A stable regularization method of downward continuation of potential field

Abstract

Downward continuation is known as one of the crucial steps in interpreting gravity or magnetic data. As the continuation depth and the influence of noise increases, the results of downward continuation become unstable. Based on the computation of the Chebyshev-Padé approximation function obtained by the Tikhonov regularization, this paper proposes a new regularized method intended for the downward continuation of potential fields. The Chebyshev-Padé approximation function is applied to calculate the continuation factor. In this study, the cross-correlation method is adopted to calculate the cut-off wavenumber, while the regularized low-pass filter is designed to calculate the downward continuation of the potential field. In order to validate this method, numerical simulation is conducted. We calculate the root mean square error of the theoretical data on the target plane and the data of downward continuation, as obtained using the improved regularization operator method, the Chebyshev-Padé approximation function method, the regularized Chebyshev-Padé approximation function method, and the method proposed in this paper, based on which a comparison is conducted. According to the simulation and experimental results, the effects of the continuation depth can be reduced significantly by the proposed method. Besides, the method demonstrates strong resistance to noise.