The application of spatial derivatives to non-potential field data interpretation

Source/body edge detection is a common feature in the processing and interpretation of potential field data sets. A wide range of spatial derivatives is available to enhance the information contained in the basic data. Here the ability of these procedures to assist with the mapping interpretation of non-potential field data is considered. The study uses airborne electromagnetic (conductivity) data but also provides a general context for other conductivity/resistivity data, provided the non-potential field nature of active and thus spatially-focused, measurements is acknowledged. The study discusses and demonstrates the application of a range of common spatial derivative procedures, including the analytic signal and upward continuation, to both magnetic and conductivity data. The ability of the tilt derivative to provide enhanced mapping of conductivity data is considered in detail. Tilt and its associated functions are formed by taking combinations of vertical and horizontal derivatives of the data set. Theoretical forward modelling studies are first carried out to assess the performance of the tilt derivative in relation to the detection and definition of concealed conductivity structure. The tilt derivative embodies automatic gain control that normalizes the detection and definition of both weak and strong conductivity gradients across an appropriate subsurface depth range. The use of high-order spatial derivatives inevitably results in a degree of noise (cultural perturbation) amplification that is survey and technique specific. Both of these aspects are considered using practical case studies of jointly obtained magnetic and conductivity data at a variety of spatial scales.