A Novel Iterative Approach for Downward Continuation of Potential Fields

This paper presents a novel iterative approach for downward continuation of potential fields. Mathematically speaking, downward continuation can be viewed as a two dimensional deconvolution problem, which is always ill-posed. In this paper, regularization idea is invoked to suppress ill posedness of downward continuation problem, and a gradient-type iterative method is constructed to solve it. Another contribution of this paper is that it proves that spatial discrete downward continuation operator has a structure of Toeplitz. Based on fast Toeplitz matrix and vector computation method, computational cost and memory cost of two dimensional convolution operation is reduced so largely that spatial iterative regularization method can be used to solve downward continuation problem in ordinaire computer. Moreover, the idea may have further effect on other kind of deconvolution problems. The present approach is compared with traditional FFT based downward continuation method, and model tests show that the new approach is more stable and robust than traditional approach.