An iterative particle filter approach for coupled hydro-geophysical inversion of a controlled infiltration experiment

The modeling of unsaturated groundwater flow is affected by a high degree of uncertainty related to both measurement and model errors. Geophysical methods such as Electrical Resistivity Tomography (ERT) can provide useful indirect information on the hydrological processes occurring in the vadose zone. In this paper, we propose and test an iterated particle filter method to solve the coupled hydrogeophysical inverse problem. We focus on an infiltration test monitored by time-lapse {ERT} and modeled using Richards equation. The goal is to identify hydrological model parameters from {ERT} electrical potential measurements. Traditional uncoupled inversion relies on the solution of two sequential inverse problems, the first one applied to the {ERT} measurements, the second one to Richards equation. This approach does not ensure an accurate quantitative description of the physical state, typically violating mass balance. To avoid one of these two inversions and incorporate in the process more physical simulation constraints, we cast the problem within the framework of a {SIR} (Sequential Importance Resampling) data assimilation approach that uses a Richards equation solver to model the hydrological dynamics and a forward {ERT} simulator combined with Archie's law to serve as measurement model. {ERT} observations are then used to update the state of the system as well as to estimate the model parameters and their posterior distribution. The limitations of the traditional sequential Bayesian approach are investigated and an innovative iterative approach is proposed to estimate the model parameters with high accuracy. The numerical properties of the developed algorithm are verified on both homogeneous and heterogeneous synthetic test cases based on a real-world field experiment.