Differential reduction to the pole: Revisited

Following a detailed investigation of the Fourier-domain differential reduction-to-the-pole (DRTP) algorithm I compared the results to those obtained using a space-domain reduction-to-the-pole algorithm. I demonstrate that DRTP reduces magnetic anomalies to the pole more effectively than the space-domain algorithm. The DRTP operator has singularities at the geomagnetic equator and enhances north-south trending features at low latitudes. The operator is modified by slightly increasing the inclination of the core field at low latitudes to suppress the singularity. This space-domain modification only affects the anomalies very close to the equator. The modified DRTP operator successfully reduces the magnetic anomalies at low latitudes to the pole. The effects of random noise added to the original magnetic anomalies are investigated in some detail, and an appropriate directional low-pass filter is used to remove the resulting enhanced noise in the reduced-to-the-pole magnetic anomalies. Very simple bodies (uniformly magnetized, cubic, or rectangular) are considered to clearly illustrate the effects of the DRTP, its modified version, and the directional low-pass filter.