Dynamical inversion of geophysical ERT data: state estimation in the vadose zone

Abstract

The imaging of the evolution of conductive fluids in porous media with electrical resistance tomography (ERT) can be considered as a dynamic inverse problem, in which the time-dependent electrical conductivity distribution in the target region is inferred from voltage measurements at electrodes placed in boreholes or on the ground surface. A petrophysical relationship is then used to relate the electrical conductivity to water saturation. We consider a state estimation approach that combines the complete electrode model for simulating ERT measurements and a hydrological evolution model for unsaturated flow. To demonstrate the approach, we consider synthetic measurements from a simulated experiment in which water is injected from a point source into an initially dry soil. The purpose is to carry out a feasible study. In the studied simple cases, the proposed method provides improved estimates of the water saturation distribution compared to the traditional reconstruction approach, which does not employ an evolution model.