Time Series Data Inversion and Monitoring Method for Cross-Hole ERT Based on an Improved Extended Kalman Filter

In recent decades, the DC resistivity method has been applied to geophysical monitoring because of its sensitivity to hydrogeological properties. However, existing inversion algorithms cannot give a reasonable image if fluid migration is sudden and unpredictable. Additionally, systematic or measurement errors can severely interfere with accurate object location. To address these issues, we propose an improved time series inversion method for cross-hole electrical resistivity tomography (cross-hole ERT) based on the Extended Kalman Filter (EKF). Traditional EKF includes two steps to obtain the current model state: prediction and correction. We improved the prediction step by introducing the grey time series prediction method to create a new regular model sequence that can infer the potential trend of underground resistivity changes and provide a prior estimation state for reference during the next moment. To include more current information in the prior estimation state and decrease the non-uniqueness, the prediction model needs to be further updated by the leastsquares method. For the correction step, we used single time-step multiple filtering to better deal with the case of sudden and rapid changes. We designed three different numerical tests simulating rapid changes in a fluid to validate the proposed method. The proposed method can capture rapid changes in the groundwater transport rate and direction of the groundwater movement for real-time imaging. Model and field experiments were performed. The inversion results of the model experiment were generally consistent with the results of dye tracing, and the groundwater behavior in the field experiment was consistent with the predicted groundwater evolution process.