Physics-Guided Deep Learning Model for Daily Groundwater Table Maps Estimation Using Passive Surface-Wave Dispersion

Monitoring groundwater tables (GWTs) remains challenging due to limited spatial and temporal observations. This study introduces an innovative approach combining an artificial neural network, specifically a multilayer perceptron (MLP), with continuous passive Multichannel Analysis of Surface Waves (passive-MASW) to construct GWT depth maps. The geologically well-constrained study site includes two piezometers and a permanent 2D geophone array recording train-induced surface waves. At each point of the array, dispersion curves (DCs), displaying Rayleigh-wave phase velocities $\left(V_R\right)$ over a frequency range of 5–50 Hz, were measured daily from December 2022 to September 2023, and latter resampled over wavelengths from 4 to 15 m, to focus on the expected GWT depths (1–5 m). Nine months of daily $V_R$ data near one piezometer, spanning both low and high water periods, were used to train the MLP model. GWT depths were then estimated across the geophone array, producing daily GWT maps. The model's performance was evaluated by comparing inferred GWT depths with observed measurements at the second piezometer. Results show a coefficient of determination (R²) of 80% at the training piezometer and of 68% at the test piezometer, and a remarkably low root-mean-square error (RMSE) of 0.03 m at both locations. These findings highlight the potential of deep learning to estimate GWT maps from seismic data with spatially limited piezometric information, offering a practical and efficient solution for monitoring groundwater dynamics across large spatial extents.