Statistical interdependence of additional errors of magnetic inclinometers and geomagnetic activity in the Arctic Zone of Russia

The geomagnetic disturbances on the northern high latitudes, many times higher than the threshold of sensitivity of borehole magnetic inclinometers, are the key impact on the quality of directional survey, particularly, in mining hard-to-recover reserves. In this connection, the objective of this research is statistical modeling aimed at the quantitative evaluation of influence exerted by geomagnetic activity on additional errors of magnetic inclinometers in the areas situated on the northern high latitudes. The proposed approach uses the statistical analysis of 1-minute geomagnetic data taken from earth-based magnetic stations in Russia’s Arctic Zone in 2015 (solar maximum). Also, the data obtained from magnetic stations in the auroral oval in 2022–2024 are analyzed. It is found that the additional error probability distribution follows a heavy-tailed long-normal plot approximated by the Pareto distribution, which proves a high probability of extremal deviations (dozens of degrees). There is a strong correlation (r = 0.78) between the SME index of magnetic storm and waste measurements. The threshold risk level (SME ≥ 500 nT) and the representative time scales of disturbances (seasonal trend with peaks at equinox, diurnal periods of 2–6 h) are determined. The main implication is the demonstrated possibility of transition from the reactive noise management to the proactive probabilistic prediction of metrological risks for drilling operation planning in the Arctic Zone of Russia. 

Vorobeva G. R., Vorobev A. V., Shekhtman L. I. Statistical interdependence of additional errors of magnetic inclinometers and geomagnetic activity in the Arctic Zone of Russia. MIAB. Mining Inf. Anal. Bull. 2026;(9):137-149. [In Russ]. DOI: 10.25018/0236_1493_2026_9_0_137.

The study was supported by the Russian Science Foundation, Grant No. 25-21-00569, https://rscf.ru/project/25-21-00569/.

G.R. Vorobeva¹, Dr. Sci. (Eng.), Assistant Professor, Professor, e-mail: gulnara.vorobeva@gmail.com, ORCID ID: 0000-0001-7878-9724, 
A.V. Vorobev¹, Dr. Sci. (Eng.), Assistant Professor, Professor of Academy of Sciences of Republic of Bashkortostan, Head of Chair, e-mail: geomagnet@list.ru, ORCID ID: 0000-0002-9680-5609,
L.I. Shekhtman¹, Cand. Sci. (Eng.), Assistant Professor, Assistant Professor, e-mail: lidia.shehrman@yandex.ru,
¹ Ufa University of Science and Technology, 450000, Ufa, Russia.

G.R. Vorobeva, e-mail: gulnara.vorobeva@gmail.com.

1. Chang J. L., Jung K. L. Highly accurate accelerometer- and magnetometer-based elevation and azimuth estimation procedure under stationary conditions. Journal of Sensor Science and Technology. 2025, vol. 34, no. 1, pp. 8—18. DOI: 10.46670/JSST.2025.34.1.8.

2. Yang C., Zeng Q., Xiong Z., Yang J. IMU/magnetometer-based azimuth estimation with norm constraint filtering. Sensors. 2024, vol. 24, no. 10, article 2982. DOI: 10.3390/s24102982.

3. Soloviev A. A. Geomagnetic support for directional drilling. Herald of the Russian Academy of Sciences. 2024, vol. 94, no. 10, pp. 885—891. [In Russ]. DOI: 10.31857/S0869587324100023.

4. Yang J., Cai J., Wang S. Online compensation of geomagnetic measurement errors while drilling. IEEE Transactions on Instrumentation and Measurement. 2024, vol. 73, pp. 1—9. DOI: 10.1109/TIM.2024.3379082.

5. Pilipenko V. A., Chernikov A. A., Soloviev A. A., Yagova N. V., Sakharov Y. A., Kudin D. V., Kostarev D. V., Kozyreva O. V., Belov A. V. Influence of space weather on the reliability of the transport system functioning at high latitudes. Russian Journal of Earth Sciences. 2023, vol. 23, no. 2, pp. 1—34. DOI: 10.2205/2023ES000824.

6. Soloviev A. A., Sidorov R. V., Oshchenko A. A., Zaitsev A. N. On the need for accurate monitoring of the geomagnetic field during directional drilling in the Russian Arctic. Izvestiya, Physics of the Solid Earth. 2022, no. 3, pp. 136—152. [In Russ]. DOI: 10.31857/S0002333722030074.

7. Poedjono B., Beck N., Buchanan A., Brink J., Longo J., Finn C. A., Worthington E. W. Geomagnetic referencing in the Arctic environment. SPE Arctic and Extreme Environments Conference & Exhibition. Moscow, Russia, 2011. SPE-149629-Pp. DOI: 10.2118/149629-MS.

8. Kudin D. V., Gvishiani A. D., Nikitina I. M., Belov I. O., Dzeboev B. A., Grudnev A. A., Dzeranov B. V., Krasnoperov R. I. Storage and processing of big data for geomagnetic support of directional drilling. Applied Sciences. 2024, vol. 14, no. 21, article 9730. DOI: 10.3390/app14219730.

9. Gjerloev J. W. The SuperMAG data processing technique. Journal of Geophysical Research: Space Physics. 2012, vol. 117, A9, article A09213. DOI: 10.1029/2012JA017683.

10. Kovalev D. V., Vorobev A. V., Valchuk A. S., Vorobeva G. R., Khannanov N. K. Assessment of the effects of space weather on the reliability of readings of magnetic inclinometers. Cosmic Research. 2025, vol. 63, no. 6, pp. 582—590. DOI: 10.1134/S001095252560177X.

11. Farcomeni A., Geraci M. Quantile ratio regression. Statistics and Computing. 2024, vol. 34, article 94. DOI: 10.1007/s11222-024-10406-8.

12. Trebault H., Finlay C., Beggan C. D., Alken P. International geomagnetic reference field: The 12th generation. Earth, Planets and Space. 2015, vol. 67, article 158. DOI: 10.1186/s40623-015-0228-9.

13. Russell C. T., McPherron R. L. Semiannual variation of geomagnetic activity. Journal of Geophysical Research. 1973, vol. 78, no. 1, pp. 92—108. DOI: 10.1029/JA078i001p00092.

14. Vorobev A. V., Soloviev A. A., Pilipenko V. A., Vorobeva G. R. Interactive computer model for aurora forecast and analysis. Solar-Terrestrial Physics. 2022, vol. 8, no. 2, pp. 81—87. DOI: 10.12737/stp-82202212.

15. Vorobev A. V., Hannanov N. K., Vorobeva G. R. An approach to decision support in directional drilling in variable geomagnetic conditions. MIAB. Mining Inf. Anal. Bull. 2026, no. 2, pp. 156—170. [In Russ]. DOI: 10.25018/0236_1493_2026_2_0_156.

16. Love J. J., Finn C. A. Real-time geomagnetic monitoring for space weather-related applications: Opportunities and challenges. Space Weather. 2017, vol. 15, pp. 1—8. DOI: 10.1002/2017SW001665.

17. Feldstein Ya. I. Discovery and first studies of the auroral oval (review). Geomagnetism and Aeronomy. 2016, vol. 56, no. 2, pp. 139. [In Russ]. DOI: 10.7868/S0016794016020048.

18. Love J. J., Chulliat A. An international network of magnetic observatories. Eos Transactions American Geophysical Union. 2013, vol. 94, no. 42, pp. 373—384. DOI: 10.1002/2013EO420001.

19. Bukhtoyarov B. N., Starikova O. R., Petrov V. G., Kudin D. V., Vinogradova A. A. Geomagnetic data for directional drilling and well positioning. Mine Surveying and Subsurface Use. 2025, no. 4, pp. 71—82. [In Russ]. DOI: 10.56195/207933322025-25-4-71-82.

20. Gvishiani A. D., Lukyanova R. Yu., Soloviev A. A. Study of the geomagnetic field and problems of directional drilling accuracy in the Arctic region. Gornyi Zhurnal. 2015, no. 10, pp. 94—99. [In Russ]. DOI: 10.17580/gzh.2015.10.17.