Determining 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.

中文翻译：

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使用延时地电断层图训练的物理信息神经网络可估计异质土壤的水饱和度、渗透率和岩石物理关系


确定土壤水力特性非常复杂，这对管理地下和农业实践提出了持续的挑战。电阻率层析成像 (ERT) 因其非侵入性、易于应用且经济高效的特性，是一种颇具吸引力的地下监测地球物理方法。然而，从原始测量中获取地电断层图需要对不适定问题进行反演，这会导致实际结构的平滑。此外，空间分辨率是根据电极放置的距离确定的，从而固有地放大了所获得的结构。本研究探讨了物理信息神经网络 (PINN) 在扩大渗透率和岩石物理关系以及使用延时地电数据监测异质土壤中的水动态方面的适用性。模拟水渗透的高分辨率数值模拟被用作基准。采用比数值模型分辨率大 10 倍的电极间距进行综合 ERT 测量，以提供 2D 电断层图。将断层图像输入 PINNs 系统以获得渗透率、岩石物理关系和含水量图。另外还训练了一个包含水含量测量的 PINN 系统来检查测量灵敏度。结果表明，PINNs 系统可以在放大的渗透率和岩石物理关系场方面产生可靠的结果。准确预测了地下的水动态，平均误差为~3%。在 PINN 训练中添加水含量测量改善了系统结果，主要是在 ERT 低敏感区域。 与使用已知的均质岩石物理关系直接将地电断层图转换为水饱和度的常见做法相比，PINNs 系统将水饱和度误差减少了 30% 以上。