Physics-guided deep learning model for daily groundwater table maps estimation using passive surface-wave dispersion

Monitoring groundwater tables (GWTs) is challenging due to limited spatial and temporal observations. This study presents an innovative approach utilizing supervised deep learning, specifically a Multilayer Perceptron (MLP), and continuous passive-Multichannel Analysis of Surface Waves (passive-MASW) for constructing 2D GWT level maps. The study site, geologically well-constrained, features two 20-meter-deep piezometers and a permanent 2D geophone array capturing train-induced surface waves. For each point of the 2D array, dispersion curves (DCs), displaying Rayleigh-wave phase velocities (V_R) across a frequency range of 5 to 50 Hz, have been computed each day between December 2022 and September 2023. In the present study, these DCs are resampled in wavelengths ranging from 4 to 15~m in order to focus the monitoring on the expected GWT levels (between -1 and -5 m). Nine months of daily V_R data around one of the two piezometers is used to train the MLP model. GWT levels are then estimated across the entire geophone array, generating daily 2D GWT maps. Model’s performance is tested through cross-validation and comparisons with GWT level data at the second piezometer. Model’s efficiency is quantified with the root-mean-square error (RMSE) and the coefficient of determination (R²). The R² is estimated at 80% for data surrounding the training piezometer, and at 68% for data surrounding the test piezometer. Additionally, the RMSE is impressively low at 0.03 m at both piezometers. Results showcase the effectiveness of DL in estimating GWT level maps from passive-MASW data, offering a practical and efficient monitoring solution across broader spatial extents.