Smoothing Objective Function for 3-D Electrical Resistivity Inversion by CNNs Regularizer

In tunnel geological forecasting, the electrical resistivity inversion method is extensively employed due to its high sensitivity to water-bearing bodies. Traditional inversion methods, such as least squares, simplify nonlinear problems into linear ones. However, they often converge to local minima, making it challenging to identify the global optimal solution, and their inversion results are highly dependent on the choice of the initial model. To address these challenges, we propose integrating convolutional neural networks (CNNs) into the conventional iterative inversion framework. Instead of directly optimizing the initial resistivity model, our approach focuses on updating the network parameters, with the resistivity model subsequently generated by the CNN. This enables the CNN structure to regularize the resistivity model, resulting in a smoother objective function. Consequently, our method exhibits greater robustness to variations in the initial model, leading to improved inversion results. Our numerical simulations and practical applications in engineering projects demonstrate that, compared to traditional inversion methods, the proposed approach is less sensitive to the initial model and achieves superior inversion outcomes, thereby validating our hypothesis.