Separation filtering using fractional order derivatives

Separation or layer filtering of regional and residual magnetic fields is an important component of magnetic interpretation. Separation filtering depends fundamentally on the concept of random distributions of sources within discrete layers, and assumes that there is no statistical difference in response along each ideal layer and no correlation between the distributions in different layers. Separation filtering becomes very difficult when there is considerable overlap in the spectra of individual depth ensembles. The degree of separation achieved depends on the depth differences and the spectral b/B ratio, the ratio of the amplitudes of the shallow and deep ensembles. A high b/B ratio is needed to separate the effects of shallow sources with minimum contamination by deeper sources. In practice, it is usually impossible to achieve complete separation because the problem is non-linear and spectra have too much overlap, but the results are still a very powerful interpretation aid when used qualitatively (Jacobsen, 1987). Selection of a suitable filter depends both on the magnetic signature of the target source and on the data quality. Both tonal (amplitude) and textural information are needed to recognise type patterns characteristic of the magnetic expression of geological features of interest.

It is well known that derivatives of potential fields enhance the field component associated with shallow features and de-emphasise the field from deeper sources. Fractional vertical derivatives provide an objective, flexible approach to shallow-layer separation filtering, as the order of the fractional derivative can be selected to match the data and optimise enhancement of the shallow field component. The method avoids the uncertainties in selecting spectral matched filter parameters. Fractional derivatives of different order can be combined to produce RGB images and this can be a significant aid to the interpretation of the data. Finally, the order of the vertical derivative can be varied across the dataset, based on local statistics, to produce balanced derivative images that show detail in both ‘smooth’ and ‘rough’ regions simultaneously.

The application of fractional-derivative separation filtering is illustrated using high-resolution aeromagnetic data covering the Ghanzi-Chobe fold belt in Botswana. Total magnetic intensity data are dominated by crystalline basement anomalies. Progressively increasing the order of fractional vertical derivatives provides rejection of deeper basement anomalies and provides better resolution of subtle supracrustal anomalies than the conventional vertical gradient. Varying the order of the vertical derivative across the dataset provides a local rather than global filtering capability, unlike conventional matched filters.