Estimation of the water table throughout a catchment using self-potential and piezometric data in a Bayesian framework

Abstract

Information about spatial variations of the water table that occur throughout catchments is useful to infer large scale flow patterns, but conventional mapping using piezometric data is invasive, slow, and expensive. Water flow in the subsurface generates an electrical current called the streaming current. The resulting self-potential (SP) (electrostatic) signals can be measured non-intrusively, quickly, and inexpensively at the ground surface. We considered two conceptual models to relate SP signals to the water table. The “infiltration model” relates SP signals to the thickness of the vadose zone, while the “water table model” relates SP signals to the distribution of the water table in unconfined aquifers. These models are first calibrated against field data before a Bayesian method is applied to update a kriged map of the water table obtained from piezometric observations using a kriged SP map. The estimated water tables based on the two conceptual models were combined into one final model using concepts from Bayesian Model Averaging. The method was applied to a small agricultural catchment (not, vert, similar1 km2) in southern France. The posterior water table estimates were improved mainly on the slopes surrounding the basin. Understanding the variations in the water table on these slopes is important because infiltration in these areas feed the basin with groundwater flow. The Bayesian framework is useful to avoid overconfident predictions when using SP data in hydrogeological estimation because it provides realistic uncertainty estimates.