Differential reduction to the pole☆
Introduction
Pole reduction is an operator which takes magnetic anomalies and changes their asymmetric form to the symmetric form which would have been observed had the causative magnetic bodies lain at the magnetic poles. The frequency domain operator is (Baranov, 1957)where A(u,v) is the amplitude at frequencies , and are the geomagnetic inclination and declination, respectively, and is tan−1(v/u). The method has several (well-known) problems when implemented in this fashion. It is unstable at low magnetic latitudes, it gives incorrect results if the causative magnetic bodies possess unknown remanent magnetisation, and lastly, because of the frequency domain implementation of the algorithm, and must remain constant throughout the area of application of the filter.
There are several approaches that can be taken to solve this latter problem. Lu et al. (2003) used a parallel computer to reduce the dataset to the pole nxm times, where the dataset contains nxm datapoints. The inclination and declination could be different at each grid point as required, and only the response centred on the current point was retained from each RTP operation. The method is effective but requires considerable computer power. The equivalent layer method can also be used to apply RTP when the field parameters vary (Von Frese et al., 1981; Silva, 1986). In this case, the inversion stage that determines the layer susceptibilities uses sources with inclination and declination that vary over the dataset. Then the forward model is calculated with all layer dipole inclinations set to −90°. The computational effort required to perform the inversion is again the main problem with the method.
If the variations of the field parameters are small, then they can be considered as perturbations about the average field values of the region. Arkani-Hamed (1988) used this idea in the frequency domain, allowing the crustal magnetisation to vary continuously over a plane, using an iterative algorithm. However, as pointed out by Swain (2000), the method is rarely used in practice because of the large data storage requirements of the algorithm and because it is unstable at low magnetic latitudes. Additionally, the iterative nature of the algorithm makes its computational requirements yet more demanding.
Section snippets
Differential RTP as a space domain perturbation
An alternative method is to apply the perturbations in the space domain rather than the frequency domain. So, using a Taylor series expansionRTPmean is the dataset reduced to the pole using the average field inclination and declination of the area. is the difference between the inclination at a given point and the average inclination, and is computed similarly. The derivatives are computed in the space
Differential pseudogravity
Once the differential reduction to the pole dataset has been computed it is relatively simple to convert to pseudogravity by vertical integration and the application of a scale factor. Pseudogravity converts the magnetic field into the gravity field that would be observed if the magnetisation distribution were to be replaced with an identical density distribution (Blakely, 1995, p. 344). It is a useful technique for the interpretation of major magneto-tectonic provinces as it simplifies anomaly
Application to aeromagnetic data from the Northern Territories, Australia
The new differential reduction to the pole algorithm was applied to the regional aeromagnetic grid of the Northern Territory, Australia. The magnetic field inclination ranges from −57° in the south to −33° in the north. The simplified geology of the Northern Territory is shown in Fig. 2a. Proterozoic Orogens of the North Australian Craton and the Central Australian Mobile Belts form the basement. The North Australian Craton is interpreted as complex accreted terranes (Myers et al., 1996) with
Conclusions
A simple algorithm for the pole reduction of magnetic datasets with variable geomagnetic inclination and declination was presented. The algorithm is computationally simple and gave good results both on synthetic data and on aeromagnetic data from Australia.
Acknowledgements
We thank the Northern Territory Geological Survey for providing the original total magnetic intensity grid and the geological overview maps.
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