Physics-Guided Neural Network Parameter Estimation of Groundwater–Strain Coupling at Moxa Geodynamic Observatory

High-resolution laser strainmeter measurements in an underground gallery at Moxa Geodynamic Observatory (Thuringia, central Germany) provide detailed records of crustal deformation. Beyond Earth tides, deformation induced by pore-pressure fluctuations produces the largest signals. These observations reveal that the relationship between groundwater transport and crustal strain is temporally fluctuating, highlighting the need for a quantitative approach to systematically characterize potential coupling.

Here, we present a physics-guided, data-driven approach for estimating effective groundwater–strain coupling from multivariate time series of groundwater levels and nanometer-scale strain measurements, based on linear Biot poro-elasticity. The approach incorporates physically guided Biot neurons into an autoregressive neural network architecture; these neurons model horizontal poro-elastic responses of fractured rock driven by groundwater variations. It dynamically adjusts to temporal changes in groundwater levels and the resulting pore-pressure-induced strain. Using orientation-specific laser strainmeter measurements and spatially distributed groundwater levels from boreholes, we estimate Biot coupling in two horizontal directions (North–South and East–West) and derive effective coupling parameters from over a decade of observatory records.

Our results provide insights into the dynamic hydro-mechanical behaviour of the shallow crust and highlight the potential of physics-guided neural architectures to support the interpretation of high-resolution deformation and stress–strain responses in geomechanical studies.