Journal of Radio Electronics. eISSN 1684-1719. 2026. №7
Full text in Russian (pdf)
DOI: https://doi.org/10.30898/1684-1719.2026.7.6
Direct Problem of Subsurface Radar Location
of Pipe Leaks in Seasonally Frozen Arctic Soils
by the Modified Method of Auxiliary Sources
K.V. Muzalevskiy, S.I. Polukeev
Kirensky Institute of Physics, Federal Research Center KSC SB RAS
660036, Russia, Krasnoyarsk, Akademgorodok 50, bld. 38
The paper was received May 31, 2026.
Abstract. This article investigates the capabilities of the modified method of auxiliary sources (MAS) for solving the direct problem of subsurface radar sounding of layered inhomogeneous media of Arctic soils, including cylindrical doubly-connected dielectrically inhomogeneous regions. In this modification of MAS, the fields of auxiliary sources (AS) are represented as a superposition of zero-order Bessel functions, zero-order Hankel functions of the first kind, and their derivatives with respect to the normal direction to the level line, which made it possible to solve the boundary value problem with open interfaces of a plane-layered inhomogeneous medium. The time-domain waveforms calculated by MAS were verified using the finite-difference method (coefficient of determination 0.998, root-mean-square deviation less than 6 V/m). It is shown that the modified MAS provides a reliable solution to the direct problem of subsurface radar sounding over a wide range of soil properties, including seasonally frozen soils, and can be used in algorithms for processing ground-penetrating radar data for monitoring pipelines and road structures in permafrost regions.
Key words: subsurface radar location, Arctic soils, method of auxiliary sources, diffraction, ultra-wideband pulses.
Financing: The work was carried out within the State Assignment of the Kirensky Institute of Physics SB RAS, calculations for the freezing active layer were carried out within the framework of research under grant No. 25-17-20029 of the Russian Science Foundation and the Krasnoyarsk Regional Science Foundation.
Corresponding author: Muzalevskiy Konstantin, email: rsdkm@ksc.krasn.ru
References
1. Iatropoulos V.G., Anastasiadou M.T., Anastassiu H.T. Electromagnetic scattering from surfaces with curved wedges using the method of auxiliary sources (MAS) // Applied Sciences. – 2020. – Т. 10. – №. 7. – С. 2309.
2. Tabatadze V., Karaçuha K., Zaridze R. Electromagnetic scattering from 2-D conducting objects of arbitrary smooth shape: complete mathematical formulation of the method of auxiliary sources for E-polarized case // Prog. Electromagn. Res. M. – 2022. – Т. 114. – С. 117-125.
3. Kouroublakis M., Tsitsas N.L., Fikioris G. Shielding effectiveness of ideal monolayer graphene in cylindrical configurations with the method of auxiliary sources // IEEE Transactions on Electromagnetic Compatibility. – 2022. – Т. 64. – №. 4. – С. 1042-1051.
4. Papakanellos P.J., Tsitsas N.L., Anastassiu H.T. The method of auxiliary sources (MAS) in computational electromagnetics: A comprehensive review of advancements over the past two decades // Electronics. – 2024. – Т. 13. – №. 17. – С. 3520.
5. Eremin Y.A. et al. A new method of internal auxiliary source-sinks (MIASS) for two-dimensional interior Dirichlet acoustic problems // Journal of Computational and Applied Mathematics. – 2021. – Т. 386. – С. 113231.
6. Eremin Y.A. et al. New scheme of the discrete sources method for two-dimensional scattering problems by penetrable obstacles // Journal of Computational and Applied Mathematics. – 2023. – Т. 417. – С. 114556.
7. Музалевский К.В. Метод дискретных источников для задачи подповерхностного радиозондирования сверхширокополосными импульсами двумерных диэлектрических тел // Радиотехника и электроника. – 2024. – Т. 69. – №. 11. – С. 1039-1052. (In Russian)
8. Kouroublakis M., Tsitsas N.L., Leviatan Y.A time-domain method of auxiliary sources for efficient analysis of transient electromagnetic scattering by moderately conductive cylinders // Engineering Analysis with Boundary Elements. – 2026. – Т. 183. – С. 106605.
9. Geçer M.E. et al. Scattering by a Dielectric Circular Cylinder in a Planar Layered Medium with MAS, MMP and T-Matrix Methods // 2025 IEEE 30th International Seminar/Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (DIPED). – IEEE, 2025. – Т. 1. – С. 14-18.
10. Cao Y. et al. Thawing of permafrost surrounding buried pipelines and a novel powerless air ventilation technique for thawing mitigation // Energy. – 2025. – Т. 320. – С. 135063.
11. Mironov V.L. et al. A dielectric model of thawed and frozen Arctic soils considering frequency, temperature, texture and dry density // International journal of remote sensing. – 2020. – Т. 41. – №. 10. – С. 3845-3865.
12. Yee K. Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media // IEEE Transactions on antennas and propagation. – 1966. – Т. 14. – №. 3. – С. 302-307.
13. Lazaridis D.S., Tsitsas N.L. The method of auxiliary sources for scattering by layered media with parallel algorithmic implementations // Journal of Electromagnetic Waves and Applications. – 2025. – Т. 39. – №. 15. – С. 1896-1915.
14. Stogryn A. Equations for calculating the dielectric constant of saline water (correspondence) // IEEE transactions on microwave theory and Techniques. – 1971. – Т. 19. – №. 8. – С. 733-736.
15. Кулижников А.М. Определение диэлектрической проницаемости материалов дорожной одежды по результатам георадиолокационных обследований на участках автомобильных дорог // Инженерные изыскания. – 2014. – №. 11. – С. 46-52. (In Russian)
16. Библиотека Численного анализа НИВЦ МГУ. Подпрограмма: ASP4E. Online: http://num-anal.srcc.msu.ru/lib_na/cat/as/asp4a.htm. (In Russian)
For citation:
Muzalevskiy K.V., Polukeev S.I. Direct problem of subsurface radar location of pipe leaks in seasonally frozen arctic soils by the modified method of auxiliary sources // Journal of Radio Electronics. – 2026. – №. 7. https://doi.org/10.30898/1684-1719.2026.7.6 (In Russian)