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.

I. Introduction

Electrical resistivity inversion (ERI) method is widely utilized across various domains, such as mineral exploration [1], environmental science and engineering [2], and hydrology [3]. This method is favored due to its cost-effectiveness, efficiency, and sensitivity to water-bearing structures. In the context of advanced geological forecasting for tunnel construction, the borehole direct current resistivity method is particularly effective. By deploying multiple advanced horizontal boreholes with high-density detection electrodes along the tunnel face, this method enables 3-D, detailed imaging of interborehole water-conducting structures, thereby providing a robust tool for forecasting and mitigating water and mud inrush hazards. Resistivity inversion methods are generally categorized into linear and nonlinear approaches. The most commonly employed technique is the traditional iterative method, which is inherently a linear inversion method. However, given the inherently nonlinear nature of resistivity inversion, this linear approach often encounters significant challenges, such as getting trapped in local optima and a strong dependence on the initial model, leading to suboptimal and inaccurate inversion results [4], [5].