Objective  In the monitoring of coal seam mining-induced deformation and failure of surrounding rocks, the borehole resistivity method stands out due to its capacity for dynamic, three-dimensional (3D) full-space measurements. However, conventional resistivity inversion for the method is generally carried out using the least squares algorithm, leading to limited accuracy in practical engineering. In recent years, neural network-based inversion has demonstrated the potential for addressing this challenge, while its performance is yet to be further improved.

Methods In this context, inversion imaging based on a back propagation-Kolmogorov-Arnold network (BP-KAN) was proposed for the borehole resistivity method, aiming to accurately monitor the range and depth of mining-induced deformation and failure of a coal seam floor. First, based on representative geological conditions of coal mines, this study constructed geoelectric models for mining-induced deformation and failure of a coal seam floor under varying advancement distances of a mining face. Forward modeling was then conducted to establish training and test datasets for the BP-KAN neural network. Subsequently, the inversion imaging results derived using the BP-KAN neural network were compared with those determined using the KAN and BP neural networks and the least squares method. Finally, in combination with the measured data derived using the borehole resistivity method from the coal seam floor of mining face 3303 in a coal mine of Shanxi Province, the inversion imaging performance of the BP-KAN neural network in engineering application was validated.

Results and Conclusions  The BP-KAN-based inversion imaging for the borehole resistivity method enables accurate characterization of the ranges, boundary morphologies, and resistivity variations of the mining-induced failure zone in the coal seam floor, thereby improving the inversion imaging accuracy of the borehole resistivity method. In the engineering application, the proposed BP-KAN-based inversion imaging revealed a floor failure depth of 15.5 m, with an absolute error of merely 0.5 m against the failure depth (15 m) derived in the field through the segmented water injection with double-end sealing using a borehole. Besides, the proposed inversion imaging method outperformed the inversion using a traditional BP neural network, which yielded a failure depth of 19 m. Furthermore, the failure range revealed by the proposed inversion imaging method was consistent with the actual evolution patterns of mining-induced failure. Therefore, the BP-KAN-based inversion imaging for the borehole resistivity method features high monitoring accuracy and reliability, offering a novel approach for the precise monitoring of the deformation and failure of coal seam floors.