Reduction-to-the-pole of regional magnetic data with variable field direction, and its stabilisation at low inclinations

A method for reducing a grid of total field magnetic data to the pole, where the field and magnetisation directions vary, was published by Arkani-Hamed in 1988. He called the method differential reduction-to-the-pole (DRTP) because the variations in direction are treated as perturbations about mean directions and the problem is solved iteratively. There appear to be advantages in applying this (or a similar method) to large regional magnetic grids, particularly at low magnetic latitudes. Nevertheless, it appears to have been rarely used. There are two problems with DRTP. Firstly, the algorithm calls for 12 two-dimensional arrays (5 real and 7 complex) so an implementation capable of dealing with a 4000 × 4000 data grid on a PC or small workstation requires careful coding. Secondly, as noted by Arkani-Hamed, the method is unstable at low inclinations where, like the standard wavenumberdomain method, it selectively amplifies noise (as well as anomalies) in the magnetic north-south direction. The problem of low inclination stabilisation is addressed using a similar technique to that used in Geosoft’s MAGMAP to stabilise its wavenumberdomain RTP filter. This introduces a pseudo-inclination into the denominator of the filter transfer function, which is increased from the true inclination in order to reduce the amplification of northsouth wavenumbers. It is not obvious that this modification should work with the DRTP algorithm because of the iterative corrections being applied, but tests with synthetic data show that it has a very similar behaviour to the uniform direction algorithm. As an example of its use the low-inclination DRTP is applied to a large regional magnetic dataset from Brazil, where the inclination varies from -40° to +20°.