Regularized 2D Savitzky–Golay derivative filter in estimating the second vertical derivative of potential field data

Abstract

ABSTRACTA robust method of estimating the second vertical derivative of two‐dimensional (2D) potential field data is proposed. The proposed method uses a 2D variant of Savitzky–Golay derivative filtering. The design of the 2D Savitzky–Golay derivative filter, unlike its one‐dimensional (1D) counterpart, is a non‐trivial exercise. This is due to the inherent complexity associated with 2D polynomial regression, which increases with the increase in the degree of the polynomial and the dimension of the filter window. The measure of complexity increases manifold, as the polynomial order increases from cubic to quintic. A larger polynomial order demands a larger dimension of the filter window patch as a minimum requirement. The large window patch which, in turn, poses computational challenges, becomes anill‐posedproblem and is computationally inefficient. To alleviate such a problem, an appropriate set of filter parameters is proposed, which ensures computational efficiency while maintaining sufficient robustness. The computational issue arising from theill‐posedcondition of the system matrix is addressed viashrinkage‐based regularization. A numerical experiment was conducted on a synthetically generated 2D dataset without and with a moderate amount of Gaussian random noise in order to check the applicability of the proposed method. The performance in terms of robustness was also compared with the other, usually considered as a benchmark, method. The proposed method is then successfully applied to determine the second vertical derivative of the high‐resolution Bouguer gravity anomaly data over an impact crater in Lake Wanapitaei, Canada. A qualitative interpretation of the second vertical derivative map over Lake Wanapitei is given.