An adaptive iterative method for downward continuation of potential-field data from a horizontal plane

Abstract

We have developed an improved adaptive iterative method based on the nonstationary iterative Tikhonov regularization method for performing a downward continuation of the potential-field data from a horizontal plane. Our method uses the Tikhonov regularization result as initial value and has an incremental geometric choice of the regularization parameter. We compared our method with previous methods (Tikhonov regularization, Landweber iteration, and integral-iteration method). The downward-continuation performance of these methods in spatial and wavenumber domains were compared with the aspects of their iterative schemes, filter functions, and downward-continuation operators. Applications to synthetic gravity and real aeromagnetic data showed that our iterative method yields a better downward continuation of the data than other methods. Our method shows fast computation times and a stable convergence. In addition, the [Formula: see text]-curve criterion for choosing the regularization parameter is expressed here in the wavenumber domain and used to speed up computations and to adapt the wavenumber-domain iterative method.

Gravity gradient and magnetic terrain effects for airborne applications — A practical fast Fourier transform technique

“…A promising method is based on a linear inverse problem formulation using Tikhonov and Arsenin's (1977) regularization developed in recent years by Liang (1989), Devriese (2009), Pašteka et al (2012), Abedi et al (2013), and Zeng et al (2013). As pointed out by Zeng et al (2013), regularization in the wavenumber domain corresponds to low-pass filtering of the data prior to downward continuation.…”

Comparative Study of the Spherical Downward Continuation

“…Since the topic of the downward continuation was and is extensively studied (see, e.g., Huestis and Parker 1979;Xu 1992;Phillips 1996;Novák et al 2001;Zeng et al 2013), we restrict ourselves to state that the difficulty of the downward continuation lies in transforming a given signal through the source-free (or harmonic) space closer to sources while preventing noise amplification. Basically, this is the reason why the topic is still worth exploring.…”

“…In this approach, the direct problem (here, the upward continuation) is solved iteratively until the input data are fitted to a possible level of agreement that is mostly corrupted by noise. Most recently, the approach was used on the plane by Xu et al (2007), Ma et al (2012), Zeng et al (2013), Zhang et al (2013) and on the sphere by Sebera et al (2014) in the case of the global downward continuation.…”

“…For the same purpose, Eshagh (2011) has proposed stochastically modified integral kernels, while Shen et al (2012) has derived the partially bias-corrected regularization. Most recently, iterative Tikhonov's regularization (King and Chillingworth 1979) was used by Pašteka et al (2012), Zeng et al (2013) for the downward continuation of magnetic data from the horizontal plane.…”

“…Most recently, the problem was treated with help from Tikhonov's regularization (Pašteka et al 2012;Zeng et al 2013), with the help from Landweber's iteration on the plane (Xu et al 2007;Zhang et al 2013) and on the sphere . Besides the approaches applicable in source-free regions (satisfying the Laplace equation), there are also numerous approaches for working with potential data inside a source region (see, e.g., Elysseieva and Pašteka 2009;Fedi and Florio 2011).…”