A fractional vertical derivative technique for regional-residual separation

The separation of the effects of deep-seated sources of potential fields from those of shallower ones is a frequent requirement when interpreting magnetic or gravity fields. A common procedure is estimating the regional, long wavelength, component of the field by analysing the data over an area larger than that of the local feature of interest. The local components are found by subtracting the estimated regional from the observed data. These approaches may have difficulties in their application, as the dataset over large areas may not be available and other local anomalies, in the enlarged area, may prevent a reliable estimate of the regional field. We present an alternative and simple approach to the regional-residual separation problem not requiring the analysis over large areas and aiming at estimating the local, rather than the regional, component. Our method exploits the natural enhancement of short wavelengths obtainable by computing vertical derivatives of potential fields. An equivalent layer source is computed from the vertical derivative and is used to estimate the local field. The optimal differentiation order can be determined by inspecting the obtained results. This parameter may assume even fractional values, so that the method results a very versatile tool. The application to a complex synthetic case and two real data examples demonstrates the utility of this approach. In summary, our method has some peculiar characteristics making it an interesting alternative to currently used approaches to regional-residual separation: (i) it is a local method, so it can work well even when processing datasets relative to areas of limited extension; (ii) unlike most current methods, estimating a smooth regional component, our method directly produces an estimate of the local field and (iii) it is highly versatile, as the key parameter, that is the fractional differentiation order, can be finely adjusted up to obtain an optimal local field