Stable calculation of horizontal derivatives of potential field data

Methods for potential field enhancement and parameter estimation routinely employ horizontal and vertical derivatives. Several regularization methods have been proposed for the latter, which is typically calculated in the wavenumber domain and is more sensitive to noise. We propose a finite-difference formula to compute horizontal derivatives that has the same theoretical accuracy as the standard centered-difference formula, but involves upward-continued data only, thus reducing noise amplification. The upward continuation height is chosen from local minima of C-norm curves of the horizontal derivatives, as in Tikhonov regularization methods. We illustrate the proposed calculation by comparing standard and stabilized maps of the total horizontal gradient, as well as other edge-detection filters applied to synthetic and real datasets. The enhancement maps obtained using the proposed approach are sharper than those using the standard approach, even when the data are previously filtered by upward continuation.