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Abstract <p>The paper presents the results of solving a structural inverse problem of magnetometry (determining the surface separating layers with different magnetization values). Using the finite element method, a “fast” regularizing iterative algorithm for solving the integral equation of the inverse problem, which does not require calculating the derivatives of the target functional, is constructed. Two iterative formulas are obtained: for near-surface and deep-seated objects. Due to the simplicity of the formulas, the algorithm can be implemented on a medium-performance personal computer. It allows obtaining an approximate solution of the problem within a few minutes. The applicability of each variant of the algorithm is assessed. Examples of solving the inverse problem for model and practical data are constructed.</p>

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On the Solution of a Three-Dimensional Structural Inverse Problem of Magnetometry for Interfaces in Horizontally Layered Media

  • 期刊论文

  • 发表日期：

    2026年1月1日

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  • P. S. Martyshko,
  • D. D. Byzov,
  • A. L. Rublev

摘要

Abstract

The paper presents the results of solving a structural inverse problem of magnetometry (determining the surface separating layers with different magnetization values). Using the finite element method, a “fast” regularizing iterative algorithm for solving the integral equation of the inverse problem, which does not require calculating the derivatives of the target functional, is constructed. Two iterative formulas are obtained: for near-surface and deep-seated objects. Due to the simplicity of the formulas, the algorithm can be implemented on a medium-performance personal computer. It allows obtaining an approximate solution of the problem within a few minutes. The applicability of each variant of the algorithm is assessed. Examples of solving the inverse problem for model and practical data are constructed.