Elsevier

Computers & Geosciences

Volume 31, Issue 8, October 2005, Pages 989-999
Computers & Geosciences

Differential reduction to the pole

https://doi.org/10.1016/j.cageo.2005.02.005Get rights and content

Abstract

Due to the dipolar nature of the geomagnetic field, magnetic anomalies located anywhere other than at the magnetic poles are asymmetric even when the magnetic source distribution is symmetrical. This complicates interpretation. Pole reduction (RTP) takes the anomaly, as measured at any latitude, and transforms it into that which would have been measured if the body had been laid at the magnetic pole i.e. the area where the field inclination is vertical and the anomalies from symmetrical bodies are symmetrical. The algorithm is usually applied in the frequency domain which has the advantage of being computationally fast, but the disadvantage of restricting the application of the algorithm to regions possessed of constant geomagnetic inclination and declination. Various frequency domain algorithms have been devised to solve this problem, but all have problems of one form or another. A simple algorithm for RTP is suggested here that employs a Taylor series expansion in the space domain (other work has used the Taylor series expansion approach in the frequency domain). The algorithm is demonstrated on synthetic data and on aeromagnetic data from the Northern Territory, Australia.

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)A(u,v)=A(u,v)(sinθ+icosθsin(φ+α))2where A(u,v) is the amplitude at frequencies (u,v), θ and φ are the geomagnetic inclination and declination, respectively, and α 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, θ and φ 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 expansionRTPvar=RTPmean+ΔincRTPinc+0.5Δinc22RTPinc2+ΔdecRTPdec+0.5Δdec22RTPdec2+RTPmean is the dataset reduced to the pole using the average field inclination and declination of the area. Δinc is the difference between the inclination at a given point and the average inclination, and Δdec 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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