Physics-Driven Deep Learning Inversion for Direct Current Resistivity Survey Data

The direct-current (dc) resistivity method is a commonly used geophysical technique for surveying adverse geological conditions. The resistivity model can be reconstructed from data by inversion, which is an important step in geophysical surveys. However, the inversion problem is a serious one that can easily lead to incorrect results. Deep learning (DL) provides new avenues for solving inverse problems, and these methods have been widely studied. Currently, most DL inversion methods for resistivity are purely data-driven and depend heavily on labels (real resistivity models). However, real resistivity models are difficult to obtain through field surveys. As an inversion network may not be effectively trained without labels, we built an unsupervised learning resistivity inversion scheme based on the physical law of electric field propagation. First, a forward modeling process was embedded into the network training to convert the predicted resistivity model to predicted data, and form a data misfit with the observation data. Unsupervised training independent of labels was realized using the data misfit as a loss function. Moreover, a dynamic smoothing constraint was imposed on the loss function to alleviate the ill-posed inverse problem. Finally, a transfer learning scheme was employed to adapt the network trained with simulated data to field data. Numerical simulations and field tests showed that the proposed method can accurately locate and depict geological targets.

I. Introduction

The direct-current (dc) resistivity method, which is characterized by low economic cost, high survey efficiency, and strong sensitivity to water-bearing structures, is one of the most commonly used solutions for geophysical surveys [1], [2]. Therefore, it has been widely used for various purposes, including traffic engineering [3], [4], [5], dam surveys [6], [7], and environmental engineering [8], [9]. An effective inversion method is the key to improving the reliability of imaging techniques. Currently, linear inversion is the main method for inverting real-world data, and it predicts models according to the physical laws of geoelectric fields. However, the inversion results are highly dependent on the initial model and only a locally optimal solution is usually obtained using this method. Moreover, imagining results usually contain artifacts that influence the geological interpretation of the results.