azimuth, which are expressed by the infinite sum of terms close to unity. The stabilizing procedure reduces to simply truncating the infinite series. The upward continuation filter attenuates the high wavenumber component of the noise and allows us to design a stabilized filter closer to the theoretical one, Besides, quantitative interpretations of source depth based on the filtered field are more reliable when using upward continuation as compared with arbitrary low-pass filters. The proposed filter was applied to synthetic data of a single prism uniformly magnetized along a supposedly known direction, and it produced a reduced-to-the-pole field very close to the theoretical field at pole. We also applied the filter to magnetic data from Dixon Seamount assuming induced magnetization only. We obtained, within the central part of the anomaly, roughly circular contours of the reduced-to-the-pole anomaly due to the nearly circular shape of the Seamount (evidenced by topographic data).