Iterative Wiener filter for unstable linear transformations of potential field data

There are many unstable linear transformations in the processing and interpretation of potential field data, such as, derivatives, reduction to the pole at low latitudes, and downward continuation. They all have the tendency to amplify the noise content in the original data. By means of the Wiener filter theory it is possible to derive optimum transformation filters for these processing technologies in the wavenumber domain. However, the realization of these optimum filters is difficult because they need to know the noise-to-signal power ratio. In this paper, we use iterative Wiener filter (IWF) to solve this problem. First, a noise variance estimation method is proposed based on the annular averaged power spectrum of potential field data. Then, we use the discrepancy principle to choose the regularization parameter for the regularized filter which is an approximation of Wiener filter. After that, the regularized transformation result is used as the initial value of IWF algorithm. Finally, a correction term is used to update the power spectrum estimation of the desired potential field data. Synthetic and field examples show that the proposed IWF algorithm yields better transformation results than the regularized method and has a stable convergence.