Using Vadose Zone Flow Model Data in ERT Inversion for Improved Estimation of Water Content Distribution

Mathematical analysis of Electrical Resistance Tomography data leads to an underdetermined inverse problem whose solution requires additional information. In addition to constraints related to the smoothness of the solution relative to the starting profile (SP), this information is provided though the SP itself which is based on apparent resistivity, geological data, or local measurements. However, this causes the solution to be very sensitive to the SP. Hydrological processes such as infiltration often lead to "front" regions in which the water content changes sharply, but the exact locations of these fronts are not known since they depend on hydraulic soil parameters. In these regions, the standard inversion procedure that desires smoothness of the profile relative to the SP are not appropriate since they penalize heavily any front shifting. The hypothesis of this work is that the accuracy of the water profile obtained by ERT inversion could be significantly improved by including a more proper SP and locally adjusting the smoothness constraints taking into account the expected profile according to a water flow model. We propose to use a water flow model based on Richard's equations to obtain a first estimate of the water profile, which leads to two levels of information: First, it is converted to electrical conductivity distribution using petrophysical equations, hence providing a physically-sound starting profile for the iterative inversion process. Second, the regions with high gradient of the water content, and hence high gradient of the EC distribution, are identified, and this information can be used to locally adjust (relax) the smoothness constraints. The subsurface is split into two types of regions: 'S' type where we have reliable information on water content from the flow model or from the measurements, and 'X' type where the wetness front is expected. In S regions we use the flow model based SP and impose smoothness constraints relative to the SP, as in standard ERT inversion methods. In X regions we consider that we only know the shape of the EC profile based on the flow model, namely we expect a sharp EC change in these regions although we do not known exactly where the change should occur. In mathematical terms, we relax the smoothness constraint in the X regions, so that the inversion procedure tends to locate the fronts in these regions. We present here 1D synthetic cases in which profiles were derived numerically from known EC distribution based on a flow model. Simulated ERT signals were obtained and the water content profile was calculated using the developed method. The results show that the proposed approach leads to better agreement between the actual and estimated EC profiles.