Differential reduction‐to‐the‐pole of regional magnetic anomalies

Abstract

I present a differential reduction‐to‐the‐pole technique that reduces regional scale magnetic anomalies to the geomagnetic pole, while taking into account the variations in the direction of the geomagnetic field and that of the magnetization of the crust over the region. The technique is developed in the spectral frequency domain as an inverse problem solved iteratively using a perturbation method. I regard the variations in the directions as finite perturbations about the mean values of the directions over the region and evaluate the nonlinear coupling terms due to these perturbations in the space domain at each iteration before transforming them into the spectral frequency domain. The technique is applied to the magnetic anomalies of three semiinfinite prisms, which are inductively magnetized and located at high, mid, and low latitudes in a region where the inclination of the ambient field changes from 10 to 90 degrees and its declination changes from −30 to +30 degrees. The differential reduction to the pole shifts the positive anomaly of the low‐latitude prism toward the north more than it shifts that of the mid‐latitude prism, which in turn is shifted northward more than that of the high‐latitude prism. The reduction also suppresses the negative lobes to the north of the mid and low‐latitude prisms and moves the positive anomalies to points directly over the prisms. I also apply the technique to the marine magnetic anomalies off the east coast of Canada. The positive magnetic anomalies in the southern part of the area are displaced northward by about 30 km, whereas those in the northern part are not moved significantly.