Reduction to the pole as an inverse problem and its application to low‐latitude anomalies

Traditionally, reduction to the pole has been accomplished either by space‐ or wavenumber‐domain filtering. In the two‐dimensional case, this procedure is stable regardless of the latitude, as long as the source strike is not parallel to the horizontal projection of the geomagnetic field. In the three‐dimensional case, however, reduction‐to‐the‐pole filtering is stable only at high magnetic latitudes. At latitudes lower than 15 degrees, it is of no practical use due to a sharply increasing instability toward the magnetic equator. The three‐dimensional instability of this filtering technique is demonstrated, and the reduction‐to‐the‐pole problem is formulated in the context of a general linear inverse problem. As a result, stable solutions are found by using well‐known stabilizing procedures developed for the inverse linear problem. The distribution of magnetization of an equivalent layer of doublets that reproduces the observed data is computed. The magnetic doublets are parallel to the magnetization direction which is assumed constant throughout the sources. The magnetic field reduced to the pole is then obtained by changing the inclinations of the geomagnetic field and the doublets to 90 degrees and recalculating the total field. The usefulness and limitations of the method at low magnetic latitudes are assessed using theoretical data. The effects of noise and anomaly truncation are also investigated for both high and low latitudes. In all cases, application of the proposed method produced meaningful results regardless of the latitude. The method is applied to field data from two different low‐latitude anomalies. The first anomaly is due to a seamount in the Gulf of Guinea with reversed magnetization. The geomagnetic field at this location is about −23 degrees. The second anomaly is an intrabasement anomaly from Parnaiba Basin, Brazil, where the magnetization is assumed to be induced by a geomagnetic field with −1.4 degree inclination. The results obtained confirm that the proposed method produces stable, meaningful, reduced‐to‐the‐pole maps.