A statistical approach to assessing the risk of extreme errors in high-latitude magnetic inclinometers

The efficiency of directional drilling in the Russian Arctic critically depends on the accuracy of magnetic inclinometers. In addition to voltage fluctuations and temperature variations, the metrological characteristics are significantly affected by ionospheric currents during geomagnetic substorms. The superposition of these factors leads to substantial errors in wellbore trajectory determination. Existing compensation methods are predominantly reactive, while proactive risk assessment approaches remain underdeveloped. This paper proposes a statistical framework for the probabilistic assessment of extreme error risks in magnetic inclinometers operating in high-latitude regions. Based on the analysis of magnetic observatory data from the maximum of the 24th solar cycle, it was established that the distributions of magnetic declination and inclination measurement errors follow a lognormal law. It was revealed that the heavy tails of the distributions (up to 19 % of the sample) are accurately described by a Generalized Pareto Distribution, indicating a high risk of extreme events. The probability of exceeding the permissible error threshold is ~6.3 % for azimuthal and ~0.81 % for zenith angles, which is unacceptable for managing the costly drilling process. The obtained results enable the creation of risk maps for integration into decision-support systems when planning drilling operations. This will minimize economic losses and mitigate emergency risks by enabling the advance prediction of periods when the use of magnetic inclinometers is associated with an increased probability of unacceptable errors.