Stable iterative downward continuation of potential field based on Runge-Kutta method

Abstract

Downward continuation is a useful transformation in the processing and interpretation of potential field data. However, this transformation is known for its inherent instability. In this paper, we proposed a stable iterative Runge-Kutta method for downward continuation that uses an average slope over the interval of continuation. Because of the truncation error, we combine the ideas of Runge-Kutta with the iterative downward continuation methods in a single method to improve the accuracy and the precision of the method. The presented method needs only the computation of the first order vertical derivatives (slope) over the whole interval of continuation using the Tikhonov regularization. To validate the efficiency of the proposed method, various tests were conducted on synthetic magnetic data as well as real aeromagnetic data. The obtained results clearly show the stability of our method for the downward continuation of potential field data.