Implicit Neural Representation to Improve the Resolution of 3D Electrical Resistivity

Electrical resistivity tomography (ERT) is a subsurface imaging geophysical technique. Traditional ERT inversion methods, such as smoothness-constrained least-squares approaches, often suffer from discretization artifacts when reconstructing electrical resistivity from resistance measurements. To address the limitations of conventional ERT inversion, this study introduces a novel super-resolution framework based on an Implicit Neural Representation (INR) to enhance 3D ERT inversion resolution beyond that achievable with standard Gauss-Newton techniques. The proposed machine learning methodology effectively integrates high-resolution two-dimensional data with coarse three-dimensional data to generate a higher-resolution resistivity representation consistent with the measured apparent-resistivity data. Validation using data from the Waste Isolation Pilot Plant (WIPP) site shows that the INR approach improves 3D inversion quality relative to Res3Dinv. For the WIPP data set, the INR model increases R² from 0.107 to 0.361, reduces RMSE from 77.21 to 33.32 Ω·m, and reduces bias from 68.34 to 13.94 Ω·m (corresponding to relative improvements of 237.4%, 56.8%, and 79.6%, respectively). Tests on a synthetic domain with increased resistivity variation show even stronger performance enhancement: R² increases from 0.149 to 0.740, RMSE decreases from 119.28 to 53.24 Ω·m, and bias decreases from 88.45 to 12.74 Ω·m (relative improvements of 396.6%, 55.4%, and 85.6%, respectively). Results demonstrate improved apparent-resistivity prediction using INR, but the method is deterministic and does not provide formal uncertainty bounds. Generalization to other electrode arrays and systematic quantification of line-density sensitivity remain future work.