Higher-order regularised differentiations of potential fields

Abstract

The differentiations of potential fields play an important role in their interpretations, as they are included in many of the enhanced transformations and edge detectors (Analytical Signal Amplitude, Tilt derivatives, Total Differentiation and others). However, the evaluation of horizontal and vertical differentiation is an unstable process. This instability was partially solved in the past by, e.g. Tikhonov regularisation for the first-order differentiations. Here, we present and compare several regularised stabilisations of higher-orders of differentiations. The methods are tested on synthetic and real data sets, where results indicate the usefulness of the presented method in the potential fields' processing and interpretation. Good properties of higher order regularised derivatives are demonstrated on selected edge-detection operator: in this case, on the modified balanced horizontal gradient operator.