Abstract :
[en] Electrical resistivity tomography (ERT) is increasingly used in the context of agriculture since the measured resistivity distribution can be linked to soil moisture, soil structure or pore water salinity. Due to its minimally invasive character, its spatial coverage and its monitoring abilities, ERT can be used to study field heterogeneity and competition between plants, quantify water fluxes throughout a growing season or distinguish preferential flow pathways in soils. Nevertheless, a lot of challenges still remain. From a mathematical point of view, the inverse problem linked to ERT is ill-posed. To solve it, the inverse problem is often regularized with a Tikhonov-type approach resulting in a smoothed resistivity distribution. However, in reality strong contrasts can exist due to e.g. compacted soil layers due to ploughing, water infiltration fronts, etc. and in that case other operators have been proposed to regularize the inversion. Taking into account spatial heterogeneity of petrophysical characteristics and providing a realistic uncertainty estimation are additional challenges, which can be addressed using stochastic approaches. Monitoring data provides further elements to constrain the inverse problem: data can be replaced by data difference and regularization may incorporate the temporal dimension for instance. However, such constraints require their compatibility with the studied temporal process, which is not always straightforward. Several alternative strategies are being developed, such as coupled hydrogeophysical inversion, or stochastic approaches using a prior falsification/validation method following a Popper-Bayes philosophy. In this presentation, we will illustrate the mentioned challenges and some recent developments in the context of agrogeophysics.
