Optimal regularization downward continuation method of potential field based on fractal radial spectrum

The downward continuation technique of potential fields is an important data processing method in the field of gravity and magnetic potential fields. The mathematical instability of this technique has always been a focus of academic attention. Regularization is one of the most effective methods to solve the instability of downward continuation of potential fields, but currently there are four different forms of regularization. Starting from the Wiener filter of downward continuation of potential fields in the sense of minimum mean square error, and combining with the fractal radial average power spectrum of the potential field source, the optimal low-pass filter for regularized downward continuation of potential fields is derived. The following conclusions are obtained through analysis: (1) The optimal regularized low-pass filter for downward continuation is only related to the burial depth of the source's centroid and the fractal structure parameter, and is independent of the continuation distance; (2) The four different regularization forms in the existing literature are all special cases of the optimal regularization downward continuation filter with specific parameters; (3) The optimal regularization downward continuation filter combined with the minimum value of the fractal-corrected radial spectrum only requires calculating the regularization parameter once to downward continue to different depths. Through the comparison experiments of theoretical models and actual measurement data for downward continuation, the results show that, compared with the existing four kinds of potential field regularization methods, the optimal regularization method proposed in this paper can obtain more stable and accurate downward continuation results.