AD-TLERT: Faster Hydrologic Imaging with Automatic Differentiation.

A new framework called AD-TLERT has been introduced, designed to enhance the efficiency and flexibility of time-lapse electrical resistivity tomography (TL-ERT) inversion. TL-ERT is a technique used to monitor subsurface hydrologic changes, but its computational demands, especially for long monitoring sequences, have been a significant challenge. AD-TLERT leverages automatic differentiation and GPU acceleration to address this, achieving a remarkable 51-fold speedup compared to existing methods. The framework unifies model parameterization, differentiable petrophysical transformations, forward modeling, data misfit, regularization, and auxiliary constraints into a single computational chain. This integration means that alternative inversion formulations can reuse the same partial differential equation derivative implementation, eliminating the need to re-derive the complete ERT sensitivity for each new case. Synthetic experiments confirmed that AD-TLERT provides more accurate water-content estimates by propagating gradients directly through embedded petrophysical relationships. A field application further demonstrated its utility in imaging snowmelt-driven hillslope wetting by combining ERT with temperature and soil-moisture observations.