On estimation of stopping criteria for iterative solutions of gravity downward continuation

Goli, Mehdi; Foroughi, Ismael; Novák, Pavel

doi:10.1139/cjes-2017-0208

Cited by 9 publications

(3 citation statements)

References 29 publications

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“…These debates, while important, are not closely related to our thesis, so we will not refute them in detail. However, we do take issue with Popadyev reiterating the historical arguments for the Molodensky system while he, and any reviewers of his paper, have ignored the massive body of work showing that they are no longer valid (Vaníček and Martinec 1994;Martinec and Vaníček 1994;Vaníček et al 1999;Huang et al 2001;Janák and Vaníček 2001;Tenzer et al 2003;Tenzer and Vaníček 2003;Tenzer et al 2005;Kingdon et al 2005;Santos et al 2006;Cheraghi et al 2007;Kingdon et al 2012;Foroughi and Tenzer 2017;Foroughi et al 2017a, b;Janák et al 2017;Goli et al 2018;Foroughi 2018;Foroughi et al 2019;Sheng et al 2019;Vaníček and Santos 2019;Goli et al 2019a, b)-the references indicated come mostly from geodesists who follow the "University of New Brunswick's (UNB) line of thought" (as this is a rebuttal paper) but it is by no means complete, as many other colleagues dedicated to the classical theory validate our assumptions. Among other things, this substantial list of references shows that several quantities Popadyev claims are "unknown" or "unknowable" can be determined with sufficient accuracy.…”

Section: Auxiliary Argumentsmentioning

confidence: 97%

Assessing Molodensky’s Heights: A Rebuttal

Kingdon¹,

Vaníček²,

Santos³

et al. 2022

International Association of Geodesy Symposia

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This paper is written as a progression of the ongoing discussion in geodesy about the merits of the Molodensky height system versus the classical height system. It is a rebuttal of a publication in the Proceedings of the IX Hotine-Marussi Symposium on Mathematical Geodesy by Victor Popadyev titled “On the Advantage of Normal Heights: Once More on the Shape of Quasigeoid.” Even though Popadyev’s paper was not presented at the symposium it was published in the proceedings regardless. It purports to address a presentation from the symposium titled “The shape of the quasigeoid”, that applied a set of criteria to judge the suitability of the quasigeoid as a vertical reference surface, ultimately finding it inferior due to its edges and folds. The proceedings paper acknowledges these irregularities in the quasigeoid, but instead argues that the Molodensky system, apart from any vertical reference surface, should be evaluated on two different and more favorable criteria, and finds it superior on that basis. Herein, we continue the ongoing discussion by clarifying some of the misunderstandings in the Popadyev paper and explaining that even on the favourable criteria proposed the Molodensky system holds no advantages over the classical system.

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Section: Auxiliary Argumentsmentioning

confidence: 97%

Assessing Molodensky’s Heights: A Rebuttal

Kingdon¹,

Vaníček²,

Santos³

et al. 2022

International Association of Geodesy Symposia

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show abstract

“…The commonly used stopping criterion includes the discrepancy principle [30] and Lcurve methods [31]. The determination of the iteration stopping criterion was usually based on the difference between estimated and observed values, and the estimated statistical data of observed data noise is usually used as the criterion for stopping the iteration process [32]. Chen et al enriched the CGLS method using flexible Krylov subspace technique and non-negative constraints, and proposed for the first time a non-negative flexible CGLS (NN-FCGLS) method.…”

Section: Introductionmentioning

confidence: 99%

A CGLS-based method for solving magnetic moments of hybrid-model magnetic targets

Lu,

Zhang,

Dai

2024

Meas. Sci. Technol.

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In order to solve the problem of magnetic moment estimation of magnetic targets, the inverse problem of magnetic moment estimation was constructed based on the hybrid model of ellipsoid and magnetic dipole array. In order to solve the ill-posed problem of the magnetic moment estimation equations, the method was designed to estimate the magnetic moment parameters of the ellipsoid and magnetic dipole array, and the improved discrepancy principle and the maximum chi-square distribution stop criterion were introduced to improve the semi-convergence behavior of the conjugate gradient least squares method. Through simulation examples of magnetic target magnetic moment estimation and ship model measurement data, the performance of two conjugate gradient least squares methods, Tikhonov algorithm and stepwise regression method, was compared and analyzed from four aspects: relative error of magnetic moment estimation, relative error of magnetic field fitting, relative error of magnetic field extrapolation, and computational time complexity. The conjugate gradient least squares method has the advantages of high accuracy of magnetic moment estimation, high immunity of magnetic moment estimation to interference, high accuracy of magnetic field fitting and extrapolation, and low computational time complexity.

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“…However, the continuation near the field source is the inverse problem of the continuation far away from the field source, which is of great discomfort. Therefore, the solution of the continuation is greatly affected by small noise and usually cannot converge stably [6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Magnetic Field Downward Continuation Iterative Method Based on Low-pass Filter

You

Wang

et al. 2023

J. Phys.: Conf. Ser.

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Magnetic field downward continuation is an important technique for expanding geomagnetic database, which can separate superimposed anomalies and enhance the resolution of local anomalies. However, the adaptability of the fixed filter operator of the existing downward continuation algorithm to the wavenumber domain frequency component of the observed data is not good enough, which leads to the poor applicability of the algorithm, resulting in poor applicability of the algorithm. The downward continuation iteration method based on a low-pass filter is proposed in this paper. First, the residual terms based on the remainder of the first and second vertical derivatives are constructed by using the stability of upward continuation; Secondly, the upward continuation low-pass filter operator, single parameter low-pass filter operator, and two-parameter low-pass filter operator are designed, and the effects of their filtering characteristics on the continuation stability are compared. At the same time, the cut-off frequency and order of the filter operator with parameters are optimized to update the iterative value. Simulation and experimental studies are carried out under different field source depths. Simulation results show that the convergence performance of this method is better when dealing with shallow source field, and the continuation accuracy is improved by 15%–25%. The stability and effectiveness of the magnetic field downward continuation method are verified by the measured data.

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On estimation of stopping criteria for iterative solutions of gravity downward continuation

Cited by 9 publications

References 29 publications

Assessing Molodensky’s Heights: A Rebuttal

Assessing Molodensky’s Heights: A Rebuttal

A CGLS-based method for solving magnetic moments of hybrid-model magnetic targets

Magnetic Field Downward Continuation Iterative Method Based on Low-pass Filter

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