Sequential Inversion for Helicopter Time-Domain Electromagnetics Based on a Regularized Extended Kalman Filtering

The helicopter time-domain electromagnetic method (HTEM) has been widely applied in challenging geological terrains, particularly in large-scale mineral exploration, underground water resource detection, and the selection of sites for underground engineering, due to its advantage of not requiring personnel to enter the detection area. Currently, the 1D inversion method with lateral constraints, which is commonly used in HTEM, faces challenges quickly delivering inversion results in the field due to its high computational demands and lengthy processing time. In this paper, we propose a sequential inversion method for HTEM based on the regularized extended Kalman filter (REKF). The REKF algorithm is used to predict the current inversion result at a given time by using the inversion result from the previous moment, and predictions are corrected with the observed data at that specific time. We also introduce a vertical roughness regularization term to avoid overfitting issues during the inversion process. Based on the sequential processing strategy of measuring while inverting, the REKF algorithm yields the optimal solution of the inversion objective function in just a few iterations, or even a single iteration, enabling near real-time calculations. In the simulation experiments, the advantages of the REKF method are demonstrated by comparing the inversion results of the REKF method with those of the extended Kalman filter method and the Occam method with lateral constraints. Finally, we perform REKF inversion on HTEM data obtained from a location in Xinjiang, China. The results demonstrate the accuracy and practicality of the REKF inversion method.