Hysteresis of the self‐potential response associated with harmonic pumping tests

Harmonic pumping tests performed in an unconfined aquifer are responsible for a non‐linear and phase shifted behavior of the self‐potential response recorded at the ground surface with respect to the change in the pressure heads of the aquifer. The observed non‐linearity of the transfer function can be reproduced with a petrophysical model in which the permeability, the capillary pressure curve, and the streaming potential coupling coefficient are modelled inside a unified framework approach based on the van Genuchten parametrization including a hysteretic behaviour with the water saturation. The field equations for the hydraulic heads and the self‐potential signals are solved with a finite‐element code, which is used to compute the time variation of the self‐potential variations over time for two numerical experiments accounting or not for hysteresis. Only the model with hysteresis can reproduce the field observations.