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.