Measurement error law and uncertainty characterization method of directional drilling trajectory in advanced investigation

To improve the trajectory control accuracy of directional drilling for advanced geological investigation, this study systematically investigates the composition, propagation law, and uncertainty characterization method of measurement errors based on theoretical calculations and engineering verification. The results indicate that the inclination measurement error primarily originates from inherent instrument errors, borehole curvature effects, and cuttings bed lifting effects. Azimuth error is significantly disturbed by geomagnetic anomalies, while hole depth error is mainly attributed to drill pipe machining tolerances and thread connection clearances. A two-plane ellipse characterization model is established based on error propagation theory. The four semiaxis lengths of the ellipse are determined through eigenvalue calculation of the borehole trajectory covariance matrix, which exhibits a nonlinear sensitivity to angle variations. Comparative analysis demonstrates that the deviation induced by hole depth measurement errors is smaller than that caused by angular errors, with the proportional contribution of these errors varying across different drilling positions. Simulation analyses of kilometer-scale straight boreholes reveal that measurement spacing exerts a dominant control on error accumulation. As the measurement spacing increases from 3 m to 18 m, the elliptical semiaxis length increases logarithmically, with a maximum growth rate of 160%. This finding verifies that dense measurement points can effectively suppress error accumulation. Field engineering tests further validate the accuracy of the proposed characterization model. Specifically, the model achieves a prediction accuracy of 50% at a confidence factor of 1 and 100% at a confidence factor of 2.