The application of fractional calculus to potential field data

Gradients of magnetic and gravity data are used routinely to enhance the edges of anomalies, or as input to interpretation techniques such as analytic signal analysis or Euler deconvolution. The most commonly used gradients are of first and second order, higher orders being used less frequently due to noise problems. This paper discusses the benefits of a generalized approach using fractional gradients, demonstrating their usefulness as an aid to interpretation, both on theoretical models and on aeromagnetic data from the Free State province, South Africa. Fractional horizontal gradients are suggested as a means of avoiding the instability problems present when magnetic data from low latitudes is reduced to the pole. They also allow the use of an improved sunshading algorithm that is less affected by noise than the standard method. Fractional vertical gradients may be used to generate both enhanced analytic signal data and enhanced Euler deconvolution solutions.