Estimation of hydraulic conductivity and water table map in a large‐scale laboratory model by means of the self‐potential method

The goal of this paper is to estimate the position of the water table and hydraulic conductivity of a homogeneous porous medium by means of the self‐potential method. The hydrogeophysical experiments were carried out at the Hydrogeosite Laboratory of the Istituto di Metodologie per l’Analisi Ambientale, Consiglio Nazionale delle Ricerche (Marsico Nuovo, Italy); the laboratory is a large‐scale model sized 10 × 7 × 3 m3 that is filled with a homogeneous medium made up of quartz‐rich sand with a medium‐high hydraulic conductivity in the order of 10−5 m s−1. Self‐potential signals generated by the groundwater flow, during a pumping test, were measured on the ground surface, on both the pumping and the recovery phases. A novel methodology to estimate the hydraulic conductivity from self‐potential measurements is proposed. Hydraulic conductivity very close to that calculated from hydraulic data, by means of Neuman‐type curves, has been obtained by solving the electrical flow equation through a linear least squares method. Moreover, a kriging with external drift geostatistical methodology has been proposed to estimate the hydraulic head distribution. The advantages given by this geostatistical method are that (1) hydraulic head distribution can be estimated without any previous electrokinetic coupling coefficient calculation and (2) the method is valid for either linear or nonlinear relationships between self‐potential and hydraulic head gradients. An original finding of this work is that the relationship between self‐potential signals and drawdown, around a pumping well, is not always linear: linearity applies only when the groundwater velocity is low, but high nonlinearity occurs when hydraulic head gradient rises up. Kriging with the external drift method could be used for the inversion of the hydraulic conductivity distribution, in a real heterogeneous aquifer, by means of an appropriate conditioning technique