Full-gradient difference inversion scheme based on time-lapse electrical resistivity tomography

ABSTRACT Time-lapse electrical resistivity tomography (ERT) has been widely used in near-surface monitoring. A methodological approach, known as the 4D inversion scheme, enables the simultaneous inversion of an entire set of ERT data and has become a commonly used time-lapse inversion scheme. However, despite using qualitative cross-time constraints to regularize neighboring resistivity models, the problem of overfitting noisy data during the inversion process remains unresolved. To address this limitation, a new time-lapse ERT inversion scheme, named the full-gradient difference (FGD) inversion scheme, is first developed based on a 4D inversion scheme. By inverting the background resistivity and subsequent resistivity differences and constructing a full-gradient Jacobian matrix at various time steps, this approach ensures that the resistivity models at most time steps need to fit multiple sets of observed data. Consequently, it mitigates overfitting noisy data and enhances noise robustness. Results from numerical and field experiments show that the FGD inversion scheme produces more stable resistivity images than the 4D inversion scheme in the presence of noise, making it suitable for application to field data. Furthermore, the FGD inversion scheme has the potential to be applied to other time-lapse geophysical methods and is theoretically applicable to geophysical methods susceptible to noise.