Physics‐Informed Neural Networks Trained With Time‐Lapse Geo‐Electrical Tomograms to Estimate Water Saturation, Permeability and Petrophysical Relations at Heterogeneous Soils

Abstract

AbstractDetermining soil hydraulic properties is complex, posing ongoing challenges in managing subsurface and agricultural practices. Electrical resistivity tomography (ERT) is an appealing geophysical method to monitor the subsurface due to its non‐invasive, easy‐to‐apply and cost‐effective nature. However, obtaining geoelectrical tomograms from raw measurements requires the inversion of an ill‐posed problem, which causes smoothing of the actual structure. Furthermore, the spatial resolution is determined from the distances in the electrode placement, thus inherently upscaling the obtained structure. This study explores the applicability of physics‐informed neural networks (PINNs) for upscaling permeability and petrophysical relations and monitoring water dynamics at heterogeneous soils using time‐lapse geoelectrical data. High‐resolution numerical simulations mimicking water infiltration were used as benchmarks. Synthetic ERT surveys with electrode spacing 10 times larger than the numerical model resolution were conducted to provide 2D electrical tomograms. The tomograms were fed to a PINNs system to obtain the permeability, petrophysical relations, and water content maps. An additional PINNs system incorporating water content measurements was trained to examine measurement sensitivity. Results have shown that the PINNs system could produce reliable results regarding the upscaled permeability and petrophysical relations fields. Water dynamics at the subsurface was accurately predicted with an average error of ∼3%. Adding water content measurements to PINNs training improved the system outcomes, mainly at the ERT low sensitivity zones. The PINNs system reduced water saturation errors by more than 30% compared to the common practice of directly translating the geoelectrical tomograms to water saturations using known, homogeneous petrophysical relations.