Separation filtering using fractional order gradients

Abstract

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 distribution in each layer. 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 spectral b/B ratio, the ratio of the amplitudes of the shallow and deep ensembles. A high b/B ratio is needed to deconvolve the effects of shallow sources with minimum contamination by deeper sources. 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. Different order fractional derivatives can be combined to produce RGB images and this can be a significant aid to the interpretation of the data. 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 improved resolution of subtle supracrustal anomalies than the conventional vertical gradient.