Functional approach to the search for the quasioptimal value of the regularization parameter in downward continuation of potential fields

Abstract

The Tikhonov regularized approach to the downward continuation of potential fields is a partial but strong answer to the instability and ambiguity of the inverse-problem solution in studies of applied gravimetry and magnetometry. The task is described with two functionals, which incorporate the properties of the desired solution, and it is solved as a minimization problem in the Fourier domain. The result is a filter in which the high-pass component is damped by a stabilizing condition, which is controlled by a regularization parameter (RP) — this parameter setting is the crucial step in the regularization approach. The ability of using the values of the functionals themselves as the tool for RP setting in the comparison with commonly used tools such as various types of LP norms is demonstrated, as well as their possible role in the source’s upper boundary estimation. The presented method is tested in a complex synthetic data test and is then applied to real detailed magnetic data from an unexploded ordnance survey and regional gravity data as well to verify its usability.