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

We combine a stabilized reduction-to-the-pole and an upward continuati on filter to produce meaningful reduced-to-the-pole fields at low magn etic latitudes. The stabilizing procedure is based on the development, in Taylor's series, of the theoretical expression for the reduction-t o-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 s tabilizing procedure reduces to simply truncating the infinite series. The upward continuation filter attenuates the high wavenumber compone nt of the noise and allows us to design a stabilized filter closer to the theoretical one, Besides, quantitative interpretations of source d epth based on the filtered field are more reliable when using upward c ontinuation as compared with arbitrary low-pass filters. The proposed filter was applied to synthetic data of a single prism uniformly magne tized along a supposedly known direction, and it produced a reduced-to -the-pole field very close to the theoretical field at pole. We also a pplied the filter to magnetic data from Dixon Seamount assuming induce d magnetization only. We obtained, within the central part of the anom aly, roughly circular contours of the reduced-to-the-pole anomaly due to the nearly circular shape of the Seamount (evidenced by topographic data).