Regularized derivatives of potential fields and their role in semi-automated interpretation methods

Evaluation of higher derivatives (gradients) of potential fields plays an important role in geophysical interpretation (qualitative and/or quantitative), as has been demonstrated in many approaches and methods. On the other hand, numerical evaluation of higher derivatives is an unstable process – it has the tendency to enlarge the noise content in the original data (to degrade the signal-to-noise ratio). One way to stabilize higher derivative evaluation is the utilization of the Tikhonov regularization. In the submitted contribution we present the derivation of the regularized derivative filter in the Fourier domain as a minimization task by means of using the classical calculus of variations. A very important part of the presented approach is the selection of the optimum regularization parameter – we are using the analysis of the C-norm function (constructed from the difference between two adjacent solutions, obtained for different values of regularization parameter). We show the influence of regularized derivatives on the properties of the classical 3D Euler deconvolution algorithm and apply it to high-sensitivity magnetometry data obtained from an unexploded ordnance detection survey. The solution obtained with regularized derivatives gives better focused depth-estimates, which are closer to the real position of sources (verified by excavation of unexploded projectiles).