On the calculation of vertical derivatives of potential fields for downward continuation and related filters

Methods for enhancing and estimating parameters of potential fields from gravimetric and magnetometric surveys typically utilize the vertical derivative (VDR) of the potential field. These derivatives amplify the high-frequency content of the field, which can be caused by shallow bodies or survey noise. Regularization methods generate approximations of derivatives that must reconcile two objectives: reducing the effect of high-frequency amplification and providing an accurate approximation. Achieving this balance is crucial for methods that require vertical derivatives of successive order, such as Taylor-series implementations of downward continuation and the enhanced horizontal derivative (EHD) filter. This paper evaluates the performance of several vertical-derivative methods for downward continuation and EHD filters using both noise-free and noisy synthetic data. In addition, gravity data over the SW Sub-basin are considered, and the findings are compared with seismic data. Our results show that the β-VDR method provides more accurate and stable derivatives under noisy conditions.